19. Radiation and Optics in the Atmosphere and 19.3 Aerosols and Clouds 1172 This Chapter Describes the Fundamentals of Ra-

1165 Radiation19. Radiation and Optics in the Atmosphere and 19.3 Aerosols and Clouds 1172 This chapter describes the fundamentals of ra- ...... diation transport in general and in the Earth’s 19.4 Radiation and Climate ...... 1174 atmosphere. The role of atmospheric aerosol and 19.5 Applied Radiation Transport: Remote clouds are discussed and the connections between Sensing of Atmospheric Properties ...... 1176 radiation and climate are described. Finally, nat- 19.5.1 Trace Gases ...... 1176 ural optical phenomena of the atmosphere are 19.5.2 The Fundamentals of DOAS ...... 1176 discussed. 19.5.3 Variations of DOAS ...... 1178 19.5.4 Atmospheric Aerosols...... 1179 19.1 Radiation Transport 19.5.5 Determination of the Distribution of Solar Photon Path Lengths 1181 in the Earth’s Atmosphere...... 1166 ...... 19.1.1 Basic Quantities Related 19.6 Optical Phenomena in the Atmosphere...1182 to Radiation Transport ...... 1166 19.6.1 Characteristics 19.1.2 Absorption Processes ...... 1166 of Light Scattering by Molecules 19.1.3 Rayleigh Scattering...... 1166 and Particles ...... 1182 19.1.4 Raman Scattering...... 1167 19.6.2 Mirages...... 1185 19.1.5 Mie Scattering...... 1168 19.6.3 Clear Sky: Blue Color and Polarization 1186 19.2 The Radiation Transport Equation ...... 1169 ...... 19.6.4 Rainbows 1187 19.2.1 Sink Terms (Extinction)...... 1169 ...... 19.2.2 Source Terms 19.6.5 Coronas, Iridescence and Glories ...1189 19.6.6 Halos 1191 (Scattering and Thermal Emission). 1169 ...... 19.2.3 Simpliﬁcation of the Radiation 19.6.7 The Color of the Sun and Sky ...... 1193 19.6.8 Clouds and Visibility 1195 Transport Equation...... 1170 ...... 19.2.4 Light Attenuation 19.6.9 Miscellaneous ...... 1196 in the Atmosphere ...... 1171 References ...... 1197

There are a multitude of processes in which electromag- where its energy is also changed. Inelastic scat- netic radiation interacts with the atmosphere: tering by molecules is called Raman scattering, where the energy of the scattered photon can • Absorption, i. e. radiation is removed from the ra- be reduced at the expense of energy transferred diation ﬁeld and converted into some other form of to the scattering molecule (Stokes scattering). energy, e.g. heat. Absorption can be due to molecules Likewise, energy can be transferred from the (ther- D Part in the atmosphere (such as ozone, oxygen, or water mally excited) molecules to the photon (anti-Stokes vapor) or aerosols (such as soot), absorption of solar scattering). energy in the atmosphere is an important process in • Thermal emission from air molecules and aerosol 19 the climate system of the Earth. particles. The emission at any given wavelength can- • Elastic scattering, which – seen from an individual not exceed the Planck function (or emission from photon – changes its direction of propagation, but a black body) for the temperature of the atmo- not its energy (and hence wavelength or ‘color’). sphere, thus noticeable thermal emission only takes Scattering can be due to molecules (Rayleigh scat- place at infrared wavelengths longer than several tering) or aerosol particles (Mie scattering) present micrometers. Due to Kirchhoff’s law only absorb- in the air. ing gases (such as CO2,H2O, O3, but not the • Inelastic scattering where, as for elastic scatter- main components of air N2,O2, Ar), can emit ing, the direction of a photon is changed but radiation. 1166 Part D Selected Applications and Special Fields

• Aerosol ﬂuorescence. Excitation of molecules (broad band) ﬂuorescence; this process will not be within aerosol particles by radiation can result in further discussed here.

19.1 Radiation Transport in the Earth’s Atmosphere In the following we introduce the basic quantities per- 19.1.3 Rayleigh Scattering tinent to the propagation of radiation in the atmosphere and discuss the fundamental laws governing radiation Elastic scattering (i. e. scattering without change of the transport in absorbing and scattering media, i. e. the photon energy) by air molecules is called Rayleigh scat- atmosphere. tering. While this is not an absorption process, light scattered out of the probing light beam will normally 19.1.1 Basic Quantities Related not reach the detector, thus for narrow beams it is justi- to Radiation Transport fied to treat Rayleigh scattering as an absorption process. 2 The Rayleigh scattering cross section σR(λ)(incm )is A light source will emit a certain amount W of energy given by [19.1]: in the form of radiation. π3 λ 2 − 2 Φ 24 n0( ) 1 1. The radiant flux is defined as the radiation en- σR(λ) = FK(λ) λ4 N2 2 2 ergy W per unit time (regardless of the direction in air n0(λ) + 2 which it is emitted): 3 8π 2 ≈ n (λ)2 − 1 F (λ) , (19.5) radiated energy dW Ws λ4 2 0 K Φ = = = W 3 Nair time interval dt s (19.1) where: λ denotes the wavelength, n0(λ) is the real part of the wavelength-dependent index of refraction of air, N Φ air 2. The irradiance B is defined as the radiant flux is the number density of air (e.g. 2.4×1019 molec/cm3 received by an (‘illuminated’) area Ae: ◦ λ ≈ . at 20 C, 1 atm), FK( ) 1 061 is a correction for Φ W anisotropy (polarisability of air molecules). B = ; (19.2) 2 2 Note that n (λ) − 1 ≈ 2[n (λ) − 1]∝N ,since Ae m 0 0 air n0 ≈ 1 [in fact n0 (550 nm) = 1.000293], and 3. The radiation intensity is (Ω = solid angle): n0 − 1 ∝ Nair, thus σR(λ) is essentially independent Φ of Nair. On that basis a simplified expression for the I = [ / ]; (19.3) 2 Ω W sr Rayleigh scattering cross section (in cm )isgivenby Nicolet [19.2] 4. The radiance is (As = radiating area): . −28 Φ W σ λ ≈ 4 02 × 10 F = . (19.4) R( ) + (19.6) 2 λ4 x Ω As m sr atD Part (All areas are assumed to be oriented perpendicular with to the direction of propagation of the radiation.) x = 0.04 19.1 for λ>0.55 μm , 19.1.2 Absorption Processes x = 0.389λ + 0.09426/λ − 0.3328 Radiation is absorbed by molecules in the atmosphere for 0.2 μm <λ<0.55 μm . (such as ozone, oxygen, or water vapor), aerosol (such For these simple estimates the Rayleigh scattering as soot) or liquid and solid water particles (cloud cross section can be written as droplets (ice crystals)). Absorption of solar ultravio- − let (UV) radiation at wavelengths below about 300 nm σ (λ) ≈ σ λ 4 R R0 by atmospheric O2 and O3 is important for life on − σ ≈ . 16 2 4 . (19.7) Earth. R0 4 4×10 cm nm for air Radiation and Optics in the Atmosphere 19.1 Radiation Transport in the Earth’s Atmosphere 1167

Rayleigh phase fuction molecule) changes its state of excitation during the scattering process. A part of the photons energy is then 90 2.0 passed from the photon to the molecule (Stokes lines, 120 60 ΔJ =+2, S-branch) or vice versa (anti-Stokes, ΔJ = 2, 1.5 O-branch). The term rotational Raman scattering (RRS) 150 30 is used if only the rotational excitation is affected 1.0 (Δv = 0). If the vibrational state also changes, the term 0.5 (rotational-) vibrational Raman scattering (VRS) is used (Δv =±1). Only discrete amounts of energy given by 0.0 180 0 the difference between the discrete excitation states can be absorbed/emitted. For air (O2 and N2) RRS frequency 0.5 shifts of up to ±200 cm−1 occur, for VRS a vibrational shift of ±2331 cm−1 for nitrogen and ±1555 cm−1 for 1.0 210 330 oxygen has to be added. The VRS is one order of mag- 1.5 nitude weaker than the RRS, and RRS is roughly one magnitude weaker than Rayleigh scattering. 240 300 2.0 In the following we give a quantitative description of 270 rotational- and vibrational-Raman scattering by O2 and Isotropic polarizability N2 [19.4–7]. The scattered power density Iv,J→v,J in Anisotropic polarizability [W/m2] scattered into the full solid angle 4π involving Fig. 19.1 Polar diagram of the Rayleigh scattering phase a transition (v, J → v, J) is given by [19.8]: function Φ(ϑ) for unpolarized incident light (dashed line, normalized to 2). The contribution of light polarized paral- Iv,J→v,J 2 ϑ lel to the scattering plane shows the sin dependence 1 −E(v,J )/kT = I σv, →v, LN g (2J + 1) e , of a Hertz dipole (dotted line, normalized to 1), with 0 J J air J Z ϑ = π/2 − ϑ being the angle between dipole axis and the (19.11) Poynting vector of the incident radiation, while the con- where I is the incident power density, N is the number tribution of light polarized perpendicular to the scattering 0 air of molecules in the scattering volume, L is the length plane (drawn line, normalized to 1) is independent of ϑ. of the volume and g is the statistical weight factor (plot by F. Filsinger) J of the initial rotational state due to the nuclear spin; J and v are the rotational and vibrational quantum num- The extinction coefﬁcient due to Rayleigh scattering bers, respectively. The factor (2J + 1) accounts for the ε (λ) is then given by R degeneracy due to the magnetic quantum numbers while [− v, / ] εR(λ) = σR(λ)Nair . (19.8) exp E( J ) kT accounts for the population of the initial state of the molecule at temperature T.Thestate The Rayleigh scattering phase function (see sum Z is given by the product of the rotational state Fig. 19.1) is given by sum Zrot and the vibrational state sum Zvib.Theabso- σv, →v, 3 lute cross section in (19.11) is given by J J ,which D Part Φ(cos ϑ) = (1 + cos2 ϑ) . (19.9) 4 can be obtained by integration of the differential cross section dσv, →v, /dΩ over the entire solid angle Ω. Taking the anisotropy of the polarisability into account J J Note that the term differential refers to the solid angle. the above equations becomes [19.3]: 19.1 The energy of the molecule is characterized by the vi- Φ(cos ϑ) = 0.7629(0.9324 + cos2 ϑ) . (19.10) brational (v) and rotational (J) quantum numbers and given by E v, J = E v + E J 19.1.4 Raman Scattering ( ) vib( ) rot( ) 1 While Raman (and Mie) scattering can be regarded as = hcν˜ v + + hcBJ(J + 1) , (19.12) 2 elastic scattering processes, where no energy is transferred between the scattering particle and the photon, assuming no coupling between rotation and vibration, inelastic scattering occurs, if the scattering particle (i. e. B is the rotational constant and ν˜ is the wave number in 1168 Part D Selected Applications and Special Fields

cm−1 of the ground state vibration. Allowed transitions Table 19.1 Comparison of the total cross section for the are, in that approximation, ΔJ = 0, ±2 resulting in the different scattering types for 770 nm, 273 K Δv = ± Q-, O- and S-branches and 0, 1 for vibrational Scattering type Cross section (cm2) Ratio (%) transitions. Due to the temperatures in the Earth’s at- Rayleigh 1.156 × 10−27 100 mosphere only the ground vibrational state is occupied O RRS 7.10 × 10−29 6.1 significantly, thus leading only to Stokes transitions of 2 N RRS 2.94 × 10−29 2.5 the vibrational states. 2 Air RRS 3.82 × 10−29 3.3 − Polarization Properties of Vibrational Raman VRS 0.1 Scattered Light and Line Filling in The polarization properties of isotropic and anisotropic ally much weaker wavelength dependence (see below) component of Raman scattered light are described and a strong dominance of the forward direction in the by (19.13), respectively: scattered light. The calculation of the Mie scattering cross section can be very complicated (involving sum- 2 Iparallel 6 + cos Θ (anisotropic) = , ming over slowly converging series), even for spherical Iperp 7 particles, but even more so for particles of arbitrary I shape. However, the Mie theory (for spherical particles) parallel = 2 Θ, (isotropic) cos (19.13) is well-developed and a number of numerical models Iperp exist to calculate scattering phase functions and extinc- where the terms parallel and perpendicular refer to the tion coefficients for given aerosol types and particle plane defined by the sun, the scattering point and the ob- size distributions see Figs. 19.2, 19.17 [19.11, 12]. The server. Thus only the isotropic part leads to enhanced computational effort is substantially reduced by the in- polarization of scattered light, especially at large scat- troduction of an analytical expression for the scattering tering angles (≈ solar zenith angle (SZA)). Since the phase function, which only depends on a few observable Q-branch of the vibrational band of the Raman-scattered parameters. Most common is the Henyey–Greenstein light consists of an isotropic fraction, this will lead to parameterization: an enhanced degree of polarization in the centre of 1 − g2 a Fraunhofer line. But due to the small cross section Φ(cos ϑ) = , (19.14) of vibrational Raman scattering, this enhancement is 4π(1 + g2 − 2g cos θ)3/2 ∼ very small (e.g. = 0.3% for the Ca–I line at 422.7nm . which only depends on the asymmetry factor g (average and a resolution of 0 01 nm) and occurs only at large cosine of the scattering function): scattering angles. Thus the observed high degrees of polarization at small solar zenith angles cannot be at- 1 1 tributed to vibrational Raman scattering [19.9]. g =cos θ= P(cos θ)cosθ dcosθ (19.15) Due to the relative small cross section of vibrational– 2 − rotational Raman scattering the additional filling in of 1 Fraunhofer or terrestrial absorption lines is around 10% see e.g. [19.11]. For isotropic scattering [Φ(cos θ) = of the filling in due to rotational Raman scattering const] the asymmetry factor g = 0 while for a tropo- atD Part (see Table 19.1). spheric aerosol a typical value might be as large as g ≈ 10. 19.1.5 Mie Scattering Tropospheric aerosol is either emitted from the sur- 19.1 face (e.g. sea salt, mineral dust, biomass burning) or Mie scattering is (after [19.10]) defined as the inter- forms in the gas phase by condensation of chemically action of light with (particulate) matter of dimensions formed hygroscopic species (primarily sulphates, ni- comparable to the wavelength of the incident radiation. trates, or oxidized organic material). The aerosol load It can be regarded as the radiation resulting from a large of the atmosphere, i. e. particle number density and size number of coherently excited elementary emitters (i. e. distribution, depends on the aerosol origin and history. molecules) in a particle. Since the linear dimension of Parameters for typical aerosol scenarios (urban, rural, the particle is comparable to the wavelength of the ra- maritime, background) can be found in the database for diation, interference effects occur. The most noticeable the radiative transfer model LOWTRAN [19.13], which difference compared to Rayleigh scattering is the usu- includes the extinction coefficients and the asymmetry Radiation and Optics in the Atmosphere 19.2 The Radiation Transport Equation 1169 factors as well as their spectral dependence. Another Polarized phase function important aspect is Mie scattering by cloud particles. 0.3 A radiative transfer model including all cloud effects 0.86 µm 0.25 known to date was, e.g., developed by Funk [19.14]. 0.67 µm Mie scattering is only partly an absorption process, 0.2 0.44 µm 0.15 but by similar arguments as in the case of Rayleigh reff = 9 µm scattering, for narrow beams it can be treated as an 0.1 σeff = 0.02 absorption process with an extinction coefficient of 0.05 0 ε λ = ε λ−α M( ) M0 (19.16) –0.05 –0.1 with the Angström exponent α being inversely related 140 145 150 155 160 165 170 to the mean aerosol particle radius. Typically α is found Scattering angle to be in the range 0.5–2.5 with an average value of Polarized phase function α = 1.3 [19.15,16]. For the ideal case of an exponential 0.3 λ = 0.67 µm σ = 0.01 aerosol size distribution: 0.25 eff eff reff = 9 µm σeff = 0.02 Δ 0.2 σeff = 0.05 N −(ν+1) = r . 0.15 σeff = 0.10 Δr 0.1 The Angström exponent is related to the Junge in- 0.05 ν ν = α + dex by 2 [19.17]. Thus an Angström exponent 0 of 1.3 would correspond to a Junge index of 3.3. –0.05 In summary a more comprehensive description of –0.1 atmospheric extinction (in the presence of a single trace 140 145 150 155 160 165 170 gas species and neglecting Raman scattering) can be Scattering angle expressed as: Fig. 19.2 Polarized Mie scattering phase function as a function of scattering angle for cloud droplet having I λ = I λ − L[σ λ c + ε λ + ε λ ] . ( ) 0( )exp ( ) R( ) M( ) a lognormal particle size distribution with an effective ra- (19.17) dius reff = 9 μm. Upper panel: phase function as a function Typical extinction coefficients due to Rayleigh and of wavelength with fixed σ = 0.02 effective size vari- − − eff Mie scattering at 300 nm are 1.3×10 6 cm 1 and ance; lower panel: as a function of effective size variance − − 1–10×10 6 cm 1, respectively. (courtesy of Bréon and Goloub, 2003)

19.2 The Radiation Transport Equation

In this section we present the basic equations describing ds by absorption and scattering. As before we refer to the radiation transport (RT) in absorbing and scattering the absorption (a) and scattering (s) coefﬁcients with D Part media as described by the above elementary processes. εa = Nσa(λ)andεs = Nσs(λ), respectively, with N be- In physical notation the RT equation is a continuity ing the number of absorber or scatterers per volume and equation with corresponding source and sink terms σi (λ) being absorption or scattering cross sections. Both 19.2 (Fig. 19.3); these source and sink terms are assumed processes are commonly referred to as extinction. Ac- to be linear in the radiant ﬂux Φ, intensity I,orradi- cordingly, we obtain the following continuity equation ance F (19.1, 19.3, 19.4). for the incoming intensity traversing the distance ds

19.2.1 Sink Terms (Extinction) dIλ =−[εa(λ) + εs(λ)]Iλ ds =−[σa(λ) + σs(λ)]nIλ ds , (19.18) First we consider the radiant flux Φ per unit space angle Ω and wavelength λ i. e., the incoming inten- where εa is the absorption coefficient, εs is the scattering sity Iλ (19.3) which is attenuated within the distance coefficient, σa(λ) is the absorption cross section of the 1170 Part D Selected Applications and Special Fields

which we integrate over all angles weighted with the Direction of primary beam ∗,λ θ∗,ϕ∗ incoming intensity Is ( ) I λ π 2π * ∗ ∗ ∗ ∗ * * λ = ε λ λ, θ ,ϕ Iλ(θ ) dIs ( ) s( )ds I ( ) θ* 0 0 ∗ ∗ S(θ ,ϕ ) ∗ ∗ ∗ × dϕ sin θ dθ (19.20) A 4π ds to obtain the intensity added to the outgoing inten- ∗ sity dIs . θ Thermal Emission d Finally the intensity due to thermal emission dI (λ, T ) Iλ–dleλ th 2 = d Φ5λ(θ) by the volume element (dV Ads) is added to the outgoing intensity

+dlθλ dIth(λ, T ) = εa(λ)Ip(λ, T )ds = εa(λ)Fp(λ, T )Ads (19.21)

where, as before, Ka denotes the absorption coefficient +dlth, λ and FP(λ, T ) denotes the Planck function 2hc2 dλ dF (λ, T) = . (19.22) P λ5 ehc/λkT − 1 Combining the above source and sink terms we obtain Fig. 19.3 Schematic drawing of the continuity equation the radiation transport equation (19.23): for radiative transfer. The continuity assumes linearity λ of processes in the intensity Iλ. When passing through dI( ) a distance ds the incoming radiation Iλ is attenuated by ex- ds =−[ε λ + ε λ ] λ + ε λ λ, + ε λ tinction (absorption and scattering), Ie,λ. The source term a( ) s( ) I( ) a( )IP( T ) s( ) ∗ π π for the outgoing light is the scattered light dIs,λ from 2 ∗ ∗ θ∗ ϕ∗ I ∗ ∗ ∗ ∗ S(θ ,ϕ ) ∗ ∗ ∗ the space angles and and thermal radiation d th,λ × I (λ, θ ,ϕ ) dϕ sin θ dθ (courtesy of Rödel, 1999) 4π 0 0 (19.23) absorber (molecule), σs(λ) is the scattering cross section of the absorber (molecule), and n is the number of absorbers per unit volume. 19.2.3 Simplification of the Radiation Transport Equation 19.2.2 Source Terms (Scattering and Thermal Emission) Frequently simplifications of the radiation transport atD Part equation are possible, if only partial systems are of In the gas phase there are two sources of radiation: ther- interest. mal emission and scattering, i. e. the radiation removed For instance at short wavelengths (UV, visible) the

19.2 from the primary beam due to scattering (19.18) reap- Planck term can usually be neglected: pears as a radiation source. dI(λ) =−[ε (λ) + ε (λ)]I(λ) + ε (λ) ds a s s Scattering π 2π Evidently, the outgoing light receives some intensity S(θ,ϕ) ∗ ∗ ∗ × F(λ, θ, ϕ) dϕ sin θ dθ. dI ,λ, by scattering from all space angles θ and ϕ .We π s ∗ ∗ 4 introduce a dimensionless scattering function S(θ ,ϕ ) 0 0 (19.24) 4π dσs(λ) Sλ(θ,ϕ) = (19.19) If thermal radiation (from the atmosphere) is of interest σs dΩ due to its long wavelength, Rayleigh and Mie scattering Radiation and Optics in the Atmosphere 19.2 The Radiation Transport Equation 1171

(by aerosol particles and cloud droplets) can frequently beam emitted by a searchlight-type differential optical be neglected absorption spectroscopy (DOAS) light source). λ dI( ) Wide Beams (WB) in the Atmosphere: = εa(λ)[AFP(λ, T) − I(λ)] . (19.25) ds The Two-Stream Model

With the definition of the optical density dτ = εa(λ)ds In the following we consider the transport of solar radia- and after division by A the above equation becomes tion in the atmosphere. Compared to the general form of the radiation transport equation (19.23) the problem is λ dF( ) simplified by assuming a flat, horizontally homogeneous = FP(λ, T) − F(λ) . (19.26) dτ and infinite atmosphere. Therefore only the vertical (z) This latter equation is also known as the Schwarzschild component of the radiance has to be considered. equation. When radiation enters the atmosphere from above, its vertical component is counted as ‘downwelling ra- 19.2.4 Light Attenuation diation’ F↓(λ, z); upon interaction with atmospheric in the Atmosphere constituents (gases or aerosol) this radiation is either absorbed or scattered (Fig. 19.5). These extinction When considering the question of the attenuation of ra- processes reduce the amount of downwelling radi- diation in the atmosphere, two (extreme) cases can be ation (according to (19.17) where the extension of distinguished, as illustrated in Fig. 19.4: wide beams the light path for non-vertical rays has to be taken (WB, as e.g. the illumination of the Earth’s atmosphere into account). While the absorbed radiation causes by the sun) and narrow beams (NB, as e.g. the light no further problems, the scattered radiation appears as a source term, which is split into two parts (taking the phase function into account): A downwelling WB part, which adds to F↓(λ, z) and an upwelling part, which is added to a second, upwelling radiation flux F↑(λ, z). Thermal emission adds to both, F↓(λ, z)and F↑(λ, z). For practical calculation the atmosphere is di- vided into layers of thickness dz, which change the

F↑(λ, zl) atD Part Fig. 19.4 Difference between Wide Beams (WB, top)as, F (λ, z) e.g., the illumination of the Earth’s atmosphere by the sun, ↓ and Narrow Beams (NB, bottom) as, e.g., the light beam 19.2 emitted by a searchlight-type light source. In the NB case the probability of a photon being scattered back into the beam after being scattered out of the beam is generally negligible, therefore extinction can be treated like absorption. In the case of a WB the lateral (i. e. perpendicular to the propagation of the incident radiation flux) radiation Fig. 19.5 The two-stream model. In a horizontally homo- flux can be neglected. Therefore the scattering has only the geneous atmosphere radiation transport can be represented effect of reflecting some of the incoming light, as can be by just two ‘streams of radiation’, the downwelling flux and calculated by, e.g., a two-stream model (see above) the upwelling flux 1172 Part D Selected Applications and Special Fields

radiance F traversing it by dF. The net radiance is The attenuation of a light beam by extinction due composed of both components (up- and downwelling to atmospheric constituents is in principle described radiances) by (19.17). For practical purposes of measurements in the atmosphere, however, (19.17) is oversimplified in λ, = (λ, ) − λ, . Fn( z) F↑ z F↓( z) (19.27) that it neglects the presence of other causes of light extinction, including absorption by other molecules Narrow Beams (NB) in the Atmosphere present in the atmosphere. In the case of a WB the lateral (i. e. perpendicular to the In the natural atmosphere many different molecu- propagation of the incident radiation flux) radiation flux lar species will absorb light. Equation (19.17) must can be neglected. Therefore the scattering has only the therefore be further extended to effect of reflecting some of the incoming light, as can be I(λ) calculated by e.g. a two-stream model (see above). = I (λ)exp − L{Σ[σ (λ)c ]+ε (λ) + ε (λ)} , In contrast, in the case of narrow beams the prob- 0 i i R M ability of a photon being scattered back into the beam (19.28) after being scattered out of the beam is generally negli- where σi (λ)andci denote the absorption cross gible (Fig. 19.4), therefore extinction can be treated as section and the concentration of the i-th species, absorption. respectively.

19.3 Aerosols and Clouds

Aerosols are a natural constituent of the Earth’s atmo- thropogenic or natural processes (e.g. the coagulation sphere and their origin is mostly natural, although lately of smaller Aitken nuclei). Natural sources for giant par- the anthropogenic contribution is increasing. An aerosol ticles are bulk-to-particle conversion (BPC) processes is defined as a stable suspension of particles, liquid or like sea-salt aerosol production, or desert dust mobi- solid, in a carrier gas like atmospheric air. Therefore lization, while human activity contributes, for example dust, haze, smoke, smog, fog, mist, and clouds can be through emission from industries, mining, biomass and considered to be specific aerosol types. The total mass of wood burning, and agricultural dust generation. natural aerosols was found be four times larger than due In the atmosphere, typical particle number con- to human activity in 1968, and by the year 2000 the an- centration decreases with increasing particle size since thropogenic contribution is estimated to have doubled. Aitken particles are newly produced; they subsequently According to Junge and Manson [19.18], aerosols can coagulate and form fewer larger particles. Accordingly be classified by sizes: particles with diameters be- Aitken particles usually dominate the total number low 0.1 mm are named Aitken particles, while those of particles in an air sample, but their contribution with sizes between 0.1–1 mm are “large” particles, and to the total aerosol volume is small, whilst an in- those larger than 1 mm are called “giant” particles. The creasing contribution is due to the large and giant aerosols may also be classified according to their origin particles. Conversely, Aitken particles often dominate atD Part into marine, continental, rural, remote, background, and the surface available for heterogeneous reactions. For urban aerosol, where each category has different char- particles with sizes ranging from a few nanometers up acteristics like chemical composition, size distribution, to tens of micrometers typical number concentrations 19.3 shapes and so on. Aitken nuclei, i. e. the smallest atmo- can be coarsely specified. For example, typical aerosol spheric aerosol particles, are naturally produced from numbers are: 1) ≈ 1.4×104 cm−3 at the (continental) supersaturated vapors by a process called gas-to-particle ground level total concentrations, 2) ≈ 6×102 cm−3 in conversion (GPC), often in connection with photochemi- remote continental regions, 3) 105 cm−3 in large cities, cal reactions between gas-phase constituents (Fig. 19.6). 4) ≈ 3×104 cm−3 in small towns, 5) ≈ 5×102 cm−3 Anthropogenic activities such as combustion and indus- over remote oceans, 6) ≈ 50 cm−3 in the clean Arc- trial processes increasingly lead to the release of aerosol tic, and 7) even lower in the remote Antarctica. The particles, or precursor gases from which aerosol particles vertical aerosol profiles (in number of particles per cu- are formed, into the atmosphere. Large aerosol particles bic centimeter of air) frequently show an exponential can be produced by combustion processes and other an- decay for the lowest 6 km of the atmosphere. Above Radiation and Optics in the Atmosphere 19.3 Aerosols and Clouds 1173

Homogeneous nucleation Bulk-to-particle gas-to-particle conversion conversion Production

Primary aerosol Acting processes Cloud and Heterogeneous condensation fog formation Coagulation Deposition of nonvolatile compounds onto the particles Several Deposition of particle cycles onto water droplets Interconnection Repeated evaporation

Aged and mixed aerosol Removal from the Dry deposition Precipitation atmosphere

Fig. 19.6 Aerosol-related processes in the atmosphere involving particle formation, processes altering particle characteristics, and removal from the atmosphere this level, background tropospheric aerosol concentra- effects in atmospheric photochemistry are most notice- tions (in the Aitken mode) are around 200–300 particles ably in: 1) the heterogeneous processing of longer-lived 3 per cm . Above the tropopause up to around 30 km, the and ozone-friendly halogen species (ClONO2,HCl, total number concentration decreases again to a mini- BrONO2,...) into ozone-harmful halogen oxides (ClO, mum below 1–10 cm−3 particles in volcanically quiet BrO) on polar stratospheric cloud particles, which is periods and 1000 cm−3 after major volcanic eruptions. a major reason for the formation of the Antarctic At any time, about 50% of the globe is cloud ozone hole, 2) uptake of acids (e.g., H2SO4, HNO3, covered. Atmospheric clouds are volumes of water- HCl, HBr,...) and of N2O5 on the stratospheric or supersaturated air containing hydrometeors, which tropospheric aerosols and cloud particles, 3) in the het- are microscopic objects (e.g. aerosol particles, cloud erogeneous conversion of SO2 into H2SO4,orNO3 and droplets, ice and snow crystals) as well as macroscopic N2O5 into HNO3 and 4) the uptake of species such as objects (snowflakes, graupel grains, raindrops, and hail- NH3HNO3,orNH4HSO4 into atmospheric aerosols and stones). The individual cloud particles have sizes with cloud particles. Eventually when these particles grow radii ranging from 0.001 mm to several hundreds of large enough (> some μm), the respective gases at- micrometers, or even centimeters, as in the case of tached or solved inside are efficiently washed out from hailstones. the atmosphere. Atmospheric clouds can be classified into four major Aerosols and clouds also have a large effect on categories: 1) low-level cloud in the lower troposphere the radiative budget of the atmosphere, primarily by D Part (< 2.5 km), 2) middle-level clouds in the middle tro- increasing the scattering of the incoming solar and posphere (2.5–8 km), 3) higher clouds in the upper outgoing thermal radiation. Clouds affect radiation troposphere (8–15 km), and 4) middle (stratospheric) both through their three-dimensional geometry and 19.3 and upper (mesospheric) atmospheric clouds, which the amount, size and nature of the hydrometeors themselves form 11 major subgroups (1.1 cumulus, which they contain. In climate models these proper- 1.2 stratocumulus, 1.3 stratus, 2.1 altocumulus, 2.2 al- ties translate into cloud cover at different levels, cloud tostratus, 2.3 nimbostratus, 3.1 cirrus and cirrostratus, water content (for liquid water and ice) and cloud 3.2 cirrocumulus, 3.3 cumulonimbus, 4.1 polar strato- droplet (or crystal) equivalent radius. The interaction spheric clouds, and 4.2 noctilucent clouds) of some 100 of clouds and radiation also involves other parame- different cloud types in total. ters (asymmetry factor of the Mie diffusion) which Both aerosols and clouds have a considerable im- depend on cloud composition, and most notably on their pact on atmospheric photochemistry and radiation. Their phase. 1174 Part D Selected Applications and Special Fields

In effect, the occurrence of aerosols and clouds in- temperature. The subtle balance between cloud impact creases the planetary albedo A of the solar short-wave on the SW and terrestrial long-wave radiation altered by (SW) radiation, and thus lead to a net cooling of the a change in any of the aforementioned parameters, the Earth. Conversely clouds, and to a much lesser degree dependence of the radiation budget on altitude at which aerosols, increase the infrared albedo B of the atmo- clouds occur and the solar inclination (latitude and sea- sphere and thus increase the downwelling atmospheric son) make clouds the most sensitive factors to affect the long-wave (LW) radiation which increases the surface global climate in both directions (cooling/warming).

19.4 Radiation and Climate

2 The atmospheric radiation budget largely determines the where S0 is the solar constant (1370 W/m ), A is the Earth’s climate. Evidently the incoming solar or short- terrestrial SW albedo (0.298), the factor 4 coming from wave (SW) radiation shining on the globe has to be geometric considerations, ε is the LW emissivity (0.96), balanced by the outgoing long-wave (LW) radiation. B is the atmospheric LW albedo (0.34), σ is Boltz- −8 2 This thermal equilibrium between incoming SW and mann’s constant (5.67 × 10 W/m /K), and Ts is the outgoing LW radiation and can be simply expressed average temperature (Ts = 286 K) of the Earth’s sur- by face. It thus becomes clear that the globe’s surface temperature Ts is given by a delicate balance of the S (1 − A)/4 = ε(1 − B)σT 4 (19.29) 0 s parameters S0, A,andB. In geological and historic

Table 19.2 Compendium of change in recognized periods in climate change and changes in the solar constant S0 Time scale/period Cause Change in solar constant Observation/problem S0

4.5Ga Secular trend in solar out- Secular 25–30% increase ‘Faint Sun problem’, i. e. liquid H2O put should not have been there, but was present since 4 Ga before present 450 ka Change in orbital eccen- < 0.7W/m2 Change in ice volume, Δ18O/16Oin tricity Δε = 0.06 (Milankovitch) H2O and CaCO3 in foraminifera 100 ka Change in orbital eccen- < 0.7W/m2 Change in ice volume, Δ18O/16Oin tricity Δε = 0.06 (Milankovitch) H2O and CaCO3 in foraminifera 41 ka Change in obliquity (ax- June insulation changed Change in ice volume, Δ18O/16Oin ◦ ial tilt) due to Earth and by 25% at 80 N, no net H2O and CaCO3 in foraminifera Jupiter’s orbital plane tilt change on annual S0 (Milankovitch) 23 ka June insulation changed by Change in ice volume, Δ18O/16Oin 2 ◦ 100 W/m at 60 N, no net H2O and CaCO3 in foraminifera change on annual S0 atD Part (Milankovitch) 1.5ka Unclear whether cause is 14Cand10Be variation in oceanic solar, ‘eigenmode’ of the sediments, 14C variation in tree

19.4 climate system? rings 210a (Suess) Unclear whether cause is 14C variation in tree rings, 14Cand 148a, and 88a solar, ‘eigenmode’ of the 10Be variation ice cores, (Gleisberg) cycles climate system? 2 22a Sun spot ‘overtone’, eigen- ΔS0 ≈ 1.5W/m , Change in atmospheric circulation? mode in solar magnetic UV radiation changes by ﬁeld oscillation 0.37–0.6% 11a (Schwabe 1843) Sun spot ‘overtone’, eigen- Change in atmospheric circulation? mode in solar magnetic ﬁeld oscillation 4w (27d) Sun rotation period Small ? Radiation and Optics in the Atmosphere 19.4 Radiation and Climate 1175

Fig. 19.7a–c Schematic overview of the SW (left part)and LW (right part) radiative transfer in the atmosphere; upper a) λBλ(Normalized) panel: (a) incoming solar SW and outgoing LW terrestrial Black body spectrum, (b) atmospheric absorption from individual gases curves at ground level (total atmosphere) and (c) at 11 km

6000K 255K times, the solar constant is known to have varied on different timescales, mostly given by changes in the Earth’s orbital parameters, as suggested by Milankovitch in 1941 [19.19] and solar activity (Table 19.2), causing 0.1 0.15 0.2 0.3 0.5 1.0 1.5 2.0 3.0 5.0 10 15 20 30 50 100 well recognized and significant effects on the Earth’s Wavelength (μm) b) climate. In this context, most notable is that the size Absorption (%) H2O CO2 100 ΔS of any of the known processes listed in Table 19.2 H O 0 80 Ground 2 has not been sufficiently large to be held solely re- 60 level sponsible for documented ΔTs changes, which were 40 ◦ inferred to be as large as some 10 C. Therefore, it 20 HOO O3 O3 0 is well accepted that the global climate system ampli- O2 O2O2 O3 O2 O2 CO2 H2O O3 N2OH2O (rotation) O2 H2O CO2 N2O fies external disturbances (forcing) through interacting N2O CO2 CH CO CH complicated positive and negative feedback cycles (Ta- c) Absorption (%) 4 4 100 ble 19.2). 80 11 km Another factor important for Ts is of course the 60 magnitude and variability of the SW albedo A (19.35). 40 20 This is largely influenced by the amount of cloud and 0 the abundance of atmospheric aerosol; the latter is ei- 0.1 0.15 0.2 0.3 0.5 1.0 1.5 2.0 3.0 5.0 10 15 20 30 50 100 ther due to increasing directly back reflection of SW Wavelength (μm) radiation to space, or by altering the cloud particle formation processes, a process called the indirect aerosol 1970s [19.20]. Changing global cloud cover is also likely effect [19.20, 21]. In the recent past changes in the to have occurred in the past. In the tropics, which are global albedo due to increasing atmospheric aerosol a particularly sensitive region for the global energy bud- abundances, mostly particles containing sulphuric acid get, the cloud cover appears to be highly variable on has been well recognized and held partly responsible timescales ranging from days to decades. Accordingly, for lower global Ts between the late 1940s to late satellite-based cloud cover records that began in the late

The global mean radiative forcing of the climate system for the year 2000, relative to 1750 Radiative forcing (W/m2) 3 Warming Halocarbons Aerosols 2 N2O atD Part CH4 Tropo- Black carbon spheric 1 CO2 from fossil Mineral Aviation-induced ozone fuel burning dust Solar

Contrails Cirrus 19.4 0 Strato- Organic Land-use spheric carbon Biomass –1 Sulphate (albedo) ozone from burning Aerosol only fossil fuel indirect effect –2 burning Cooling High Medium Medium Low Very Very Very Very Very Very Very Very low low low low low low low low Level of Scientific Understanding Fig. 19.8 External factors which force climate change (adopted from IPCC, 2001) 1176 Part D Selected Applications and Special Fields

1970s are still insufficiently long to establish unambigu- In 1896, the atmospheric greenhouse effect of CO2 ously an observation-based relation between a changing was already recognized by S. Arrhenius. Accordingly A and Ts [19.22]. it is undisputed in the scientific community that rising The atmospheric LW albedo B is responsible for atmospheric CO2 concentrations affect the atmospheric the greenhouse effect of the atmosphere. If B were LW budget and thus Ts. Radiative transfer calculations zero, then according to (19.35), Ts would be 255 K, show that the CO2 increase from preindustrial 280 ppm clearly cooler than the habitable Earth is able to provide to presently 370 ppm alone gives rise to a present ra- 2 (Ts = 287 K). The value of B is due to the combined ac- diative forcing of 1.4W/m and for all greenhouse tion of the most important atmospheric greenhouse gases gases of 2.4W/m2 ([19.20], Fig. 19.8). Naively adding H2O, CO2,CH4,O3,N2O, and many others, mostly the respective radiative forcing in (19.18) leads to man-made, trace molecules [19.20]. It appears that, even a ΔTs =+0.7 K, precisely the value that is reported though each greenhouse gas has its own specific spec- for the global average temperature rise in the past trum, they combine in a way that only a small fraction 150 y [19.20]. However, due to the complicated inter- of the outgoing LW radiation is not absorbed in the actions in the climate system, it is disputed how the atmosphere, i. e., radiation in the atmospheric window global climate system is and will react in detail to future (8–14 μm) (Fig. 19.7). man-induced LW radiative forcing.

19.5 Applied Radiation Transport: Remote Sensing of Atmospheric Properties 19.5.1 Trace Gases a series of unique advantages including high (i. e. ppt- level in many cases) sensitivity, very specific detection Measurements of trace gas concentrations (and other of a given molecule, inherent calibration, and wall-free quantities such as aerosol distribution or the intensity operation. These properties, in combination, are diffi- of the radiation field in the atmosphere) are the ex- cult to obtain in techniques based on other principles. perimental prerequisites for the understanding of the Here we describe a particular technique, differential op- physico-chemical processes in the Earth’s atmosphere. tical absorption spectroscopy (DOAS), which has been At the same time the determination of trace gas con- successfully used in atmospheric measurements for sev- centrations in the atmosphere constitutes a challenge eral decades now, while new applications continue to be for the analytical techniques employed in several re- introduced. spects: It is well known (e.g. Perner et al. [19.23]) that species (such as OH radicals) present at mixing 19.5.2 The Fundamentals of DOAS rations ranging from as low as 0.1 ppt (one ppt corresponds to a mixing ratio of 10−12, equivalent to about The DOAS technique [19.26, 27] makes use of the 2.4×107 molecules/cm3) to several ppb (1 ppb corres- structured absorption of trace gases. Typically spectra ponds to a mixing ratio of 10−9) can have a significant are recorded which encompass several hundred spec- atD Part influence on the chemical processes in the atmosphere. tral channels. Evaluation is done by fitting the spectral Thus, detection limits from below 0.1 ppt to the ppb structure of the trace gases, thus making use of all the range are required, depending on the application. On the spectral information. DOAS has proven to be particu- 19.5 other hand, measurement techniques must be specific, larly useful for the determination of the concentration i. e. the result of the measurement of a particular species of unstable species such as free radicals or nitrous acid. should neither be positively nor negatively influenced In addition, the abundance of aromatic species can be by any other trace species simultaneously present in the determined at high sensitivity (see below). DOAS, like probed volume of air. Given the large number of differ- all spectroscopic techniques, relies on the absorption of ent molecules present at the ppt and ppb level, even in electromagnetic radiation by matter. Quantitatively the clean air, meeting this requirement is also not trivial. absorption of radiation is expressed by the Lambert– Presently many highly sophisticated techniques for Beers law: the measurement of atmospheric trace species are in use. λ = λ [− σ λ ] , Among these, spectroscopic techniques [19.24,25] offer I( ) I0( )exp L ( )c (19.30) Radiation and Optics in the Atmosphere Applied Radiation Transport 1177 where I(λ) is the intensity after passing through a layer shows rapid variations with λ, for instance due to an ab- of thickness L, while I0(λ) denotes the initial inten- sorption line. The meaning of rapid and slow (or rather sity emitted by the light source. The species to be smooth and structured) variation of the absorption cross measured is present at the concentration (number den- section as a function of wavelength is, of course, a ques- sity) Nc. The quantity σ(λ) denotes the absorption cross tion of the observed wavelength interval and the width section at the wavelength λ; it is a characteristic prop- of the absorption bands to be detected. Note that extinc- erty of any species. The absorption cross section σ(λ) tion due to Rayleigh and Mie scattering can be assumed can be measured in the laboratory, while the determina- to be slowly varying with λ. Thus (19.30) becomes tion of the light path length L is trivial in the case of I(λ) = I (λ)exp −LΣ σ (λ)N the arrangement of an artificial light source and detec- 0 i ci − {Σ[σ λ ]+ε λ + ε λ } tor (Fig. 19.9, arrangement a). Once those quantities are ×exp L i0( )ci R( ) M( ) known, the trace gas concentration c can be calculated × A(λ) , (19.32) from the measured ratio I (λ)/I(λ). In contrast to lab- 0 where the first exponential function describes the ef- oratory spectroscopy, the true intensity I (λ), as would 0 fect of the structured, differential absorption of trace be received from the light source in the absence of any species, while the second exponential constitutes the absorption, is usually difficult to determine when meas- slowly varying absorption of atmospheric trace gases as urements are made in the open atmosphere or in smog well as the influence of Mie and Rayleigh scattering de- chambers. The solution lies in measuring the so-called scribed by the extinction coefficients ε (λ)andε (λ), differential absorption. This quantity can be defined as R M respectively. The attenuation factor A(λ) describes the the part of the total absorption of any molecule rapidly (slow) wavelength-dependent transmission of the optical varying with wavelength and is readily observable, as system used. Thus we can define a quantity I as the will be shown below. Accordingly, the absorption cross 0 intensity in the absence of differential absorption: section of a given molecule (numbered i) can be split λ into two portions: I0( ) σ λ = σ λ + σ λ , = I (λ)×A(λ) i ( ) i0( ) i ( ) (19.31) 0 ×exp − L{Σ[σi0(λ)Nci ]+εR(λ) + εM(λ)} . where σi0(λ) varies only slowly with the wavelength λ, (19.33) for instance describing a general slope, while σi (λ)

a) c) DOAS 2 I0 I

Detector Pollution Plume b)

DOAS 1 D Part 19.5 Detector Retro- reflector arrays

Fig. 19.9a–c The active DOAS principle can be applied in several light-path arrangements and observation modes using artiﬁcial light sources such as arc lamps or incandescent lamps in a searchlight-type arrangement, or lasers. The light- path-averaged trace gas concentration is determined in the ‘traditional’ setup (a). In situ concentrations are measured with multiple reﬂection cells (b). The new ‘tomographic’ arrangement (c) employing many DOAS light paths allows mapping of (two- or three-dimensional) trace gas distributions 1178 Part D Selected Applications and Special Fields

Fortunately the effect of slowly varying absorbers, i. e. systems can be used to fold the light path into a small vol- the exponential in (19.33), can be removed by high-pass ume [19.28]. An example of detection limits attainable filtering the spectral data, thus only the first exponen- with multi-reflection systems is given in Table 19.3. tial function in (19.32) remains, which is essentially Lambert–Beers law [(19.30) for more than one ab- 19.5.3 Variations of DOAS sorber]. It should be noted that the length of the light path is more difficult to determine – or might actually The DOAS technique can be adapted to a large variety not have a precise meaning – in applications where di- of measurement tasks; as a consequence there are many rect or scattered sunlight is used (arrangements d, e, and variants of the DOAS technique in use. These can be f and Fig. 19.11), in this case the column density S of grouped into active techniques, which employ their own the trace gas light sources (e.g. Xe-arc lamps or incandescent lamps), ∞ and passive techniques, which rely natural light sources (e.g. sunlight, moonshine or starlight). S = N (l)dl (19.34) c The most common active DOAS light-path arrange- 0 ments include (Fig. 19.9): can still be determined. In the case of a constant trace = gas concentration Nc0 (l) c0 along a path length L the a) The traditional active long-path systems (usually = column density simply becomes S Nc0 L. folded once); In order to obtain sufficient sensitivity, light-path b) Active systems using multi-reflection cells (e.g. lengths L of the order of several 100 m to several 1000 m white cells); are usually required. For measurements in the free at- c) Recently the first tomographic systems allowed the mosphere, assuming the arrangement a in Fig. 19.9, the determination of 3-D trace gas distributions by trace gas concentration is averaged over the whole length multiple-beam active DOAS. of the light path, which makes the measurement less susceptible to local emissions. On the other hand meas- The most common passive DOAS light path arrange- urements must frequently be made in a small volume ments include (Fig. 19.10): (e.g. in photo-reactors); in these cases multi-reflection d) Zenith scattered light (ZSL)-DOAS is well-suited to study stratospheric trace gases. For instance a global d) f) network of ZSL-DOAS instruments continuously watches the distribution of stratospheric species (e.g. O3,NO2,BrO,OClO). e) Multi-AXis (MAX)-DOAS allows determination of trace gases and their vertical distribution in e.g. Detector the atmospheric boundary layer or the detection of plumes from cities, stacks, or volcanoes. In addi- e) tion Airborne Multi-AXis (AMAX)-DOAS is a new technique for application from aircraft. atD Part f) Direct sunlight observation of trace gases from balloon platforms allows the determination of trace gas Detector profiles. 19.5 An extremely important, new application is satellite- Fig. 19.10d–f The passive DOAS technique can be applied in sev- borne DOAS, pioneered by the GOME and SCIA- eral light path arrangements and observation modes using natural MACHY instruments [19.29,30] that allow observation light sources such as sunlight or moonlight. The zenith scattered of global stratospheric and tropospheric trace gas distri- light (ZSL-DOAS) set-up (d) is most suited for the determination butions (Fig. 19.11): of stratospheric species, while the Multi-AXis (MAX-DOAS) arrangement (e) provides highly sensitive trace gas measurements in g) The most basic observation geometry is the nadir the atmospheric boundary layer. Direct sunlight observation of trace view. Here, sunlight backscattered from the Earth gases from balloon platforms (f) allows the determination of trace and its atmosphere is analyzed by DOAS to yield gas profiles in the atmosphere trace gas slant column densities. Ideally all light Radiation and Optics in the Atmosphere Applied Radiation Transport 1179

recorded by the satellite spectrometer traversed the atmosphere twice. g) h) h) Satellites also allow the observation of scattered sunlight in a limb-viewing geometry. This allows the determination of trace gas proﬁles (although generally only for the stratosphere). i) Occultation (sunset, sunrise or starlight) measurements from satellites are an attractive possibility.

In addition it is now possible to determine the photon i) path-length distribution in clouds by ground-based observation of O2 and O4 bands. Here effectively DOAS is Sciamachy reversed: instead of the usual configuration where an un- known concentration is measured while the length of the light path is (at least approximately) known, the photon Fig. 19.11g–i Satellite-based DOAS has become an important tech- path-lengths are determined by observing the absorption nique for probing the atmospheric composition on a global scale. due to an absorber with known concentration, such as The most basic observation geometry is the nadir view (g),here oxygen (O2) or oxygen dimers (O4). sunlight backscattered from the Earth and its atmosphere is analyzed by DOAS to yield trace gas slant-column densities. Ideally all 19.5.4 Atmospheric Aerosols light recorded by the satellite spectrometer traversed the atmosphere twice. Satellites also allow the observation of scattered sunlight in a The atmospheric aerosol concentration is frequently limb-viewing geometry (h). This allows the determination of trace monitored by light detection and ranging (LIDAR) gas profiles (although generally only for the stratosphere). Occulta- instruments operated from the ground, aircrafts, or satel- tion (sunset, sunrise or starlight) measurements (i) from satellite lites [19.32]. In their most basic configuration they are another attractive possibility to determine trace gas vertical measure the ratio of total extinction due to Mie and profiles

Table 19.3 Selection of species of atmospheric relevance measurable by DOAS and detection limits. Differential absorption cross-sections and corresponding detection limits (assuming 32 passes in a multi-reﬂection cell with a 8 m base path) for a series of species to be investigated by DOAS in the Valenciasmog chamber. A dielectric mirror coating or DOAS measurements in the open atmosphere would allow longer light paths, resulting in correspondingly improved detection limits Species Wavelength Differential abs. cross Detection limit σ = − = of prominent section ( i ) L (40 8) × 8 m 256 m band (nm) (10−20 cm2/molec.) (ppt) ClO 280 350 200 BrO 328 1040 80

IO 427 1700 50 D Part

SO2 300 68 1000

NO2 430 17 2700

HONO 352 41 2000 19.5

O3 282 10 8000 Glyoxalb ca. 470 ≈ 10 ≈ 8000 Benzene 253 200a 400 Toluene 267 200a 400 Phenol 275 3700a 20 Xylenes 260–272 ≈ 100a ≈ 800 Benzaldehyde 285 500a 160 a data from Trost et al. 1997, R. Volkamer, personal communication 2000 b from [19.31] 1180 Part D Selected Applications and Special Fields

Fig. 19.12 Schematic setup of the DLR-Oberpfaffenhofen aircraft-borne LIDAR system (OLEX). APD: avalanche Aircraft window photo diode; PM: photomultiplier (courtesy G. Ehret/DLR Oberpfaffenhofen)

The Ozone Lidar EXperiment (OLEX) LIDAR is used as an aerosol and ozone LIDAR (Fig. 19.12). The 1064 nm system consists of two laser transmitters: 1) a Nd:YAG Telescope 308 nm + 532 nm +354 nm laser operating at a repetition rate of 10 Hz in the fundamental, second harmonic, and third harmonic with output energies of 200 mJ at 1064 nm, 120 mJ at 532 nm, and 180 mJ at 355 nm, and 2) a XeCl laser operating at 10 Hz, emitting 200 mJ at 308 nm. The receiver system Nd:YAG is based on a 35 cm Cassegrain telescope with a field F 354 nm laser Aperture of view (FOV) of 1 mrad and a focal length of 500 cm. The system uses five detection channels: one channel for 1064 nm, two channels for 532 nm in two polariza- PM CeCl F 1064 nm laser tion planes, one channel for 355 nm, and one for 308 nm. Aperture The 308 and 355 nm channels are specifically dedicated F 308 nm Aperture APD to ozone profiling in the stratosphere, while the other wavelengths are used for aerosol and cloud monitoring. PM The acquisition electronics can acquire each single sig- nature, with the lasers firing at a 50 Hz repetition rate, Polarizing PM beamsplitter and the aerosol distributions measured by the system F 532 nm are available in real time. The total weight of the sys- Aperture Aperture tem is about 270 kg and the total power consumption F 532 nm above 1.6kW. PM In the present example, the OLEX LIDAR was assembled on board the DLR-Falcon aircraft in a down- looking mode that enabled aerosol backscattering Rayleigh scattering versus the calculated expectation measurements below the aircraft cruise altitude. On of pure Rayleigh scattering for a set of absorbing and 24 September 1999, a flight was undertaken leading from non-absorbing wavelengths. Oberpfaffenhofen near Munich to the Adriatic Sea. The

Altitude (km) 400 300 200 100 0 km (m/s) European alps Po basin Elevated layer 18.2 5 18.7 atD Part 13.2 4 11.5 6.4 3 3.7 19.5 0.8 2 2.4 1.6 1 2.3 0.5 0 47 46 45 44 nr. Innsbruck nr. Venice/Coastline Northern adriatic sea Fig. 19.13 Tropospheric aerosol distribution recorded by OLEX at λ = 1024 nm during a flight of the Falcon aircraft from Oberpfaffenhofen to the Adriatic Sea on 24 September 1999. The color codes qualitatively indicates the aerosol concentration with the large aerosol concentrations given in yellow and the small in blue color Radiation and Optics in the Atmosphere Applied Radiation Transport 1181 main scientific objective was to investigate the spatial Transmission distribution of made-made aerosols emitted from traffic, 1.0 industry and house burning into the lower troposphere. The major detected features were inhomogeneously RR 9.9 RQ 5.6 RR 5.5 PQ 3.4 PP 29.29 PP PQ 17.18 RQ 9.10 0.8 27.27 PP PQ 28.27 PQ 28.28 aerosol-loaded air masses located in the alpine mountain PR 211.11 RQ 15.16 valleys and the fairly uniform planetary bound- Si I Mg I ary layer (PBL) stretching over the whole alpine 0.6 PQ 33.32 33.33 PP ridge (Fig. 19.13). Both aerosol layers nicely mark PQ 31.30 31.31 PP the vertical layering of a vertically layered lower PQ 29.28 29.29 PP 0.4 troposphere typical for a high-pressure system at mid- K I latitudes in fall. Another interesting feature was the 27.26 PQ 27.26PQ 27.27 PP 0.2 Measurement structure of the planetary boundary layer (PBL) located PQ 25.24 25.25 PP Simulation over the Adriatic Sea (≈ 2000 m above sea level), which 768.0 768.5 769.0 769.5 770.0 770.5 overlaid a very thin marine boundary layer (250–300 m Wavelength (nm) above sea level). This feature resulted from an advection Resisual (OD) of polluted PBL air masses originating from the North 0.008 Italian Apennines and the Po Basin by synoptic westerly 0.004 winds [19.33]. 0.000 19.5.5 Determination of the Distribution –0.004 of Solar Photon Path Lengths –0.008 768.0 768.5 769.0 769.5 770.0 770.5 Wavelength (nm) A novel application of differential optical absorption PDF 1.0 spectroscopy (DOAS) is the measurements of path- Model Γ = 2.84 × VOD length distributions of solar photons (photon PDF) 2 0.5 0.5 transmitted to the ground [19.34–38]. The knowledge = 8.28 × VOD 0.5 of a photon PDFs is of primary interest in the cloudy atmospheric radiative transfer, atmospheric absorption of solar radiation energy and thus for climate. The 0.0 method relies on the analysis of highly resolved oxy- 0246810 gen A-band (762–775 nm) spectra (Fig. 19.14) observed Path length (VOD) ◦ with a telescope with a small field of view (1 )in Fig. 19.14 Measured and modeled oxygen A-band spectrum (up- zenith-scattered sky light. It uses the fact that solar pho- per panel), inferred residual spectrum (middle panel) and inferred tons are randomly scattered by molecules, aerosols and photon PDF for the observation between 12:32 and 12:33 UT over cloud droplet during their atmospheric transport. Since Cabauw/NL on 23 September 2001. The black vertical line indi- a fraction of the solar photons become absorbed in the at- cates the optical path for the direct sunlight. Photon path lengths are mosphere, largely depending on the atmospheric opacity given in units of vertical atmosphere (VOD) or air mass (AM) for a given wavelength, for each wavelength solar photons travel on different average, long distances in the storm Cb (cumulus nimbus) clouds, average photon path D Part atmosphere. Spectral intervals with a largely changing lengths of up to 100 km have been observed, while for atmospheric opacity but known absorber concentration Sc (stratus clouds) typically photon paths are 50–100% and spectroscopic constants, such as that given by the larger than for the direct and slant path of the sun’s 19.5 oxygen A-band, thus contain information on the pho- rays. Moreover, it appears that even though the spa- ton PDFs. Recent studies have been showing that the tial distribution of cloud droplets is inhomogeneous atmospheric photon PDFs are highly correlating with with the moments of the density behaving like multi- the total amount of liquid water in the atmosphere, the fractals, photon PDFs tend to be mono-fractals, mostly spatial arrangement of clouds, cloud inhomogeneity and due to the so-called radiative smoothing of optically solar illumination [19.34–38]. For example, for thunder- thick clouds [19.39]. 1182 Part D Selected Applications and Special Fields

19.6 Optical Phenomena in the Atmosphere

Phenomena based on atmospheric optics can be observed nearly every day and everywhere. Examples are Absorption water droplets ice crystals rainbows, halos, mirages, coronas, glories, the colors of Scattering of light from dendrites the sky, sunsets and twilight phenomena, green ﬂashes, Reflection sun, moon dust particles noctilucent clouds, polar lights, and many more. All Refraction by / from Diffraction electrons these different phenomena are due to interaction of light atoms with matter present in the atmosphere (Fig. 19.15). Emission of light from molecules In the following, a brief survey of light scattering by ions molecules and particles with regard to optical phenomena in the atmosphere will be given. More details on Fig. 19.15 Possible interaction processes of light with con- light scattering by particles can be found in a number of stituents of air monographs [19.40–43]. Several books have focussed on one or more optical phenomena (e.g. [19.44–54]). 19.6.1 Characteristics of Light Scattering Some older original publications are available as a col- by Molecules and Particles lection of articles [19.55] and the proceedings of the regular conferences on atmospheric optics have been Nearly all optical phenomena in the atmosphere are published in special issues of the journals of the Optical due to light scattering – mostly sunlight and some- Society of America [19.56–63], most of them recently times moonlight – with the constituents of air. In the put together on a CD-ROM [19.64]. Several videos and following, a brief general survey of light scattering pro- movies deal with selected phenomena [19.65–69], some cesses in the atmosphere will be given. Consequences articles focus on connections to the ﬁne arts [19.70–73], for various optical phenomena of the atmosphere will be a number of books focus on simple experiments as well systematically discussed in the respective sections ac- as observations [19.74,75] and a number of internet sites cording to the constituents of the air that are responsible with a lot of material are also available, Table 19.4. (Table 19.5).

Table 19.4 List of internet sites on atmospheric optics 1. http:// www.polarimage.fi (Images of many phenomena) 2. http:// www.atoptics.co.uk (Images and simulations) 3. http:// www.engl.paraselene.de (Images) 4. http:// www.philiplaven.com (Images and simulations) 5. http:// www.funet.fi/pub/astro/html/eng/obs/meteoptic/links.html (Finnish amateur observer site) 6. http:// www.ursa.fi/english.html (Finnish astronomical association) 7. http:// www.meteoros.de (German halo observer network) 8. http:// mintaka.sdsu.edu/GF/ (Green flashes) 9. http:// thunder.msfc.nasa.gov (Nasa lightning page) atD Part 10. http:// www.fma-research.com/ (Lightning, in particular sprites) 11. http:// www.sel.noaa.gov/ (Space weather)

19.6 12. http:// www.spaceweather.com/ (Space weather) 13. http:// sunearth.gsfc.nasa.gov/ (Nasa Sun Earth connection, outreach) 14. http:// www.mreclipse.com/ (Eclipses) 15. http:// www.geo.mtu.edu/weather/aurora/ (Auroras) 16. http:// www.exploratorium.edu/auroras/index.html (Auroras) 17. http:// www.amsmeteors.org/ (American meteor society) 18. http:// www.imo.net/ (International meteor organization) 19. http:// liftoff.msfc.nasa.gov/academy/space/solarsystem/meteors/Showers.html (Meteor showers, Nasa) Radiation and Optics in the Atmosphere 19.6 Optical Phenomena in the Atmosphere 1183

Table 19.5 Classiﬁcation of optical phenomena of the atmosphere. Depending on the homogeneity of the air, different light interaction processes correspond to various phenomena, which are indicated by examples

1. Pure homogeneous air • refraction ⇒ mirages, shape changes of sun/moon at horizon Sect. 19.6.2 • scattering ⇒ blue sky Sect. 19.6.3 2. Inhomogenous atmosphere: Air plus water droplets • refraction and reﬂection ⇒ rainbows Sect. 19.6.4 • forward scattering/diffraction ⇒ coronas Sect. 19.6.5 • backward scattering/diffraction ⇒ glories Sect. 19.6.5 3. Inhomogenous atmosphere: Air plus ice crystals • refraction and reﬂection ⇒ halos Sect. 19.6.6 • forward scattering/diffraction ⇒ coronas Sect. 19.6.5 4. Inhomogenous atmosphere: Air plus aerosols • absorption, scattering ⇒ sky colors Sect. 19.6.7 • absorption, scattering ⇒ visibility Sect. 19.6.8 • forward scattering/diffraction ⇒ coronas Sect. 19.6.5 5. Ionized air • ionization/excitation by solar wind, emission ⇒ auroras Sect. 19.6.9 • ionization/excitation by discharges, emission ⇒ lightning Sect. 19.6.9

Molecular Scattering anthropogenic droplets/particles with an enormous va- For pure air, scatterers are mostly N2 and O2 molecules, riety in composition. Typical aerosol particles have size the greenhouse gases CO2 and H2Oaswellassome distributions in the range 0.1–10μm with an average traces of other gases such as Ar [19.76]. These scatter- around 1 μm (e.g. [19.83]). The vertical distribution of ers are all much smaller than the wavelength of visible the particle components of air may also be described by light and one speaks of a molecular atmosphere [19.77]. some kind of exponential formula [19.77], however, the The vertical distribution of the gaseous components of scaling height of 1–2 km is much smaller than that for air follows the barometric formula with a scaling height molecules. of about 8 km. The scattering of sunlight from the bound The scattering of light from particles in these size electrons of atoms/molecules is usually called Rayleigh ranges differs dramatically from molecular scattering, scattering [19.1, 78, 79]. (For historical notes on the since the particle size is comparable to or larger than the problem of the blue sky, see [19.80].) wavelength of the light. Since atoms/molecules within particles are very close to each other, they are excited D Part Scattering from Particles coherently, i. e. the total scattering from all molecules Normal air usually also contains a variety of different within a particle is quite different from the sum of the particles, the most predominant being water droplets, scattering of all individual molecules within the particle. 19.6 ice crystals and snow ﬂakes (dendrites). The size of the In 1908, G. Mie gave the solution of classical electro- water droplets ranges from several micrometers (cloud dynamics for the simplest case, referring to spherical droplets) to well above 1 mm (raindrops); ice crystals shapes of the particles [19.10]. Henceforth, this type of are very often of hexagonal symmetry with sizes on the light scattering from particles is mostly known as Mie order of 10–100 μm. scattering. This name is sometimes also used for exten- In addition, the atmosphere also contains other liquid sions to nonspherical particle shapes. For nonabsorbing and solid particles called aerosols [19.20, 76, 81, 82]. particles, which are small compared to the wavelength, These include many types of particles from dust, oil the Mie scattering gives the same results as Rayleigh droplets from forest ﬁres, volcanic ashes as well as scattering. In the general case, however, it shows pro- 1184 Part D Selected Applications and Special Fields

nounced differences regarding wavelength dependence, length, scattering from water droplets is essentially angular dependence, degree of polarization of the scat- independent of wavelength. tered radiation as well as scattering cross section per molecule [19.40–42, 77]. Angular Dependence. Figure 19.17 gives a schematic overview of how the angular dependence of scattering Comparison of Rayleigh and Mie Scattering changes with particle size. Molecules scatter unpo- Wavelength Dependence. Figure 19.16 gives a sche- larized light nearly isotropically (see also Fig. 19.1) matic example of the scattering of light by water whereas large particles scatter rather asymmetrically molecules as well as water droplets of, say, 10 μm. in the forward direction. For a given particle size, the Whereas molecules or very small particles scatter light scattering also depends on wavelength. mostly according to the inverse fourth power of wave- Degree of Polarization. For Rayleigh scattering, and as- Relative scattering signal suming perfectly spherical air molecules, light scattered at an angle of 90◦ would be perfectly polarized [19.84]. 1 However, air molecules already show an anisotropy, re- Water droplets ducing the polarization to only about 94% [19.77, 79]. For larger particles, the degree of polarization varies considerably as a function of scattering angle for Water molecules ﬁxed size. These patterns, however, strongly depend on size [19.40, 41, 77]. In addition, the degree of po- 0 larization at a ﬁxed angle varies as a function of 400 500 600 700 800 wavelength. Wavelength (nm) Fig. 19.16 Schematic wavelength dependence for light Scattering Cross Section per Molecule:. The enormous scattering from water molecules and water droplets of, e.g., differences between incoherent and coherent scattering μ 10 msize become apparent when comparing light scattering from isolated molecules to those of the same molecules within a particle, e.g. water molecules within a water droplet Rayleigh scattering or a raindrop [19.77]. For example, the scattering per molecule that belongs to a cloud droplet of 1 μmis about 109 times larger than scattering by an isolated water molecule and still a factor of about 100 larger than a molecules in a 1 mm raindrop.

Single and Multiple Scattering, Optical Mean Φ Յ λ/50 Free Path and Air Mass Light from the sun (or moon) has to traverse the atmosphere before reaching the eye of an earthbound atD Part observer. It is attenuated by scattering and absorption, Φ λ/4 depending on the number of scatterers present in the line of sight. If absorption can be neglected, one may use the

19.6 scattering coefficient Φ 5λ βS = Nσ, (19.35) where N is the number of scatterers per unit volume and σ is the extinction cross section, 1/βS defines the scattering mean free path, i. e. the average distance a photon Mie scattering has to travel before being scattered. (If absorption is Fig. 19.17 Schematic overview of the angular dependence included, an additional absorption coefficient βA is in- of light scattering from molecules and very small particles troduced and βS will be replaced by β = βS +βA.) Using (Rayleigh scattering) to larger particles (Mie scattering) βS, one may define the optical thickness τ between two Radiation and Optics in the Atmosphere 19.6 Optical Phenomena in the Atmosphere 1185 points A and B of the atmosphere as Normal optical thickness 0.4 B Molecular atmosphere τ = β (x)dx . (19.36) S 0.3 A

The optical thickness is a measure of the physical thick- 0.2 ness in units of the scattering mean free path. For light along a radial path, i. e. coming from the zenith, the 0.1 amount of air to be traversed is least and one refers to the normal optical thickness, which is also called the 0.0 optical depth. For a pure molecular atmosphere, this is 400 500 600 700 800 depicted in Fig. 19.18. In the visible spectral range, its Wavelength in nm values are small compared with unity, hence, a photon Fig. 19.18 Normal optical thickness of a purely molecular is unlikely to be scattered more than once, i. e. single atmosphere (data from [19.3]) scattering predominates. The amount of air to be traversed by light, the so discussed. Scattering effects by particles are neglected called air mass, depends on the sun’s elevation. Air mass here. (AM) is deﬁned to be unity for the light source in the In homogeneous media, the forward propagation of zenith. It increases for smaller sun elevation angles. As light is expressed in terms of the refractive index n a matter of fact, it is the optical thickness, relative to (for tables of n [19.3]). n depends on temperature T its zenith value. The exact value depends on the surface (in K), pressure p (in mbar) and humidity. Equa- pressure. At 5◦ elevation (85◦ zenith angle) its value is tion (19.37) [19.87] gives an approximation for n of about 10 and it ultimately reaches a value of about 40 dry air at grazing incidence [19.51, 77, 85, 86], i. e. for the case 77.6p − of sunrise or sunset. In this case, the light must pass n = 1 + ×10 6 . (19.37) about 40 times the amount of air compared to the case T of the zenith. For example, T = 300 K and p = 1030 mbar yields Combining the air mass with the normal optical n ≈ 1.000266. Increasing the air temperature by 40 K thickness gives the optical thickness for arbitrary sun (e.g., air directly above the ground which is heated elevation. Since AM reaches large values, optical thick- by the sun) gives n ≈ 1.000235 (for humid air, the nesses may become large compared with unity, i. e. numbers only change slightly). These small changes of multiple scattering events become likely for low sun Δn ≈ 3×10−5 are responsible for all kinds of mirages. elevations. The most simple mirage effect is known from astronomy: if an observer looks at an object in the sky 19.6.2 Mirages at a certain altitude, the actual position of the object is lower in the sky. This is due to the refraction of light Mirages are due to the propagation of light waves in air upon propagation in the atmosphere with a gradient in n that has gradients in the index of refraction [19.44–48, giving rise to curved light paths. D Part 51]. In general, light which is propagating in clear air At the zenith, the deviation is zero, at 45◦ zenith (no particles) is partly scattered according to Rayleigh distance it amounts to 1 (1 minute of an arc) increasing ◦ scattering, while the rest propagates undisturbed in the to more than 38 at an angle of 90 . This has to be 19.6 forward direction. The scattered light consists of side- compared with the angular size of the sun or moon, ways scattering and forward scattering, the latter being which is about 30, i. e. half a degree. Since the refraction in phase with the incident light. As a consequence, light is only about 28 at a zenith distance of 89.5◦,thesun in clear air is slightly weakened by sideways scattering, or the moon in an otherwise undisturbed atmosphere the forward-propagating light being the superposition (no inversion layers) will thus be ﬂattened [19.47], see of the incident light and the forward-scattered light. also [19.88–92]. The weakening due to sideways scattering will be Mirages are images of objects which may be seen discussed below (blue sky). Here, the phenomena as- in addition to the real objects. They can be seen when- sociated with the forward-propagating light will be ever there are temperature differences in the atmosphere, 1186 Part D Selected Applications and Special Fields

telephoto lenses are used. The mirages are often distorted and flicker due to local density fluctuations in the air. Theoretical progress in understanding mirages came with the computer. The propagation of light rays in a given atmosphere, defined by the vertically varying index of refraction n(z), is computed theoretically using ray-tracing methods. The various methods [19.93–96] differ by their choice of geometry and n(z). Such simulations prove very helpful in understanding the general characteristics of mirages, like e.g. so-called mock mirages [19.97, 98]. Recent research has explained many unusual mirage phenomena quantitatively, including long-range mirages like the Novaya–Zemlya effect from atmospheric duct- ing [19.99–102] and small-scale movements seen within superior mirages when atmospheric gravity (buoyancy) waves are present [19.103, 104]. Superior mirages seen over large distances (70–100 km) can result from fairly complex atmospheric temperature profiles [19.95]. Also, the origin of double inferior mirages as well as unusual horizontal Fig. 19.19 Inferior mirage: a palm tree scatters sunlight in stripes in inferior mirages has been analyzed theoret- all directions. The atmosphere is heated close to the ground. ically [19.96]. Very recently, focus had been on very Therefore the index of refraction is smaller there, giving rise precise measurements and comparison to modeled astro- to curved light paths. Direct and refracted light can enter nomical refraction of the setting sun [19.105, 106] and the eye of an observer, which is interpreted as an object on the occurrence of very bright superior mirages [19.107]. top of an inverted image (after [19.48]) In addition to analysis of observations and theoretical models, inferior mirages and superior mirages which give rise to unusual gradients in the index of re- with multiple images may also be studied quan- fraction. Similarly to astronomical refraction, gradients titatively or as demonstration experiments in the in n give rise to curved light paths. If warm air is above laboratory [19.65, 108–112]. the ground, n is smaller close to the ground than above it. This leads to inferior mirages like the well-known 19.6.3 Clear Sky: wet streets on hot summer days. The formation of in- Blue Color and Polarization ferior mirages is illustrated in Fig. 19.19. A prominent feature of a mirage is the so-called vanishing line of the Light scattering in pure gases is due to the electrons object [19.48]. Light below certain object points has no in atoms and molecules. As a result, the scattered light atD Part chance whatsoever to reach the eye of the observer, i. e. intensity varies approximately as 1/λ4 (Fig. 19.16), i. e., parts of the object cannot be seen, irrespective of the red light is scattered much less than blue light [19.1,78, direction into which the light is scattered. 79]. When looking at the daylight sky illuminated by the 19.6 In the case of an inversion layer in the atmosphere, sun one mostly sees scattered light and, hence, a blue the air at a given height is warmer than below, which sky (In Sect. 19.6, the qualitative term intensity which is may give rise to superior mirages. Similarly to infe- often not properly defined (see [19.113]), does usually rior mirages, the propagation of light with curved paths mean either radiance, given in W/m2 sr, or spectrally in this case can give rise to multiple images on top of resolved radiance in W/m2 sr nm). the object. In nature, combinations of inferior and supe- The scattered light is strongly polarized at a scat- rior mirages may occur. Also, heated vertical walls may tering angle of 90◦ [19.84]. Concerning the whole result in lateral mirages. sky, the polarization varies and also has neutral points, The angular size of mirages is usually about named after Arago and Babinet [19.44, 46, 51]. In real- ◦ 0.5–1.0 . For observations, binoculars and cameras with ity, even if very clean air is used, the maximum degree Radiation and Optics in the Atmosphere 19.6 Optical Phenomena in the Atmosphere 1187 of polarization is about 94%, see Sect. 19.6.1. The atmo- 8–12 sphere usually also contains an appreciable number of 7 6 particles, which show Mie scattering with different an- 5 δ gular polarization dependencies. In addition, there may 4 be contributions of multiply scattered light as well as b 3 backscattering from the surface of the Earth. Overall, the 2 degree of polarization typically reaches values around 1 80%. Obviously, this depends on the concentration of particles and is thus related to the transmission of the 2* atmosphere [19.114]. More details on scattering effects and recent research will be given in Sect. 19.6.7. 3* 19.6.4 Rainbows 4* 11* 8* 12* 10* 9* Rainbows are due to scattering of sunlight from rain- 5* drops in the atmosphere [19.43–48,51]. The drops are in 6* 7* μ Scattering angle δ the size range between 10 m (white fogbow/cloud bow) 180 and several millimeters. One usually assumes spherical Minimum: 137.48° (n = 1.33) droplets, however, drop shapes may vary depending on 170 at b/R = 0.86 size [19.115, 116] or they may even oscillate [19.117]. 160 Drop formation and size distributions have been extensively studied [19.118]. The effect of nonsphericity on 150 rainbow phenomena is discussed, e.g., in [19.119, 120]. 140 The observed bows are mostly due to single scattering events. Hence, the complex problem of light 130 scattering from millions of raindrops in a rain shower 120 can be reduced to the scattering of sunlight from a single 0.0 0.2 0.4 0.6 0.8 1.0 raindrop. Since raindrops are large compared to the Normalized impact parameter b/R wavelength of light, geometrical optics already gives Fig. 19.20 Simple explanation of a rainbow from a single raindrop a rough description. Figure 19.20 depicts a single rain- in terms of geometrical optics. Parallel light rays, characterized by drop and parallel light rays from the sun. the impact parameter b, are scattered due to refraction, internal The rays are characterized by their impact param- reflection and refraction (for clarity other light paths are omitted). eter b. Each ray is reflected and refracted upon hitting The scattering angle δ as a function of b exhibits a shallow minimum, an interface between air and water. For clarity, only i. e. many incoming light rays with different values of b will be the light paths that give rise to the primary rainbow scattered in the same direction are sketched. They are defined by refraction into the droplet, internal reflection and refraction back into the rection. As a consequence, an observer who is looking air. Similarly higher-order rainbows may be constructed at a cloud of raindrops that is illuminated from the back by allowing for multiple internal reflections. The cen- by sunlight, will observe a bow of angular size 42◦ D Part tral ray (1) is not deflected by the refractions and exits (Fig. 19.21). at a scattering angle of 180◦ with respect to the inci- The rainbow angle, i. e. the minimum of δ in the plot dent ray. Ray number (2) suffers a scattering angle of of Fig. 19.20, can be easily calculated (e.g. [19.47,121]) 19.6 about 170◦ and so on. For increasing impact param- with geometrical optics by finding the minimum of the eter the scattering angle δ decreases until a minimum is scattering angle δ(αinc) with respect to the angle of inci- reached at an impact parameter of about 0.86 R (ray 7). dence αinc of the light rays onto the droplet. Assuming The flatness of this shallow minimum (Fig. 19.20) at nair ≈ 1 one finds for the primary bow an angle of about 138◦ is responsible for the fact that δ(α ) = 2α − 4α + π, with much more light is scattered into this direction – geo- inc 2 inc refr metrically along the surface of a cone – than in others, n2 − 1 since many incoming light rays of slightly differing cos αinc = . (19.38) impact parameters will emerge in the same output di- 3 1188 Part D Selected Applications and Special Fields

From sun

From sun 42° 138°

42°

Antisolar point

Fig. 19.21 Observation of a rainbow. Each raindrop scatters light preferably in a cone of the rainbow angle. Hence, an observer will see more light when looking in the direction of the surface of a cone that is centered in a droplet. The whole rainbow is due to millions of drops, the effect of which is an observable bright feature, geometrically on the surface of another cone centered in the eye of the observer and making an angle of 42◦ with regard to the antisolar point (after [19.48]). Its surface touches the surfaces of the scattered light cones of each individual droplet

Here αrefr denotes the angle of the refracted ray Mie theory [19.10, 40, 41], however, its numerical so- within the raindrop and n is the index of refraction lutions in terms of scattering efficiencies as a function of water. For n = 1.33, Snell’s law gives a scat- of angle for size distributions of the droplets and fi- ◦ tering angle of δ(αinc) = 137.5 . Due to dispersion nite angular size of the solar disk had to wait for the (n650 nm = 1.331, n400 nm = 1.343) the rainbow angles development of computers. Similarly, Debye developed depend on wavelength. Taking into account the finite size of the sun of about 0.5◦ one finds an angular width of about 2.2◦ for the primary bow. The analy- Intensity of scattered light sis is easily extended to higher-order rainbows [19.47], most of which may, however, only be observed in the laboratory [19.110, 122–125]. atD Part Several rainbow features can only be explained by wave optics. Light from the rainbow is apprecia- Geometrical optics bly polarized perpendicular to the plane of incidence, 19.6 since the angle of incidence for the internal reflection is close to the Brewster angle [19.126]. Also, careful Wave optics measurements showed that the light intensity shows an interference pattern, named after Airy [19.50,127,128], which differs markedly from the prediction of geometrical optics (Fig. 19.22). Until the beginning of the 20th century, wave optics features were computed using Airy’s theory, which Rainbow angle Scattering angle gives reasonable results for droplet sizes down to 10 μm; Fig. 19.22 Differences between the theories of Descartes for smaller sizes, it fails. Improvements came with and Airy for the scattered light intensity of raindrops Radiation and Optics in the Atmosphere 19.6 Optical Phenomena in the Atmosphere 1189 a tool of how to decompose the partial wave ampli- Intensity (logarithmic scale!) tudes for scattering of a plane wave into individual +2 Forward scattering: contributions of certain types. This later led to the com- +1 plex angular-momentum theory [19.129]. Application Coronas Ϯ of the mathematics of catastrophe theory to light scat- 0 Rainbows Back +1 with Airy scattering: tering showed that the rainbow is a manifestation of the rings Glories so-called fold caustic [19.130]. +2 Here, results of the full electrodynamic treatment, –3 i. e. Mie theory, are presented [19.40,41,131–133]. Fig- Radius: ure 19.23 depicts results for monochromatic blue light –4 2 μm of λ = 450 nm, scattered by a lognormal distribution of –5 8 μm μ water droplets with mean radii ranging from 2 mto –6 40 μm 200 μm. The full width at half maximum of the size 200 μm distribution is 10% of the mean radius. –7 Obviously, large droplets show Airy rings at the rain- –8 0° 21° 48° 72° 86° 120° 144° 168° bow angles. For other wavelengths, these curves would 12° 36° 60° 84° 108° 132° 156° 180° be slightly shifted due to dispersion. The overlapping Scattering angle δ of the interference rings for all wavelengths leads to Fig. 19.23 Angular distribution of blue light scattered by water so-called supernumerary arcs (e.g. [19.134, 135]). De- droplets with mean radii ranging from 2 μmand8μm (fog and cloud creasing the droplet size leads to a broadening of the droplets) to 200 μm (small raindrops) (computation by E. Tränkle) rainbows due to diffraction. In this case, the overlapping of all wavelengths leads to a white rainbow, also called light [19.138, 139]. Even infrared rainbows have been a fog bow. If the size becomes too small, no rainbows detected [19.140]. are observable. The other features in Fig. 19.23 will be In addition to analysis of observations and theoret- discussed in Sect. 19.6.5. ical models, rainbow phenomena may also be studied There are many other interesting features of rain- in the laboratory either for quantitative comparison to bows. For example the first-order rainbow often visually theory or just as demonstration experiments using either appears brighter at the base of the bow than at the top of single droplets or cylinders of water or other mater- the bow. This is due to the fact that, in a rain shower, rain- ials [19.109, 110, 122–124, 136, 141, 142]. drops are distorted in shape to oblate spheroids. Light Present investigations of rainbow phenomena deal, reaching an observer from the base of a rainbow tra- e.g., with experiments on higher-order rainbows verses a water droplet in the horizontal plane where the from acoustically levitated water drops [19.143] or droplet cross section is circular. In contrast, light from cylinders [19.144,145] and total internal reflection rain- the top of the rainbow traverses the water droplet in bows [19.146] as well as new simulations of rainbows the vertical plane where the droplet cross section is el- and fogbows [19.147, 148]. liptical. Since the scattered light intensity due to the internal reflection is less in the elliptical cross section 19.6.5 Coronas, Iridescence and Glories than that in the circular cross section the base of the rainbow is brighter than the top of the bow (the longer The forward and backward scattering of small water D Part optical path from the top may also lead to increased droplets can also give rise to very distinct fea- extinction). tures [19.43, 44, 47, 48, 51]. First, colored concentric Similar explanations [19.136] are possible for other rings, called coronas, around the sun or the moon with 19.6 features such as, e.g., that the supernumeraries of the angular distances up to, e.g., 15◦ may be observed, when first-order rainbow often appear most vividly at the top looking through thin clouds. The middle whitish part of the bow or that supernumeraries of the second-order around the light source is often called an aureole. If, rainbow are almost never seen. Also, the effects of the second, colorful clouds are observed at larger distances electric fields [19.137] and acoustic forces accompany- from the sun (up to 45◦), one usually speaks of cloud ing thunderstorms can have observable consequences iridescence. Third, backscattering that leads to colorful on rainbows [19.117]. Visibility and general brightness concentric rings at angles close to 180◦ with respect to of rainbows depend on multiply scattered and absorbed the light source are called glories. Figure 19.24 gives an 1190 Part D Selected Applications and Special Fields

ored rings of computer simulations to those of photos of Fogbow/Rainbow natural observations [19.150]. Sun An aureole may be produced by relatively large light particles that tightly compress the rings, or by the presence of a broad particle size distribution that causes the Glory colored rings to overlap. Simple diffraction theory has problems for drops Corona Water with sizes only slightly greater than the incident wave- droplet length. In this case, Mie theory must be applied, since the amplitudes of the diffracted and transmitted light are comparable in the forward-scattering direction, leading to interference between the two components that can significantly alter the scattering pattern. Forward scattering Back scattering The nature of the cloud particles that cause coro- Fig. 19.24 Overview of geometries of light-scattering phe- nas has been the subject of controversy [19.152, 153]. nomena from a water droplet Observations of some coronas due to very high clouds suggested that not only supercooled spherical cloud overview of the light-scattering geometries of rainbows, droplets, but also ice crystals may be responsible for coronas and glories due to water droplets. coronas. However, ice crystals can assume a variety of shapes and orientations that should not give Coronas very pure coronal colors. The issue was settled by In its most spectacular form, coronas can be observed experiments which simultaneously used polarization as a concentric series of three or four brilliantly colored LIDAR data as well as photographic evidence of rings around the sun or moon. In its simplest form, the coronas to demonstrate that cirrus clouds composed corona is just represented by the aureole, which is a white of hexagonal ice crystals with particle sizes rang- disk near the sun or moon bordered by a bluish ring and ing from 12 to 30 μm (which is unusually small for terminated by a reddish-brown band. most cirrus clouds) can generate multiple-ringed col- Coronas are easily explained using Mie the- ored coronas [19.152]. Later the study also included ory [19.149, 150]. Coronas occur as strong forward- aircraft probes of the particles [19.153]. In one case scattering phenomena (Fig. 19.23) for very small nearly a weak corona and a halo display (see below) of monodisperse sizes of typically about 10 μm. More sim- the hexagonal crystals were observed simultaneously ply, coronas are treated as diffraction phenomena by within the same cloud. This is possible, since labora- water droplets. The first minimum for light of wave- tory experiments indicate a lower limit of about 20 μm length λ diffracted by a circular aperture of diameter for the sizes of ice crystals that can produce halo 2R = D is given by effects. Some while ago, it was also noted that coronas need D sin φ = 1.22λ. (19.39) not be spherical. Elliptical coronas have been reported For droplets of nearly uniform size, the diffraction an- at special times in early summer. They were explained atD Part gles φ obviously depend on wavelength, giving rise as diffraction phenomena from nonspherical birch and to rather pure perceived colors of the coronas. In this pine pollen grains [19.154–156]. Also, split coronas due case, the average droplet size may be estimated from the to local variations of droplet size or changes between 19.6 angular size of the rings from (19.39). To obtain the ap- water and ice have been observed [19.157]. Recently, proximate angle for the red band of the solar corona, new simulations have been reported [19.158]. Special it is customary to use λ = 570 nm in (19.39) since the coronas, called Bishop’s rings, can be produced by vol- positions of the red bands are believed to correspond canic ashes, as has been reported after the explosion of to the minima for green light [19.151]. (Alternatively to Krakatau in 1883. 570 nm, 490 nm has been proposed [19.152].) For example, 2R = 10 μmgivesφ ≈ 4◦. (Note that there will be Iridescence deviations between the correct Mie theory and diffrac- Cloud iridescence is a brilliant display, which occurs tion theory for droplets with sizes of 10 μm and below.) quite often when appropriate thin clouds are close to A much better way to judge droplet sizes is to fit the col- the sun or moon or if edges of thick clouds happen to Radiation and Optics in the Atmosphere 19.6 Optical Phenomena in the Atmosphere 1191 have rather monodisperse droplets. Iridescence is also Glories are present in Fig. 19.23 as oscillatory structures observed, though more rarely, at much larger angular in the angular range from about 160 to 180◦ for droplets separation from the sun of up to 45◦ and it may be of 4 and 16 μm size. The more uniform the droplet size, easily observed and analyzed within contrails [19.151]. the more rings may be observed. If interpreted using diffraction, like coronas, the drop Knowing from coronas that colorful rings may also sizes 2R are in the range 2–4 μm. These sizes are indeed be produced by fairly monodisperse assemblies of ice quite rare, though possible near the edges of growing or crystals and even tree pollen, one may ask whether the evaporating clouds. glories that are often observed from airplane windows Whereas, coronas are generally observed at smaller may also be due to ice crystals in high-altitude cirrus angles for mostly monodisperse droplet populations clouds. with sizes of about 10 μm, iridescence usually occurs From the above interpretation of Mie theory, the at larger angles and requires cloud droplet sizes on the glory is due to circumferential, i. e., surface-wave ray order of a few microns in diameter with broad size paths which are unique to spheres. Glories are, hence, distributions. These conditions are often found in the produced by spherical scatterers. Based on photographic vicinity of the visible cloud margin where there is also evidence, it was therefore investigated [19.164] whether a sharp gradient of the drop sizes. Thus, coronas and glories may be also due to spherical or near-spherical iridescence appear to require quite different cloud mi- ice crystals? In conclusion it was found that ice grows in crophysical conditions to be present, and should also amorphous and presumably spherical shapes only at un- be most frequently observed in different angular re- likely frigid temperatures. Recent studies have, however, gions [19.151]. Recent studies deal with coronas and suggested that small near-spherical ice particles (diam- iridescence in mountain wave clouds [19.157] as well as eters ranging from 9 to 15 μm) can sometimes, though rare iridescence cases in cirrus clouds [19.159, 160]. very rarely, occur near the tops or along the margins of some ice clouds, and these may give rise to observable Glories glories. Very recently, new simulations for glories were The colored rings of glories, sometimes also called spec- reported [19.147, 165, 166]. tre of the Brocken are observed in a backscattering geometry, if sunlight illuminates fog or clouds with very 19.6.6 Halos small water droplets. Nowadays, observations can be performed easily when flying in airplanes and observing Halos are caused by the refraction and/or reflection of the shadow of the plane on nearby clouds. sunlight by ice crystals in the atmosphere [19.43–48,51, Early interpretations could not use Mie theory (since 52, 66, 167]. They can already be understood in terms computers were not available), but tried to understand of geometrical optics. Ice crystals that cause good halo the phenomenon in simpler terms. The assumption of displays are usually hexagonal plate or column crystals diffraction of reflected light by the droplets (diffraction with sizes in the range of 20–100 μm [19.168]. Such from circular apertures) did not work, since intensities crystals form very often, depending on the temperature and angular distances of the pattern are different. How- and the amount of water vapor in the air [19.169]. Good ever, diffraction from circular rings could explain the documentation with micrographs can be found in the phenomenon [19.40, 161]. For this to happen, glories literature [19.52, 170]. must be due to light entering the raindrops at grazing in- A great number of different halos may be observed D Part cidence (this interpretation was later supported by Mie in nature and in the laboratory since there is an enor- theory [19.162]). Then, the scattered light is more or mous variety of possible types of ray paths through the less exiting at the opposite side of a droplet, i. e. at scat- crystals and crystals may have different orientations in 19.6 tering angles of 180◦. In terms of geometrical optics, the air. this is not possible, however, wave theory allows for The most simple halos are parhelia, also called surface waves at the boundary. In the backward direc- sun dogs, which are often observed in cirrus clouds tion, all contributions interfere constructively to produce (and sometimes in contrails [19.171]). They are due to the glory. These model assumptions were supported by oriented plate crystals, i. e. crystals falling with their experiments with microscopic water droplets supported principal axes vertical. This orientation mode is often by submicroscopic spider webs [19.163]. Later on, this possible and is, e.g., similar to movements of leaves (or model was further developed very successfully [19.129]. sky divers), which maximize their air resistance as they Nowadays, glories are explained by using Mie theory. fall [19.118]. If light rays from the sun enter a prism face 1192 Part D Selected Applications and Special Fields

a circular halo, centered at the light source, for oriented Scattering angle δ(°) 90 crystals, light will be deflected to both sides of the light source, giving rise to parhelia. The color of the parhelia, reddish towards the sun and bluish tails at the outside, δ is due to dispersion, i. e. different minimum deviation Ice crystal angles for the various wavelengths. 60 n = 1.31 δmin(90°-prism) = 46° Similarly, other halos, often referred to as arcs, are due to other ray paths. A very brief survey of some common halos (today, more than 40 different types are known) is shown in Fig. 19.26. The circumzenith arc 30 (No. 7 in Fig. 19.26) is due to rays which enter the top δ (60°-prism) = 22° min basal face and exit a prism face of crystals with vertical symmetry axis. For random orientation, ray paths which refer to such a 90◦ prism lead to circular halos of 46◦ (No. 3 in Fig. 19.26). Pure reflection halos – not colored, 0 0 306090since refraction does not contribute – are e.g. sun pil- Angle of incidence (°) lars (No. 4 in Fig. 19.26). They arise when sunlight is Fig. 19.25 Ray paths within hexagonal ice crystals (n = 1.31) show reflected at grazing incidence from the horizontal faces an angle of minimum deviation of 22◦. For clarity, other light paths of plate crystals oriented with their axes vertical. Simi- are omitted larly oriented crystals also give rise to the parhelic circle (No. 5 in Fig. 19.26), which is due to reflected sunlight of a crystal and exit an alternate prism face, the situation from crystal faces lying in the vertical plane. corresponds to refraction from a 60◦ prism. The scat- Singly oriented column crystals – column crystals tering angle as a function of angle of incidence shows with axes horizontal but otherwise unconstrained – give a flat minimum (Fig. 19.25) that is at a scattering angle rise to the upper and lower tangent arcs. Much more of 22◦ for ice crystals with n = 1.31. Similarly to the ex- rarely, column crystals orient with two prism faces hori- planation of the rainbow, more light is deflected in this zontal. Crystals having these Parry orientations give rise direction. Therefore an observer looking at the sun or to Parry arcs. Still other crystal orientation modes are the moon through a thin cirrus cloud will see more light possible. Furthermore, crystals occasionally have pyra- at an angular distance of 22◦ from the light source. For midal faces that produce halos at other angular distances, randomly oriented crystals, the resulting display will be referred to as odd-radius halos. The modern theory of halos started in the 17th century [19.44,172]. In recent decades, enormous progress has been made. This is due to computer techniques, the 7 application of more traditional, conceptual mathematics [19.173], experiments which collected atmospheric ice crystals during observation of halo displays in cold climates, and to dedicated observers who have docu- atD Part 3 6 mented many new halos. 5 1 2 4 Sun Probably the biggest step was made by the introduction of computer simulations which allow the 19.6 computation of complex halos from many different types of crystal shapes, sizes and orientation. They gave a lot of new information, especially regarding intensity variations within a given halo [19.48,174,175]. Various arcs Observer could be directly related to the crystals and the ray paths that were producing them. The theoretical displays could Fig. 19.26 A schematic survey of some halos which may be be easily compared with photographs or drawings of real observed (1: 22◦ halo, 2: parhelia, 3: 46◦ halo, 4: sun pillar, halo displays. 5: parhelic circle, 6: circumscribed halo, 7: circumzenithal Many excellent displays were documented by arc). These displays all depend on sun elevation Finnish or German observer networks ([19.176], see Radiation and Optics in the Atmosphere 19.6 Optical Phenomena in the Atmosphere 1193 also Table 19.4) and scientists in Antarctica [19.52]. to [19.86, 114] Computer simulations were also used to explain old ϕ, T(ϕ, h) = T(0, h)AM( h) (19.40) documented displays dating back to the 18th century [19.177]. Analysis of halos also include polarization Results for the transmission of red (λ = 630 nm), effects, started by systematic studies in the seven- green (λ = 530 nm) and blue (λ = 430 nm) light for ties [19.53,178]. Halo polarimetric studies should allow a molecular atmosphere and AM = 1, (ϕ = 0◦, zenith), the detection and identification of birefringent crystals AM = 10 (ϕ ≈ 85◦)andAM= 38 (ϕ = 90◦, horizon) in extraterrestrial atmospheres [19.179–181]. Very re- are given in Table 19.6. cently, the focus had been on comparison of observations Whereas the zenith sun is still regarded as white, the with the simulation of halo polarization profiles, the size sun’s spectrum near the horizon is drastically changed in and shape of the crystals in the model being based on favor of red and green light. Above the horizon, yellow sampled ice crystals [19.182]. colors may be observed and close to the horizon, red Halo phenomena have also been studied in the lab- dominates. Since, simultaneously, the radiance of the oratory for quantitative comparison to theory and as sun decreases drastically, the brightness also decreases demonstration experiments using prisms or hexagons with ϕ. Naked-eye observations are, however, still not made of glass, lucite or other materials [19.43, 66, 109, possible in very clear air even if h = 0 (sea level). In 110, 112]. general, however, haze due to water vapor and aerosols leads to additional weakening. 19.6.7 The Color of the Sun and Sky Aerosols are very important for optical variations within the atmosphere [19.15,16]. The difference of ob- The Color of the Sun servations and theoretical spectra, including selective Light scattering in the atmosphere is responsible for the absorption of molecules within the air, is attributed to color of the sun or moon, as perceived by earthbound aerosols [19.114]. observers. Outside the atmosphere, solar irradiation has Extraordinary color changes of the sun can some- a very broad spectrum, ranging from UV to the deep times occur, if clouds of nearly uniformly sized particles infrared [19.183]. Neglecting processes in the sun’s at- are present in the line of sight. For example, the forest mosphere, it more or less resembles the emission of fires in Canada in 1950 ejected large numbers of oil a black body of about 5900 K. This radiation is inter- droplets in the air. These were transported over long preted as white by human eyes (the exact color may be distances and led to blue sun observations even in Edin- computed from spectra according to color metric for- burgh [19.74,184]. Similar events may be due to volcanic mulae, see e.g. [19.76]). In the Earth’s atmosphere, the eruptions. radiation is absorbed and scattered. Compared to the outside spectrum, the irradiation curve is lowered and Sky Colors shows characteristic absorption features, mostly from Obviously, sky colors are due to many factors [19.43– H2O, CO2 and oxygen (see Fig. 19.7). 49, 51]. A simple qualitative explanation of typical sky Color changes occur depending on air mass, i. e. colors at sunset can be given according to Fig. 19.27. sun elevation. Starting with a purely nonabsorbing molecular atmosphere, atmospheric transmission has been computed for air mass AM = 1 [19.3]. Therefrom the D Part transmission at arbitrary zenith angles ϕ and starting at height h of an observer may be computed according Line of sight 19.6

Table 19.6 Transmission of a molecular atmosphere Horizon (h = 0) for sun in zenith (AM = 1: ϕ = 0◦)orclose ◦ ◦ Observer to the horizon (AM = 10: ϕ = 85 ,AM= 38: ϕ = 90 ), T(ϕ = 0◦) after [19.3] λ(nm) T(AM = 1) T(AM = 10) T(AM = 38) 630 0.945 0.625 0.117 530 0.892 0.320 0.013 Fig. 19.27 Geometry for qualitative explanation of sky col- 430 0.764 0.068 0.000036 ors after sunset (see text for details) 1194 Part D Selected Applications and Special Fields

The sun has just set, i. e. it is below the horizon. Sun- cumulations, carried by the wind, thus undergoing light still illuminates portions of the atmosphere. The constant qualitative changes, including condensation color that an observer perceives in a given direction is processes [19.114]. As a consequence, the extinction co- due to contributions of scattered and attenuated light efficient for various atmospheric compositions, e.g., for along a line of sight in the respective direction. In sim- different types of clouds, and low- or high-altitude haze ple terms, the amount of radiation entering the observers varies considerably [19.76]. For simplicity, let us now eye depends on, first, the light path through the at- assume just a single aerosol layer. Its influence on sky mosphere before scattering, second, the height of the colors is simply to intensify the red and yellow colors scattering event, which determines the density of scat- in the forward direction. This is due to the fact that the terers, third, the scattering angle, and fourth, the optical scattering angles are rather small and that aerosol par- thickness along the line of sight, i. e. the attenuation due ticles show very strong forward scattering, compared to to scattering and/or absorption. The subtle interplay of Rayleigh scattering (Fig. 19.17). these four parameters determines the spectrum of light Similar qualitative arguments may also be applied to reaching the eye of an observer and hence the perceived the phenomenon of the so-called blue mountains. Dur- color. ing the day, the sky is illuminated by the sun. If the Different locations along the line of sight will con- line of sight to a distant mountain is close to the hori- tribute to the scattered light with varying intensity as zon, the radiation entering the eye of an observer is well as spectral composition. The light beam most dis- due to two contributions. First, it consists of the light tant from the Earth will reach the line of sight, nearly originally scattered by the mountain towards the ob- unattenuated, and a broad spectrum is available for scat- server. This light is attenuated due to scattering along tering. Due to the large height, only a small amount the line of sight. Second, the observer will see sunlight of radiation is scattered towards the observer, with blue that is scattered by the air along the line of sight. This dominating. This light is further attenuated before reach- air light will be blue in a Rayleigh atmosphere. Observ- ing the observer. The final spectral composition of the ing a scenery with mountains at various distances will light depends on the optical thickness that must be tra- change the amount of the two contributions: the more versed. However, blue is most strongly attenuated, i. e. distant, the smaller the first will be and the more im- overall this light will not contribute much and will not portant the second contribution (see the discussion on dominate the color. The closer the light passes to the visibility in Sect. 19.6.8). As a consequence, distant ob- ground, the more its spectrum is shifted towards the red. jects will appear to have a faint blue color [19.45, 51]. Although less light will intersect the line of sight com- This scheme can be used to get a measure for the pared to the large height rays, it will contribute more, thickness of the atmosphere [19.186]. since it interacts at lower heights, i. e. with a much Very often, one observes that sky light close to the larger density of scatterers. Taking into account the fur- horizon is whitish. This can be understood in a similar ther shift of the scattered light spectrum towards the way. Since no objects except the sky are observed, the red due to scattering along the line of sight shows that first contribution from the above argument vanishes and the sky color will be dominated by yellowish and red only air light has to be considered. Sunlight which is colors. scattered in a length interval close to the observer con- The brightness and color of the clear sky has also tributes a large amount of blue light due to Rayleigh atD Part been investigated for various zenith angles ϕ [19.185]. scattering at low heights above the ground. Light which For high sun elevations, the zenith sky of a pure Rayleigh is scattered at larger distances from the observer is scat- atmosphere is blue (as observed for clear air), however, tered at larger heights, i. e. contributes smaller amounts

19.6 it would turn yellowish after sunset. This is in contrast of predominantly blue light. In addition this light is at- to the observed blue color. The solution of this puz- tenuated and spectrally modiﬁed by additional scattering zle are the Chappuis absorption bands of ozone in the along the line of sight. As a result, light which originates wavelength range between 500 and 700 nm. For high far from the observer contributes small amounts of mul- sun elevations, the ozone absorption contribution to sky tiply scattered mostly red light. All contributions along light is small compared to Rayleigh scattering whereas the line of sight add up to give an overall white color. it dominates for very low sun elevations. Since light from distant portions will cease to contribute Aerosols within the atmosphere are usually not if scattered out of the line of sight, the overall brightness distributed homogeneously, but in the form of ac- has a limit [19.45, 51, 77]. Radiation and Optics in the Atmosphere 19.6 Optical Phenomena in the Atmosphere 1195

Observations from Mauna Loa of the polarization 19.6.8 Clouds and Visibility and color ratio during twilight often show deviations from the clear-sky average. These were attributed to Clouds cloud or haze shadow effects and the importance of Clouds are visible aggregates of water droplets or ice stratospheric dust layers was emphasized [19.187]. crystals, suspended in the air and grown around con- Stratospheric dust clouds from volcanic eruptions do densation nuclei [19.118]. Fog or clouds have droplet strongly affect the degree of polarization of sky light sizes around or above 10 μm, with densities ranging and also shift the positions of neutral points by more from 10 to 1000 droplets/cm3. On average we will as- than 15◦ [19.188]. Such investigations strongly profit sume 300 droplets/cm3 [19.203]. Droplets of 5–10 μm from the development of LIDAR systems and the radius will then correspond to volume fractions f of − − respective theories of backscattering from small par- about 10 7 –10 6. ticles [19.189–192]. Clouds exhibit several optical phenomena, the most Modern experiments simultaneously measure the obvious being their white color, but certain types of sky light radiance distribution at three wavelengths, clouds show particular phenomena. Cirrus and cirru- the degree of polarization, and the plane of polariza- stratus clouds may give rise to coronas, iridescence tion [19.193]. Recently, the color coordinates of sky and halos, contrails of aircraft engines are cirrus-like light have been investigated, showing that sky light trails of condensed vapor with characteristics similar colors have a wide range of chromaticity curves, de- to cirrus clouds, and cumulonimbus clouds relate to pending strongly on location. Sometimes difficulties thunderstorms, i. e. lightning. Here, the color of clouds, arise in separating luminance changes from chromatic- their absorption and extinction will be briefly discussed. ity changes [19.194]. Astonishingly, clear daytime skies The effect of photon path length distributions within show a local maximum of radiance near the astronomical clouds is discussed in the contribution of U. Platt and horizon. Its angular width and elevation vary with the K. Pfeilsticker (Sect. 19.5.5). solar elevation, azimuth relative to the sun, and aerosol If illuminated by white light, clouds appear white optical depth. This is understood in terms of second- (lower brightness is often interpreted as grey or dark). order scattering processes [19.195]. Since water droplets are mostly nonabsorbing in the When the sun is seen through thin clouds, it usually visible, the color must be due to scattering. Scattering of has a sharp edge, but occasionally is fuzzy. This is due to light from monodisperse water droplets of about 10 μm certain clouds with ranges of cloud optical thicknesses shows Ripple structures (Fig. 19.16) [19.40,41], for size depending on the cloud particle sizes [19.196]. distributions this is washed out and scattering is mostly Present investigations of sky light deal, e.g., with independent of wavelength in the visible spectral range. digital imaging of clear-sky polarization [19.197], twi- Although this is a sufficient condition for clouds to be light modeling [19.198] as well as color and luminance white, it is not necessary [19.204]. As a matter of fact, asymmetries in clear [19.199] and overcast [19.200] a suspension of Rayleigh scatterers (such as fat droplets skies. Sky light measurements have also been reported in milk), i. e. selective scatterers, also give a white color for Mars, based on data from the Viking and Pathfinder due to multiple scattering. missions. The Martian atmosphere has a high dust- The criterion for multiple scattering to take place is particle content resulting in very high sky brightness and that the optical thickness τ is large compared to unity. the sky colors vary strongly with the angular position of A molecular atmosphere had τ<1, therefore the ex- D Part the sun [19.201]. planation of the blue sky needs only single scattering Theoretical modeling of atmospheric extinction events. For clouds, τ for a distance x can be esti- greatly profited from computer technology. Nowadays, mated by the following argument: within clouds, the 19.6 the transmission of the atmosphere is modeled by ex- extinction coefficient is more or less constant, hence tensive databases. The most prominent of these are the τ = βx. The extinction coefficient β can be estimated HITRAN and LOWTRAN databases [19.76, 202]. In from Mie theory calculations. Droplets of about 10 μm particular, the LOWTRAN program calculates the trans- in diameter have extinction cross sections of about mission spectrum for molecular absorption, Rayleigh twice the geometrical cross section (this is the extinc- − scattering and aerosol extinction at a moderate resolution tion paradox, [19.41]), i. e. of the order of 10 6 cm2. of 20 cm−1. For concentrations of 300/cm3, this leads to extinction 1196 Part D Selected Applications and Special Fields

coefficients β of the order of 0.05 m−1.Averysim- and absorption of the components of the air (vertically, ple estimate [19.77] can also be made by starting from the atmosphere is optically much thinner, hence we may β = Nσ and substituting the number density N by the see the stars at night). In meteorology, visibility refers to volume fraction f ≈ N∅3 and the cross section by ap- the observation of distant dark objects against a bright proximately the geometrical cross section σ ≈ ∅2 to background, usually the sky. The basis for a theoretical find derivation [19.77,205–209] is the contrast ratio C,giving the normalized difference between the background in- β ≈ f/∅ (19.41) tensity of the object and the intensity of the air light from for f = 10−6 and 10-μm particles, this also gives the the line of sight. One finds for the resulting maximum order of 0.1/m. distance D Hence, a cloud of several meters thickness corres- D =−ln(C)/β , (19.42) ponds to the optical thickness of the whole normal −β atmosphere. The transmission is given by T = e x where β is the scattering coefficient. The sensitivity of − and for β = 0.05 m 1 a distance of 20 m leads to τ = 1 the human eye has a maximum at λ = 555 nm, therefore − (T = 1/e), x = 100 m to τ = 5(T ≈ 7×10 3), and one usually evaluates (19.42) for green light. D then − x = 200 m to τ = 10 (T ≈ 5×10 5), which is sufficient just depends on the threshold contrast C,i.e.thelowest to obscure the disk of the sun [19.77]. Low transmis- visual brightness contrast, a person can see. It is common sion automatically leads to high reflection, i. e. thick to assume C = 0.02 although it varies from individual clouds have a high albedo which explains the bright to individual. This gives D = 3.912/β.ValuesofD for white color observed from airplanes above clouds. In various β are shown in Table 19.7. Obviously, there is conclusion, multiple scattering dominates for any cloud an enormous range of distances from several meters in that is optically thick and composed of nearly nonab- dense fog to several hundred kilometers in very clear air. sorbing particles; upon illumination by white light it Hence, the visibility is an indicator of the aerosol and/or will look white. The color of clouds may change during water droplet content. sunrise and sunset if spectrally filtered light illuminates the clouds, giving rise to spectacular sceneries. 19.6.9 Miscellaneous The very small transmission of sunlight through thick clouds also accounts for the fact that the bases There is a great number of other optical phenomena of such clouds are usually very dark. If droplets near the associated with the atmosphere. In the following, these base grow to form raindrops, the extinction coefficient will be very briefly described and references will be changes. The volume fraction stays about the same, but given. raindrops have a size of, say, 1 mm, hence β in a rain Green flashes or green suns are phenomena when shower is about a factor 100 smaller than within the either the last rays at sunset or the first rays at sunrise clouds. This explains, why it is easily possible to look look green or when, at low sun elevations, the upper rim through very heavy rainfalls. of the sun looks green. In the first case, just a very small portion of the sun is above the horizon, in the second Visibility case, the sun’s disk is usually highly distorted due to Visibility is a measure of how far one can see through the mirage effects. The explanations of these phenomena atD Part air. Even in the clearest air – assuming that no aerosol require refraction and the scattering of the sunlight as particles are present and that one is not restricted by the well as mirage effects [19.103, 210, 211]. Earth’s curvature – the horizontal visibility is limited to Noctilucent clouds are blue, white or silvery looking 19.6 a few hundred kilometers. This is due to the scattering clouds within the stratosphere at heights of about 80 km

Table 19.7 Typical values for visibility in molecular atmosphere and examples if aerosols (natural/anthropogenic) and water droplets are present β D Molecular atmosphere 0.013 km−1 300 km Extremely excellent visibility Some particles 0.050 km−1 80 km Excellent visibility Many particles 0.500 km−1 8km Poor visibility Thick fog 0.050 m−1 80 m Extremely poor visibility Radiation and Optics in the Atmosphere References 1197 which can still be illuminated by sunlight 1–2 h after with electrons from the solar wind [19.51, 226, 227]. sunset [19.212–214]. They often show wavelike features At times of increased solar activity, they may also with wavelengths in the range from 1–100 km. be observed at low latitudes. These events are accu- Interesting colorful phenomena may be observed rately predictable, since the solar wind needs time to during eclipses. For example, the colors and brightness reach the Earth (see the websites on space weather of lunar eclipses are directly related to the scatter- in Table 19.4). ing of sunlight within the Earth’s atmosphere [19.215, Lightning, one of the most common and spectacular 216]. Other examples include polarization of sky natural phenomena, is due to electric charging effects in light [19.217,218], twilight phenomena [19.219], and il- thunderstorm clouds. The exact microphysical processes luminance measurements [19.220] during solar eclipses. that are responsible for the charging are still under dis- Shadows are regions in space that are shielded pute [19.228–230]. Recent research has revealed a whole from light. They give rise to very prominent daily-life new class of phenomena: lightning-related transient lu- phenomena in atmospheric optics such as the crepus- minous events (TLE), including sprites, blue jets, elves, cular rays, sometimes called sun beams or shadow trolls etc. [19.231]. These TLE extend from the top beams [19.45,48,51,221] or the fact that mountain shad- of thunderclouds at heights of up to 100 km and raise ows are always triangular, irrespective of the contour of serious questions about possible hazards for aerospace the mountain [19.222, 223]. operations. In addition, promising efforts are under way A very personal experience, based on our visual sys- concerning lightning protection by initiation of the dis- tem, is the so-called moon illusion, i. e. the fact that charge using intense femtosecond lasers [19.232]. the sun or the moon looks much bigger near the hori- Meteors are sometimes faint, sometimes brilliant zon than when it is higher in the sky [19.224,225]. This streaks of light with luminous trails in the night sky. phenomenon is not reproduced on photos. Meteor incorporates all phenomena when a cosmic par- In addition to phenomena with external light sources ticle enters the atmosphere. Outside the atmosphere, they such as the sun, moon or stars, a number of opti- are called meteoroids and, if they reach ground, mete- cal phenomena in the atmosphere produce light. The orites. The visual effects are due to heating of particles most well known are auroras, multicolored, diffuse and in the atmosphere due to frictional forces. Small par- slowly moving lights, usually seen only in high altitudes ticles heat up until they evaporate. Thereby, they collide against the clear dark night sky. They are due to air with air molecules and ionize a channel of air. Light is molecules and atoms, which are excited by collisions then emitted upon recombination [19.233, 234].

References

19.1 Lord Rayleigh, J. W. Strutt: On the transmission port European Space Agency (ESA), Noordvijk, The of light through an atmosphere containing small Netherlands, Contract 109996/94/NL/CN (1995) particles in suspension and on the origin of 19.6 H. Haug, K. Pfeilsticker, U. Platt: Vibrational Raman the blue of the sky, Philos. Mag. XLVII, 375–384 scattering in the atmosphere, (1996) unpublished (1899) 19.7 C. E. Sioris, W. F. J. Evans: Filling in of Fraunhofer 19.2 M. Nicolet: On the molecular scattering in the ter- and gas-absorption lines in sky spectra as caused restrial atmosphere: An empirical formula for its by rotational Raman scattering, Appl. Opt. 38, atD Part calculation in the homosphere, Planet. Space Sci. 2706–2713 (1999) 32, 1467–1468 (1984) 19.8 H. W. Schrötter, H. W. Klöckner: Raman scattering 19.3 R. Penndorf: Tables of the refractive index for cross-sections in gases. In: Raman Spectroscopy

standard air and the Rayleigh scattering coefficient of Gases and Liquids, ed. by A. Weber (Springer, 19 for the spectral region between 0.2 and 20 µm and Berlin, Heidelberg 1979) their application to atmospheric optics, J. Opt. Soc. 19.9 D. Clarke, H. M. Basurah: Polarisation measure- Am. 47, 176–182 (1957) ments of the ring effect in the daytime sky, Planet. 19.4 M. Bussemer: Der Ring-Effekt: Ursachen und Space. Sci. 37, 627–630 (1989) Einfluß auf die spektroskopische Messung strato- 19.10 G. Mie: Beiträge zur Optik trüber Medien, speziell sphärischer Spurenstoffe Ph.D. Thesis (Univ. Hei- kolloidaler Metalllösungen, Ann. Phys. 25, 377–445 delberg, Heidelberg 1993) (1908) in German 19.5 J. Burrows, M. Vountas, H. Haug, K. Chance, 19.11 H. C. Van de Hulst: Multiple Light Scattering, L. Marquard, K. Muirhead, U. Platt, A. Richter, Tables, Formulas and Applications,Vol.1,2(Aca- V. Rozanov: Study of the Ring Effect, Final Re- demic, London 1980) 157 Nonlinear4. Nonlinear Opt Optics This chapter provides a brief introduction into the basic nonlinear-optical phenomena and discusses 4.4.6 Optical Phase Conjugation ...... 169 some of the most significant recent advances and 4.4.7 Optical Bistability and Switching .... 170 breakthroughs in nonlinear optics, as well as novel 4.4.8 Stimulated Raman Scattering...... 172 applications of nonlinear-optical processes and 4.4.9 Third-Harmonic Generation devices. by Ultrashort Laser Pulses...... 173 Nonlinear optics is the area of optics that 4.5 Ultrashort Light Pulses studies the interaction of light with matter in in a Resonant Two-Level Medium: theregimewheretheresponseofthematerial Self-Induced Transparency system to the applied electromagnetic field is and the Pulse Area Theorem...... 178 nonlinear in the amplitude of this field. At low 4.5.1 Interaction of Light light intensities, typical of non-laser sources, the with Two-Level Media ...... 178

properties of materials remain independent of 4.5.2 The Maxwell and Schrödinger A Part the intensity of illumination. The superposition Equations for a Two-Level Medium 178 principle holds true in this regime, and light waves 4.5.3 Pulse Area Theorem ...... 180 can pass through materials or be reflected from 4.5.4 Amplification 4 boundaries and interfaces without interacting with of Ultrashort Light Pulses each other. Laser sources, on the other hand, can in a Two-Level Medium ...... 181 provide sufficiently high light intensities to modify 4.5.5 Few-Cycle Light Pulses the optical properties of materials. Light waves in a Two-Level Medium ...... 183 can then interact with each other, exchanging 4.6 Let There be White Light: momentum and energy, and the superposition Supercontinuum Generation...... 185 principle is no longer valid. This interaction of light 4.6.1 Self-Phase Modulation, waves can result in the generation of optical fields Four-Wave Mixing, at new frequencies, including optical harmonics of and Modulation Instabilities incident radiation or sum- or difference-frequency in Supercontinuum-Generating signals. Photonic-Crystal Fibers ...... 185 4.6.2 Cross-Phase-Modulation-Induced Instabilities ...... 187 4.1 Nonlinear Polarization 4.6.3 Solitonic Phenomena in Media and Nonlinear Susceptibilities ...... 159 with Retarded Optical Nonlinearity. 189 4.2 Wave Aspects of Nonlinear Optics ...... 160 4.7 Nonlinear Raman Spectroscopy ...... 193 4.3 Second-Order Nonlinear Processes ...... 161 4.7.1 The Basic Principles ...... 194 4.3.1 Second-Harmonic Generation...... 161 4.7.2 Methods of Nonlinear Raman 4.3.2 Sum- and Difference-Frequency Spectroscopy ...... 196 Generation and Parametric 4.7.3 Polarization Nonlinear Raman Amplification...... 163 Techniques...... 199 4.7.4 Time-Resolved Coherent 4.4 Third-Order Nonlinear Processes ...... 164 Anti-Stokes Raman Scattering...... 201 4.4.1 Self-Phase Modulation ...... 165 4.4.2 Temporal Solitons...... 166 4.8 Waveguide Coherent Anti-Stokes 4.4.3 Cross-Phase Modulation ...... 167 Raman Scattering ...... 202 4.4.4 Self-Focusing...... 167 4.8.1 Enhancement of Waveguide CARS 4.4.5 Four-Wave Mixing...... 169 in Hollow Photonic-Crystal Fibers... 202 158 Part A Basic Principles and Materials

4.8.2 Four-Wave Mixing and CARS 4.11 High-Order Harmonic Generation ...... 219 in Hollow-Core Photonic-Crystal 4.11.1 Historical Background...... 219 Fibers ...... 205 4.11.2 High-Order-Harmonic Generation in Gases ...... 220 4.9 Nonlinear Spectroscopy 4.11.3 Microscopic Physics ...... 222 with Photonic-Crystal-Fiber Sources...... 209 4.11.4 Macroscopic Physics...... 225 4.9.1 Wavelength-Tunable Sources and Progress in Nonlinear Spectroscopy 209 4.12 Attosecond Pulses: 4.9.2 Photonic-Crystal Fiber Frequency Measurement and Application ...... 227 Shifters ...... 210 4.12.1 Attosecond Pulse Trains 4.9.3 Coherent Anti-Stokes Raman and Single Attosecond Pulses...... 227 Scattering Spectroscopy 4.12.2 Basic Concepts with PCF Sources ...... 211 for XUV Pulse Measurement ...... 227 4.9.4 Pump-Probe Nonlinear 4.12.3 The Optical-Field-Driven XUV Streak Absorption Spectroscopy Camera Technique...... 230 using Chirped Frequency-Shifted 4.12.4 Applications of Sub-femtosecond Light Pulses XUV Pulses: Time-Resolved from a Photonic-Crystal Fiber ...... 213 Spectroscopy of Atomic Processes ... 234 4.12.5 Some Recent Developments...... 236 4.10 Surface Nonlinear Optics, Spectroscopy, and Imaging ...... 216 References ...... 236 atA Part

4 Although the observation of most nonlinear-optical 1963 provided 20%–30% efficiency of frequency con- phenomena requires laser radiation, some classes of version [4.5, 6]. The early phases of the development nonlinear-optical effects were known long before the and the basic principles of nonlinear optics have been invention of the laser. The most prominent examples of reviewed in the most illuminating way in the classi- such phenomena include Pockels and Kerr electrooptic cal books by Bloembergen [4.7] and Akhmanov and effects [4.1], as well as light-induced resonant absorp- Khokhlov [4.8], published in the mid 1960s. tion saturation, described by Vavilov [4.2, 3]. It was, Over the following four decades, the field of nonlin- however, only with the advent of lasers that systematic ear optics has witnessed an enormous growth, leading studies of optical nonlinearities and the observation of to the observation of new physical phenomena and giv- a vast catalog of spectacular nonlinear-optical phenom- ing rise to novel concepts and applications. A systematic ena became possible. introduction into these effects along with a comprehen- In the first nonlinear-optical experiment of the laser sive overview of nonlinear-optical concepts and devices era, performed by Franken et al. in 1961 [4.4], a ruby- can be found in excellent textbooks by Shen [4.9], laser radiation with a wavelength of 694.2nm was Boyd [4.1], Butcher and Cotter [4.10], Reintjes [4.11] used to generate the second harmonic in a quartz crys- and others. One of the most recent up-to-date reviews of tal at the wavelength of 347.1 nm. This seminal work the field of nonlinear optics with an in-depth discussion was followed by the discovery of a rich diversity of the fundamental physics underlying nonlinear-optical of nonlinear-optical effects, including sum-frequency interactions was provided by Flytzanis [4.12]. This generation, stimulated Raman scattering, self-focusing, chapter provides a brief introduction into the main optical rectification, four-wave mixing, and many others. nonlinear-optical phenomena and discusses some of the While in the pioneering work by Franken the efficiency most significant recent advances in nonlinear optics, as of second-harmonic generation (SHG) was on the or- well as novel applications of nonlinear-optical processes der of 10−8, optical frequency doublers created by early and devices. Nonlinear Optics 4.1 Nonlinear Polarization and Nonlinear Susceptibilities 159

4.1 Nonlinear Polarization and Nonlinear Susceptibilities

Nonlinear-optical effects belong to a broader class of We now represent the polarization P as a sum electromagnetic phenomena described within the gen- P = P + P , (4.8) eral framework of macroscopic Maxwell equations. The L nl Maxwell equations not only serve to identify and classify where PL is the part of the electric dipole polarization nonlinear phenomena in terms of the relevant nonlinear- linear in the field amplitude and Pnl is the nonlinear part optical susceptibilities or, more generally, nonlinear of this polarization. terms in the induced polarization, but also govern the The linear polarization governs linear-optical phe- nonlinear-optical propagation effects. We assume the nomena, i. e., it corresponds to the regime where the absence of extraneous charges and currents and write optical properties of a medium are independent of the , the set of Maxwell equations for the electric, E(r t), field intensity. The relation between PL and the electric and magnetic, H(r, t), fields in the form field E is given by the standard formula of linear optics: ∂ 1 B ∇ × E =− , (4.1) P = χ(1)(t − t )E(t )dt , (4.9) c ∂t L 1 ∂D ∇ × B = , (4.2) where χ(1)(t) is the time-domain linear susceptibility c ∂t tensor. Representing the field E and polarization P in ∇·D = 0 , (4.3) L the form of elementary monochromatic plane waves, ∇·B = 0 . (4.4) A Part E = E (ω) exp (ikr − ωt) + c.c. (4.10) Here, B = H + 4π M,whereM is the magnetic dipole polarization, c is the speed of light, and and 4.1 t PL = PL(ω)exp ikr − ωt + c.c. , (4.11) D = E + 4π J(ζ)dζ, (4.5) we take the Fourier transform of (4.9) to find −∞ P (ω) = χ(1)(ω)E(ω) , (4.12) where J is the induced current density. Generally, the L equation of motion for charges driven by the electromag- where netic field has to be solved to define the relation between (1) (1) the induced current J and the electric and magnetic χ (ω) = χ (t)exp(iωt)dt . (4.13) fields. For quantum systems, this task can be fulfilled by solving the Schrödinger equation. In Sect. 4.5 of this In the regime of weak fields, the nonlinear part of the chapter, we provide an example of such a self-consistent polarization Pnl can be represented as a power-series expansion in the field E: analysis of nonlinear-optical phenomena in a model two-level system. Very often a phenomenological ap- (2) Pnl = χ (t − t1, t − t2) : E(t1)E(t2)dt1 dt2 proach based on the introduction of field-independent or local-field-corrected nonlinear-optical susceptibilities + χ(3) − , − , − can provide an adequate description of nonlinear-optical (t t1 t t2 t t3) processes. . Formally, the current density J can be represented .E(t1)E(t2)E(t3)dt1 dt2 dt3 + ... , (4.14) as a series expansion in multipoles: χ(2) χ(3) ∂ where and are the second- and third-order J = (P −∇·Q) + c (∇ × M) , (4.6) nonlinear susceptibilities. ∂t Representing the electric field in the form of a sum where P and Q are the electric dipole and electric of plane monochromatic waves, quadrupole polarizations, respectively. In the electric = ω − ω + , dipole approximation, we keep only the first term on E Ei ( i )exp(ikir i t) c.c. (4.15) the right-hand side of (4.6). In view of (4.5), this gives i the following relation between the D, E,andP vectors: we take the Fourier transform of (4.14) to arrive at (2) (3) D = E + 4π P. (4.7) Pnl(ω) = P (ω) + P (ω) + ... , (4.16) 160 Part A Basic Principles and Materials

where ω 1, k 1 (2) (2) P (ω) = χ (ω; ωi ,ωj ) : E(ωi )E(ω j ) , (4.17) . (3) (3) . P (ω) = χ (ω; ωi ,ωj ,ωk).E(ωi )E(ω j )E(ωk) , (2) (4.18) ω 3, k 3 χ(2) ω; ω ,ω = χ(2) ω = ω + ω ω 2, k 2 ( i j ) ( i j ) (2) = χ (t1, t2)exp[i(ωi t1 + ω j t2)]dt1 dt2 (4.19)

is the second-order nonlinear-optical susceptibility and Fig. 4.1 Sum-frequency generation ω1 + ω2 = ω3 in a medium with a quadratic nonlinearity. The case of ω = ω χ(3) ω; ω ,ω ,ω = χ(3) ω = ω + ω + ω 1 2 ( i j k) ( i j k) corresponds to second-harmonic generation = χ(3) t , t , t ( 1 2 3) χ(2) = χ(2) ω ; ω ,ω nonlinear susceptibilities SFG ( SF 1 2)and χ(2) = χ(2) ω ; ω , −ω exp[i(ωi t1 + ω j t2 + ωkt3)]dt1 dt2 dt3 (4.20) DFG ( DF 1 2), respectively. The third-order nonlinear polarization defined by is the third-order nonlinear-optical susceptibility. (4.18) is responsible for four-wave mixing (FWM), The second-order nonlinear polarization defined stimulated Raman scattering, two-photon absorption, atA Part by (4.17) gives rise to three-wave mixing processes, and Kerr-effect-related phenomena, including self- optical rectification and linear electrooptic effect. phase modulation (SPM) and self-focusing. For the In particular, setting ωi = ω j = ω0 in (4.17) and particular case of third-harmonic generation, we set

4.2 ω = ω (4.19), we arrive at 2 0, which corresponds to ωi = ω j = ωk = ω0 in (4.18) and (4.20) to obtain second-harmonic generation, controlled by the nonlin- ω = 3ω0. This type of nonlinear-optical interaction, in χ(2) = χ(2) ω ; ω ,ω ear susceptibility SHG (2 0 0 0). In a more accordance with (4.18) and (4.20), is controlled by χ(3) = χ(3) ω ; ω ,ω ,ω general case of three-wave mixing process with the cubic susceptibility THG (3 0 0 0 0). ωi = ω1 = ω j = ω2, the second-order polarization de- A more general, frequency-nondegenerate case can cor- ﬁned by (4.17) can describe sum-frequency generation respond to a general type of an FWM process. These (SFG) ωSF = ω1 + ω2 Fig. 4.1 or difference-frequency and other basic nonlinear-optical processes will be con- generation (DFG) ωDF = ω1 − ω2, governed by the sidered in greater details in the following sections.

4.2 Wave Aspects of Nonlinear Optics In the electric dipole approximation, the Maxwell equa- axis, we represent the field E in (4.21) by tions (4.1–4.4) yield the following equation governing ( , ) = ( , ) ( − ω ) the propagation of light waves in a weakly nonlinear E r t Re eA z t exp ikz t (4.22) medium: and write the nonlinear polarization as 2 2 2 1 ∂ E 4π ∂ PL 4π ∂ Pnl ∇ × (∇ × E) − − = . ( , ) = ( , ) − ω , c2 ∂t2 c2 ∂t2 c2 ∂t2 Pnl r t Re ep Pnl z t exp ikpz t (4.21) (4.23) The nonlinear polarization, appearing on the right-hand where k and A(z, t) are the wave vector and the envelope side of (4.21), plays the role of a driving source, inducing of the electric field, k p and Pnl(z, t) are the wave vector an electromagnetic wave with the same frequency ω as and the envelope of the polarization wave. the nonlinear polarization wave Pnl(r, t). Dynamics of If the envelope A(z, t) is a slowly varying func- a nonlinear wave process can be then thought as a result tion over the wavelength, |∂2 A/∂z2||k∂A/∂z|,and 2 2 2 of the interference of induced and driving (pump) waves, ∂ Pnl/∂t ≈−ω Pnl, (4.21) is reduced to [4.9] controlled by the dispersion of the medium. ∂ ∂ π ω2 Assuming that the fields have the form of quasi- A 1 A 2 i + = Pnl exp (iΔkz) , (4.24) monochromatic plane waves propagating along the z- ∂z u ∂t kc2 Nonlinear Optics 4.3 Second-Order Nonlinear Processes 161

− where u = (∂k/∂ω) 1 is the group velocity and will be employed to analyze the wave aspects of Δk = kp − k is the wave-vector mismatch. the basic second- and third-order nonlinear-optical In the following sections, this generic equation phenomena. of slowly varying envelope approximation (SVEA)

4.3 Second-Order Nonlinear Processes

4.3.1 Second-Harmonic Generation reference with z = z and η = t − z/u ΔkL Δ In second-harmonic generation, a pump wave with a fre- 2 sin 2 i kL A (L) = iγ A L exp , (4.29) quency of ω generates a signal at the frequency 2ω 2 2 10 ΔkL 2 2 as it propagates through a medium with a quadratic nonlinearity (Fig. 4.1). Since all even-order nonlinear where L is the length of the nonlinear medium. susceptibilities χ(n) vanish in centrosymmetric me- The intensity of the second-harmonic ﬁeld is then dia, SHG can occur only in media with no inversion given by symmetry. ΔkL 2 Assuming that diffraction and second-order dis- sin I (L) ∝ γ 2 I 2 2 L2, (4.30) persion effects are negligible, we use (4.24) for 2 2 10 ΔkL

2 A Part a quadratically nonlinear medium with a nonlinear SHG χ(2) = χ(2) ( ω; ω, ω) where I is the intensity of the pump field. susceptibility SHG 2 to write a pair of 10 coupled equations for the slowly varying envelopes of Second-harmonic intensity I2, as can be seen from 4.3 the pump and second-harmonic fields A1 = A1(z, t)and (4.30) oscillates as a function of L Fig. 4.2 with a period = π/|Δ |=λ | − | −1 λ A2 = A2(z, t): Lc k 1(4 n1 n2 ) ,where 1 is the pump wavelength and n1 and n2 are the values of the refractive ∂ ∂ A1 + 1 A1 = γ ∗ ( Δ ) , index at the frequencies of the pump field and its second i 1 A1 A2 exp i kz (4.25) ∂z u1 ∂t harmonic, respectively. The parameter Lc, defining the ∂A ∂A length of the nonlinear medium providing the maximum 2 + 1 2 = γ 2 (− Δ ) , i 2 A1 exp i kz (4.26) SHG efficiency, is referred to as the coherence length. ∂z u2 ∂t where Second-harmonic intensity (arb. units) 2 2πω Lc2 = 2Lc1 γ = 1 χ(2) (ω; ω, −ω) (4.27) 0.4 1 2 2 k1c and 0.3 πω2 4 (2) γ = 1 χ (4.28) 2 2 SHG k2c 0.2 are the nonlinear coefficients, u1 and u2 are the group Lc1 velocities of the pump and second-harmonic pulses, 0.1 respectively, and Δk = 2k1 −k2 is the wave-vector mismatch for the SHG process. 0.0 If the difference between the group velocities of the 0 123456 pump and second-harmonic pulses can be neglected for L/Lc a nonlinear medium with a given length and if the intensity of the pump field in the process of SHG remains Fig. 4.2 Second-harmonic intensity as a function of the much higher than the intensity of the second-harmonic length L of the nonlinear medium normalized to the coher- 2 2 field, we set u1 = u2 = u and |A1| =|A10| = const. ence length Lc for two values of Lc:(dashed line) Lc1 and in (4.25) and (4.26) to derive in the retarded frame of (solid line) Lc2 =2Lc1 162 Part A Basic Principles and Materials

Although the solution (4.29) describes the simplest Pump amplitude Second-harmonic amplitude regime of SHG, it is very instructive as it visualizes (arb. units) (arb. units) the signiﬁcance of reducing the wave-vector mismatch Δk for efﬁcient SHG. Since the wave vectors k1 and 1.0 1.0

k2 are associated with the momenta of the pump and = second-harmonic fields, p1 = k1 and p2 k2, with 0.8 0.8 Δ = being the Planck constant, the condition k 0, known as the phase-matching condition in nonlinear 0.6 0.6 optics, in fact, represents momentum conservation for the SHG process, where two photons of the pump field are requited to generate a single photon of the second 0.4 0.4 harmonic. Several strategies have been developed to solve the 0.2 0.2 phase-matching problem for SHG. The most practi- cally significant solutions include the use of birefringent 0.0 0.0 nonlinear crystals [4.13, 14], quasi-phase-matching in 0 1 2 3 4 z/z periodically poled nonlinear materials [4.15, 16] and sh waveguide regimes of nonlinear interactions with the Fig. 4.4 The amplitudes of the pump and second-harmonic phase mismatch related to the material dispersion com- fields as functions of the normalized propagation distance atA Part −1 pensated for by waveguide dispersion [4.7]. Harmonic z/zsh with zsh =[γρ10(0)] generation in the gas phase, as demonstrated by Miles and Harris [4.17], can be phase-matched through an second-harmonic intensity as a function of the length 4.3 optimization of the content of the gas mixture. Fig- L of the nonlinear medium. This scaling law holds ure 4.3 illustrates phase matching in a birefringent true, however, only as long as the second-harmonic crystal. The circle represents the cross section of the intensity remains much less than the pump intensity. refractive-index sphere n0(ω) for an ordinary wave at As |A2| becomes comparable with |A1|, depletion of the pump frequency ω. The ellipse is the cross sec- the pump field has to be taken into consideration. tion of the refractive-index ellipsoid ne(2ω)foran To this end, we introduce the real amplitudes ρ j and extraordinary wave at the frequency of the second har- phases ϕ j of the pump and second-harmonic fields, monic 2ω. Phase matching is achieved in the direction A j = ρ j exp iϕ j , with j = 1, 2. Then, assuming that where n0ω = ne(2ω), corresponding to an angle θpm u1 = u2 = u and γ1 = γ2 = γ, we derive from (4.25) with respect to the optical axis c of the crystal in and (4.26) Fig. 4.3. When the phase-matching condition Δk = 0 is satis- ρ1 (η, z) = ρ10 (η) sech [γρ10 (η) z] , (4.31) fied, (4.29) and (4.30) predict a quadratic growth of the ρ2 (η, z) = ρ10 (η) tanh [γρ10 (η) z] . (4.32) c The solutions (4.31) and (4.32) show that the entire energy of the pump field in the phase- matching regime can be transferred to the second θ harmonic. As the pump field becomes depleted ηo(ω) Fig. 4.4, the growth of the second-harmonic field saturates. Effects related to the group-velocity mismatch become significant when the length of the nonlinear = τ /| −1 − −1| medium L exceeds the length Lg 1 u2 u1 , τ ηe(2ω) where 1 is the pulse width of the pump field. The length Lg characterizes the walk-off between the pump and second-harmonic pulses caused by the group-velocity Fig. 4.3 Phase-matching second-harmonic generation in mismatch. In this nonstationary regime of SHG, the a birefringent crystal amplitude of the second harmonic in the constant-pump- Nonlinear Optics 4.3 Second-Order Nonlinear Processes 163

field approximation is given by A2(z, t) = A20(t), and the solution of (4.36) yields z z − − A (z, t) = γ A2 t − z/u + ξ u 1 − u 1 ( , ) = γ − / + ξ −1 − −1 2 i 2 10 2 2 1 A3 z t i 3 A10 t z u3 u3 u1 0 0 ×exp(−iΔkξ) dξ. (4.33) − / + ξ −1 − −1 × A20 t z u3 u3 u2 Group-velocity mismatch may lead to a considerable ×exp(−iΔkξ) dξ. (4.40) increase in the pulse width of the second harmonic τ2.ForL Lg, the second harmonic pulse width, The efficiency of frequency conversion, as can be seen −1 −1 Δ ≈ τ2 ≈|u − u |z, scales linearly with the length of the from (4.40) is controlled by the group delays 21 2 1 | −1 − −1| Δ ≈| −1 − −1| Δ ≈| −1 − nonlinear medium and is independent of the pump pulse u2 u1 L, 31 u3 u1 L,and 32 u3 −1| width. u2 L between the pulses involved in the SFG process. In particular, the laser fields cease to interact with each 4.3.2 Sum- and Difference-Frequency other when the group delay Δ21 starts to exceed the Generation and Parametric pulse width of the faster laser pulse. Amplification In difference-frequency generation (DFG), two input fields with frequencies ω1 and ω2 generate a nonlinear In sum-frequency generation Fig. 4.1, two laser fields signal at the frequency ω3 = ω1 −ω2.Thisprocessisof with frequencies ω and ω generate a nonlinear

1 2 considerable practical significance as it can give rise to A Part signal at the frequency ω3 = ω1 + ω2 in a quadrati- intense coherent radiation in the infrared range. In the cally nonlinear medium with a nonlinear susceptibility limiting case of ω1 ≈ ω2, this type of nonlinear-optical (2) (2) χ = χ (ω3; ω1,ω2). In the first order of dis- interaction corresponds to optical rectification, which SFG 4.3 persion theory, the coupled equations for slowly has been intensely used over the past two decades for varying envelopes of the laser fields A1 = A1(z, t)and the generation of terahertz radiation. = , = , A2 A2(z t) and the nonlinear signal A3 A3(z t)are If the field at the frequency ω1 is strong and re- written as mains undepleted in the process of nonlinear-optical ∂ ∂ interaction, A (z, t) = A (t), the set of coupled equa- A1 + 1 A1 = γ ∗ ( Δ ) , 1 10 i 1 A3 A2 exp i kz (4.34) tions governing the amplitudes of the remaining two ∂z u1 ∂t ∂A2 1 ∂A2 ∗ fields in the stationary regime is written as + = γ A A ( Δkz) , (4.35) ∂ ∂ i 2 3 1 exp i ∂ ∂ z u2 t A2 + 1 A2 = γ ∗ ( Δ ) , i 2 A1 A3 exp i kz (4.41) ∂A3 1 ∂A3 ∂z u ∂t + = γ A A (− Δkz) , (4.36) 2 ∂ ∂ i 3 1 2 exp i ∂ ∂ z u3 t A3 + 1 A3 = γ ∗ (− Δ ) , i 3 A1 A2 exp i kz (4.42) where ∂z u3 ∂t 2πω2 where, γ = 1 χ(2) (ω ; ω , −ω ) , (4.37) 1 k c2 1 3 2 πω2 1 2 2 (2) 2 γ = χ (ω ; ω , −ω ) , (4.43) 2πω 2 k c2 2 1 3 γ = 2 χ(2) (ω ; ω , −ω ) , (4.38) 2 2 2 2 3 1 k2c 2πω2 γ = 3 χ(2) (ω ; ω , −ω ) πω2 3 3 1 2 (4.44) 2 (2) k c2 γ = 3 χ (4.39) 3 3 k c2 SFG 3 are the nonlinear coefficientsm and Δk = k1 −k2 −k3 is are the nonlinear coefficients, u1, u2,andu3 and k1, k2, the wave-vector mismatch for the DFG process. and k3 are the group velocities and the wave vectors of With no signal at ω3 applied at the input of the non- ω ω ω the fields with frequencies 1, 2,and 3, respectively, linear medium, A3(0, t) = 0, the solution to (4.41) and and Δk = k1 + k2 − k3 is the wave-vector mismatch for (4.42) in the stationary regime is given by [4.12] the SFG process. Δk As long as the intensity of the sum-frequency field A (z) = A (0) cosh (κz) + i sinh (κz) , 2 2 2κ remains much less than the intensities of the laser fields, (4.45) the amplitudes of the laser fields can be can be as- A (z) = iA (0) sinh (κz) , (4.46) sumed to be given functions of t, A1(z, t) = A10(t)and 3 2 164 Part A Basic Principles and Materials

where As can be seen from (4.50), optical parametric ampli- ∗ fication preserves the phase of the signal pulse. This κ2 = 4γ γ |A |2 − (Δk)2 . (4.47) 2 3 1 property of optical parametric amplification lies at the Away from the phase-matching condition, the amplifica- heart of the principle of optical parametric chirped-pulse tion of a weak signal is achieved only when the intensity amplification [4.19], allowing ultrashort laser pulses to of the pump field exceeds a threshold, be amplified to relativistic intensities. It also suggests 3 2 n1n2n3c (Δk) a method of efficient frequency conversion of few-cycle I > I = , (4.48) 1 th 2 field waveforms without changing the phase offset be- π3 χ(2) ω ω 32 DFG 2 3 tween their carrier frequency and temporal envelope, making few-cycle laser pulses a powerful tool for the where we took investigation of ultrafast electron dynamics in atomic χ(2) ω ; ω , −ω ≈ χ(2) ω ; ω , −ω = χ(2) . ( 2 1 3) ( 3 1 2) DFG and molecular systems. In the nonstationary regime of optical paramet- Above, this threshold, the growth in the intensity I2 of a weak input signal is governed by ric amplification, when the pump, signal, and idler fields propagate with different group velocities, useful γ γ ∗ | |2 2 3 A10 2 and important qualitative insights into the phase rela- I2 (z) = I2 (0) sin (κz) + 1 . (4.49) κ2 tions between the pump, signal, and idler pulses can This type of three-wave mixing is often referred to as be gained from energy and momentum conservation, ω = ω +ω = + optical parametric amplification. A weak input field, re- 1 2 3 and k1 k2 k3. These equalities dictate atA Part ferred to as the signal field (the field with the amplitude the following relations between the frequency deviations δω j = , , A2 in our case), becomes amplified in this type of pro- j in the pump, signal, and idler fields ( 1 2 3): cess through a nonlinear interaction with a powerful 4.4 δω1 = δω2 + δω3 (4.52) pump field (the undepleted field with the amplitude A1 in the case considered here). In such a scheme of optical and parametric amplification, the third field (the field with δω / = δω / + δω / . the amplitude A3) is called the idler field. 1 u1 2 u2 3 u3 (4.53) We now consider the regime of optical paramet- In view of (4.52) and (4.53), we find ric amplification ω1 = ω2 + ω3 where the pump, signal and idler pulses are matched in their wave vectors and δω2 = q2δω1 (4.54) group velocities. Introducing the real amplitudes ρ j and phases ϕ j of the pump, signal, and idler fields, and A j = ρ j exp iϕ j ,where j = 1, 2, 3, assuming that δω = q δω , (4.55) γ2 = γ3 = γ in (4.35) and (4.36), A1(z, t) = A10(t)and 3 3 1 A (0, t) = 0, we write the solution for the amplitude of − − − − 3 where q = (u 1 − u 1)/(u 1 − u 1), q = 1 −q . the signal field as [4.18] 2 1 3 2 3 3 2 In the case of a linearly chirped pump, (η, ) = (η) γρ (η) . 2 A2 z A20 cosh [ 10 z] (4.50) ϕ1(t) = α1t /2, the phases of the signal and idler ϕ = α 2/ α = α The idler field then builds up in accordance with pulses are given by m(t) mt 2, where m qm 1, m = 2, 3. With q 1, the chirp of the signal and idler (η, ) = ∗ (η) ϕ (η) γρ (η) . m A3 z A20 exp [i 10 ] sinh [ 10 z] pulses can thus considerably exceed the chirp of the (4.51) pump field.

4.4 Third-Order Nonlinear Processes

Optical nonlinearity of the third order is a univer- for symmetry reasons. Third-order nonlinear processes sal property, found in any material regardless of its include a vast variety of four-wave mixing processes, spatial symmetry. This nonlinearity is the lowest- which are extensively used for frequency conversion of order nonvanishing nonlinearity for a broad class of laser radiation and as powerful methods of nonlinear centrosymmetric materials, where all the even-order spectroscopy. Frequency-degenerate, Kerr-effect-type nonlinear susceptibilities are identically equal to zero phenomena constitute another important class of third- Nonlinear Optics 4.4 Third-Order Nonlinear Processes 165 order nonlinear processes. Such effects lie at the heart of In the retarded frame of reference, z = z and optical compressors, mode-locked femtosecond lasers, η = t − z/u, the solution to (4.60) is written as and numerous photonic devices, where one laser pulse is 2 used to switch, modulate, or gate another laser pulse. In A (η, z) = A0 (η) exp iγ˜ |A0 (η)| z , (4.62) this section, we provide a brief overview of the main third-order nonlinear-optical phenomena and discuss where A0(η) is the initial ﬁeld envelope. some of their practical applications. Since the group-velocity dispersion was not included in (4.60), the shape of the pulse envelope remains un- 4.4.1 Self-Phase Modulation changed as the pulse propagates through the nonlinear medium. The intensity-dependent change in the refrac- The third-order nonlinearity gives rise to an intensity- tive index gives rise to a nonlinear phase shift dependent additive to the refractive index: ϕnl (η, z) = γSPM I0 (η) z , (4.63) n = n0 + n2 I (t) , (4.56) γ = πn /λ I η where n0 is the refractive index of the medium in the where SPM 2 2 and 0( ) is the initial intensity 2 (3) absence of light ﬁeld, n2 = (2π/n0) χ (ω; ω, ω, −ω) envelope. is the nonlinear refractive index, χ(3)(ω; ω, ω, −ω)is The deviation of the instantaneous frequency of the the third-order nonlinear-optical susceptibility, referred pulse is given by to as the Kerr-type nonlinear susceptibility, and I(t) ∂ϕnl (η, z) ∂I0 (η) A Part is the intensity of laser radiation. Then, the nonlinear δω (η, z) =− =−γ z . (4.64) ∂ SPM ∂η (intensity-dependent) phase shift of a pulse at a distance t L is given by A quadratic approximation of the pulse envelope, 4.4 ω Φ (t) = n I (t) L . (4.57) c 2 η2 I (η) ≈ I (0) 1 − , (4.65) 0 0 τ2 Due to the time dependence of the radiation inten- 0 sity within the light pulse, the nonlinear phase shift is also time-dependent, giving rise to a generally time- where τ0 is the pulse width, which is valid around the dependent frequency deviation: maximum of the laser pulse, gives a linear chirp of the ω ∂I Δω (t) = n L . (4.58) c 2 ∂t Spectral intensity (arb. units) The resulting spectral broadening of the pulse can be 10 estimated in the following way:

ω I0 Δω = n L , (4.59) c 2 τ 1 where I0 is the peak intensity of the light pulse and τ is the pulse duration. The first-order dispersion-theory equation for the 0.1 slowly varying envelope A(t, z) of a laser pulse prop- 1 432 agating in a medium with a Kerr-type nonlinearity is written as [4.9] 0.01 ∂A 1 ∂A + = iγ˜ |A|2 A , (4.60) 1.00 1.01 1.02 1.03 1.04 1.05 1.06 ∂z u ∂t Wavelength (μm) where u is the group velocity of the laser pulse and Fig. 4.5 Self-phase-modulation-induced spectral broaden- . μ 3πω ( ) ing of a laser pulse with a central wavelength of 1 03 m(an γ˜ = χ 3 (ω; ω, −ω, ω) . (4.61) 2 input spectrum is shown by curve 1) in a fused-silica opti- 2n0c −16 2 cal fiber with n2 = 3.2×10 cm /W: γSPM I0(0)z = 1.25 is the nonlinear coefficient. (curve 2), 2.50 (curve 3), and 6.25 (curve 4) 166 Part A Basic Principles and Materials

pulse to pulses propagating through the nonlinear dispersive medium with an invariant or periodically varying shape: I0 (0) δω (η, z) ≈−2γ ηz . (4.66) optical solitons. SPM τ2 0 Optical solitons is a special class of solutions to the The spectrum of a self-phase-modulated pulse is given nonlinear Schrödinger equation (NLSE) by ∂ ∂2 q 1 q 2 i + + |q| q = 0 . (4.68) ∞ 2 ∂ξ 2 ∂τ2

S (ω) = I (η) exp [iωη + iϕnl (η)] dη . (4.67) The NLSE can describe the evolution of optical wave packets including the dispersion β(ω) of optical waves 0 in a bulk material or in a waveguide structure through Figure 4.5 illustrates SPM-induced spectral broaden- the power series expansion ing of a short laser pulse with a central wavelength of 1 1.03 μm, typical of ytterbium fiber lasers, in a fused- β (ω) ≈ β (ω0) + (ω − ω0) silica optical fiber with nonlinear refractive index u = . −16 2/ 1 2 n2 3 2×10 cm W. + β2 (ω − ω0) + ... , (4.69) Thus, self-phase modulation results in spectral 2 broadening of a light pulse propagating through a hol- where ω0 is the central frequency of the wave = ∂β/∂ω| −1 low fiber. This effect allows compression of light pulses packet, u ( ω=ω0 ) is the group velocity, atA Part β = ∂2β/∂ω2| through the compensation of the phase shift acquired and 2 ω=ω0 . Thus, with the NLSE (4.68) by the pulse in a hollow fiber. Compensation of a lin- projected on laser pulses propagating in a nonlinear ear chirp, corresponding to a linear time dependence of medium, q is understood as the normalized pulse en- /

4.4 1 2 the instantaneous frequency, is straightforward from the velope, q = A/(P0) , with ξ being the normalized ξ = / = τ2/|β | technical point of view. Such a chirp arises around the propagation coordinate, z Ld, Ld 0 2 be- maximum of a light pulse, where the temporal pulse en- ing the dispersion length, P0 and τ0 defined as the velope can be approximated with a quadratic function pulse width and the pulse peak power, respectively, and of time [see (4.65, 4.66)]. τ = (t − z/u)/τ0. It is physically instructive to consider the compres- The canonical form of the fundamental soliton solu- sion of chirped light pulses in the time domain. Since the tion to (4.68) is [20] frequency of a chirped pulse changes from its leading ξ edge to its trailing edge, dispersion of our compressor q (ξ,τ) = sech (τ) exp i . (4.70) 2 should be designed in such a way as to slower down the leading edge of the pulse with respect to the trailing The radiation peak power required to support such a soli- edge of the pulse. In other words, the group velocities ton is given by for the frequencies propagating with the leading edge P = |β | /(γτ2) . (4.71) of the pulse should be lower than the group velocities 0 2 0 for the frequencies propagating with the trailing edge Solitons retain their stable shape as long as their of the pulse. This can be achieved by designing a dis- spectrum lies away from the spectrum of dispersive persive element with the required sign of dispersion and waves that can propagate in the medium. High-order appropriate dispersion relation. Systems of diffraction dispersion perturbs solitons, inducing Cherenkov-type gratings and, recently, multilayer chirped mirrors [4.20] wave-matching resonances between solitons and disper- are now widely used for the purposes of pulse compres- sive waves [4.21, 22]. Under these conditions solitons sion. In certain regimes of pulse propagation, self-phase tend to lose a part of their energy in the form of blue- modulation and pulse compression may take place in the shifted dispersive-wave emission. For low pump-field same medium. powers, the generic wave-matching condition for such soliton–dispersive wave resonances is written [4.22] 4.4.2 Temporal Solitons Ω = 1/2ε,whereΩ is the frequency difference between the soliton and the resonant dispersive wave and ε is The nonlinear phase shift acquired by a laser pulse prop- the parameter controlling the smallness of perturbation agating through a medium with a Kerr nonlinearity can of the nonlinear Schrödinger equation, which can be be balanced by group-velocity dispersion, giving rise represented as ε =|β3/6β2| for photonic-crystal fibers Nonlinear Optics 4.4 Third-Order Nonlinear Processes 167

2 2 (PCFs) with second-order dispersion β2 = ∂ β/∂ω and change in the refractive index induced by a laser pulse 3 3 third-order dispersion β3 = ∂ β/∂ω . This dispersive- with an intensity envelope I(t) varying in time, self- wave emission of solitons is an important part of focusing is related to a nonlinear lens induced by a laser supercontinuum generation in nonlinear optical fibers, beam with a spatially nonuniform intensity distribu- including photonic-crystal fibers. tion I(r). Given a transverse intensity profile I(r), the nonlinear additive to the refractive index is written as 4.4.3 Cross-Phase Modulation n (r) = n0 + n2 I (r) . (4.74) Cross-phase modulation (XPM) is a result of nonlinear- If the field intensity peaks at the center of the beam at optical interaction of at least two physically distinguish- r = 0, the nonlinear change in the refractive index also able light pulses (i. e., pulses with different frequencies, reaches its maximum at r = 0, yielding a focusing or polarizations, mode structures, etc.) related to the phase defocusing lens, depending on the sign of n2. modulation of one of the pulses (a probe pulse) due to The stationary regime of self-focusing is governed the change in the refractive index of the medium induced by [4.9] by another pulse (a pump pulse). ∂A Δn + Δ =− 2 , The cross-action of a pump pulse with a frequency 2ik ⊥ A 2k A (4.75) ∂z n0 ω1 on a probe pulse with a frequency ω2 gives rise to Δn = n I = n˜ |E|2 Δ⊥ a phase shift of the probe pulse, which can be written where 2 2 , is the transverse part of as [4.23]. the Laplacian.

We consider a Gaussian beam and assume that this A Part 3πω2 Φ (η, z) = 2 χ(3) ω ; ω ,ω , −ω beam retains its proﬁle as it propagates through the XPM 2 s s p p c k2 nonlinear medium, z

2 2 4.4 ζ A0 r × A η − , 0 dζ, (4.72) A (r, z) = exp − + iψ (z) , p σ f (z) 2 2 ( ) 2a0 f z 0 (4.76) (3) where χ (ωs; ωs,ωp, −ωp) is the third-order nonlinear- where a0 is the initial beam size, f (z) characterizes optical susceptibility of the medium; 1/σ = 11/u1 − the evolution of the beam size along the propagation 1/u2; u1 and u2 are the group velocities of the pump and coordinate z [ f (0) = 1], and the function ψ(z) describes probe pulses, respectively; and k2 is the wave number of the spatial phase modulation of the ﬁeld. the pump pulse. Taking the time derivative of the nonlinear phase shift, we arrive at the following expression In the paraxial approximation, r a0 f (z), (4.75) for the frequency deviation of the probe pulse and (4.76) give [4.18] − − 2 2 − 2 3πω d2 f Ldf Lnl δω (η, z) =− 2 χ(3) ω ; ω ,ω , −ω = , XPM 2 s s p p (4.77) c k2 dz2 f 3 (z) 2 z 2 = π 2/λ = [ / | |2 ]1/2 × σ Ap (η, 0) − Ap η − , 0 . (4.73) where Ldf 2 a0 and Lnl a0 2n0 (n2 A ) are σ the characteristic diffraction and nonlinear lengths, re- Similarly to self-phase modulation, cross-phase spectively. modulation can be employed for pulse compression. Solving (4.77), we arrive at The dependence of the chirp of the probe pulse on the 2 z P0 pump pulse intensity can be used to control the parame- f 2 (z) = 1 + 1 − , (4.78) ters of ultrashort pulses [4.24]. Cross-phase modulation Ldf Pcr also opens the ways to study the dynamics of ultrafast where P0 is the total power of the laser beam and nonlinear processes, including multiphoton ionization, cλ2 P = (4.79) and to characterize ultrashort light pulses through phase cr 2 16π n2 measurements on a short probe pulse [4.25]. is the critical power of self-focusing. The focal length 4.4.4 Self-Focusing of the nonlinear lens is given by = Ldf . Lsf / (4.80) Self-focusing is a spatial counterpart of self-phase mod- P 1 2 0 − 1 ulation. While SPM originates from the time-dependent Pcr 236 Part A Basic Principles and Materials

[4.330]. With this tool it should be possible to precisely throughput) [4.346]. Applications are flourishing, go- control the motion of energetic electron wave packets ing from the determination of vibration frequencies in around atoms on attosecond timescales just as the motion molecules [4.347] to microscopy [4.348, 349] and even of nuclear wave packets in molecules can be controlled recently to seeding of X-ray laser plasmas [4.350] and within a few femtoseconds. The single sub-femtosecond possibly, in the future, free-electron lasers. electron bunches and (XUV/X-ray) photon bursts that Attosecond pulses have been studied in more de- arise from the recently gained ability to control elec- tails with different techniques [4.351, 352] and the tron wave packets will enable the scientific community method to isolate a single pulse refined [4.353, 354]. to excite and probe atomic dynamics on atomics time Their time-frequency characteristics have been mapped scales. out [4.355–357] and ways to control both the individual pulses [4.358] and the train structure [4.359] 4.12.5 Some Recent Developments have been developed. The shortest isolated pulse produced to date is 130 as, using the polarization gating Attosecond science is rapidly evolving [4.344] and the technique for the temporal confinement [4.360, 361]. last three years have seen important progress both in Applications now include characterization of elec- the performances of femtosecond and attosecond light tromagnetic fields [4.362], tomography of molecular pulses based on high-order harmonic generation in gases orbitals [4.363], molecular dynamics studies of simple and in their applications in different scientific areas. molecules [4.364, 365], dynamical studies and interfer- Harmonic sources now reach pulse energies in ometric measurements of electron wavepackets [4.366, atA Part the microjoule range [4.345] and their spectra ex- 367], and time-resolved inner-shell spectroscopy in tend to energies of several keV (though with a lower atoms and solids [4.368]. 4 References

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4.20 T. Brabec, F. Krausz: Intense few-cycle laser fields: ultra-short pulses in dispersion-engineered pho- Frontiers of nonlinear optics, Rev. Mod. Phys. 72,545 tonic crystal fibres, Nature 424, 511–515 (2003) (2000) 4.41 D. A. Akimov, E. E. Serebryannikov, A. M. Zheltikov, 4.21 H. H. Chen, Y. C. Lee: Radiations by solitons at the M. Schmitt, R. Maksimenka, W. Kiefer, K. V. Dukel’skii, zero group-dispersion wavelength of single-mode V. S. Shevandin, Yu.N. Kondrat’ev: Efficient anti- optical fibers, Phys. Rev. A 41, 426–439 (1990) Stokes generation through phase-matched four 4.22 N. Akhmediev, M. Karlsson: Cherenkov radiation wave mixing in higher-order modes of a microstruc- emitted by solitons in optical fibers, Phys. Rev. A ture fiber, Opt. Lett. 28, 1948–1950 (2003) 51, 2602–2607 (1995) 4.42 J. K. Ranka, R. S. Windeler, A. J. Stentz: Visible 4.23 G. P. Agrawal: Nonlinear Fiber Optics (Academic, continuum generation in air-silica microstructure Boston 1989) optical fibers with anomalous dispersion at 800 nm, 4.24 N. I. Koroteev, A. M. Zheltikov: Chirp control in third- Opt. Lett. 25, 25–27 (2000) harmonic generation due to cross-phase modulatio, 4.43 W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, Appl. Phys. B 67, 53–57 (1998) T. A. Birks, T. P. M. Mann, P. St. J. Russell: Supercon- 4.25 S. P. Le Blanc, R. Sauerbrey: Spectral, temporal, and tinuum generation in photonic crystal fibers and spatial characteristics of plasma-induced spectral optical fiber taperss: a novel light source, J. Opt. blue shifting and its application to femtosecond Soc. Am. B 19, 2148–2155 (2002) pulse measurement, J. Opt. Soc. Am. B 13, 72 (1996) 4.44 A. M. Zheltikov: Supercontinuum generation, Appl. 4.26 M. M. T. Loy, Y. R. Shen: Theoretical interpretation Phys. B 77, 2 (2003), special issue ed. by of small-scale filaments of light originating from A. M. Zheltikov moving focal spots, Phys. Rev. A 3, 2099 (1971) 4.45 S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Har- vey, J. C. Knight, W. J. Wadsworth, P. St.J. Russell:

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About the Authors

Andreas Assion Chapter C.12 Authors Femtolasers Produktions GmbH Andreas Assion joined Femtolasers in January of 2005. Prior to joining Femtolasers, Vienna, Austria he worked with ultrafast lasers on the observation and control of quantum optical [email protected] phenomena in atoms and molecules. He earned his diploma and doctorate studying molecular dynamical effects, including coherent control of complex molecules. After a post-doctoral position with the German Space Agency, he completed his Habilitation 2004.

Thomas E. Bauer Chapter A.5,Sect.5.7

JENOPTIK Polymer Systems GmbH Thomas Bauer is a physicist working at Jenoptik Polymer Systems GmbH (former Coating Department WAHL optoparts) as head of coating department. His main areas of interest are plastic Triptis, Germany optics in general and coating of plastic optics in particular. [email protected]

Thomas Baumert Chapter C.12

Universität Kassel Professor Baumert received is Ph.D. with Prof. Gerber, University of Institut für Physik Freiburg, Germany in 1992. Further positions in his carreer were: Kassel, Germany 1992–1993, post doc with Prof. Zewail, Caltech, Pasadena; 1993–1997, [email protected] “Habilitation”, University of Würzburg, Germany; 1998–1999, head of LIDAR group, DLR Oberpfaffenhofen, Germany; 1999 Full Professor of Experimental Physics at University of Kassel, Germany. His research area: Femtosecond spectroscopy and ultrafast laser control of matter. Awards: Gödecke thesis award (1992), Heisenberg-Scholarship of DFG (1997–1998), Philip-Morris-Award (2000).

Dietrich Bertram Chapter C.10

Philips Lighting Prior to joining the CTO offic at Philips Lighting as technical office Aachen, Germany solid-state lighting, Dietrich Bertram headed a project on LED light [email protected] sources at Philips Research. His background education is physics, where he obtained a masters degree at Marburg University in epitaxy of III-V materials and a Ph.D. from the Max-Planck Institute of Solid State Research, Stuttgart, Germany.

Klaus Bonrad Chapter A.5,Sects.5.9.2, 5.10

Schott Spezialglas AG Klaus Bonrad studied chemistry in Darmstadt and received his Ph.D. in Mainz at Division Luminescence Technology the Max-Planck-Institute of Polymer Research for synthesis and characterisation of Mainz, Germany electrooptical macrocycles. After a post-doc position at Virginia Polytechnic Institute [email protected] and State University in Blacksburg/USA he worked for IBM and SCHOTT Spezialglas AG in the f eld of organic light emitting diodes developing large area displays in Mainz.

Matthias Born Chapter C.10

Philips Research Laboratories Aachen Matthias Born is a physicist and joined Philips Research Aachen, Germany, in 1992. Aachen, Germany He is leading several projects about plasma physics and diagnostics of gas discharges [email protected] with a major topic on mercury-free lamps for general and automotive lighting applications. He is also working as a professor for physics at the Heinrich-Heine-University of Düsseldorf. 1280 About the Authors

Annette Borsutzky Chapter C.11,Sect.11.9

Technische Universität Kaiserslautern Annette Borsutzky studied physics in Bielefeld and Hannover, Fachbereich Physik Germany, where she received in 1992 her Dr. rer. nat. working on Kaiserslautern, Germany nonlinear frequency mixing in crystals and gases. Joining the university [email protected] of Kaiserslautern studies of optical parametric oscillators, diode- pumped solid state lasers as well as the characterization of new Authors nonlinear and laser active materials are at the center of her work.

Hans Brand Chapter C.11,Sect.11.4

Friedrich-Alexander-University of Hans Brand received the degrees Dipl.-Ing. in 1956, Dr.-Ing in 1962 and Erlangen-Nürnberg LHFT Dr.-Ing. habil. in 1962 at the RWTH Aachen, Germany. In 1969 he Department of Electrical, Electronic became professor at the Chair for Microwave Engineering at the FAU and Communication Engineering Erlangen, Germany. His main f elds of research are microwaves, Erlangen, Germany [email protected] millimeter wave and terahertz components and systems as well as gas laser and infrared laser technology. In 1996 he became Fellow of the IEEE. He is emeritus since 1998.

Robert P. Breault Chapter B.7

Breault Research Organization, Inc. Robert P. Breault is the Chairman and founder of the Breault Research Organization. Tucson, AZ, USA He works on stray light analysis and suppression. He is the author of the APART stray [email protected] light analysis program, used to analyze the Hubble telescope and many others. He received the B.S. in mathematics from Yale University, and his M.S. and Ph.D. in optical sciences from the University of Arizona. He is a fellow of SPIE and founder and Co-chairman of the Arizona Optics Industry Association.

Matthias Brinkmann Chapter A.5,Sects.5.1, 5.1.9, 5.10

University of Applied Sciences Darmstadt Dr. Brinkmann is a professor of optical engineering at the University of Applied Mathematics and Natural Sciences Sciences Darmstadt, Germany. He obtained his Ph.D. degree in Physics from the Darmstadt, Germany Ruhr-Universität Bochum,Germany in 1997 for his work on high-temperature [email protected] superconductors. Prior to joining the University of Applied Sciences Darmstadt, he worked as a staff scientist and research manager at Schott Glas corporate research in Mainz, Germany. His main scientifi focus covered thermal material properties of glass and microstructured optical glass for photonic applications. His current research activities include integrated waveguide optics and diffractive microoptics for various Photonic applications.

Uwe Brinkmann Chapter C.11,Sect.11.7

Bovenden, Germany Uwe Brinkmann obtained his education in physics at the universities [email protected] Munich, Heidelberg, Hannover, and worked in laser research at the Universität Cologne before joining Lambda Physik, Göttingen, as Head of Research and Development. Since 1988 self-employed, he edited the German periodical Laser und Optoelektronik over 20 years and is a contributing editor to Laser Focus World since 1987.

Robert Brunner Chapter B.8,Sect.8.1

Carl Zeiss AG Robert Brunner graduated from the University of Ulm in 1994 and Central Research and Technology received his Ph.D. degree in the fiel of near-fiel optical microscopy. Jena, Germany Since 1998 he works at the Research Center of Carl Zeiss, where he is [email protected] the responsible Lab Manager for microstructured optics. His current research interests are hybrid diffractive/refractive optics, subwavelength structures, refractive microoptics, and high resolution optics. About the Authors 1281

Geoffrey W. Burr Chapter D.20

IBM Almaden Research Center Geoffrey W. Burr received his B.S. in Electrical Engineering (EE) and B.A. in Greek San Jose, CA Classics from the State University of New York at Buffalo in 1991. That year Eta [email protected] Kappa Nu selected him as the Alton B. Zerby Outstanding EE Senior in the U.S. He received his M.S. and Ph.D. in Electrical Engineering from the California Institute of Technology in 1993 and 1996, respectively, under the supervision of Professor

Demetri Psaltis. Since that time, Dr. Burr has worked at the IBM Almaden Research Authors Center in San Jose, California, where he is currently a Research Staff Member. He has worked extensively in holographic data storage, volume holography, signal processing and systems tradeoffs in data storage, and optical information processing. Dr. Burr’s current research interests also include nanophotonics, numerical modeling for design optimization, and phase-change nonvolatile memory. He is a member of SPIE, OSA, IEEE, Eta Kappa Nu, and Tau Beta Pi.

Karsten Buse Chapter A.5,Sects.5.9.3

University of Bonn Karsten Buse received his Ph.D. from the University of Osnabrück, Germany. Institute of Physics Since 2000 he is holding the Heinrich Hertz professorship for physics at the Bonn, Germany University of Bonn. His research focus is on nonlinear-optical and photosensitive [email protected] dielectric materials like nonlinear and photorefractive crystals. He authored and co-authored more than 150 publications and more than 20 patents in this field

Carol Click Chapter A.5,Sects.5.1.2, 5.1.3, 5.10

Schott North America Dr. Click received her Ph.D. from the University of Missouri – Rolla in Regional Research and Development ceramic engineering focused in contamination in phosphate laser Duryea, PA, USA glasses. She is now involved in the research and development necessary [email protected] to commercialize Schott’s inorganic low-temperature reactive bonding technology for producing light-weighted Zerodur optics and precision optical components.

Mark J. Davis Chapter A.5,Sects.5.5, 5.10

Schott North America Mark Davis earned his Ph.D. in Geology from Yale University in 1996, focusing on Regional Research and Development the kinetics of nucleation in glass-forming melts and related topics. Since then, his Duryea, PA, USA research has centred on the development of new glass-ceramic materials for a range of [email protected] applications, in addition to continued efforts towards a more fundamental understanding of crystallization processes.

Wolfgang Demtröder Chapter D.13,Sects.13.1, 13.2

TU Kaiserslautern Wolfgang Demtröder studied Physics, Mathematics and Science of Music at the Department of Physics Universities of Münster, Tübingen and Bonn. He received his Ph.D. in 1961 with Kaiserslautern, Germany Prof. Paul in Bonn. He was research assistant in Freiburg, visiting fellow at JILA in [email protected] Boulder, Colorado and since 1970 he is Professor of Physics at the University of Kaiserslautern, and visiting Professor at the Universities at Stanford (USA), Kobe (Japan), New South Wales in Sydney (Australia) and at the Technical University in Lausanne (Switzerland). His field of research are high resolution laser spectroscopy of molecules and metal-clusters, time resolved spectroscopy, spectroscopy of collision processes. He received the Max Born Prize in 1994 and the Heisenberg Medal 2001. 1282 About the Authors

Henrik Ehlers Chapter A.6

Laser Zentrum Hannover e.V. Henrik Ehlers is working in the fiel of optical thin films He studied Department of Thin Film Technology physics in Hannover, Germany, and is currently head of the Process Hannover, Germany Development Group in the department of Thin Film Technology at the [email protected] Laser Zentrum Hannover. The focus of the group is on R&D in modern deposition processes, in situ process monitoring, and advanced process Authors automation.

Rainer Engelbrecht Chapter C.11,Sect.11.4

Friedrich-Alexander-University of Rainer Engelbrecht studied electrical engineering at the University of Erlangen-Nürnberg Erlangen-Nürnberg and received his diploma and Dr. degree in 1995 Department of Electrical, Electronic and and 2001, respectively. The doctoral thesis was on gas analysis in CO2 Communication Engineering lasers by diode laser spectroscopy. His current research field are Erlangen, Germany [email protected] nonlinear fibe optics, Raman f ber lasers and low-noise photo receivers.

Martin Fally Chapter D.20,Sect.20.1

University of Vienna Martin Fally earned both his Ph.D. in physics (1996) and his habilitation in solid-state Faculty of Physics, Department for physics (2003) from the Vienna University, Austria. Since then he is Associate Experimental Physics Professor at the Department for Experimental Physics. In 2003–2004 he held Vienna, Austria a Mercator Visiting- Professorship at the University of Osnabrück, Germany. He [email protected] authored or co-authored more than 40 publications in the f elds of structural phase transitions (experimental and theoretical), quasi one-dimensional systems (theoretical), neutron-scattering, neutron-diffraction, photorefractive materials, holographic scattering (experimental and theoretical). In 2001 he was awarded the Prize of the City of Vienna for research in natural sciences.

Yun-Hsing Fan Chapter A.5,Sects.5.3, 5.10

University of Central Florida Ms. Yun-Hsing Fan is currently a Ph.D. candidate at the School of Optics/CREOL, College of Optics and Photonics University of Central Florida. Her current research is to develop novel electronic Orlando, USA liquid crystal (LC) lenses and fast-response infrared phase modulators for optical [email protected] communications. Her future work will focus on polarization-independent LC lens and fast switching polymer-network LC modulators for far-infrared and visible regions.

Enrico Geißler Chapter B.8,Sect.8.2

Carl Zeiss AG Enrico Geißler completed his studies of electrical engineering at the Central Research and Technology University of Applied Sciences Jena, Germany, in 1998. Since Jena, Germany graduation he has been at the Research Center of Carl Zeiss, where he is [email protected] currently Senior Scientist for Digital Visualization Systems. His current research interests are spatial light modulators and MEMS.

Ajoy Ghatak Chapter B.8,Sect.8.7

Indian Institute of Technology Delhi Ajoy Ghatak has published more than 170 research papers in Physics Department international journals and is the co-author (with Professor Thyagarajan) New Delhi, India of six books. He is a Fellow of the Optical Society of America (OSA) [email protected] and is the recipient of the 2003 OSA Esther Hoffman Beller award, the International Commission for Optics Galileo Galilei award and the CSIR S.S. Bhatnagar award. His areas of interests are fibe optics and quantum mechanics. About the Authors 1283

Alexander Goushcha Chapter B.9

SEMICOA Dr. Alexander Goushcha (aka Gushcha) is a Chief Scientist and CTO at SEMICOA, Costa Mesa, CA, USA a California-based manufacturer of high-reliability silicon transistors and [email protected] optoelectronics. He obtained his Ph.D. degree in Physics from the Institute for Physics, Ukrainian Academy of Sciences in Kyiv (Ukraine). He has been working in the f elds of semiconductor physics and technology, biophysics and molecular

electronics, and nonlinear optics at the Institute for Physics, Kyiv, Ukraine, MPI Authors Strahlenchemie, Mülheim a.d. Ruhr, Germany, and UC Riverside, CA. Dr. Goushcha is the author of about 100 technical papers in referred journals and holds 10 patents and patent applications.

Daniel Grischkowsky Chapter D.17

Oklahoma State University Daniel R. Grischkowsky is a Regents Professor and the Bellmon Professor of Electrical and Computer Engineering Optoelectronics at Oklahoma State University. He received his B.S. from Oregon State Stillwater, OK, USA University in 1962 and his Ph.D. degree in physics from Columbia University in 1968. [email protected] In 1969 he joined the IBM Watson Research Center, Yorktown Heights, New York, where he developed and experimentally verifie the adiabatic following model in 1972. In 1982 his research group developed the optical-fibe pulse compressor, and later in 1989 developed the technique of THz time-domain spectroscopy (THz-TDS). In 1993 he relocated to Oklahoma State University to pursue THz-TDS applications. He is a fellow of The American Physical Society (APS), The Institute of Electrical and Electronics Engineers (IEEE) and The Optical Society of America (OSA). He was awarded the Boris Pregel Award (1985) by the New York Academy of Sciences for the development of the optical fibe pulse compressor, the R.W. Wood Prize (1989) from OSA for distinguished contributions to the f eld of optical pulse compression, particularly for pioneering work on the use of optical fiber for generating ultrashort pulses of light, and the William F. Meggers Award (2003) from OSA for seminal contributions to the development and application of THz time-domain spectroscopy.

Richard Haglund Chapter A.1

Vanderbilt University Professor Halund earned his Ph.D. in experimental nuclear physics from Department of Physics and Astronomy the University of North Carolina, Chapel Hill. He was staff member, Nashville, TN, USA Los Alamos National Laboratory from 1975 to 1984. Since 1984 he is [email protected] Professor of Physics at Vanderbilt University. He was Alexander von Humboldt awardee in 2003. His current research activities are in nonlinear optics in metal and metal-oxide nanoparticles; size and dimensional effects in metal-insulator transitions; and ultrafast mid-infrared laser processing of polymers and organic materials.

Stefan Hansmann Chapter C.11,Sect.11.3

Al Technologies GmbH Stefan Hansmann received his Ph.D. from the Technical University of Darmstadt, Germany Darmstadt for his work on simulation and realization of DFB laser [email protected] diodes. He worked 10 years in the fiel of optoelectronics at the research center of Deutsche Telekom and become the head of a research group focusing on the application of photonic technologies in telecommunication. Thereafter he served as a technical manager in several companies of III/V semiconductor industry and is now the chief technical office of AL Technologies GmbH in Darmstadt, commercializing high speed InP based semiconductor laser technology. 1284 About the Authors

Joseph Hayden Chapter A.5,Sects.5.1, 5.4, 5.10

Schott North America Dr. Joseph Hayden has a B.S. in Physics from Saint Joseph’s University and a Ph.D. in Regional Research and Development Chemical Physics from Brown University. He joined the Schott Group in 1985, where Duryea, PA, USA he has worked in glass composition and process development with emphasis on laser, [email protected] nonlinear and technical glasses. He is presently an Executive Scientist at Schott’s North American Regional R&D site in Duryea, Pennsylvania. Authors

Joachim Hein Chapter C.11,Sect.11.13

Friedrich-Schiller University Jena Dr. Joachim Hein is a scientist at the faculty of physics of the University of Jena since Institute for Optics and Quantum many years. He is working on femtosecond-lasers, new laser materials for broad-band Electronics amplificatio and applications of ultra-high peak power light sources. He is an expert Jena, Germany for diode-pumped high-energy laser systems as well as solid-state laser design and [email protected] modelling.

Stefan W. Hell Chapter D.16

Max Planck Institute Stefan W. Hell is credited with having both conceived and validated the for Biophysical Chemistry firs viable concept for breaking Abbe’s diffraction-limited resolution Göttingen, Germany barrier in a light-focusing microscope. He leads the Department of [email protected] NanoBiophotonics at the Max Planck Institute for Biophysical Chemistry as well as the High-Resolution Optical Microscopy division at the German Cancer Research Center (DKFZ) in Heidelberg.

Jürgen Helmcke Chapter C.11,Sect.11.14

Physikalisch-Technische Bundesanstalt Until his retirement at the end of 2003, Dr. Jürgen Helmcke headed (PTB) Braunschweig the department “Quantum Optics and Length Unit” at the Former Head Quantum Optics and Length Physikalisch-Technische Bundesanstalt in Braunschweig, Germany. Unit (retired) His main interests are in the field of precision laser spectroscopy, laser Braunschweig, Germany [email protected] cooling, optical and atom interferometry, and optical frequency measurements. From 1977 to 1978 he spent a year as NATO scholar with Dr. John L. Hall at the Joint Institute of Astrophysics in Boulder, CO. In 1999, together with F. Riehle, H. Schnatz, and T. Trebst, J. Helmcke received the Helmholtz Price of Metrology for the paper “Atom interferometer in the time domain for precision measurements”.

Hartmut Hillmer Chapter C.11,Sect.11.3

University of Kassel Professor Hillmer received his doctor and habilitation degrees from Stuttgart and Institute of Nanostructure Technologies Darmstadt University, respectively. He worked 10 years in telecommunication and Analytics (INA) industry (German Telekom and NTT Japan) on design, implementation and Kassel, Germany characterization of fast and tunable semiconductor lasers. As a full professor at Kassel [email protected] University since 1999, he deals with optical MEMS and nanotechnology and is a coordinator in the Hess Nano Network (nnh-9). He published more than 200 papers, holds 14 patents and received the European Grand Prix of Innovation Awards 2006

Günter Huber Chapter C.11,Sect.11.2

Universität Hamburg Guenter Huber is Professor of Physics at the Institute of Laser-Physics, University of Institut für Laser-Physik Hamburg, Germany. His research on solid-state lasers includes the growth, Department Physik development and optical spectroscopy of laser materials, new diode-pumped lasers in Hamburg, Germany the near infrared and visible spectral region, as well as up-conversion lasers. He is [email protected] Fellow of the Optical Society of America and received the Quantum Electronics and Optics Prize of the European Physical Society in 2003. About the Authors 1285

Mirco Imlau Chapter D.20,Sect.20.1

University of Osnabrück Dr. Imlau studied physics at the University of Cologne, where he Department of Physics received his Osnabrück, Germany Ph.D. for work on centrosymmetric photorefractive crystals. Since 2002 [email protected] he is Junior-Professor at the University of Osnabrück and team leader of the photonics work group. His research is focused on the fiel of condensed matter and optics, in particular on nonlinearities of optical Authors materials (optical damage, nonlinear light scattering, photoswitchable compounds, unconventional photorefractive materials, space charge waves). Having his expertise in holography, he authored more than 40 publications in refereed journals, 4 book articles, and 8 international patents.

Kuon Inoue Chapter B.8,Sect.8.6

Chitose Institute of Science and Kuon Inoue received his Ph.D. from the University of Tokyo, Japan in Technology 1970. Since 1967, he worked at the Department of Physics, Shizuoka Department of Photonics University. In 1984, he joined the faculty of the Research Institute for Chitose, Japan Electronic Sciences, Hokkaido University. After retirement in 2001, he [email protected] is now a guest Professor at Chitose Institute of Science and Technology and is a Fellow of the Toyota Physics and Chemistry Research Institute. He has worked in solid-state physics, laser spectroscopy in solids, and photonic crystals.

Thomas Jüstel Chapter C.10

University of Applied Sciences Münster Thomas Jüstel received his Ph.D. in coordination chemistry in 1995 in the group of Steinfurt, Germany Prof. Dr. K. Wieghardt. He worked on luminescent materials for light sources and [email protected] emissive displays in the Philips Research Laboratories Aachen, Germany from September 1995 to February 2004. In March 2004 he became a Professor for Inorganic Chemistry at the University for Applied Sciences in Münster, Germany. His present research deals with phosphors for LEDs and luminescent nanoparticles.

Jeffrey L. Kaiser Chapter C.11,Sect.11.5

Spectra-Physics Jeffrey Kaiser is a product manager in the Spectra-Physics division of Newport Division of Newport Corporation Corporation. He has held a variety of positions in marketing, product development, Mountain View, CA, USA engineering, and manufacturing for gas lasers. He holds several patents in gas-laser [email protected] technology. He received his M.S. in Applied Physics from Stanford University and B. S. in Physics from Purdue University. 1286 About the Authors

Ferenc Krausz Chapter A.4,Sect.4.2

Max-Planck-Institut für Quantenoptik Ferenc Krausz was awarded his M.S. in Electrical Engineering at Garching, Germany Budapest University of Technology in 1985, his Ph.D. in Quantum [email protected] Electronics at Vienna University of Technology in 1991, and his “Habilitation” degree in the same f eld at the same university in 1993. He joined the Department of Electrical Engineering as Associate Authors Professor in 1998 and became Full Professor in the same department in 1999. In 2003 he was appointed as Director of Max Planck Institute of Quantum Optics in Garching, Germany, and since October 2004 he has also been Professor of Physics and Chair of Experimental Physics at Ludwig Maximilian’s University of Munich. His research has included nonlinear light-matter interactions, ultrashort light pulse generation from the infrared to the X-ray spectral range, and studies of ultrafast microscopic processes. By using chirped multilayer mirrors, his group made intense light pulses comprising merely a few wave cycles available for a wide range of applications and utilized them for pushing the frontiers of ultrafast science into the attosecond regime. His most recent research focuses on attosecond physics: the control and real-time observation of the atomic-scale motion of electrons. He co-founded Femtolasers GmbH, a Vienna-based company specializing in cutting-edge femtosecond laser sources.

Eckhard Krätzig Chapter A.5,Sects.5.9.3

University of Osnabrück Eckhard Krätzig received his Ph. D. degree in physics from the Johann Physics Department Wolfgang Goethe University of Frankfurt/Main, Germany in 1968. Osnabrück, Germany Then he joined the Philips Research Laboratories Hamburg, where he [email protected] headed the Solid State Physics Group. Since 1980 he has been a Professor of Applied Physics at the University of Osnabrück. During the last years his research interests were focused on photorefractive effects and light-induced charge-transport phenomena.

Stefan Kück Chapter C.11,Sect.11.2

Physikalisch-Technische Bundesanstalt Dr. Kück is working group leader for laser radiometry at the Physikalisch-Technische Optics Division Bundesanstalt, the German National Metrology Institute. He obtained his Ph.D. in Braunschweig, Germany 1994 and habilitated in 2001 in the f eld of solid-state lasers. His main research topic [email protected] is the development of new methods, procedures and standards for the high-precision measurement of laser power and laser pulse energy.

Anne L’Huillier Chapter A.4,Sect.4.2

University of Lund Anne L’Huillier defended her Ph.D. thesis in Paris in 1986. She worked at the Department of Physics Commissariat à l’Energie Atomique in Saclay, France, until 1995 and then moved to Lund, Sweden Lund University, Sweden, where she became professor in 1997. Her current research [email protected] is on the generation of high-order harmonics of laser light in gases and its application to attosecond science. In 2003, she got the Julius Springer prize for Applied Physics together with F. Krausz. She became member of the Royal Swedish Academy of Sciences in 2004.

Bruno Lengeler Chapter D.18

Aachen University (RWTH) Bruno Lengeler is emeritus professor of physics and former head of II. Physikalisches Institut a physics institute at Aachen university. He is a solid-state physicist who Aachen, Germany has worked for many years on spectroscopy and imaging with [email protected] synchrotron radiation, in particular on the development of parabolic refractive X-ray lenses. He was Director of Research at the European Synchrotron Radiation Facility. About the Authors 1287

Martin Letz Chapter A.5,Sects.5.1.1, 5.1.4, 5.1.6, 5.1.7, 5.10

Schott Glas Dr. Martin Letz studied physics at the universities of Braunschweig, Materials Science, Central Research Stuttgart (Germany) and Tartu (Estonia) and f nished his Ph.D. in 1995 Mainz, Germany at Stuttgart University in the f eld of theoretical solid state physics with [email protected] a work on magnetic polarons. In the following he worked as a postdoctoral fellow at Queen’s University, Kingston (Canada) and at the University of Mainz (Germany). During this time he performed Authors investigations on statistical physics of strongly correlated quantum-mechanical systems of strongly correlated classical systems, light scattering and on the dynamics of the glass transition in molecular fluids In 2001 Martin Letz joined the central research of Schott Glass.

Gerd Leuchs Chapters A.2, A.3

University of Erlangen-Nuremberg Gerd Leuchs studied physics and mathematics at Cologne and received his Ph,D. in Institute of Optics, Information and 1978. After research years in USA, he headed the German gravitational wave Photonics detection group, then became technical director at Nanomach AG, Switzerland. Since Erlangen, Germany 1994 he has been Professor of Physics at the University of Erlangen, since 2003 also [email protected] director of the Max Planck research group of optics, information and photonics.

Norbert Lindlein Chapters A.2, A.3

Friedrich-Alexander University of Norbert Lindlein received in 1996 his Ph.D. from the Friedrich-Alexander University Erlangen-Nürnberg Erlangen-Nürnberg (Germany). In 2002 he finishe his habilitation in physics and is Max-Planck Research Group a member of the Physics Faculty of the University of Erlangen-Nürnberg since. His Institute of Optics Information and research interests include the simulation and design of optical systems, diffractive Photonics Erlangen, Germany optics, microoptics and optical measurement techniques using interferometry or [email protected]. Shack-Hartmann wavefront sensors. uni-erlangen.de

Stefano Longhi Chapter C.11,Sect.11.1

University of Politecnico di Milano Stefano Longhi is Associate Professor of Physics of Matter at the Department of Physics Polytechnic Institute of Milan. He has authored more than 100 papers in Milano, Italy the f elds of laser physics, photonics, nonlinear and quantum optics. longhi@ﬁsi.polimi.it Professor Longhi is Fellow of the Institute of Physics and member of the J. Physics-B editorial board. In 2003 he was awarded with the Fresnel Prize of the European Physical Society.

Ralf Malz Chapter C.11,Sect.11.6

LASOS Lasertechnik GmbH Ralf Malz studied physics at the Friedrich-Schiller-Universität Jena 1984-1989 and Research and Development received his Ph.D. in1993 at the same university. Then he worked at Carl-Zeiss-Jena Jena, Germany and later LASOS in the fiel of CO2 waveguide and slab lasers. His current work is on [email protected] argon-ion, HeNe lasers, diode-laser modules and f ber coupling.

Wolfgang Mannstadt Chapter A.5,Sects.5.1.4, 5.8, 5.10

Schott AG Dr. Wolfgang Mannstadt studied physics and received his Ph.D. from the Philipps Research and Technology Development University in Marburg. His main research fiel is the materials simulation with ab Mainz, Germany initio DFT methods. He received a Feodor-Lynen fellowship from the Humboldt [email protected] Foundation and worked as a research assistent in the group of Prof. A.J. Freeman at the Northwestern University in Evanston. His current work in the R&D department at Schott is focuses on the simulation of materials properties with DFT and nanostructured optical materials. 1288 About the Authors

Gerd Marowsky Chapter C.11,Sect.11.7

Laser-Laboratorium Göttingen e.V. Dr. Gerd Marowsky graduated in 1969 from the University of Göttingen, Germany Göttingen, Germany in the field of experimental and theoretical [email protected] physics and mineralogy, and is currently director of Laser-Laboratorium Göttingen. He has made numerous scientifi contributions to the general fiel of lasers and high-fiel interactions. Current research interests Authors include quantum electronics in general, lasers, laser applications in environmental research, nonlinear optics, nonlinear inorganic and organic materials, and applications of short-duration ultraviolet laser pulses. Dr. Marowsky is well know in Canada as the Sector-Coordinator in Materials–Physical Technologies, a Science and Technology Agreement that supports numerous collaborations between Canadian and German scientists. Gerd Marowsky is also professor at the University of Göttingen, Germany and holds adjunct professor positions in Electrical and Computer Engineering at both Rice University, Houston and the University of Toronto.

Dietrich Martin Chapter B.8,Sect.8.4

Carl Zeiss AG Dietrich Martin received the B.Sc. (University of Technology, Dresden) Corporate Research and Technology in 1992, the M.Sc. (University of Oldenburg) in 1997. He earned his Ph. Microstructured Optics Research D. from the University of Kassel in 2002 working on optical properties Jena, Germany of alkali metal clusters. He joined the Corporate R&D Department of [email protected] Carl Zeiss and is engaged in research on microstructured and variable optical components.

Bernhard Messerschmidt Chapter B.8,Sect.8.3

GRINTECH GmbH Bernhard Messerschmidt studied physics at the Jena University, Germany and Research and Development, Management graduated with a Ph.D. in 1998 from the Fraunhofer Institute of Applied Optics in Jena, Germany Jena on modelling and optimization of ion exchange processes in glass for the [email protected] generation of GRIN lenses. From 1994 to 1995, he was a research fellow at the Institute of Optics, University of Rochester, New York. In 1999, he established the company Grintech as a co-founder and is currently one of the principal managers of Grintech and responsible for research and development.

Katsumi Midorikawa Chapter C.11,Sect.11.12

RIKEN Dr. Katsumi Midorikawa is a director and chief scientist of the Laser Technology Laser Technology Laboratory Laboratory at RIKEN. He received his Ph. D. degree from Keio University in Saitama, Japan Electrical Engineering. His research interests currently focus on ultrashort [email protected] high-intensity laser – matter interaction and its application, including the generation of coherent X-ray and femotosecond laser processing.

Gerard J. Milburn Chapter D.14

The University of Queensland Milburn’s research is largely in the field of quantum optics, quantum Center for Quantum Computer measurement and control, and quantum computing and has published Technology more than 200 papers and three books. He is a Fellow of the Australian School of Physical Sciences Academy of Science and The American Physical Society. He is St. Lucia, QLD, Australia [email protected] currently an Australian Research Council Federation Fellow at The University of Queensland. About the Authors 1289

Kazuo Ohtaka Chapter B.8,Sect.8.6

Chiba University In 1965 Dr. Kazuo Ohtaka graduated from Department of Applied Center for Frontier Science Physics, University of Tokyo where he was assistant professor since Photonic Crystals 1967. Since 1998 he was Professor of Department of Applied Physics of Chiba, Japan Chiba University and since 2000 he is Professor of the Center for [email protected] Frontier Science, Chiba University. In 2000 he obtained the Best Papers Award of the Physical Society of Japan. He is currently working in the Authors fiel of photonic crystals, their fundamentals and applications.

Motoichi Ohtsu Chapter D.15

Department of Electronics Engineering Dr. Ohtsu is a Professor of the University of Tokyo. As a founder of nanophotonics, he The University of Tokyo is a director of several national projects for nanophotonic devices, storage and Tokyo, Japan fabrication. He has authored more than 400 technical papers and 50 books. He holds [email protected] 100 patents. He is a fellow of the Optical Society of America and has been awarded more than ten prizes from academic institutions including the I. Koga gold metal from URSI. He was also awarded the Medal with Purple Ribbon from the Japanese Government.

Roger A. Paquin Chapter A.5,Sects.5.9.4, 5.10

Advanced Materials Consultant Roger Paquin is an independent materials consultant specializing in materials and Oro Valley, AZ, USA processes for dimensionally stable components for optical and precision instrument [email protected] systems, with emphasis on Be, SiC and composites for mirrors and structures. He has published over 50 papers and book chapters and teaches short courses on the subject. Mr. Paquin is a Fellow of SPIE, The International Society for Optical Engineering.

Klaus Pfeilsticker Chapter D.19,Sect.19.1

Universität Heidelberg Dr. Klaus Pfeilsticker is a professor of physics at the University of Institut für Umweltphysik Heidelberg since 2004. Before he worked at the Max-Planck-Institut für Fakultät für Physik Kernphysik, Heidelberg, the Alfred Wegner Institut, Bremerhaven, the und Astronomie Research Center, Jülich and at the National Oceanic and Atmospheric Heidelberg, Germany [email protected] Administration (NOAA), Boulder. His main research interests are the photochemistry and the radiative transfer of the atmosphere. His recent research focuses on the photochemistry, budget and trend of reactive halogen species in the upper troposphere and stratosphere, the spectral solar irradiance and its variability, and photon path length distribution of solar photons in clear and cloudy skies.

Ulrich Platt Chapter D.19,Sect.19.1

Universität Heidelberg Dr. Ulrich Platt is a professor of physics at the University of Heidelberg since 1989, Institut für Umweltphysik before he worked at the research Center Jülich and at the University of California, Fakultät für Physik Riverside. His main interests are atmospheric chemistry of free radicals and und Astronomie spectroscopic measurements of atmospheric constituents. He is the co-inventor of the Heidelberg, Germany [email protected] DOAS technique. His current research centres on reactive halogen species in the troposphere and their role in the tropospheric chemistry as well as on remote sensing of trace gas distributions in the atmosphere.

Markus Pollnau Chapter C.11,Sect.11.2.4

University of Twente Markus Pollnau obtained his Diploma and Ph.D. in physics from the Universities of MESA+ Institute for Nanotechnology Hamburg, Germany, and Bern, Switzerland, respectively. Following research at the Enschede, The Netherlands University of Southampton, UK, and the Swiss Federal Institute of Technlogy, [email protected] Lausanne, Switzerland, he was appointed full professor at the University of Twente, The Netherlands, in 2004. Currently, he works on light generation in integrated dielectric structures. He has co-authored over 200 international publications. 1290 About the Authors

Steffen Reichel Chapter A.5,Sects.5.1.1, 5.1.6, 5.1.7, 5.1.8, 5.10

SCHOTT Glas Dr. Reichel is an electrical engineer with extensive experience in optics Service Division Research and electromagnetics. He got his Ph.D. in Er-doped f ber amplifier and and Technology Development worked on several topics in electromagnetics, wave and laser optics, Mainz, Germany optical fiber /waveguides, and geometrical optics. He is Senior [email protected] Member of the IEEE and worked for Lucent Technologies and is now Authors manager of the Physical Science Group at Schott.

Hans-Dieter Reidenbach Chapter D.21

University of Applied Sciences Cologne Dr. Reidenbach is Professor at the University of Applied Sciences Institute of Communications Engineering Cologne and head of the research laboratory Medical Technology. He Institute of Applied Optics and Electronics obtained the Dr.-Ing. degree from the University of Erlangen. His Cologne, Germany scientifi work resulted in new applications of laser beams, incoherent [email protected] optical radiation and high frequency currents in operative endoscopy, transanal surgery and interstitial thermotherapy. Currently his research is on optical irradiation and psychophysical behaviour.

Hongwen Ren Chapter A.5,Sects.5.9, 5.10

University of Central Florida Dr. Hongwen Ren received his Ph.D. degree from Changchun Institute of Optics, Fine College of Optics and Photonics Mechanics and Physics, Chinese Academy of Sciences in 1998. After that, he was Orlando, FL, USA faculty member of the North Liquid Crystal R&D Center, Chinese Academy of [email protected] Sciences as an assistant professor. In August 2001, he joined the College of Optics & Photonics, University of Central Florida (UCF) as a research Scholar. Dr. Ren’s current research interests and projects are liquid crystal/polymer dispersions, nanoliquid crystal device, and adaptive e-lens.

Detlev Ristau Chapter A.6

Laser Zentrum Hannover e.V. Detlev Ristau is a physicist with an extensive research background in optical thin fil Department of Thin Film Technology technology. He received his Ph.D. from the University of Hannover in 1988 and Hannover, Germany authored more than 200 technical papers. Current research activities include the [email protected] development and precise control of ion processes as well as the measurement of the power handling capability and losses of optical components.

Simone Ritter Chapter A.5,Sects.5.3, 5.10

Schott AG Dr. Simone Ritter studied Chemistry in Leipzig and Tübingen and Division Research and Technology received her Ph.D. 1994 for syntheses, characterization, structures and Development reactivity of complexes with rhenium-nitrogen-multi-bonds. For the last Material Development 7 years, she worked as scientifi referent for coloured and optical Mainz, Germany [email protected] glasses at Schott. Her research involves development and characterization of glasses with new optical properties.

Evgeny Saldin Chapter C.11,Sect.11.11

Deutsches Elektronen Synchrotron (DESY) Dr. Evgeny Saldin is an expert in the f eld of physics of charged particle Hamburg, Germany beams, accelerators, and free electron lasers. He has authored a book on [email protected] free electron lasers and more than a hundred papers in peer-reviewed. About the Authors 1291

Roland Sauerbrey Chapter C.11,Sect.11.13

Forschungszentrum Roland Sauerbrey is the Scientifi Director of the Forschungszentrum Dresden-Rossendorf e.V. Dresden-Rossendorf and a professor at the Technical University of Dresden. After Dresden, Germany receiving his Ph.D. in physics from the University of Würzburg in 1981 he worked as [email protected] a professor at Rice University in Houston, Texas. In 1994 he moved to the Friedrich-Schiller-University in Jena where he stayed until 2006 as a professor of

physics. During the last 20 years he has been actively involved in the emerging fiel of Authors relativistic light – matter interaction and the development of ultrashort pulse, ultrahigh-intensity lasers. He is a fellow of the Optical Society of America and the Institute of Physics.

Evgeny Schneidmiller Chapter C.11,Sect.11.11

Deutsches Elektronen Synchrotron (DESY) Evgeny Schneidmiller is an expert in the f eld of physics of charged particle beams, Hamburg, Germany accelerators, and free electron lasers. He has authored a book on free electron lasers [email protected] and more than a hundred papers in peer-reviewed journals.

Bianca Schreder Chapter A.5,Sects.5.1.5, 5.6, 5.10

Schott Glas Dr. Bianca Schreder studied Chemistry in Würzburg and received her Division Research and Technology Ph.D. from the Department of Physical Chemistry for her work on Development Laser Spectroscopy on II–VI-Semiconductor Nanostructures. She is Material Development now working in the Research and Development Department at Schott Mainz, Germany [email protected] Glas, Mainz. Her work involves investigation and development of glass systems with special optical properties.

Christian G. Schroer Chapter D.18

Dresden University of Technology Christian G. Schroer made his doctoral studies in mathematical physics Institute of Structural Physics at the Research Centre Jülich (doctoral degree University of Cologne Dresden, Germany in 1995). After a visit as postdoctoral fellow to the University of [email protected] Maryland, he worked as a research and teaching assiociate at Aachen University in the f eld of X-ray optics and microscopy. After his Habilitation in 2004, he was a staff scientist at DESY in Hamburg until he responded to a call to the chair of Structural Physics of Condensed Matter at Dresden University of Technology in early 2006.

Markus W. Sigrist Chapter C.11,Sect.11.10

ETH Zurich, Institute of Quantum Markus W. Sigrist is Professor of Physics at ETH Zurich (Switzerland) and Adjunct Electronics Professor at Rice University in Houston (USA). His current research involves Department of Physics development and implementation of tunable mid-infrared laser sources and sensitive Zurich, Switzerland detection schemes for spectroscopic trace gas analyses in environmental, industrial [email protected] and medical applications. He published 2 books and over 150 papers. He is Fellow of OSA and Topical Editor of Applied Optics. 1292 About the Authors

Glenn T. Sincerbox Chapter D.20,Sect.20.2

University of Arizona Glenn Sincerbox is currently a Professor Emeritus of the College of Optical Sciences Optical Sciences of the University of Arizona where he was a Professor of Optical Sciences and the Tucson, AZ, USA Director of the Optical Data Storage Center; a Center that performed leading-edge [email protected] research on advanced optical storage materials, systems and techniques. Prior to that, Mr. Sincerbox was with IBM Research for 34 years holding numerous technical and Authors management positions.He has published over 50 technical papers and presented over 60 papers. He holds 40 US Patents and has 70 patent publications. His research was primarily in the f eld of optical storage with emphasis on holographic storage. He is a fellow of the OSA and has been active for over 15 years in the International Commission for Optics holding positions as vice president and treasurer.

Elisabeth Soergel Chapter B.8,Sect.8.5

University of Bonn Elisabeth Soergel studied physics at the Ludwig-Maximilian-University Institute of Physics in Munich. She received her Diploma and Ph.D. from the Max-Planck Bonn, Germany Institute for Quantum Optics in Garching in the fiel of scanning probe [email protected] microscopy. After a postdoc stay at the IBM research laboratory in Rüschlikon, Switzerland, she joined the University of Bonn in 2000 with the main research fiel on visualization of ferroelectric domains by scanning probe techniques.

Steffen Steinberg Chapter C.11

LASOS Lasertechnik GmbH Steffen Steinberg studied physics and received his doctoral degree at Jena, Germany Friedrich-Schiller-University Jena, with a work on manipulation of laser [email protected] light with integrated optical devices. Later his work concentrated on different applications of gas and solid-state laser technology especially laser display technology and f ber optical devices. Currently he is working as Sales Manager at LASOS in Jena, Germany.

Sune Svanberg Chapter D.13,Sect.13.3

Lund University Sune Svanberg made his Ph.D. in Physics at Göteborg University in 1972. He became Division of Atomic Physics professor and head of the Atomic Physics Division, Lund University, in 1980. He is Lund, Sweden also Director of the Lund Laser Centre, a European Large Scale Infrastructure. He is [email protected] fellow of the American Physical Society and the Optical Society of America, member of 5 academies and three-fold honorary doctor. His present research field include basic atomic laser spectroscopy and applications of laser spectroscopy to environmental and medical research.

Orazio Svelto Chapter C.11,Sect.11.1

Politecnico di Milano Orazio Svelto is Professor of Quantum Electronics at the Politecnico di Milano and Department of Physics the Director of the Milan Section at the Institute of Photonics and Nanotechnologies Milan, Italy (IFN), Milan, Italy, belonging to the Italian National Research Council (CNR). His orazio.svelto@ﬁsi.polimi.it current research activities include ultrashort-pulse generation and applications, physics of laser resonators and techniques of mode selection, laser applications in biology and biomedicine, and physics of solid-state lasers, also including the generation of femtosecond laser pulses, down to the record value of 3.8 fs recently established by the group, and to the applications of these ultrashort pulses. He is the author of Principles of Lasers (1998). Professor Svelto is Fellow of the Optical Society of America and the Institute of Electrical and Electronics Engineers, and a member of several Italian academies including the “Accademia dei Lincei”. He was the recipient of the Italgas Prize for research and technology innovation, the Quantum Electronics Prize of the European Physical Society and the Charles H. Townes Award of the Optical Society of America. About the Authors 1293

Bernd Tabbert Chapter B.9

Semicoa Bernd Tabbert received his Ph.D. from the University of Heidelberg, Engineering Department Germany in 1994. For several more years his research focused on Costa Mesa, CA, USA optical studies of impurity atoms and bubbles in cryogenic liquids [email protected] including a project at the University of California, Los Angeles. He is now working as an engineering manager for a semiconductor manufacturer developing sensors for medical X-ray applications. Authors

K. Thyagarajan Chapter B.8,Sect.8.7

Indian Institute of Technology Delhi Professor Thyagarajan has published more than 125 research Physics Department publications and is the co-author (with Professor Ajoy Ghatak) of six New Delhi, India books. He has held visiting positions at Thomson-CSF, France and the [email protected] University of Florida. He is a Fellow of the Optical Soceity of America and was awarded the title of “Off cier dans l’ordre des Palmes Académiques” by the French Government in 2003. His current research interests are optical fibe amplifier and guided wave nonlinear optics.

Mary G. Turner Chapter B.7

Engineering Synthesis Design, Inc. Dr. Turner has been involved with the development of optical software and conducted Tucson, AZ, USA training on optical design and optical software for the previous 12 years. She wrote [email protected] a chapter on “Optical Aberrations” in The Optics Encyclopedia and on “Reflectin and Catadioptric Objectives” in the Optical Engineer’s Desk Reference. She is a fellow of SPIE and a member of SID and OSA.

Giuseppe Della Valle Chapter C.11,Sect.11.1

Polytechnic Institute of Milan Dr. Giuseppe Della Valle received his Ph.D. in Physics from the Polytechnic Institute Department of Physics of Milan, Italy, in 2005. He is currently Assistant Professor of Physics at the Physics Milan, Italy Department of the same Institute.. His research activity is mainly devoted to solid- [email protected] state lasers and optical devices based on doped glass substrates operating in the near infrared for telecom and metrological applications.

Michael Vollmer Chapter D.19,Sect.19.2

University of Applied Sciences Michael Vollmer studied physics in Heidelberg where he received his Brandenburg Ph.D. and habilitation, working on optical spectroscopy of metal Department of Physics clusters. Presently he is Professor of Experimental Physics working in Brandenburg, Germany the f elds of infrared thermal imaging, spectroscopy, atmospheric optics, [email protected] and didactics of physics. He is author of two books and member of the editorial boards of several journals.

Silke Wolff Chapter A.5,Sects.5.2, 5.10

SCHOTT Spezialglas AG Dr. Silke Wolff, laureate of R&D award, is an expert in glass devel- Department of Research & Technology opment with an origin in analytical chemistry. Her main areas of Development, Material Development research are innovative optical glasses, including market and Optical Glasses customer-related material development, application, optimization Mainz, Germany [email protected] of production processes and patent protection. Actual topics are exceptional optical properties, suitability for reheat hot forming and/or precision moulding and environmental compatibility. 1294 About the Authors

Matthias Wollenhaupt Chapter C.12

Universität Kassel Matthias Wollenhaupt did research in high-resolution laser spectroscopy with Institut für Physik applications to aerospace and atmospheric chemistry. His current research in Kassel, Germany femtosecond laser spectroscopy is focused on pulse-shaping techniques for the design [email protected] of tailored femtosecond laser pulses as a tool to control ultrafast light-induced processes. His scientifi interests range from basic research, such as quantum control

Authors of molecular dynamics to applications of non-linear optics and materials processing.

Shin-Tson Wu Chapter A.5,Sects.5.9, 5.9.1, 5.10

University of Central Florida Dr. Wu is a Fellow of the IEEE, SID and OSA. He is a recipient of the IEEE College of Optics and Photonics Outstanding Engineer Award, SID Special Recognition Award, ERSO (Taiwan) Orlando, FL, USA Special Achievement Award, Hughes Team Achievement Award, and Hughes Annual [email protected] Outstanding Paper Award. Professor Wu has co-authored 2 books: “Reflect ve Liquid Crystal Displays” (2001), and “Optics and Nonlinear Optics of Liquid Crystals” (1993), 4 book chapters, over 200 journal papers, and 18 issued patents.

Helen Wächter Chapter C.11,Sect.11.10

ETH Zurich, Institute of Quantum Helen Wächter is a Ph.D. student at the Institute of Quantum Electronics Electronics of ETH Zurich after receiving her physics diploma from Department of Physics ETH in 2003. Her main research interests are in the f eld of IR laser Zurich, Switzerland spectroscopy and trace-gas monitoring. This includes the development [email protected] of new coherent light sources by difference frequency generation (DFG) and new sensitive detection schemes. Her emphasis is on isotope-selective trace-gas analysis.

Mikhail Yurkov Chapter C.11,Sect.11.11

Deutsches Elektronen Synchrotron (DESY) Dr. Mikhail Yurkov is an expert in the f eld of physics of charged Hamburg, Germany particle beams, accelerators, and free electron lasers. He has authored [email protected] a book on free electron lasers and more than a hundred papers in peer-reviewed journals.

Aleksei Zheltikov Chapter A.4,Sect.4.1

M.V. Lomonosov Moscow State University Aleksei Zheltikov’s current research is related to nonlinear-optical processes in Physics Department photonic-crystal f bers and nanostructures. Moscow, Russia [email protected]