Applications of Photonics Technologies 2019

Introduction: what is light and basic properties

Cristina Masoller [email protected] www.fisica.edu.uy/~cris

MÀSTER UNIVERSITARI EN ENGINYERIA DE SISTEMES AUTOMÀTICS I ELECTRÒNICA INDUSTRIAL

MÀSTER UNIVERSITARI EN ENGINYERIA AERONÀUTICA

MÀSTER UNIVERSITARI EN ENGINYERIA INDUSTRIAL Introducing myself

• Originally from Montevideo, Uruguay

• PhD in physics (lasers, Bryn Mawr College, USA 1999)

• Since 2004 @ Universitat Politecnica de Catalunya

• Profesora Catedratica, Physics Department, research group on Dynamics, Nonlinear Optics and Lasers

• Web page: http://www.fisica.edu.uy/~cris/ Introducing our research group Dynamics, Nonlinear Optics and Lasers

Senior researchers / PhD students: 11/8 Introducing our research group

. Research topics: Nonlinear phenomena (photonics, biophysics, complex systems)

. Lab facilities in Gaia Building, UPC Terrassa:

. Website: https://donll.upc.edu

4 Learning objectives and references

. To understand the basic properties of light, which will allow us to understand photonic techniques and applications.

. There is no required text. The slides are based on previous courses by Prof. Ramon Vilaseca (UPC Prof. Emerito), the slides of Prof. Rick Trebino (Georgia Tech, USA) and freely available material in the Optical Society (OSA) web page.

5 what is light? Particles and waves

Particles are localized in space and time (classical physics). Particles have well-defined trajectories.

Waves are extended in space and time. Waves have poorly defined trajectories.

waves bend around corners (diffraction) Two ways in which energy is transported

Point-mass interaction, which transfers energy and momentum: particles.

Extended regions wherein energy is transferred by vibrations and rotations (collective motions of particles): waves. Poll

Is light constituted by particles or by waves?

9 The nature of light: Huygens

Huygens promoted the wave theory.

He felt that light propagates as a wave from the point of origin. Christiaan Huygens He realized that light slowed (1629-1695) down on entering dense media. He explained polarization, reflection, refraction, and double refraction. The nature of light: Newton

Newton promoted the particle theory of light. Particles of light would travel in straight lines or rays. Explained (what were thought to be) sharp shadows. Explained reflection and refraction. Isaac Newton (1642-1727)

"I procured me a triangular glass prism to try therewith the celebrated phenomena of colours." (Newton, 1665) Interference of light beams

Thomas Young discovered interference of light—the ability of two light beams to either add or subtract.

Thomas Young (1773-1829)

His famous two-slit interference experiment proved convincingly that light is a wave. Young showed that light diffracted precisely as predicted by Fresnel’s wave theory. 13 Diffraction from one or two slits

One slit

Two slits

In 1803, Thomas Young measured the two-slit pattern, which convincingly confirmed the wave nature of light (how could particles yield such a pattern?), ending centuries of debate as to whether light was a particle or a wave. In 19th-century Maxwell unified electricity and magnetism

In free space:

where E is the electric field, B James Clerk Maxwell 2 is the magnetic field, c = and c (1831-1879) is the velocity of light. Maxwell showed that the electromagnetic “field” is a wave that propagates at the speed of light.

22 The electric ( ) and magnetic ( ) ff1 E B 0 fields obey the wave equation: xt222 v

Electric field E Wavelength (l) Magnetic field B y x z

Different wavelengths (distances between the peaks) or frequencies (the rate at which the peaks pass by) correspond to different colors, many of which we can’t see. Example of an harmonic Plane Wave that is a solution of Maxwell’s equations

E(z,t) = i E0 cos(kz-wt+)

B(z,t) = j B0 cos(kz-wt+) 푩 퐸0 푘(휔) (퐵0= ) Space 퓋  Wavelength: 휆 2휋 푛 휔 ·휔  Wavenumber: 푘 ≡ = 휆 푐 Velocity  Wavevector: 풌 = 푘풌෡  “Phase” velocity: 푐 Time 퓋 = 휆 · 휈 = 푛(휔) 푬  Period: 푇  Frequency: 휈 = 1/푇 In vacuum:  Angular frequency: 휔 = 2휋휈 퓋 = c =  Initial phase: 휑 299792,458 km/s Vertical and Horizontal Polarizations

Electric-field vector

The simplest x polarizations

y z

Light can have Electric-field vector any sum of these two waves with any relative x phase. y z Linear polarization

Adding two components in phase and with the same amplitudes yields 45º polarization.

Electric-field vector The orientation of the field vector is 45º to the x and y x axes.

y z Right circular polarization

Adding two fields that have equal Ex (,)cos()z tEkzt0 w amplitude and are 90° out of phase Ey (,)sin()z tEkzt  0 w gives a rotating field. Electric-field vector This polarization is also called positive helicity. x

y z Left circular polarization and elliptical polarization

Ex (,)cos()z tEkzt0 w Electric-field vector Ey (,)sin()z tEkzt0 w This polarization is also called negative helicity.

x

y z

Unequal arbitrary-relative-phase E-field variation over time components yield elliptical y polarization

Ex (z , t ) E0x cos( kz w t  x ) x

Ey (z , t ) E0 yy cos( kz w t  ) The Intensity of a Wave

How loud is a sound? How bright is a laser beam? We need a measure of the intensity of a wave. For a light wave, the intensity is given by:

1 2 where  is the permittivity IcE 2  0 of the medium

For other types of waves, the constants are different, but the intensity is always proportional to the square of the amplitude: IA 2 Real Waves vs. Plane Waves

A plane wave has flat wave-fronts throughout all space. It also has infinite energy. It doesn’t exist.

A real wave is localized. We can approximate a laser beam as a plane wave vs. z times a Gaussian in x and y:

exp(x2/w2) xy22 E( x , y , z , tEi )exp[ kzt0 ()exp  2  w ] w  w  x

z w y

Localized wave-fronts x Laser beam spot on wall Pulsed Waves exp(t2/t2) Gaussian in time: If we can localize the t wave in space by t multiplying by a Gaussian E in x and y, we can also localize it in time by multiplying by a Gaussian in time (but it must be of z or t the form, z – vt or t  z/v):

(/t  z v)2 xy22 E( x , y , z , t )expexp[ Ei0 exp kz  2 2 ( wt)] t w

This is the equation for a laser pulse about t long. A spherical wave (also solution of Maxwell's equations)

E (r , t ) Re E0 / r exp[ i ( krw t )] where k is a scalar, and r is the radial coordinate.

The directions of E and B must still be ┴ to the propagation direction, so the A spherical wave has polarization varies with angle. spherical wave-fronts. Unlike a plane wave, whose amplitude remains constant as it propagates, a spherical wave weakens: its intensity decreases as 1/r2. The spectrum indicates the frequencies present in a wave

Plane waves are monochromatic

(have only one frequency). Light electric field electric Light

Time

This wave has many frequencies. And the frequency increases in time (from red to blue). Superposition of waves with different frequencies

27 The Electromagnetic Spectrum

Visible light: ~380 to ~780 nm. Spectra from common sources of visible light

29 The Sun spectrum

Of the light at Earth’s surface, infrared comprises 49.4%, while visible light is 42.3%. Ultraviolet is the remaining 8%. 31 Another wave property of light: the Doppler effect

Increased sound frequency if a source, such as a train (with whistle blowing), approaches a receiver and a decreased frequency as the source recedes.

Christian Andreas Doppler (1803-1853) Waves from a source at rest

Viewers at rest everywhere see the waves with their appropriate frequency and wavelength. The Doppler Effect

. A receding source yields a red-shifted (longer-wavelength) wave, and an approaching source yields a blue- shifted (shorter- wavelength) wave. . A source passing by emits blue- then red-shifted waves. The Doppler shift has a many uses

Example: use it to sense rotation

Red-shifted reflected light Incident light Blue-shifted reflected light Rotation

Astronomers use it to measure recession velocities of distant galaxies and other astronomical objects.

So light is a wave, no? By the mid-19th century, light was well-known to be a wave. But what exactly is “waving”?

For a long time scientists searcher for the “luminiferous ether”, the hypothetical substance through which electromagnetic waves travel.

Now is well-known that electromagnetic waves can propagate through empty space!

36 Thermal radiation: “Blackbody” Radiation

When matter is heated, it not only absorbs light; it also emits it.

The name “blackbody” comes from the assumption that the body absorbs at every frequency and hence would look black at low temperature. What does blackbody radiation look like?

Depending on the temperature, look like this:

Hot

T (ºK) T (ºK)

Light bulb Sun Almost everything is a blackbody! The sun, the earth, light bulbs, etc. The earth is cooler so emits in the IR. Images we see of the earth are of reflected light, which masks the IR. The same holds for humans. Comparison of light sources for lighting

. A filament bulb has two kinds of losses: • losses due to the IR and UV radiation • heat-conduction losses in the filament, as a high intensity must be reached in order to reach a high temperature (2000-3000K). . In contrast, discharge lamps and, mainly, LEDs, do not have so much heat conduction losses (smaller currents, as the radiation efficiency in the VIS is larger), and also they do not have IR and UV radiation losses. . Therefore they are much more efficient.

39 X-ray image depicting the evolution of electric light bulbs

incandescent light bulb fluorescent light bulb LED light bulb

40 Herminso Villarraga-Gómez, Nikon Metrology, Optics and Photonics News Nov. 2019 The Sun spectrum

The effective temperature of the Sun (5777 K) is the temperature a black body of the same size should have to yield the same total emissive power. Rayleigh theory of blackbody spectrum

In 1900, Lord Rayleigh used the classical theories of electromagnetism and thermodynamics to show that the blackbody spectrum should be:

Classical Rayleigh- 8πckT Jeans IT(,)l  formula l l 4

Rayleighwhere k-Jeans= Boltzmann’s Formula constant Experimental

Spectral irradiance Spectral data

Wavelength (nm) UV UV Visible IR This worked at longer wavelengths but not at short ones. This problem became known as the “ultraviolet catastrophe” and is one of many effects that classical physics can’t explain. Shortly afterward, Planck found that he could obtain blackbody emission if light was actually a flux of particles.

8π/hc25l ITl (,)l  exp/1hckl T B   where h is a constant now known as Planck’s constant.

(he didn’t really believe such a crazy idea, and no one else did).

Max Planck (1858–1947) In 1905, Einstein showed that Planck’s theory was correct Einstein explained the photoelectric effect by requiring that light be composed of particles of energy ħw, where ħ = h/2π, and w is the frequency.

Illuminate a surface Albert Einstein with light. (1879-1955) Look at the electrons that emerge.

Classically, the kinetic energy of the electrons should increase with the light intensity and not depend on the light frequency. Photo-Electric Effect Observations

The kinetic energy (K) of the electrons is independent of the

light intensity. K K depends only on the a frequency of the light.

w0 Light frequency w There is a threshold Kaw frequency of the light, Electron kinetic energy energy kinetic Electron below which no electrons were ejected.

Classical physics could not explain these facts. Einstein theory of the photoelectric effect

Energy after = Energy before

Electron kinetic energy Photon energy

K w

Electron potential energy to be overcome before escaping So light is simultaneously a wave and a particle! Light particles are called photons. Photons have energy and momentum (but no mass)

Eh  E  w Ehh  Momentump ccl The effect of the momentum is “radiation pressure” that, at everyday size scales and low frequencies, is very small. Exercise: use p =F/t to estimate the pressure produced by visible light (600 nm) and compare with atmospheric pressure.

Photons also carry angular momentum

h = 6.62607004 × 10-34 m2 kg / s 1 atm = 105 Pa 47 EXPERIMENTAL MANIFESTATIONS OF THE “PARTICLE” CHARACTER

Very very dim Photographs taken in dimmer light look grainier

Very very bright 19th-century scientists also could not explain spectra of light emitted by gases.

Chemical elements emit light with specific wavelength when heated

Wavelength

3 min video that explains absorption and emission spectra: https://www.osa.org/en-us/media_library/youth_education/?videoId=2477197723001 If a light-wave acted like a particle, why shouldn’t matter-particles act like waves?

In 1923, de Broglie (Nobel 1929) suggested that mass particles should have wave properties similar to those of light. The wavelength of a matter wave is called de Broglie wavelength: Louis de Broglie (1892-1987) where h = Planck’s constant and p is the particle’s momentum.

E where E is the Wave frequency: w  particle’s energy. If electrons are waves, then they should exhibit wave phenomena, like diffraction.

George P. Thomson (1892–1975) observed electron diffraction from celluloid, gold, aluminum, and platinum.

In 1925, Davisson and Germer observed electrons diffracting (much like x-rays) from nickel crystals. Making atoms interfere

. Atoms are too hot, move too fast and their tiny de Broglie wavelength made observation of their wave-like nature practically impossible.

. In the 70s/80s Steven Chu, Claude Cohen-Tannoudji and William Phillips (Nobel Prize 1997) used light to trap and to cool atomic gases to near absolute zero.

. This opened the door to ultra-sensitive matter-wave atom interferometers.

52 Quantum mechanics

. Quantum mechanics has its own laws, which need only approach classical laws as the system increases in size to classical dimensions.

. Particles have quantum states (energy levels), and emit or absorb energy when they change state.

Excited level

Ground level

53 In the case of a particle, what is waving?

Probability! The probability P(x) dx of a particle being between x and x + dx is: P(x)  (x) 2

x2 The probability of the particle 2 being between x and x is: ()xdx 1 2  x1  is the solution of a wave equation (Schrödinger’s equation)

Erwin Schrödinger (1887-1961)  yields probability distribution functions

Probability density for the hydrogen atom for three different stationary electron states. Quantum mechanics is everywhere and essential to all modern technology.

Economists estimate that semiconductor- based technologies (developed thanks to quantum mechanics) are responsible for ~80% of the entire US economy. Geometrical optics (ray optics) is the simplest version of photonics.

Ray optics Considers handle re- photons flection and refraction, but not Requires interference or diffraction Maxwell’s Ray Equations optics However, when it does work, it’ll handle complex problems much more easily than even wave Requires the optics. wave equation Ray Optics Optical system

Light ray Optic axis

Light rays correspond to positions and directions in space of laser beams. Each optical system has an optic axis, which usually passes through the centers of lenses or mirrors. All light rays will be assumed to have small displacements (x) and angles () from it. This is called the Paraxial Approximation: sin() ≈ . Reality vs ray optics

Ray optics neglects the wave Rays nature of light. Ray optics As a result, the ray picture implies that a lens can focus a beam to a point with zero diameter and so obtain infinite intensity and infinitely good ~0 spatial resolution.

In reality the smallest possible focal spot is actually about l/2. Reality Same for the best spatial resolution of an image. This is fundamentally due to the wave nature of light, which is not included in geometrical optics. > ~l/2 But is much easier to use. Summary

. Light has both, wave properties (diffraction, Dopper) and particle properties (photoelectric effect).

. Optics and photonics.

. Particles also have wave properties (they are described by probabilities that are solutions of a wave equation). Light-matter interactions Everything we see is the result of the interaction of light with matter. The electromagnetic field interacts with the electrical charges (electrons, ions) of matter (be it inorganic, biological,...)

Matter

“Fields” Quantum and semi-classical descriptions of light- matter interactions

Interactions between light and particles are described by “full” quantum mechanics or by “semi-classical” theories where light is described by classical Maxwell’s equations (wave) while particles are described by quantum Schrödinger’s equation (quantum energy levels, “two-level particles”).

63 Why is light absorbed or transmitted by a particular medium?

. Light causes matter to vibrate. Matter in turn emits light, which interferes with the original light. . The interaction is described by Absorption coefficient − Absorption coefficient, a Refractive index a − Refractive index, n. w n–1 A Light Wave Exciting an Electron

A light wave causes an electron to oscillate because F = qE.

x

z or t The amplitude and phase of the electron’s oscillation depend on the nearby nucleus, which also attracts the electron. And it’ll depend on the electron’s natural oscillation frequency and the incident light frequency. An oscillating electron emits its own wave. This wave will have the same frequency as the incident light wave but will usually be out of phase with it. z or t x

The resulting cancellation attenuates the beam. This is absorption, a. It also slows the velocity of light by a factor that we call refractive index, n. What determines a and n? Resonance

. When the frequency of the incident light matches that of an electron, resonance occurs, and the electron’s oscillation amplitude is huge. . Same as the resonance of a forced oscillator. . The forced oscillator is one of the most important problems in physics. It is the concept of resonance.

Tacoma Bridge oscillated and Millennium Bridge (London 2000) collapsed (1940) because oscillatory oscillated because of the lateral winds blew at its resonance frequency. movement of pedestrians. 67 The Absorption Coefficient, a, and the Refractive Index, n, depend on the frequency of the light.

The absorption coefficient is maximal on resonance. The refractive index has a complex dependence on frequency.

On resonance (w  w0), the molecule absorbs the strongest. Absorption coefficient Refractive a index Light speeds up!

w0 Light slows down Light frequency w n–1 Electrons have many resonance frequencies

Regions of strong absorption (and anomalous dispersion)

a n

Normal Normal Normal dispersion dispersion dispersion

1 Refractive index, index, Refractive 0 w1 w2 w3 w Absorption coefficient, coefficient, Absorption Infrared Visible Ultraviolet X-ray

The tendency of n to vary with wavelength is called dispersion. n increases with frequency, except in anomalous dispersion regions. Refractive index of glasses

n ≈ 1.5 for the glass we usually encounter. Consequences and applications of the refractive index

Light bends when it passes  n through a surface between 1 1 media of different refractive n2 indices. 2 n3

nn1122sinsin    Snell’s Law n4

n5

Object Image

This is why lenses work. And it’s hard to catch a fish. Snell’s Law causes things to look bent in water.

Our eyes assume that light takes a straight- line path. Reflection for a Glass-to-Air Interface

1.0

nglass  1.5 > nair  1 r

.5 For large i, the sin(t) in Snell's Law is > 1: (n =n  1.5 ; n =n  1) sin(t)  (ni /nt) sin(i) > 1! i glass t air 0 No transmitted-beam angle!

Reflection coefficient, Reflection coefficient, -.5 Total internal reflection when i > the critical angle:

sin(crit)  (nt /ni) sin(t) crit  arcsin(nt /ni)

-1.0 max = 1

Incidence angle, i Total Internal Reflection nn1122sinsin   

What happens when n1 sin(1) > n2?

In this case, sin(2) > 1, and no transmitted beam can occur.

n2 = 1 Total Internal Reflection

n1 = 1.5

Total internal reflection is 100% efficient, that is, all the light is reflected. It’s the basis of optical fibers! First demonstration of total internal reflection

. In 1841, Daniel Colladon was the first to guide light through jets of water via total internal reflection to entertain a lecture hall in Geneva.

. This trick has been used in illuminated fountains.

. You can try this at home with a plastic bottle and laser pointer.

75 Optical Fibers

Core: Thin glass center of the fiber that carries the light

Cladding: Surrounds the core and reflects the light back into the core

Buffer coating: Plastic protective coating

The only requirement is:

ncore > ncladding Propagation of Light in an Optical Fiber

Light travels through the core, reflecting off the walls. The walls absorb very little light from the core, allowing the light wave to travel large distances.

Some light loss can occur if the curvature is too high. Some signal degradation occurs due to imperfectly constructed glass used in the cable. The best optical fibers show very little light loss—less than 10%/km at 1.550 m. Optical fibers in medicine

. The first fiberscope was invented in 1953. . It is a flexible optical fiber bundle with an eyepiece on one end and a lens on the other that is used to examine small, difficult-to-reach places. . In 1957: optical medical imaging takes off. Basil Hirschowitz designed the first fully flexible fiber optic endoscope. The hair-thin glass fibers were coated in such a way as to illuminate and allow an unobstructed view inside organs like the esophagus.

78 Fiber in modern medicine

. Researchers in China have developed laser- based ultrasound sensor for photoacoustic imaging.

. It relies on fiber optic ultrasound detection, exploiting the thermoelastic acoustic effects of laser pulses.

79 Optics and Photonics News, April 2019 Fiber in modern medicine: endoscopic surgical robot

. Researchers in Korea have developed a flexible endoscopic surgical robot for robot- assisted surgery.

. In an in vivo test, they successfully performed surgery on a porcine gallbladder.

80 Optics and Photonics News, April 2019 Fiber in modern medicine: machine learning and fiber imaging

. Artificial intelligence (AI) and machine learning (ML) are being used to reconstruct images transmitted through an optical fiber for long distances.

. By mimicking the human brain’s ability to process images, AI and ML techniques are improving endoscopic imaging for medical diagnosis.

(Want to know more about signal processing tools? New “optative” course will be offered next semester -Q2 2020)

81 Anti-Reflection Coatings

The lenses in the glasses on the right appear to be missing. They’re not! There are anti-reflection coatings on both the front and back surface of each lens.

Such coatings have been common on photography lenses and are now common on eyeglasses, TVs, etc. Anti-Reflection Coatings

n0 layer nl From Maxwell’s equations it can h be shown that, at normal incidence, the reflectance is 0 if ns substrate h  l /4 and 2 nls n0 n

So an AR-coating requires: and Multilayer Coatings

Air Typical laser mirrors and camera lenses use many l/4 layers, n0 usually with nL alternating high and n low refractive indices. H nL n The reflectance H and transmittance nL vs. wavelength nH can be tailored to Glass substrate n taste! s 85 The Fabry-Perot Interferometer (Etalon)

A Fabry-Perot interferometer is a pair of parallel reflective surfaces. An etalon is one consisting of a piece of glass with parallel sides. For normal incidence and high reflectance of Transmitted each surface, the Incident wave: E wave: E0t 0 condition for constructive Reflected interference at the output

wave: E0r is: n = 1 n n = 1 air air l0m  nL/ m

L : round-trip path length Etalon free spectral range and linewidth

4R F  (1) R 2 F is coefficient of finesse and R is the reflectivity of the surfaces

The free spectral range is the wavelength l=l 2/L range between consecutive peaks 0 The linewidth l is the accuracy with which an etalon can measure wavelength. Dispersion: variation of refractive index with wavelength

Because the bending of light (refraction) at an interface depends on the refractive index, dispersion allows prisms to separate white light into its components.

Angularly dispersed beam

White light n(l)

Dispersive element Another consequence of dispersion (the variation of the refractive index with frequency) is the variation of the group velocity with frequency.

A chirped pulse

Short Not so pulse short pulse

vg(blue) < vg(red)

Because short pulses have large ranges of frequencies, dispersion is a bigger issue for them than for nearly monochromatic light. Group-velocity dispersion is undesirable in telecommunications systems.

Train of input pulses dispersion turns short pulses into long ones.

All materials have positive dispersion in the visible and near-IR.

Many km of fiber

Fiber must be very carefully designed to compensate for dispersion. Train of output pulses Dichroism and Birefringence: the “spring constant” can be different for different directions.

ny(w) ny 1

w

nx(w) x- and y-polarizations see nx different resonances and 1 hence different absorption (dichroism) and different refractive index (birefringence). w w0y w0x Birefringence can separate the two polarizations into separate beams.

Due to Snell's Law, light of different polarizations will bend by different amounts at an interface.

e-ray

ne o-ray

no

no > ne

This can be useful or irritating. Polarizers are built with asymmetrical crystals

Optic Axis

Uniaxial crystal Uniaxial crystals have one refractive index for light Extraordinary polarized along the optic polarization k axis (ne) and another for light polarized in either of the two directions perpendicular k to it (no). Ordinary polarizations Birefringent Materials

Refractive Indices of Uniaxial Crystals (20ºC; l = 589.3nm)

______Material no ne Tourmaline 1.669 1.638 Calcite 1.6584 1.4864 Quartz 1.5443 1.5534 Sodium nitrate 1.5854 1.3369 Ice 1.309 1.313 Rutile 2.616 2.903 The polarization purity of the transmitted beam is Calcite is particularly useful the highest priority. The because it’s also transparent trade-off is that the rejected over the entire visible spectrum beam is often not so pure and even into the UV (~300nm). and often is blocked by the manufacturer. “Polariscope” or “Polarimeter”

. Stress-induced birefringence in a glass piece placed between two crossed polarizers

. Normally, the view through such crossed polarizers is uniformly dark.

. This can be used to check the quality of transparent objects (eyeglasses, crystals, plastics). 95 Polarization Mode Dispersion

Imagine just a tiny bit of birefringence, n, but over a distance of 1000 km… n as small as 10-12 can rotate the polarization by 90º!

This is a big problem because newer broadband optical- fiber communications detect only one polarization and so don’t see the orthogonal polarization. Worse, as the temperature changes, the birefringence changes, too. Why are plants green?

97 Green plants

are green because they contain a pigment called chlorophyll. Chlorophyll absorbs certain wavelengths of light within the visible light spectrum but green light is not absorbed but reflected, making the plant appear green.

98 What determines the color of an object?

Absorption! The wavelengths that are not absorbed will be reflected and/or scattered into our eyes.

These filters transmit only one color region

The smaller the absorption coefficient the higher the transmission 99 Wavelengths and frequencies of visible light (cut-offs are rather arbitrary) Chromaticity: quantitative specification of the color of an object

Chromaticity consists of two independent parameters that originate from human vision (colorfulness and saturation)

Line represents the chromaticity of black-body light at various temperatures

101 Color representations Red = (255, 0, 0)

Additive color (RGB) is for light Blue = (0, emitting sources. Red and 0, 255) green light add to yield yellow, etc. Green = (0, 255, 0)

CMYB="Cyan Magenta Yellow Black." These are the four basic colors used for printing color images. Unlike RGB, which is used for creating images on computer screens, CMYK colors are "subtractive." This means the colors get darker as you blend them together.

102 Absorption of light in water varies massively with wavelength

Water is clear in 1 km the visible, but not in other IR UV X-ray spectral regions. 1 m

Radio Microwave Notice that the 1 mm penetration depth varies by over ten

1 µm orders of

magnitude! Penetration depth into water into depth Penetration

1 km 1 m 1 mm 1 µm 1 nm Wavelength Visible spectrum Materials that are opaque in the visible are often transparent in the IR.

IR Lenses Near-IR Archaeology from Space

Archaeologists use near-IR light to reveal previously undiscovered ancient structures. Plants grow differently over buried buildings and walls— different root depths and leaf and bark composition. Also, sand over buildings can look different in the near-IR.

Visible image Near-IR image

Sarah Parcak has helped find 17 potential pyramids, 3,000 settlements, and 1,000 lost tombs in Egypt. Modern town By choosing a high-power laser that is absorbed by a material, we can laser-weld or cut.

Here, a CO2 laser cuts metal

Laser surgery works on the same principle Another consequence of absorption: the Greenhouse Effect

The greenhouse effect occurs because windows are transparent in the visible, but absorbing in the IR (~10mm), where the ground re-emits after absorbing visible light.

IR light is absorbed by the glass, so much of its energy is trapped by the greenhouse.

Greenhouses can remain quite warm even in winter. Why CO2 is a Greenhouse Gas?

Sun Earth

CO2 absorption at the peak of the earth’s emitted radiation. 108 Light Scattering Particle, bubble, droplet, or molecule When light encounters matter, matter not only re-emits light in the forward direction (leading to absorption and Light refractive index), but it source also re-emits light in all other directions. This is called scattering.

Light scattering is everywhere. Why is the sky blue?

. Sunlight reaches Earth's atmosphere and is scattered in all directions by all the gases and particles in the air.

. Blue light is scattered more than the other colors because it travels as shorter, smaller waves.

. This is why we see a blue sky most of the time.

110 Interference: sum of two or more waves

. Waves pass through each other unchanged.

. This is because the wave equation is linear: 22ff1 0 xt222 v

 the sum of solutions of the wave equation is also a solution.

111 Constructive vs. Destructive Interference

Waves that combine in phase add up to Constructive relatively high intensity. = interference

Waves that combine 180° out of phase cancel out Destructive and yield zero intensity. = interference

Waves that combine with Incoherent different phases yield interference (if intermediate intensity and = many waves an intermediate have random (different) phase. phases) Two point sources (different separations) emitting spherical waves

When combining a wave with a delayed replica of itself, the intensity has fringes. Waves crossing at an angle: Big angle, small fringes; small angle, big fringes. Ixkx()1cos(2sin)   The fringe spacing, : Large angle: l/ (2sin) 2 As the angle decreases to zero, the fringes become larger and larger, until finally, at  = 0, the intensity pattern becomes constant. Small angle:   = 0.1 mm is about the minimum fringe spacing you can see: 2 sin   l / (2  )  0.5 mm / 200   1/ 400 rad  0.15  very small! Application of interferences: Interferometry

Measurement of very small distances, displacements or vibrations, surface profiles, by interferences.

Very high resolution!!! ( nm)

Object Laser Many industrial and biomedical applications.

Photodetector Two counter-propagating waves yield a standing wave.

The wave does not propagate.

l

 x Boundary conditions limit the frequencies that can occur

A laser has two mirrors, each with the same boundary condition: the field is zero at each.

Mirror Mirror m

z 0 L The left mirror means using sin(kz):

Etot (z , tEkzt )2sin()cos() 0 w

But the right mirror means that: 0 z L kL = (2p/lL = mp And the possible frequencies are:

Or: lm = 2L/m m = c/lm = mc/2L where m is any integer. Laser Frequencies The frequencies are separated by:

m+1  m = (m+1)c/2L  mc/2L = c/2L = 1/T where L is the length of the laser cavity and T is the round-trip time.

Which frequencies can be emitted depends on the laser medium.

Laser spectra

Here, additional filtering has yielded a single Intensity frequency.

Frequency What happens when light insides on a periodic array km of scatterers? Scatterer a  Diffraction Grating D C  Constructive interference m k occurs if the pathlength i m difference is an integer Incident i a B number of wavelengths: wave-front Potential ABCDml A diffracted wave-front i

AB = a sin(m) amsin(mi ) sin(  ) l Scatterer CD = a sin(i)

For other angles, scattering is destructive.

A grating can have “solutions” for one or many values of m. Diffraction Gratings

A diffraction grating is an object with periodic optical properties and spectrally disperse light much more than prisms do. Real Diffraction Gratings

m = -1 m = 0 m =1 m = 2

White light diffracted by a real grating

The dots on a CD are equally spaced (although some are missing), so it acts like a diffraction grating. Diffraction of a Wave by a Slit

Whether waves in water or l  slitsize electromagnetic radiation in air, passage through a slit yields a diffraction pattern that will appear more dramatic as the size of the slit approaches (decreases to) the wavelength l  slit size of the wave.

l  slit size Diffraction from one or two slits

One slit

Two slits

In 1803, Thomas Young measured the two-slit pattern, which convincingly confirmed the wave nature of light (how could particles yield such a pattern?), ending centuries of debate as to whether light was a particle or a wave. Diffraction by a circular aperture

Airy disc

The first dark ring is seen, from the aperture, under an angle  푘퐷 With γ = · 푠푖푛휃 , (with respect to the axis) such 2 that: 푘= 2p/l, 퐷 = 2푎 = aperture 휆 푠푖푛 휃 = 1.22 diameter, 퐽1 = Bessel function 퐷

83.8% of total intensity lies within the first maximum. Consequence of diffraction: maximum resolving power of an optical instrument

Lens The image of point can never be a point ! O’

O D (due to diffraction by Object the aperture of the point lens D) Image point PSF (“Point Spread Function”) Double-pass retina imaging Image of a point source projected on the retina after reflection from retina (therefore, double pass through the ocular media). “ideal output” from CCD: Point Spread Function

Measures the optical quality of the eye.

2-3% retinal reflection  laser light (limited in wavelength and power by the patient’s comfort).

127 The speckle problem the roughness of the retina in the scale of the wavelength of the laser light produces interference “noise” known as speckle.

128 Image of two very close points

Lateral resolution R of a microscope (with Rayleigh criterion to distinguish two close point objects that there is a 26.3% dip):

l l R  0.61 R  0.82 NA NA With incoherent light With coherent light

Numerical aperture of a lens: NA = n sin  n is the ambience refractive index

 R ≳ 200 nm is the maximum resolution in the VIS domain. R

max ~70º, noil = 1.52  NAmax ~ 1.45

 Rmax ~ l/2 ~ 200 nm (for blue light) Beautiful proof that electrons are waves: imaging using electrons

Imaging using light waves is well known. But optical microscopes’ resolution is only l/2 ~ 200 nm. Electrons have much smaller wavelengths, and electron microscopes can achieve resolutions of ~0.05 nm.

Electron micrograph of pollen grains with ~0.1nm resolution Super-resolution optical images (Nobel Prize 2014): resolution better than 200 nm and can be used «in vivo». Newton’s Rings

Placing two pieces of glass together yields interesting colorful ring patterns.

Glass is rarely flat and is usually slightly curved. Constructive interference occurs when the front- and back-surface reflections are in phase, that is, for an integral number, m, wavelengths of path difference.

Beam You see the reflected from Beam color l when top glass back reflected constructive from surface Incident interference bottom beam occurs for it. glass front surface Back surface of top L piece of glass Front surface of bottom piece of glass Summary

. The semi-classical interaction of light with matter is described by the absorption coefficient and the refractive index.

. Resonance phenomena is crucial to understand light absorption.

. Light propagation is described by wave phenomena: interference, reflection, transmission, diffraction and scattering. Photonics Classical physics can not explain spectra of light emitted by gases

Wavelength

Quantum physics explains spectra lines as due to transitions between “energy levels” Spontaneous emission

When an atom in an excited state falls to a lower energy level, it emits a photon of light with energy equal to E (=h). Excited level “two-level” atom or particle: strong but useful Photon simplification of quantum

energy levels Energy Ground level

This is also called fluorescence. Absorption

When an atom encounters a photon of light (with the appropriated energy, i.e., frequency) it can absorb the photon’s energy and jump to an excited state.

Excited level

Photon Energy Ground level

Absorption lines in an otherwise continuous light spectrum due to a cold atomic gas in front of a hot broadband source. Einstein showed that another process, stimulated emission, can also occur.

When a photon encounters an atom in an excited state, the photon can induce the atom to emit its energy as another photon of light, resulting in two identical photons.

Excited level Photon Photon Photon

Ground level

Einstein first proposed stimulated emission in 1916. Three fundamental processes

Spontaneous Stimulated emission Absorption emission

Photon Photon Photon Photon Photon

The blackbody radiation results from a combination of spontaneous emission, stimulated emission, and absorption occurring in a medium at a given temperature. 139 Stimulated emission can lead to a chain reaction = laser emission (Light Amplification by Stimulated Emission of Radiation) If a medium has many excited particles, one photon can become many. This is the essence of a laser.

The factor by which an input beam is amplified by a medium is called the gain and is represented by G. The Laser A laser is a medium that stores energy, in a “cavity” formed by two mirrors. A partially reflecting mirror lets some light out.

Back Output mirror mirror I1 = G I0 I0 I1 Laser medium with gain, G

I3 I3 = G I2 I2 R = 100% R < 100%

Losses in intensity occur (due to absorption and output light). The laser will lase if, in a round trip:

Gain > Loss at Threshold Gain = Loss. Population Inversion 2 N2

Pump Laser To achieve the threshold condition stimulated emission must exceed 1 N1 absorption.

There should be more particles in the excited state

N2 > N1

This condition is called inversion. Inversion does not occur naturally (particles tend to be in the ground low-energy state). It’s inherently a non-equilibrium state. In order to achieve inversion, we must “pump” the laser medium and choose our medium correctly. Emission wavelength of lasers

UV Excimer

Nd:YAG tripled 0,4 Diode laser (blue)

VIS Diode laser (green)

Nd:YAG doubled lasers

He-Ne Dye Diode laser (red) 0,7

Alexandrite Ti:Sapphire Gadolinium Nd:GdVO4

Ytterbium Nd:YVO4 (IR) Nd:YAG IR Fibre laser

Ytterbium Nd:YVO4 lasers Chemical lasers

1,5 Optical fiber Diode Er:YAG CO2 l m Quantum Cascade (down to THz) A laser is “a gain medium” + optical cavity

Back Output mirror mirror

Laser medium with gain, G

R = 100% R < 100%

. The cavity provides “feedback” for the amplification of the stimulated emitted photons . The cavity selects the possible emission frequency (longitudinal modes) . It determines the beam shape (transverse modes)

145 Laser cavity: longitudinal modes

L

“Fabry- Perot” l cavity Resonance l condition:

(m=5) 2L = m l = m 퓋/ l’

(m=8) 퓋 휈 = 푚 푚 2퐿 2 L Frequency of the l “Ring” longitudinal mode cavity of order m (m = 1,2, 3,...) Unidirectional element Gain spectrum, loses and cavity modes

Total gain E2 (due to the amplifying Gain of the amplifying h(   /2 medium and the cavity) medium (given by the  21 21 width of the atomic

transition, 21 Fabry-Perot E1 Gain Transmittance 1

FP 21 loses

0    m-1 m m+1 v   “FSR” 21 2L

 CO2 laser: 1 longitudinal mode amplified

 He-Ne laser:  2-6 longitudinal modes amplified simultaneously  Nd:YAG laser (high power) : many longitudinal modes amplified simultaneously Monocromaticity The monocromaticity of the laser emission depends of the gain

spectral width 21 and of the spectral width of the cavity, FP .

Gain and  21 loses FP

0  m-1 m  21 Final laser I emission intensity, I LASER (< 10-15 

0  m-1 m v  2L

Single-mode emission Multi-mode emission Laser spectra

Monocromatic (monomode) Multimode

Optical spectrum analyzer (optical signals) LIGO (Laser Interferometer Gravitational-Wave Observatory) used an ultra-narrow laser for the detection of gravitational waves

LIGO's laser stability is one of several factors, critical for LIGO's ability to detect gravitational waves.

150 Laser cavity: transverse modes

Some cavities allow to generate the superposition of several Gaussian “Donut” transverse modes. mode mode Transverse irradiance profiles

What we want: What we often have: Gaussian beam filamentation

Radial (transverse) coordinate Radial (transverse) coordinate

152 Directionality, divergence and beam quality factor (M2)

The half-angle beam divergence is:

. M2 represents the degree of variation of the propagation of a beam with respect to an ideal Gaussian beam. 2 . For a single mode TEM00 (Gaussian) laser beam, M =1. . Because the divergence is inversely proportional to the spot

size (w0), a Gaussian beam that is focused to a small spot diverges rapidly as it propagates away from the focus.

153 A non-Gaussian Gaussian

This particular profile, which has an almost perfectly gaussian shape, is in fact composed by an incoherent superposition of higher-order

Laguerre-gaussian modes (specifically 44% of the TEM01 mode, 17% TEM10, 19% TEM11, 11% TEM20, and 6% TEM21), and absolutely no TEM00 at all. This beam will remain almost perfectly gaussian as it propagates but since it has an M2 ≈ 3.1, it will diverge ≈3.1 times as rapidly with distance as a true TEM00 beam.

154 Source: Siegman OSA tutorial. Laser high beam directionality + high power = dangerous weapon

30 kW; target reached over a mile away

Laser Focus World News March 2015

155 What’s the difference between light from a laser and a light bulb?

156 Coherent vs. Incoherent Light

Laser

Coherent light: Incoherent light: 1. It’s intense (or dark). 1. It’s relatively weak. 2. It’s unidirectional. 2. Not uni-directional (difficult to colimate). 3. Total irradiance N2. 3. Total irradiance N . 4. Total irradiance is the sum of individual fields. 4. Total irradiance is the sum of individual irradiances.

E = E1 + E2 + … + EN I ≈ I1 + I2 + … + IN Intensity and Irradiance units

The radiant power includes all wavelengths.

The luminous power includes only those the eye can see. The Candela (cd) is the SI unit of luminous intensity (power per steradian, sr=SI unit of solid angle). 1 candela = 1/683 W/steradian.

1 Lumen (lm) = 1 cd x sr. A full sphere has a solid angle of 4π steradians, so a light source that uniformly radiates one candela in all directions has a total luminous flux of 1 cd × 4π sr = 4π cd⋅sr ≈ 12.57 lm

1 Lux = 1 Lumen/m2. 1 Nit = 1 Candela/m2. Irradiance of the sum of two waves

Same polarizations Perpendicular polarizations Coherent addition III12   Same * III12 colors c Re E12 E 

Incoherent addition

Different colors

Interference only occurs when the waves have the same wavelength and polarization. Temporal (or longitudinal) coherence

l l 1 2 l3 l4 l5 lc t 1 t2 t3 t4 t t 5 Average c Lasers can have long coherence times—as coherence length long as one second, which is >1014 cycles! coherence time

- Typical values (commercial lasers): lc  1 - 100 cm 3 - A very stable laser: lc  10 km !! - Other light sources: lc ≳ 10 mm Spatial coherence

A plane wave is also considered perfectly spatially coherent and so has an infinite spatial coherence length and area. The spatial coherence length is the transverse distance over which the beam wave-fronts remain flat: Wave-fronts

Spatial xc Coherence Length: xc x k

Since there are two transverse dimensions, the spatial

coherence area, Ac = xc yc is the area over which wave- fronts remain flat. Spatial and Temporal Coherence Wave-fronts Spatial and Only a plane x Temporal c wave is Coherence perfectly tc coherent. Temporal Coherence; xc Spatial Incoherence tc Spatial

Coherence; xc Temporal Incoherence tc Spatial and xc Temporal x Incoherence

t, z tc The spectral phase distinguishes a short pulse from a light bulb “Mode-locked pulse”

Intensity vs. time

Locked Short

phases pulse Frequency

Time

Intensity vs. time

Random Light bulb

phases Frequency

Time Continuous wave (cw) vs. pulsed laser emission

cw - ms - s - ns - ps - fs - (as)

Only a few field oscillations Shortest light pulses: − Directly from a laser: few fs (1 fs =10-15 s) − With additional pulse compression techniques outside the laser cavity (Nobel 2017): tens of as (1 as =10-18 s)

Optics can be much faster than electronics Attosecond light has been used to trace electrons’ motion inside atoms (Hentschel et al, Nature 2001) The shorter the f(t) F(w) pulse, the broader the spectrum Short pulse ∆풕   ≳ 0.3 t w

f(t)=Gaussian  Medium- F(w) is a Gaussian length pulse t w

(This is the essence of the Uncertainty Long Principle of pulse Quantum Mechanics) t w Fourier transforms 1

1 rect(t)

-.5 0 .5 t w

1

-1 0 1 t -2p 2p w

cos(w0t)

t w 0 w w 0 0 0 Negative frequencies contain no additional information for real functions Optical spectrum and RF spectrum

If E(w) is the (complex) Fourier transform of the electric field E(t), then the optical spectrum is S(w) = |E(w)|2

The radio-frequency (RF) spectrum is the spectrum of 2 the intensity, I=|E| . 2 SRF(w) = |I(w)|

Spectrum analyzer (electrical signals) Optical spectrum analyzer (optical signals) How to obtain spatially and temporally coherent light from a light bulb?

temporally

A lens can then collimate the beam to a plane wave.

the pinhole An etalon (aperture) is can be used called a as l filter. spatial filter. When coherence is detrimental: laser speckle pattern

When a laser illuminates a rough surface, it yields a speckle pattern due to coherent interference of reflections from a rough surface (in the scale of the wavelength).

Laser illumination Incoherent illumination Speckle Here, poor spatial and temporal coherence yield a better image. The speckle pattern contains information of the object that generates the speckle

171 Attometer precision demonstrated using speckle-based spectrometer / wave-meter

Laser light is passed through the optical fiber (orange), and is recorded on the camera. The speckle pattern produced is shown on the screen.

The speckle pattern is produced by interference between the guided modes Source: phys.org, march 2019 of a multimode fiber.

B. Redding and H. Cao, “Using a multimode fiber as a high-resolution, low-loss spectrometer,” Opt. Lett. 37, 3384 (2012). Speckle patterns generated by scattering particles and recorded with different exposure times can be used to extract information about the dynamics of the sample.

F. Perakis et al, Diffusive dynamics during the high-to-low density transition in amorphous ice, PNAS 114, 8193 (2017). 173 Speckle can be used for spying your neighbor

. Recover sound from video signals: http://people.csail.mit.edu/mrub/VisualMic/ . And the other way around: Researchers have shown that they can hack your smart speaker just by shining lasers at it (sciencealert 6/Nov/2019) How does it work? Smart speaker mics have micro-electro-mechanical systems, or MEMs, built into. These are tiny components that can interpret light as sound, which means they can be manipulated by something as simple as a laser pointer.

Bachelor and Master projects available. 174 Summary

. A laser is composed by a gain medium and an optical cavity.

. To generate laser light spontaneous and stimulated emission need to overcome absorption. Therefore, population inversion (more particles in the high-energy state than in the low- energy state) is needed for lasing.

. The geometry of the optical cavity determines the emitted “modes” (single-mode, multi-mode, longitudinal & transverse).

. Lasers emit monochromatic, directional, spatially and temporally coherent light.