Phys 322 Chapter 13 Lecture 37
Modern optics More on Lasers
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Name Presentation topic date Abdallah, Daniel ultrafast optics 5-Dec Brown, Timothy adaptive optics 3-Dec Chen, Qingyu OCT 28-Nov Foote, Evan LCDs 30-Nov Kim, Eu-Young fiber lasers 7-Dec Lazar, Dennis lasers 28-Nov Lee, Gen Joo magn. Res. Spect. 3-Dec Navarro, Tyler optical computing 5-Dec Ohlwine, Ross x-ray imaging 5-Dec Simiele, Eric tomography Sun, Yubo metamaterials 3-Dec Tempel, Nicholas holography 30-Nov Tran, Tu holography 30-Nov Laser System
1. Active (gain) medium that can amplify light that passes through it 2. Energy pump source to create a population inversion in the gain medium 3. Two mirrors that form a resonator cavity Amplifier vs. Generator
No (or negative) feedback:
Positive feedback: Achieving Laser Threshold
An inversion isn’t enough. The laser output and additional losses in intensity due to absorption, scattering, and reflections, occur.
I0 I1 Laser medium
I3 Gain, G = exp(gL), and I2 R = 100% Absorption, A = exp(-L) R < 100%
The laser will lase if the beam increases Gain > Loss in intensity during a round trip, that is, if:
This called achieving Threshold. It means: I3 > I0. Here, it means:
I30 Iexp( gL ) exp( L ) R exp( gL ) exp( L ) I 0 2(gL ) ln(1/ R ) Gain spectrum can be very broad Broadening of the gain spectrum Laser Cavity
Longitudinal cavity modes
Longitudinal modes in Fabry-Perot cavity
Hole burning in the gain spectrum Transverse modes How to make a laser operate in a single basic transverse mode? LASER = Light Amplification by Stimulated Emission of Radiation
Laser is a device which transforms energy from other forms into (coherent and highly directional) electromagnetic radiation. •Chemical energy •Electron beam •Electric current •Electromagnetic radiation …
•1917 – A. Einstein postulates photons and stimulated emission •1954 – First microwave laser (MASER), Townes, Shawlow, Prokhorov •1960 – First optical laser (Maiman) •1964 – Nobel Prize in Physics: Townes, Prokhorov, Basov
Laser radiation
•Monochromaticity •Directionality •Coherence Monochromaticity Directionality
Radiation comes out of the laser in a certain direction, and spreads at a defined divergence angle ()
This angular spreading of a laser beam is generally very small compared to other sources of electromagnetic radiation, and described by a small divergence angle
W 2 Lamp: W = 100 W, I ~ 0.1mW/cm at R = 2 m R2 He-Ne Laser: W = 1 mW, r = 2 mm, R = r + R /2 = 2.1 mm, I = 8 mW/cm2 Fraunhofer diffraction of a laser beam
A laser beam typically has a Gaussian radial profile: 22 xy00 2w1 Ex(,00 y ) exp 2 2w0 w0 No aperture is involved. z What will its electric field be far away? 22 kkxy 2 Ekkxy,(,) Y Exy Ek(,xy k ) exp w0 4 The Fourier transform of a In terms of x1 and y1: Gaussian is a Gaussian. 2 22 22 k xy 2 xy 11 or 11 Ex(,11y ) exp2 w 0 Ex(,11 y ) exp 2 z 4 w1 2z z where: w1 kw00 w Angular divergence of a laser beam
The beam diverges. What will its divergence w1 angle be? 2w0
z z Recall that: w 1 w0
w z/w The half-angle will be: tan( ) 1 0 zz
The divergence half-angle will be: w 0 Gaussian Beams
•The Gaussian beam is the solution to the wave equation, or equivalently, the Fresnel integral, for a wave in free space with a Gaussian profile at z = 0.
x
The beam has a waist at z = 0, where the spot size is w0. It then expands to w = w(z) with distance z away from the laser. The beam radius of curvature, R(z), also increases with distance far away. Gaussian Beam Math
•The expression for a real laser beam's electric field is given by:
expikz i ( z ) xy22 xy 22 Exyz(, ,) exp 2 ik wz() w () z 2 Rz () •w(z) is the spot size vs. distance from the waist, Recall the •R(z) is the beam radius of curvature, and phase factor in (z) is a phase shift. front of the diffraction integrals. •This equation is the solution to the wave equation when we require that the beam be well localized at some point (i.e., its waist). Gaussian Beam Spot, Radius, and Phase
•The expressions for the spot size, radius of curvature, and phase shift: 2 wz() w0 1 z / zR 2 Rz z zR / z
(zzz ) arctan( /R )
where zR is the Rayleigh Range, and it's given by:
2 zwR 0 / Gaussian Beam Collimation
Twice the Rayleigh range is the distance over which the beam remains about the same size, that is, remains "collimated.“ 2 22/zwR 0 Collimation Collimation Waist spot Distance Distance size w0 = 10.6 µm = 0.633 µm ______Longer wavelengths .225 cm 0.003 km 0.045 km expand faster than 2.25 cm 0.3 km 5 km shorter ones. 22.5 cm 30 km 500 km ______
• Tightly focused laser beams expand quickly. • Weakly focused beams expand less quickly, but still expand. • As a result, it's very difficult to shoot down a missile with a laser. Coherence E Ai cos( it i )
Laser radiation is composed of waves at the same wavelength, which start at the same time and keep their relative phase as they advance. Interference Young Interference Experiment Michelson Interferometer For a completely coherent wave, defining its phase along particular surface at specific time, automatically determine its phase at all points in space at all time.
•Temporal Coherence is related to monochromaticity. •Spatial Coherence is related to directionality and uniphase wavefronts.
Coherence time tc ~ 1/, where is linewidth of laser radiation
Coherence Length (Lc) is the maximum path difference
which still shows interference: Lc = ctc = c/
Typical laser linewidths: from MHz to many GHz Record values ~ kHz Laser Types
Lasers can be divided into groups according to different criteria:
1. The state of matter of the active medium: solid, liquid, gas, or plasma. 2. The spectral range of the laser wavelength: visible, Infra-Red (IR), etc. 3. The excitation (pumping) method of the active medium: Optical pumping, electric pumping, etc. 4. The characteristics of the radiation emitted from the laser. 5. The number of energy levels which participate in the lasing process. Classification by active medium
• Gas lasers (atoms, ions, molecules) • Solid-state lasers • Semiconductor lasers – Diode lasers – Unipolar (quantum cascade) lasers • Dye lasers (liquid) • X-ray lasers • Free electron lasers Types of Lasers • Solid-state lasers have lasing material distributed in a solid matrix (such as ruby or neodymium:yttrium-aluminum garnet "YAG"). Flash lamps are the most common power source. The Nd:YAG laser emits infrared light at 1.064 nm. • Semiconductor lasers, sometimes called diode lasers, are pn junctions. Current is the pump source. Applications: laser printers or CD players. • Dye lasers use complex organic dyes, such as rhodamine 6G, in liquid solution or suspension as lasing media. They are tunable over a broad range of wavelengths. • Gas lasers are pumped by current. Helium-Neon lases in the visible
and IR. Argon lases in the visible and UV. CO2 lasers emit light in the far-infrared (10.6 mm), and are used for cutting hard materials. • Excimer lasers (from the terms excited and dimers) use reactive gases, such as chlorine and fluorine, mixed with inert gases such as argon, krypton, or xenon. When electrically stimulated, a pseudo molecule (dimer) is produced. Excimers lase in the UV. The Ruby Laser
Invented in 1960 by Ted Maiman at Hughes Research Labs, it was the first laser.
Ruby is a three-level system, so you have to hit it hard. Solid state lasers
Nd ions in YAG crystal host Gas Lasers
The laser active medium is a gas at a low pressure (A few milli-torr).
The main reasons for using low pressure are: •To enable an electric discharge in a long path, while the electrodes are at both ends of a long tube. •To obtain narrow spectral width not expanded by collisions between atoms.
The first gas laser was operated by T. H. Maiman in 1961, one year after the first laser (Ruby) was demonstrated.
The first gas laser was a Helium-Neon laser, operating at a wavelength of 1152.27 [nm] (Near Infra-Red). Pumping by electric discharge The Helium- Neon Laser Energetic electrons in a glow discharge collide with and excite He atoms, which then collide with and transfer the excitation to Ne atoms, an ideal 4-level system.
Argon ion laser
High power, but low efficiency Carbon Dioxide Laser
The CO2 laser operates analogously. N2 is pumped, transferring the energy to CO2. CO2 Laser
Gas lasers exist in nature!
•Stellar atmospheres •Planetary atmospheres •Interstellar medium CO2 laser in the Martian atmosphere
The atmosphere is thin and the sun is dim, but the gain per molecule is high, and the pathlength is long. Detuning from line center (MHz) Semiconductor lasers Conventional semiconductor laser
CB diode laser: material
VB
Quantum cascade laser: unipolar semiconductor laser using intersubband transitions CB QC- laser:
layer thickness Free electron lasers
Applications •Industrial applications •Medical (surgery, diagnostics) •Military (weapons, blinders, target pointers,…) •Daily (optical communications, optical storage, memory) •Research … Inertial confinement for nuclear fusion Laser Fusion D + T ==> 4He + n + 17.6 [MeV]