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The Temporal Coherence Time and the Spatial Coherence Length Phys 322 Chapter 13 Lecture 36 Modern optics Lasers Reminder: Please complete the online course evaluation Last lecture: Review discussion (no quiz) 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 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 Gain spectrum can be very broad Broadening of the gain spectrum Laser Cavity Laser Cavity Longitudinal cavity modes Longitudinal modes in Fabry-Perot cavity Transverse modes Challenge: How to make a laser operate in a single basic transverse mode? Laser radiation - properties •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 L = 2 m R2 He-Ne Laser: W = 1 mW, r = 2 mm, R = r + L /2 = 2.1 mm, I = 8 mW/cm2 = 0.1 mrad 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 2zz 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: w1 w0 w zw/ The half-angle will be: tan( ) 1 0 zz The divergence half-angle will be: w0 Laser radiation - properties •Monochromaticity •Directionality •Coherence 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. Coherence review Conditions for interference 1) For producing stable pattern, the two sources must have nearly the same frequency. 2) For clear pattern, the two sources must have similar amplitude. 3) For producing interference pattern, coherent sources are required. Temporal coherence: Time interval in which the light resembles a sinusoidal wave. (~10 ns for natural light) Longitudinal coherence length: lc= ctc. Spatial coherence: longitudinal and transverse The correlation of the phase of a light wave between different locations. The coherence time is the reciprocal of the bandwidth (related to monochromaticity). The coherence time is given by: c 1/v where is the light bandwidth (the width of the spectrum). Sunlight is temporally very incoherent because its bandwidth is very large (the entire visible spectrum). Lasers can have coherence times as long as about a second, which is amazing; that's >1014 cycles! The Temporal Coherence Time and the Spatial Coherence Length The temporal coherence time is the time the wave-fronts remain equally spaced. That is, the field remains sinusoidal with one wavelength: Temporal Coherence Time, c The transverse spatial coherence length is the distance over which the beam wave-fronts remain flat: Since there are Transverse Spatial two transverse Coherence Length dimensions, we can define a coherence area. Spatial and Spatial and Temporal Temporal Coherence Coherence: Temporal Coherence; Spatial Beams can be Incoherence coherent or only partially coherent (indeed, Spatial even incoherent) Coherence; in both space and Temporal time. Incoherence Spatial and Temporal Incoherence Interference Young Interference Experiment Coherence (chapter 12) Completely incoherent waves: no interference fringes Completely coherent waves: interference fringes best pronounced Add glass plate Laser Laser Add glass plate Lamp Lamp temporal coherence Coherence I = I1 +I2 + I12 I E t E t 12 1 2 T cross-correlation I E t E t 12 1 2 T Temporal coherence length is reflected in cross-correlation Visibility I I Visibility: V max min Imax Imin 2 I1 I2 V 12 I1 I2 Complex degree of coherence: E t E*t 1 2 T 12 2 2 E1 E2 T T Coherent limit: |12| = 1 Incoherent limit: |12| = 0 Partial coherence: 0<|12|<1 Examples | | = 0.062 |12| = 0.703 |12| = 0.132 12 Spatial coherence: extended source For double slit: ab V sinc l The spatial coherence depends on the emitter size and its distance away. The van Cittert-Zernike Theorem states that the spatial coherence area Ac is given by: D22 c d 2 where d is the diameter of the light source and D is the distance away. Basically, wave-fronts smooth out as they propagate away from the source. Starlight is spatially very coherent because stars are very far away. The Michelson stellar interferometer 1. Case of double star (equal intensities) angular distance interference disappears when: h 0 between the stars 2 angular diameter 2. Single star, interference disappears when: h 1.22 0 of the star Betelgeuse -Orion, the first star for which diameter was established in 1920 h 1.22 0 h = 121”, = 570 nm 0 22.6108 rad 0.047" From known distance: diameter = 240 million miles (280 times larger than sun) Michelson Interferometer 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/DVD/BlueRay 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 Semiconductor lasers: Diode laser Semiconductor lasers Conventional semiconductor laser CB diode laser: material VB Quantum cascade laser: unipolar semiconductor laser using intersubband transitions CB QC- laser: layer thickness 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) 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].
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