LASERS. Amplifiers: Broad-band communications (avoid down-conversion)

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1 L- LASERS Representative applications: Amplifiers: Broad-band communications (avoid down-conversion) Oscillators: Blasting: Energy States: Hydrogen atom Frequency/distance reference, local oscillators, illuminators, transmitters, CD/DVD players, sensors Laser machining, labeling, weapons, laser fusion (pellet compression). Peak > 0 5 W, average > kw; high intensity because I E ionization, 0 e.v free electron ground state -3.6 e.v. 40 MHz i i Water vapor H O H O H - States: electronic (visible, UV) vibrational (visible) bending (IR) rotational (microwave) Chromium atoms in lattice (e.g. ruby), Erbium atoms in glass

2 STIMULATED EMISSION AND ABSORPTION Rate Equation: Assume: Two-level system, E > E, and n i = atoms m - in state i Then: dn /dt = - An - B(n n ) [m - s - ] (collisionless system) Spontaneous emission Induced emission Spontaneous emission, states i to j: A ij = ω 3 D ij (/3hεc 3 ) [s - ] (Decay time τ A = A - ) D ij [C m] = quantum dipole moment (electric or magnetic) Note: τ A ω -3 Stimulated emission and absorption: E - - Photon flux density F: F = [photons m s ] η o hf B coefficient: B ij =Fσ ij Fg ij (f) A ij /ω 3 Line shape g ij (f): very brief visible τ s, long microwave τ s g(f) = πδ 4 ( Δ f) ij f (f f o) n A n (Lorentzian) n g ij(f)df = f o g ij (f) Δf f B n L-

3 ENERGY LEVEL POPULATION AND WIDTH Linewidth Broadening Mechanisms: Electron energy E in semiconductor Conduction band Δf Isolated atoms ΔE = hf f o f Level Populations Kinetic Temperature T k : Thermal equilibrium Boltzmann distribution: ni nj Valence band Energy band curvature broadens the linewidth = e ( i j) E E kt T = kinetic temperature if collisions dominate T = radiation temperature if radiation dominates f ij n i n j if T rad, n > n if T rad < 0 k Collisions phase changes, Fourier transform Δf E i [J] State energy n e -E/kT n L-3

4 BASIC LASER AMPLIFIER PHYSICS Amplification Process: Optical fiber input amplification, exponential growth Intensity-limited amplification [Each is a separate atom or molecule; need n > n for amplification] Pump (repopulates level ) hf hf hf 4hf 6hf amplification linear growth n replacement-rate limited amplification Amplification frequency f [Hz]: E E = hf [J], h = [Js] P(z) exponential growth P(z) P in e (g-α)z linear z (g is gain, α is attenuation) L-4

5 Two-Level Lasers: PUMPING OF LASERS Radiation pumping alone never yields n > n (some -level lasers spatially isolate n group) Three-Level Lasers: Pumping the -3 transition yields n n 3 Large A 3 populates L so n >> n n 3 0 More levels can utilize transitions with larger A s Large A 3 fills L, and large A 4 empties L 4 Laser Power Efficiency (P out /P in ): Pump Pump f pump >f o Pump lasing Pump Lasing? 3 Large A 3 lasing A 3 A 4 Intrinsic efficiency: η i =f L /f p (P nhf [W]) < 3 A B/A : η B = B /(A B ) < 3 A 3 A/A 3: η A = A 3 /(A 3 A 3 ) < Total efficiency: η = η i η B η A A Pump photons s - B >> A ω 3, so x-ray B =Fσ lasers need pump power hfb hfa ω 4 dn /dt = - An - B(n n ) 3 4 L-5

6 Laser Oscillation: LASER OSCILLATORS Lossless: Lossy: With perfect mirrors at both ends a lossless amplifier must oscillate and saturate L Amplifier Round-trip gain must exceed round-trip loss (threshold condition); gain pump power P p, so need P p >P thresh P T Mirrors: Exit mirror has power transmission coefficient T > 0 At threshold, Gain Loss, so: P ( T)e (g-α)l P round-trip gain = e (g-α)l /( T) for oscillation Q-switching: Set mirror reflectivity low round-trip gain < threshold. When laser is fully pumped, increase mirror reflectivity over threshold, yielding very large Q-switched pulse P out P thresh P pump L-6

7 L-7 Resonances LASER RESONANCES Oscillator Resonant Frequencies f: Laser line shape, width = Δf Cavity resonances Laser Output Spectrum: mλ m = L (mirrors short circuits) λ L cm m =, f m = (N = refractive index) m LN f c i fi = LN 0 8 Hz (00 MHz) for -meter fiber; 50 GHz line spacing for 0.5-mm diodes If every atom can amplify at all frequencies, then the strongest round-trip gain wins line narrowing (homogeneous line broadening) If atoms can amplify only a portion of the band, then all lines over threshold can yield output (inhomogeneous line broadening) Line narrowing

8 L-8 EXAMPLES OF LASERS Electrically Pumped Solid-State Lasers: Forward-biased GaAs p-n junction injects carriers into conduction band Compact (grain of sand) ~50 percent efficiency >00 W/cm for arrays mw/micron for diodes -000 mw typical Astrophysical Masers: E Active region Conduction p-type band electrons - holes E F n-type Valence band Mirrors at both ends z Stellar Pumping: UV-IR pumped: H O, OH, CO, etc. Interstellar collisions: OH, etc. Chemical lasers: Weapons (high energy, fast) E F star

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