Lecture 15 Stimulated Emission Devices- Lasers! Stimulated emission and light amplification! Einstein coefficients! Optical fiber amplifiers! Gas laser and He-Ne Laser! The output spectrum of a gas laser! Laser oscillation conditions! Semiconductor lasers, (laser diodes)! Rate equation*! Light emitters for optical fiber communications
Stimulated Emission! Electrons can absorb photons from medium! Accelerated electrons emit light to return their ground state! Spontaneous emission occurs through a relaxation process! A photon can stimulate an electron to radiate in phase (coherent)! Two levels is not enough to create population inversion!!
The LASER Principle! Cr +3 ions in Al 2 0 3 crystal (Ruby Laser)! Transition from E 1 to E 3 is driven by optical pumping.! From E 3, Cr +3 ions rapidly decay to energy level E 2.! The states E 2 are long-lived state,, they quickly become populated! Population inversion can be achieved when Cr +3 ions are accumulated in E 2 state.! A spontaneously emitted photon can trigger an avalanche of coherent photons! Optical gain or photon amplification is achieved! Process is repeated.
3-Level Lasers: The Ruby Laser! A more realistic energy diagram for the Cr 3+ ion in the ruby crystal (Al 2 O 3 ).! The laser action needs an optical cavity to reflect the stimulated radiation back and forth to build-up the total radiation within the cavity.! A typical construction for a ruby laser, which uses an elliptical reflector, and has the ruby crystal at one focus and the pump light at the other focus.
4-Level Laser System a Pulsed A three energy level laser system Ruby Laser Pulsed or CW Mode A four energy level laser system Nd 3+ :YAG laser (Yttrium Aluminate Garnate, Y 3 Al 5 O 11 ) YAG
Einstein Coefficients ρ(ν) is the photon energy density per unit frequency
Einstein Coefficients at Equilibrium
Einstein Coefficients in Equilibrium Consider equilibrium Boltzmann statistics R 12 = R 21 N 2 / N 1 = exp[-(e 2 - E 1 )/k B T] Planck s black body radiation law ρ eq (υ) = 8πhυ 3 c 3 exp hυ k B T 1
Einstein Coefficients in Equilibrium Consider equilibrium Boltzmann statistics R 12 = R 21 N 2 / N 1 = exp[-(e 2 - E 1 )/k B T] Planck s black body radiation law ρ eq (υ) = 8πhυ 3 c 3 exp hυ k B T 1 Black Body Radiation exp exp hυ k B T hν k B T = 8πhυ 3 1 c 3 ρ eq (υ) +1 = N 1 N 2 N 1 = N 2 ( ) ( ) +1 C υ υ ρ eq where C( υ) = 8πhυ 3 c 3
Einstein Coefficients in Equilibrium Consider equilibrium Boltzmann statistics R 12 = R 21 N 2 / N 1 = exp[-(e 2 - E 1 )/k B T] Planck s black body radiation law ρ eq (υ) = 8πhυ 3 c 3 exp hυ k B T 1 Black Body Radiation
Einstein Coefficients in Equilibrium B 12 = B 21 A 21 B 21 = 8πhυ 3 c 3 R 21 (stim) R 21 (spon) = B N 21 2ρ(υ) A 21 N 2 = B 21ρ(υ) c 3 = A 21 8πhυ ρ(υ) 3 R 21 (stim) R 12 (absorp) = N 2 N 1
Einstein Coefficients at Non-Equilibrium
Population Inversion & LASERs
Spontaneous Decay Time R 12 = -dn 1 /dt and R 21 = -dn 2 /dt R 21 = rate at which N 2 is decreasing by spontaneous and stimulated emission Consider N 2 changes by spontaneous emission dn 2 /dt = -A 21 N 2 = - N 2 /t sp, t sp = 1/A 21 = spontaneous decay time; or the lifetime of level E 2.
Absorption Cross Section Total Power Absorbed AΔI = -( Iσ ab N 1 )AΔx ΔI IΔx ab N1 = σ = α
Emission Cross Section ΔI IΔx = σ em N 2
Optical Gain Coefficient Definition g = ΔI IΔx net Optical Gain G = exp( gl)
Erbium Doped Fiber Amplifier (EDFA)
Erbium Doped Fiber Amplifier (EDFA)! Optical amplifier is based on erbium (Er +3 ion)- doped fiber amplifier.! Medium causes Stark Effect in silica-aluminate(sio 3 -Al 2 O 3 ) or silica-germania (SiO 3 -GeO 2 )! Energy bands occurs! E 1 -E 0 (30-40meV) population ratio 1 to 4. E 3 is narrow. E 2 is long-lived energy level (10ms)
Erbium Doped Fiber Amplifier (EDFA) Typical absorption and emission cross sections, s ab and s em respectively, for Er 3+ in a silica glass fiber doped with alumina (SiO 2 -Al 2 O 3 ). (Cross section values for the plots were extracted from B. Pedersen et al, J. Light. Wave Technol. 9, 1105, 1991. The spectral characteristics of gain, G in db, for a typical commercial EDF, available from Fibercore as IsoGain TM fiber.forward pumped at 115 mw and at 977 nm. The insertion losses are 0.45 db for the isolator, 0.9 db for the pump coupler and splices.