SummaryKramers-Kronig Relation (KK relation)"（0)kyk'=k[1The Significance of x(v)21GainSaturationin HomogeneousLaserMediaY0(0)r(u)1+1,11(0)tvIu-v k(A0/2)/1+1./1.0GainconstantuniformlydropsinhomogeneousbroadeningcaseGain Saturation in Inhomogeneous Laser MediaYo(U)Tpivr(u)1+I/10-Dk(A0/2)/1+1,110SpectralHoleBurningEffect
Summary Kramers-Kronig Relation (KK relation) The Significance of c(n) Gain Saturation in Homogeneous Laser Media Gain Saturation in Inhomogeneous Laser Media 1 / ( ) ( ) ( ) 0 s + I I = 0 0 | | ( / 2) 1 / s I I − + Gain constant uniformly drops in homogeneous broadening case s 1 I / I ( ) ( ) 0 + = Spectral Hole Burning Effect 0 0 | | ( / 2) 1 / s I I − + 2 2 2 "( ) ] 2 '( ) ' [1 n k i n k k c c = + −
Lecture 8Chapter V Theory of Laser Oscillationand Its Control in Continuous andPulsed RegimesHighlightsFabry-PerotLaser2.OscillationFrequency3.OptimumOutputCouplingMode Locking5. Q-Switch Laser
Lecture 8 Chapter V Theory of Laser Oscillation and Its Control in Continuous and Pulsed Regimes Highlights 1. Fabry-Perot Laser 2. Oscillation Frequency 4. Mode Locking 5. Q-Switch Laser 3. Optimum Output Coupling
$5.1Fabry-PerotLaserMirror1Mirror2-3ik'31k-2ikTtrrEtrrEettrrEe-2ik'l-iktrEeQtrE-ikt,t,E,e-in!'E,t,E,eeInputPlaneOuputPlanepropogateconstantfarawayfrom(0k-iα/2XFresonantk'=k+kik22n?2Complexdielectricsusceptibility2nx(o)= x-ixfromlasertransitionaQα:distributedpassivelossesofthemedium-i2kE, =tt,E,e-ik+rre
§5.1 Fabry-Perot Laser Ei Ei t 1 ik l i t E e ' 1 − ik l i t t E e ' 1 2 − ik l i t r E e ' 1 2 ik l − i t r E e 2 ' 1 2 − ik l i t rr E e 2 ' 1 1 2 − ik l i t rr E e 3 ' 1 1 2 − ik l i t t rr E e 3 ' 1 2 1 2 − l Mirror 1 Mirror 2 Input Plane Ouput Plane 2 2 "( ) 2 '( ) ' 2 2 c c i n ik n k = k + k − − : distributed passive losses of the medium l e − [1 ] 2 4 ' 2 2 1 2 ' 1 2 ' 1 2 = + + + −i k l −i k l −i k l t i E t t E e rr e r r e k −i / 2 propogate constant far away from resonant c() = c'−ic" Complex dielectric susceptibility from laser transition
$5.1Fabry-Perot Laser-ik'lik+k)l(-α)112t,t,e1EE,=E-i2k'l2i(k+△k)l(-α)rire2kx"(の)x(o)Ak=k(N, -N.g(u)n8元m2nspIn population inversion medium:-α>0E, >E;However,inaFabry-Perotetalon(1- R)2(1-R)22 +4Rsin(S/2)I≤I2i(k+△k)lαOscillationrre
− = − = − + − − + − − − i k k l l i k k l l i k l i i k l t i rr e e t t e e E rr e t t e E E 2 ( ) ( ) 1 2 ( ) ( ) / 2 1 2 2 ' 1 2 ' 1 2 1 1 §5.1 Fabry-Perot Laser ( ) 8 ( ) "( ) 2 2 2 2 1 c g n t N N n k s p = − = − 2 2 '( ) n k k c = (1 ) 4 sin ( / 2) (1 ) 2 2 2 R R R I I i t − + − = In population inversion medium: − 0 Et Ei However, in a Fabry-Perot etalon t i I I 1 2 ( ) ( ) 1 2 = − i k+k l − l rr e e Oscillation
$ 5.1 Fabry-Perot LaserThresholdCondition(gainbecomesequaltothelosses)Phasecondition2(k + △k)l = 2m元rre(r-α) =1()=α-_ln rr2GainconditionPopulationInversioncondition28元mspN,=(N2-N)aInr2g(0)22Otherform8πn*"tN,=(N2-N),= 7t.g(0)rrt.is call decay time of light intensity
§5.1 Fabry-Perot Laser 1 ( ) 1 2 = − l rr e Threshold Condition (gain becomes equal to the losses) Phase condition 2(k + k)l = 2m Gain condition 1 2 ln 1 ( ) rr l = − ln ) 1 ( ( ) 8 ( ) 2 1 2 2 2 1 rr g l n t N N N s p t = − t = − ( ) 8 ( ) 3 2 2 2 1 c t g n t N N N c s p t = − t = Other form Population Inversion condition − 1 2 ln 1 1 rr n l c t c tc is call decay time of light intensity