1、,Summary,Kramers-Kronig Relation (KK relation),The Significance of c(n),Gain Saturation in Homogeneous Laser Media,Gain Saturation in Inhomogeneous Laser Media,Gain constant uniformly drops in homogeneous broadening case,Spectral Hole Burning Effect,Lecture 8,Chapter V Theory of Laser Oscillation an
2、d 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,5.1 Fabry-Perot Laser,: distributed passive losses of the medium,5.1 Fabry-Perot Laser,In population inversion medium:,However, in a Fa
3、bry-Perot etalon,Oscillation,5.1 Fabry-Perot Laser,Threshold Condition (gain becomes equal to the losses),Phase condition,Gain condition,Other form,Population Inversion condition,tc is call decay time of light intensity,5.1 Fabry-Perot Laser,Numerical Example: Population Inversion,He-Ne Laser,Dopple
4、r Broadening Width,Calculate,Transmission,Reflectivity,5.1 Fabry-Perot Laser,5.2 Oscillation Frequency,Many frequencies exist, we want to know the frequency also satisfied gain condition :,mth resonance frequency of the passive Fabry-Perot etalon,5.2 Oscillation Frequency,is the center frequency of
5、the atomic lineshape function,Assume that the cavity length is adjusted so that one of its resonance frequencies is very close near . We hope that the oscillation frequency will also be close to .,is a slowly varying function of when,Oscillation Frequency,5.2 Oscillation Frequency,Passive resonator
6、linewidth :,Frequency Pulling,Round trip phase shift,5.3 Three- And Four-Level Lasers,In four-level laser system,Lifetime t2 is much longer than the lifetime t1,Oscillation starts as long as,Population on level 1 can be neglected,In three-level laser system,Population on level 1 cannot be neglected,
7、Oscillation starts at,5.3 Three- And Four-Level Lasers,So that the pump rate at threshold in a three-level laser must exceed that of a four-level laser,Minimum expenditure power of three-level system,Minimum expenditure power of four-level system,When t2=tsp, the above two equations are equal to the
8、 power emitted through fluorescence by atoms within the volume at threshold. It is referred as the critical fluorescence power.,In case of four-level laser,5.3 Three- And Four-Level Lasers,Numerical Example: Critical Fluorescence Power of an Nd3+:Glass Laser,Calculate:,5.4 Power in Laser Oscillators
9、,When the pumping intensity is increased beyond threshold point, laser will break into oscillation and emit power. We will derive the relation of laser output power to the pumping intensity.,Rate Equations (four level system),Steady state solution,Necessary condition for population inversion,5.4 Pow
10、er in Laser Oscillators,Effective pumping rate,In order to keep population inversion unchange, assume Wi is allowed to increase once R exceeds its threshold value,Below oscillation threshold,and,When R increase until,Gain Loss and steady state assumption violate,5.4 Power in Laser Oscillators,In ide
11、alized model,and,Critical fluorescence power,Threshold pumping rate,Example:,5.5 Optimum Output Coupling in Laser Oscillators,Total loss can be attributed to two different sources:,(a) The inevitable residual loss due to absorption and scattering in the laser media and mirrors, as well as diffractio
12、n losses in the finite diameter reflectors;,(b) The useful loss due to coupling of output power through the partially transmissvie reflector.,as small as possible,(1) Zero coupling (no transmission), threshold will be minimum, pe will be maximum, but no output; (2) Large coupling, threshold will be
13、larger than pumping level, oscillation will cease, output is zero again; (3) Exist an optimum coupling value, where output is maximum.,5.5 Optimum Output Coupling in Laser Oscillators,Recall oscillation condition,In case of small loss,Pe is the total power given off by the atoms due to stimulated emission,5.5 Optimum Output Coupling in Laser Oscillators,Total loss per pass,Output power is thus as,Recall,Cross section,5.5 Optimum Output Coupling in Laser Oscillators,Maximizing Po with respect to T,
