1. Summary Kramers-Kronig Relation (KK relation)
Gain Saturation in Homogeneous Laser Media
Gain constant uniformly drops in homogeneous broadening case
Gain Saturation in Inhomogeneous Laser Media
Spectral Hole Burning Effect

2. Lecture 8
Chapter V Theory of Laser Oscillation and Its Control in Continuous and Pulsed Regimes
Highlights
1. Fabry-Perot Laser
2. Oscillation Frequency
3. Optimum Output Coupling
4. Mode Locking
5. Q-Switch Laser

3. §5.1 Fabry-Perot Laser : distributed passive losses of the medium
Mirror 1
Mirror 2
Input Plane
Ouput Plane
propogate constant far away from resonant
Complex dielectric susceptibility from laser transition
: distributed passive losses of the medium

4. §5.1 Fabry-Perot Laser Oscillation In population inversion medium:
However, in a Fabry-Perot etalon
Oscillation

5. tc is call decay time of light intensity
§5.1 Fabry-Perot Laser
Threshold Condition (gain becomes equal to the losses)
Phase condition
Gain condition
Population Inversion condition
Other form
tc is call decay time of light intensity

6. §5.1 Fabry-Perot Laser Numerical Example: Population Inversion
He-Ne Laser
Doppler Broadening Width
Calculate

7. §5.1 Fabry-Perot Laser
Transmission
Reflectivity

8. §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

9. §5.2 Oscillation Frequency
is the center frequency of 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

10. §5.2 Oscillation Frequency
Passive resonator linewidth :
Frequency Pulling
Round trip phase shift

11. In four-level laser system In three-level laser system
§5.3 Three- And Four-Level Lasers
Pump
transition
Ground state 1 2 E2 t2 3
Energy E1 t1
E1 >> kT
Four-level System
Three-level System
In four-level laser system
In three-level laser system
Lifetime t2 is much longer than the lifetime t1
Population on level 1 cannot be neglected
Population on level 1 can be neglected
Oscillation starts at
Oscillation starts as long as

12. §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 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

13. Numerical Example: Critical Fluorescence Power of an Nd3+:Glass Laser
§5.3 Three- And Four-Level Lasers
Numerical Example: Critical Fluorescence Power of an Nd3+:Glass Laser
Calculate:

14. §5.4 Power in Laser Oscillators
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

15. §5.4 Power in Laser Oscillators
Effective pumping rate
Below oscillation threshold
and
When R increase until
Gain > Loss and steady state assumption violate
In order to keep population inversion unchange, assume Wi is allowed to increase once R exceeds its threshold value

16. §5.4 Power in Laser Oscillators
In idealized model
and
Critical fluorescence power
Threshold pumping rate
Example:

17. Total loss can be attributed to two different sources:
§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 diffraction losses in the finite diameter reflectors;
as small as possible
(b) The useful loss due to coupling of output power through the partially transmissvie reflector.
(1) Zero coupling (no transmission), threshold will be minimum, pe will be maximum, but no output; (2) Large coupling, threshold will be larger than pumping level, oscillation will cease, output is zero again; (3) Exist an optimum coupling value, where output is maximum.

18. Recall oscillation condition
§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

19. §5.5 Optimum Output Coupling in Laser Oscillators
Total loss per pass
Output power is thus as
Recall
Cross section

20. Maximizing Po with respect to T
§5.5 Optimum Output Coupling in Laser Oscillators
Maximizing Po with respect to T