1. Chapter 12. Multimode and Transient Oscillation
Pulsed oscillation : Relaxation oscillation, Q-switching, Mode locking ?
12.2 Rate Equations for Intensities and Populations
(10.5.8) =>
( ), G1=G2=0, A => G21

2. 12.3 Relaxation Oscillation
Assume, N1<<N2 => g(n) ~ s(n)N2
12.3 Relaxation Oscillation
Steady-state solution ;

3. Perturbation method ;
(12.2.5) =>
since
Similarly,

4. where
Sol)
where
Intensity :
homework

5. 12.4 Q Switching <Qualitative explanation>
Q switching : A way of obtaining short, powerful pulses
Sudden switching of the cavity Q(loss) from a low(high) value to high(low) value.
Principle of Q switching : Suppose we pump a laser medium inside a very lossy
cavity. Laser action is precluded even if the upper level population N2 is
pumped to a very high value (nearly small signal value). Suddenly we lower
the loss to a value permitting laser oscillation. We now have a small-signal
gain much larger than the threshold gain for oscillation.
<Qualitative explanation>
Define,
(12.2.5a) =>

6. Pumping and spontaneous decay of N2 during the pulse interval is negligible,
since the pulse is short enough.
(12.2.5b) =>

7. 12.5 Methods of Q Switching - Rotating mirrors w ~ 10,000 rpm
- Electro-optical switching
- Saturable absorber (Passive Q-switching)
; saturate the absorption (bleaching)

8. 12.7 Phase-Locked Oscillators
Mode Locking : Locking together of the phases of many cavity longitudinal modes.
=> Even shorter laser pulse than can be achieved by Q switching.
<Phase-locked harmonic oscillator>
Displacements of N harmonic oscillators with equally spaced frequencies ;
where,
The sum of the displacements ;

9. # Peaks : at
# Temporal width :
# Maximum total oscillation amplitudes equals to N times the amplitude of a single oscillator
# This maximum amplitudes occur at intervals of time T
# This temporal width of each spike get sharper as N is increased

10. 12.8 Mode Locking <Shortest pulse length>
The maximum number of longitudinal modes :
The shortest pulse length :
Examples)
1) He-Ne laser,
2) Ruby laser,
3) Dye laser,

11. <Mode-locked laser oscillation>
Electric field of m-th longitudinal mode :
where,
Assume, the mode fields all have the same magnitude and polarization, and also
=> Total electric field in the cavity ;
where,

12. Similarly,
where,

13. has maxima occurring at
cavity round trip time

14. 12.9 AM Mode Locking AM(amplitude modulation) :
modulation index
AM(amplitude modulation) :
is modulated periodically
If W=D (wm+1-wm=pc/L), each mode becomes strongly coupled to its nearest-neighbor modes, and it turns out that there is a tendency for the modes to lock together in phase.

15. 12.10 FM Mode Locking FM(frequency modulation) :
The phase of the fieldis modulated periodically
: Bessel function of the first kind of order n
control !

16. 12.11 Methods of Mode Locking
1) Acoustic loss modulation (AO modulator)
diffraction
acoustic wave
# A standing wave in a medium induces the refractive index variation ;
# Diffraction angle ;
# Modulation frequency ;
control !
ex) L ~ 1 m => D ~ 9x108 rad/s
=> ns=D/4p = 75 MHz (quartz oscillator)

17. 2) Electro-optical phase modulation (Pockels cell)
Refractive index of electro-optic medium ;
where,
: applied electric field
where,
3) Saturable absorbers
Absorption coefficient of saturable absorber ;
Suppose that there are two oscillating cavity modes ;

18. Time averaged intensity :
Intensity is modulated
=> Absorption coefficient can be also modulated