激光原理课件chapter8

N R p
(8.4.2)
We should let t p , for t p , N(t) does not undergo any further appreciable increase and the pump power would be wasted through spontaneous decay. According to Eq.(8.4.2), to achieve a sufficiently large inversion, a large is required. 6
(5) When this photon number decreases to a sufficiently low value (roughly when f<f0), the pumping process again becomes dominant over the stimulated-emission process. The population inversion can now begin growing again and the whole series of events considered in features (1)-(5) repeats itself. The photon number f(t) is then seen to display a regular sequence of peaks (or laser spikes) of decreasing amplitude; consecutive peaks are approximately equally spaced in time. The output power therefore shows a similar time behavior. This aspect of regular oscillation for the output power is usually referred to as a damped relaxation oscillation.
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Principles and Technologies of lasers
Chapter 8 Transient Laser Behavior
Va is the volume of the mode in the active medium, N(t) is the population inversion at time t, f(t) is the photon number.
for t 0
where tp is the pump pulse duration. For a four-level laser, from Eq.(7.2.16a), population inversion
N (t ) N 1 exp( t / )
(8.4.1)
where is the upper laser level lifetime. Let dN/dt=0 in Eq.(7.2.16a), we can have
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Principles and Technologies of lasers
Chapter 8 Transient Laser Behavior
(4) After this photon peak, the population inversion is driven below Nc by the continuing high rate of stimulated emission. Thus the laser goes below threshold, and the photon number decreases.
Step-function pump rate
0, for / t 0 R p (t ) R p , for / t 0
(7.2.1) are nonlinear since they involve products of fN. Consequently, one must often resort numerical computation.
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N(t)Va N0Va=6.66x10
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[NVaf

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f(t)
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f0=5.8x10
0 0 2
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t (sec)
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Principles and Technologies of lasers
Chapter 8 Transient Laser Behavior
Since this operation involves switching the cavity Q-factor from a low to a high value, the technique is usually called Q-switching.
This technique allows one to generate laser pulses with a duration comparable to the photon decay time (i.e., from a few nanoseconds to a few tens of nanoseconds) and high-peak power (in the megawatt range).
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Principles and Technologies of lasers
Chapter 8 Transient Laser Behavior
8.4. Q-SWITCHING Suppose now that a shutter is introduced into the laser cavity. If the shutter is closed, laser action is prevented, so the value of the population inversion may far exceed the threshold population holding when the shutter is absent. If the shutter is now opened suddenly, the laser will exhibit a gain that greatly exceeds losses; stored energy may then be released in the form of a short and intense light pulse.
For a three-level system, the initial conditions are N(0)=-Nt, f(0)=fi (fi is some integer, e.g. 1) For a four-level system, the difference is N(0)=0. It means the time origin in the figure is shifted to time t=2s. There are five steps (1)-(5).
Principles and Technologies of lasers
Chapter 8 Transient Laser Behavior
8.1. INTRODUCTION The transient cases are divided into two categories: (1) relaxation oscillations, g-switching, gain-switching, and cavity-dumping (single-mode laser is involved) (2) mode-locking (many mode laser is involved), where the pump rate and/or cavity losses are time-dependent. 8.2. RELAXATION OSCILLATIONS
Principles and Technologies of lasers
Chapter 8 Transient Laser Behavior
Thus, Q-switching can be used effectively with electric-dipole-forbidden laser transitions, where t falls in ms (for most solid-state lasers and CO2 gas lasers). But semiconductor, dye and He-Ne, Ar are electric-dipole-allowed, t falls in ns, they are not be suitable for Q-switching. Fast switching------g is instantaneous Slow switching------g decays in a relatively long time
(1) After time t = 2 s, the population inversion keeps growing due to the pumping process while the photon number remains at its initial low value, as determined by quantum field fluctuations, until the inversion crosses the threshold value (N0Va = 6.66 x 10^15 in the figure). From this time on, roughly for t> 3.5 s, the population exceeds the threshold value, so the number of cavity photons can begin to grow. From either Eq. (7.2.16b) (four-level laser) or Eq. (7.2.24b) (quasi-three-level laser), we find in fact that df/dt > 0 when N> Nc, where Nc is the critical or threshold inversion. (2) After threshold is exceeded, the photon number requires some time to grow from its initial value (fi= 1) to a value, e.g., equal to the steady-state value (f0= 5.8 x 10^14 in the figure); meanwhile the population continues growing due to the pumping process. (3) When the photon number becomes large enough (roughly when f>f0), the stimulated emission process becomes dominant over the pumping process. The population then begins to decrease and, at the time corresponding to the maximum of f(t), N(t) is seen to have decreased to Nc. This can be readily shown from either Eq. (7.2.16b) or Eq. (7.2.24b), since, when df/dt = 0, one has N = Nc.