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RP ProPulse – Numerical Simulation of Pulse Propagation

Example Case: Active Mode Locking

In this simple example, we consider an actively mode-locked laser. The laser resonator is described in the script as follows:

resonator: ring
* Crystal: gain(l) = g(l)
   [P_sat_av = P_sat_g, KK = 0]
* Modulator: mod(t) = t_mod(t)
* OC: T_out = T_OC
resonator end

This refers to some variable values, the definitions of which are not shown here. The gain function g(l) has a limited bandwidth of 0.2 nm, and the modulator modulates the resonator round-trip losses with 100 MHz and peak losses of 10%.

The initial pulse duration was chosen to be somewhat longer than in the steady state. It is found that the steady-state value of the pulse duration agrees with the result of Kuizenga–Siegman theory (see the diagram below).

evolution of pulse duration

The script code required for that diagram is pretty simple:

; ---------------------------
diagram 1:
"Evolution of Pulse Parameters"
x: 0, 20000
"number of round trips", @x
y: 0, 300
"pulse duration (ps)", @y
legpos 200, 160
tau_th := 0.45 *
  ((0.5 * T_OC) / (0.25 * A_mod))^0.25
  / sqrt(f_mod * df_g)
 { theoretical value for steady-state
   pulse duration according to 
   Kuizenga-Siegman theory }
f: tau_th / ps,
  "steady-state value from theory",
  style = dashed, width = 3
f: (getpulse(x / rt_per_step,0);
    tau()) / ps,
  "numerical simulation",
  color = blue, width = 3

Also, we can see the temporal pulse profile after 2000 resonator round trips (which are calculated within a few seconds on an ordinary PC):

profile of output pulse

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