Self-pulsation

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Self-pulsation takes place at the beginning of laser action. As the pump is switched on, the gain in the active medium rises and exceeds the steady-state value. Then the number of photons in the cavity increases, depleting the gain below the steady-state value, and so on. The laser pulsates; the output power at the peaks can be orders of magnitude larger than that between pulses. After several strong peaks, the amplitude of pulsation reduces, and the system behaves as a linear oscillator with damping. Then the pulsation decays; this is the beginning of the continuous-wave operation The self-pulsation is a transient phenomenon in the continuous-wave lasers.

Contents

The simple model of self-pulsation deals with number X of photons in the laser cavity and number ~Y~ of excitations in the gain medium. The evolution can be described with equaitons:

~\begin{array}{rcl} {{\rm d}X}/{{\rm d}t}&=& ~ KXY-UX\\  {{\rm d}Y}/{{\rm d}t}&=& \!- KXY-VY+W~ \end{array} ~

where

~K = \sigma/(s t_{\rm r})~ is coupling constant,
~U = \theta L~ is rate of relaxation of photons in the laser cavity,
~V = 1/\tau~ is rate of relaxation of excitation of the gain medium,
~W = P_{\rm p}/({\hbar\omega_{\rm p}})~ is the pumping rate;
~t_{\rm r}~ is the round-trip time of light in the laser resonator,
~s~ is area of the pumped region (good mode matching is assumed);
~\sigma~ is the emission cross-section at the signal frequency ~\omega_{\rm s}~.
~\theta~ is the transmission coefficient of the output coupler.
~\tau~ is the lifetime of excitation of the gain medium.
Pp is power of pump absorbed in the gain medium (which is assumed to be constant).

Such equations appear in the similar form (with various notations for fariables) in textbooks on laser physics, for example, the nonography by A.Siegman [1]:

~ \begin{array}{l} X_0=\frac{W}{U}-\frac{V}{K}\\ Y_0=\frac{U}{K} \end{array}

Decay of small pulsation occurs with rate ~ \begin{array}{l} \Gamma=KW/(2U)\\ \Omega=\sqrt{w^2-\Gamma^2} \end{array}~

where w=\sqrt{KW-UV} Practically, this rate can be orders of magnitude smaller than the repetition rate of pulses. Ih this case, the decay of the self-pulsation in a real lasers is determined by other physical processes, not taken into account with the initial equations above.

Fig.4. Outpuf ipower of the pulsed laser versus time measired in millisecond. Red and green: two oscillograms of the microchil laser . Black: scaled prediction from the model with the oscillator Toda. All curves are centered to the maximum of the first spile.
Fig.4. Outpuf ipower of the pulsed laser versus time measired in millisecond. Red and green: two oscillograms of the microchil laser [2]. Black: scaled prediction from the model with the oscillator Toda. All curves are centered to the maximum of the first spile.

The only numerical soluitons were believed to exist for the strong pulsation, spiking. The strong spiking is possible, when U/V \ll 1, id est, the lifetime of excitations in the active emdium is large compared to the lifetime of photons inside the cavity. The spiking is possible at low dumping of self-pulsation, in the corresponding both parameters u and ~v^{}~ sohuld be small.

The intent of realization of the oscillator Toda at the optical bench is shown in Fig.4. The colored curves are oscillograms of two shouts of the quasi-continuous diode-pumped microchip solid-state laser on Yb:YAG ceramics, described by [2]. The thick black curve represents the approximation within the simple model with oscillator Toda. Only qualitative agreement takes place.

Change of variables ~ \begin{array}{l} X=X_0 \exp(x)~\\ Y=Y_0+X_0 y\\ t=z/w \end{array} lead to the equation for oscillator Toda, [3], [4]. At weak decay of the self-pulsation (even in the case of strong spiking]], the solution of corresponding equation can be appriximated through elementary function. The error of such approximation of the solution of the initial equaitons is small compared to the precition of the model.

The pulsation of real the ouptut of a real lasers in the transient regime usually show significant deviation from the simpel model above, although the model gives good qualitative description of the phenomenon of self-pulsaiton.

oscillator Toda
solid-state lasers
disk lasers

  1. ^ A.E.Siegman (1986). Lasers. University Science Books. ISBN 0-935702-11-3.
  2. ^ a b D.Kouznetsov; J.-F.Bisson, K.Takaichi, K.Ueda (2005). "Single-mode solid-state laser with short wide unstable cavity". JOSAB 22 (8): 1605-1619.
  3. ^ G.L.Oppo; A.Politi (1985). "Toda potential in laser equations". Zeitschrift fur Physik B 59: 111-115.
  4. ^ D.Kouznetsov; J.-F.Bisson, J.Li, K.Ueda (2007). "Self-pulsing laser as oscillator Toda: Approximation through elementary functions". Journal of Physics A 40: 1-18.
  • Koechner, William. Solid-state laser engineering, 2nd ed. Springer-Verlag (1988).

http://www.tcd.ie/Physics/Optoelectronics/research/self_pulse.php (self-pulsation in semiconductor lasers)

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