Self-pulsation

This article may require cleanup to meet Wikipedia's quality standards. The specific problem is: formatting, grammar, coherence. Please help improve this article if you can. (September 2012) (Learn how and when to remove this message)

Self-pulsation is a transient phenomenon in

.

Equations

The simple model of self-pulsation deals with number ${\displaystyle X}$ of photons in the laser cavity and number ${\displaystyle ~Y~}$ of excitations in the

. The evolution can be described with equations:

${\displaystyle ~{\begin{aligned}{{\rm {d}}X}/{{\rm {d}}t}&=KXY-UX\\{{\rm {d}}Y}/{{\rm {d}}t}&=-KXY-VY+W\end{aligned}}}$

where ${\displaystyle ~K=\sigma /(st_{\rm {r}})~}$ is coupling constant,
${\displaystyle ~U=\theta L~}$ is rate of relaxation of photons in the

,
${\displaystyle ~V=1/\tau ~}$ is rate of relaxation of excitation of the ,
${\displaystyle ~W=P_{\rm {p}}/({\hbar \omega _{\rm {p}}})~}$ is the pumping rate;
${\displaystyle ~t_{\rm {r}}~}$ is the round-trip time of light in the ,
${\displaystyle ~s~}$ is area of the pumped region (good mode matching is assumed);
${\displaystyle ~\sigma ~}$ is the emission cross-section at the signal frequency ${\displaystyle ~\omega _{\rm {s}}~}$.
${\displaystyle ~\theta ~}$ is the transmission coefficient of the output coupler.
${\displaystyle ~\tau ~}$ is the lifetime of .
${\displaystyle P_{\rm {p}}}$ is power of pump absorbed in the (which is assumed to be constant).

Such equations appear in the similar form (with various notations for variables) in

Steady-state solution

${\displaystyle {\begin{aligned}X_{0}&={\frac {W}{U}}-{\frac {V}{K}}\\Y_{0}&={\frac {U}{K}}\end{aligned}}}$

Weak pulsation

Decay of small pulsation occurs with rate

${\displaystyle {\begin{aligned}\Gamma &=KW/(2U)\\\Omega &={\sqrt {w^{2}-\Gamma ^{2}}}\end{aligned}}}$

where

${\displaystyle w={\sqrt {KW-UV}}}$

Practically, this rate can be orders of magnitude smaller than the repetition rate of pulses. In 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.

Strong pulsation

The transient regime can be important for the quasi-continuous lasers that needs to operate in the pulsed regime, for example, to avoid the overheating.[2]

The only numerical solutions were believed to exist for the strong pulsation, spiking. The strong spiking is possible, when ${\displaystyle U/V\ll 1}$, i.e., the lifetime of excitations in the active medium 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 ${\displaystyle u}$ and ${\displaystyle ~v^{}~}$ should be small.

The intent of realization of the

. Only qualitative agreement takes place.

Toda Oscillator

Change of variables

${\displaystyle {\begin{aligned}X&=X_{0}\exp(x)\\Y&=Y_{0}+X_{0}y\\t&=z/w\end{aligned}}}$

lead to the equation for Toda oscillator.^[4][3] At weak decay of the self-pulsation (even in the case of strong spiking), the solution of corresponding equation can be approximated through elementary function. The error of such approximation of the solution of the initial equations is small compared to the precision of the model.

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

See also

• Solid-state lasers
• Disk laser

References

• Koechner, William. Solid-state laser engineering, 2nd ed. Springer-Verlag (1988).

External links

• https://web.archive.org/web/20070514062058/http://www.tcd.ie/Physics/Optoelectronics/research/self_pulse.php (self-pulsation in semiconductor lasers)