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. 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.
Self-pulsation is a transient phenomenon in continuous-wave lasers.

Equations

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

where

is coupling constant,

is rate of relaxation of photons in the laser cavity,

is rate of relaxation of excitation of the gain medium,

is the pumping rate;

is the round-trip time of light in the laser resonator,

is area of the pumped region (good mode matching is assumed);

is the emission cross-section at the signal frequency .

is the transmission coefficient

Transmission coefficient

The transmission coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered...

 of the output coupler

Output coupler

An output coupler is a partially reflective mirror used in lasers to extract a portion of the laser beam from the optical resonator....

.

is the lifetime of excitation

Excited state

Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....

 of the gain medium.

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 variables) in textbook

Textbook

A textbook or coursebook is a manual of instruction in any branch of study. Textbooks are produced according to the demands of educational institutions...

s on laser physics

Laser Physics

Laser Physics is an international scientific journal published by Nauka/Interperiodica. It is distributed through the Springer.-Topics covered:The journal specializes in laser physics, but also publishes papers about:...

,
for example, the nonography by A.Siegman

Steady-state solution

Weak pulsation

Decay of small pulsation occurs with rate

where


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
.
The only numerical solutions were believed to exist for the strong pulsation, spiking.
The strong spiking is possible, when , id est,
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
and
should be small.

The intent of realization of the oscillator Toda

Oscillator Toda

In physics, the Toda oscillator is special kind of nonlinear oscillator; it is vulgarization of the Toda field theory, which is a continuous limit of Toda's chain, of chain of particles, with exponential potential of interaction between neighbors. These concepts are named afterMorikazu 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

Integrated circuit

An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

solid-state laser

Solid-state laser

A solid-state laser is a laser that uses a gain medium that is a solid, rather than a liquid such as in dye lasers or a gas as in gas lasers. Semiconductor-based lasers are also in the solid state, but are generally considered as a separate class from solid-state lasers .-Solid-state...

 on Yb:YAG ceramics, described by.
The thick black curve represents the approximation within the simple model with oscillator Toda

Oscillator Toda

In physics, the Toda oscillator is special kind of nonlinear oscillator; it is vulgarization of the Toda field theory, which is a continuous limit of Toda's chain, of chain of particles, with exponential potential of interaction between neighbors. These concepts are named afterMorikazu Toda...

.
Only qualitative agreement takes place.

Oscillator Toda

Change of variables

lead to the equation for oscillator Toda

Oscillator Toda

In physics, the Toda oscillator is special kind of nonlinear oscillator; it is vulgarization of the Toda field theory, which is a continuous limit of Toda's chain, of chain of particles, with exponential potential of interaction between neighbors. These concepts are named afterMorikazu Toda...

,
,
.
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.

External links

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

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