Self-pulsation takes place at the beginning of
laser action.As the pump is switched on, the gainin 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.
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:
is coupling constant,
is rate of relaxation of photons in the
is rate of relaxation of excitation of the
is the round-trip time of light in the
is area of the
pumped region(good mode matchingis assumed);
emission cross-sectionat the signal frequency.
transmission coefficientof the output coupler.
lifetimeof excitationof 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
textbooks on laser physics,for example, the nonography by A.Siegmancite book
publisher=University Science Books
id= ISBN 0-935702-11-3] :
Decay of small pulsation occurs with rate
wherePractically, this rate can be orders of magnitude smaller than the repetition rate of pulses. In this case, the decayof the self-pulsation in a real lasers is determined by other physical processes, not taken into account with the initial equations above.
The transient regime can be important for the quasi-continuous lasers that needs to operate in the pulsed regime, for example, to avoid the overheatingcite journal
coauthors=J.-F.Bisson, K.Takaichi, K.Ueda
title=Single-mode solid-state laser with short wide unstable cavity
JOSAB|volume=22| issue=8| pages=1605–1619
600px|right|thumb|Fig.4._Output_power_of_the_pulsed_laser_versus_time_measured_in_milliseconds.Red_and_green:_two_oscillograms_of_the_microchip_laser_cite journal|url=http://www.iop.org/EJ/abstract/-search=15823442.1/1751-8121/40/9/016| author=D.Kouznetsov|coauthors=J.-F.Bisson, J.Li, K.Ueda|title=Self-pulsing laser as oscillator Toda: Approximation through elementary functions|journal=
Journal of Physics A|volume=40|pages=1–18| year=2007|doi=10.1088/1751-8113/40/9/016] .Black: scaled prediction from the model with the oscillator Toda.All curves are centered to the maximum of the first spike.]
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 Todaat 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 laseron ceramics, described bycite journal|url=http://www.iop.org/EJ/abstract/-search=15823442.1/1751-8121/40/9/016| author=D.Kouznetsov|coauthors=J.-F.Bisson, J.Li, K.Ueda|title=Self-pulsing laser as oscillator Toda: Approximation through elementary functions|journal= Journal of Physics A|volume=40|pages=1–18| year=2007|doi=10.1088/1751-8113/40/9/016] .The thick black curve represents the approximation within the simple model with oscillator Toda.Only qualitative agreement takes place.
Change of variableslead to the equation for
oscillator Toda,cite journal|url=http://worldcat.org/issn/0722-3277| author=G.L.Oppo|coauthors=A.Politi|title=Toda potential in laser equations
Zeitschrift fur PhysikB|volume=59|pages=111–115| year=1985|doi=10.1007/BF01325388] ,cite journal|url=http://www.iop.org/EJ/abstract/-search=15823442.1/1751-8121/40/9/016| author=D.Kouznetsov|coauthors=J.-F.Bisson, J.Li, K.Ueda|title=Self-pulsing laser as oscillator Toda: Approximation through elementary functions|journal= Journal of Physics A|volume=40|pages=1–18| year=2007|doi=10.1088/1751-8113/40/9/016] .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.
oscillator Toda solid-state lasers disk lasers
*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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