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Quantum Electronics

Effect of the cross-relaxation rate on the transverse radiation dynamics of a wide-aperture laser

A P Zaikin, Nonna E. Molevich

Published Aug 31, 2004• 9 citations
Publisher

Abstract

The effect of a finite polarisation relaxation time on the transverse structure of the optical field of a wide-aperture laser is considered. The conditions are found for the emergence of periodic autowaves for positive and negative frequency detuning. These conditions are shown to depend strongly on the cross-relaxation rate. It is established that the dynamics of finite-aperture lasers at high cross-relaxation rates is satisfactorily described by simplified models in which the polarisation is adiabatically eliminated.

DOI
10.1070/qe2004v034n08abeh002663

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The effect of a finite polarisation relaxation time on the transverse structure of the optical field of a wide-aperture laser is considered. The conditions are found for the emergence of periodic autowaves for positive and negative frequency detuning. These conditions are shown to depend strongly on the cross-relaxation rate. It is established that the dynamics of finite-aperture lasers at high cross-relaxation rates is satisfactorily described by simplified models in which the polarisation is adiabatically eliminated.
The processes of the formation of optical field structures in the transverse profile of wide-aperture laser radiation are studied within the model described by the system of Maxwell-Bloch equations. The main types of instabilities appearing above the second lasing threshold and corresponding mechanisms controlling the laser dynamics at negative frequency detuning are considered. The characteristic lasing modes and conditions of the spontaneous formation of transverse optical structures are determined.
The regions of stability of homogeneous generation regimes in a wide-aperture laser with a saturable absorber, including a semiconductor laser with a vertical output of radiation, are determined depending on the relative relaxation rate of carriers in active and passive media and on the frequency detunings of working transitions in these media with a resonant frequency of radiation, taking into account its polarization state. The excitation thresholds for relaxation and polarization oscillations are determined within the four-level model. Keywords: wide-aperture laser, saturable absorber, relaxation and polarization oscillations
The space-time behavior of a wide-gain-section, single-longitudinal-mode laser is investigated. Analysis of the full Maxwell-Bloch model in one transverse spatial dimension identifies a traveling-wave solution beyond the first laser threshold, for positive detuning from resonance, which appears to be a globally attracting state of the laser. On the negative-detuning side we observe an initial bifurcation to a homogeneous plane-wave state. A second instability threshold can be identified by linearizing about the respective solutions for both positive and negative detuning. We also find that the standard approach to adiabatic elimination, whereby the polarization equation is adiabatically eliminated, can lead to a spurious high-transverse-wave-number instability in the reduced equations. The derivation of an adiabatically reduced set of equations to remove the instability on the positive-detuning side is a nontrivial matter.