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Известия Самарского научного центра Российской академии наук

Устойчивость поперечных оптических структур в широкоапертурных лазерах

Анчиков Дмитрий Александрович, Кренц Антон Анатольевич, Пахомов Антон Владимирович

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

The work deals with numerical and analytical research of optical field patterns in transverse light profile of wide-aperture lasers. On the basis of numerical simulation of Maxwell-Bloch’s system of equations spatiotemporal dynamic has been observed at positive and negative frequency detuning.

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Вестник Саратовского государственного технического университета•Jan 1, 2010•0 citations
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.
Pattern formation in large-aspect-ratio single-mode inhomogeneously broadened lasers is studied by means of the integro-differential Maxwell-Bloch equations. As the inhomogeneous linewidth increases, the neutral stability curve shows a relaxation in the traveling wave selection allowing structures with different sizes to grow. We have performed numerical simulations with a simplified model based on a few discrete groups of atoms at different resonant frequencies to observe transverse dynamics above threshold for good and bad cavity configurations. We obtain, in general, that close to threshold the inhomogeneous broadening leads to a more complex pattern in comparison to the homogeneous broadening case. At higher pumpings, a stabilization in the number of spatial frequencies taking part in the transverse pattern is found. The influence of the laser aperture on temporal dynamics is also studied. It is shown how the typical self-pulsing regime present in single-mode inhomogeneously broadened lasers is destroyed for a wide enough aperture.
It is well known that transverse intensity profiles of lasers may show a nontrivial spatial structure. Usually, depending on the degree of symmetry, the spatial patterns have been associated with modes of a passive resonator or combinations of them which cause oscillations in the laser intensity (mode beating).1 It was recently shown2 that the fluctuations may be due, instead, to the nonlinear coupling between atoms and the field. Here we show that a spontaneous symmetry-breaking process is also at the origin of the formation of complex spatiotemporal dynamics in which oscillations at a single frequency, quasiperiodicity, and chaos may coexist within in the same spatial structure. We compare our experimental results with those obtained from bifurcation theory and numerical integration of the Maxwell–Bloch equations. The transition from a simple (Gaussian) profile to a complex (turbulent) profile is studied by means of the average intensity patterns, frequencies, and phases of the local intensity and cross-correlation functions.
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.
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.