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Physical Review A

Local-field effects in pattern formation in large-aspect-ratio lasers

Óscar G. Calderón, E. Cabrera, M. A. Antón, J. M. Guerra

Published Apr 22, 2003• 11 citations
Publisher

Abstract

Transverse effects in the laser dynamics due to near dipole-dipole interactions are studied considering the presence of permanent electric dipole moments. The semiclassical two-level Maxwell-Bloch equations are used and a single longitudinal mode is assumed. A traveling wave is selected at threshold when the sum of the cavity detuning and the near dipole-dipole parameter is larger than zero. As a consequence of this, transverse pattern can occur even when the laser frequency is larger than the frequency of the atomic transition. Also, a cutoff in the laser field spectrum arises. We found that the near dipole-dipole interactions significantly modify the stability picture of the traveling waves. Numerical simulations have been carried out and the effect of the near dipole-dipole on the pattern formation is addressed.

DOI
10.1103/physreva.67.043812

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Transverse effects in the laser dynamics due to near dipole-dipole interactions are studied considering the presence of permanent electric dipole moments. The semiclassical two-level Maxwell-Bloch equations are used and a single longitudinal mode is assumed. A traveling wave is selected at threshold when the sum of the cavity detuning and the near dipole-dipole parameter is larger than zero. As a consequence of this, transverse pattern can occur even when the laser frequency is larger than the frequency of the atomic transition. Also, a cutoff in the laser field spectrum arises. We found that the near dipole-dipole interactions significantly modify the stability picture of the traveling waves. Numerical simulations have been carried out and the effect of the near dipole-dipole on the pattern formation is addressed.
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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.
Transverse effects in the laser threshold, originated by electronic-vibrational coupling in the active centers, are analyzed theoretically by means of the semiclassical two-level Maxwell-Bloch equations. A single longitudinal mode is considered. It is found that the first laser threshold suffers modifications depending on the electronic-vibrational coupling strength. This coupling imposes certain conditions for the selection of a particular transverse spatial state and provides the minimum wavelength that can appear in the transverse pattern. The nature of the bifurcation and the stability of the homogeneous and critical traveling waves are analyzed.
We analyze the effect of injected atomic coherence on transverse patterns of a broad area laser by means of the semiclassical two-level Maxwell-Bloch equations. A single longitudinal mode is considered. The injected atomic coherence forces a spatially homogeneous profile to appear and locks the field phase to a single value. Above a pump threshold value a very rich scenario of patterns is developed. Near threshold we find stationary patterns such as rhombic and hexagonal lattices. Well above threshold nonstationary patterns such as complex highly ordered vortex lattices traveling along the cross section, and nearly traveling waves appear.
Complex order-parameter equation descriptions of pattern evolution in large-aspect-ratio two-level and Raman lasers are derived systematically as solvability conditions in a multiple-scales asymptotic expansion of the original Maxwell-Bloch laser equations in powers of a small parameter. These amplitude equations, although strictly valid near threshold for lasing, are shown to capture the essential features of pattern instability and evolution well beyond lasing threshold. A technical difficulty that can arise in the Raman laser, namely, subcriticality of the bifurcation near the critical wave number, is not addressed in the present paper and the order-parameter equations as derived are valid only when this situation does not arise. Analytical expressions for long-wavelength phase instabilities of the underlying traveling-wave pattern, which appears as the natural nonlinear lasing mode when the detuning of the laser from the gain peak is positive, are obtained from the coefficients of a Cross-Newell phase equation. Phase and amplitude instability boundaries, when computed via the original laser equations, the complex order-parameter equations and the phase equation, are shown to be consistent for all cases studied with the exception of the case when a subcritical bifurcation approaches the critical wave number kc{\mathit{k}}_{\mathit{c}}kc​.
In this paper we analyze the transverse pattern-forming characteristics of a two-level and single-longitudinal-mode laser. The corrections to the classical empty cavity modes due to pumping and losses are specifically considered, leading to different excitation rates for the different transverse modes. The near-threshold excitation rates provide a selection mechanism that is studied and compared to the results from numerical simulations of the Maxwell-Bloch equations. \textcopyright{} 1996 The American Physical Society.