Pattern Formation in the Transverse Section of a Laser with a Large Fresnel Number

Abstract

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Transverse Patterns in Nonlinear Optical Resonators

“…The predicted laser TW patterns have been observed in experiments with large-Fresnel-number cavities [126][127][128]. The TW solutions are also found in passive resonators described by the same order parameter equation, such as nondegenerate optical parametric oscillators (OPOs) [35,129].…”

Coupling of Polarization and Spatial Degrees of Freedom of Highly Divergent Emission in Broad-Area Square Vertical-Cavity Surface-Emitting Lasers

“…We interpret these intriguing observations by taking into account that reflections of waves at the side aperture and DBRs couple the polarization orientation of wave vectors already in linear order. Therefore, the 90 rule reported in [1] is valid only in a tiny range of transverse wave vectors parallel to one of the boundaries. Our argument shows also that single-wave number solutions are not possible, which provides justification for the phenomenological construction of superposition states to explain the scared structures in [4].…”

“…The main mechanism determining the length scale of spatial structures for broad-area devices is provided by the alignment of the cavity resonance and the gain maximum [1,2]. If the cavity resonance is redshifted versus the gain maximum (positive detuning >0) tilted waves are favored to on-axis emission, which leads to pattern formation.…”

“…with the polarization direction being orthogonal to k ? [1]. We will refer to this as the ''90 rule'' in the following.…”

“…Vertical-cavity surface-emitting lasers (VCSELs) are a special kind of semiconductor lasers which combine a high potential for applications with intricate dynamical behavior of fundamental interest in physics. The coherence of broad-area VCSELs is limited by the appearance of high order transverse modes [1,2] being a manifestation of selforganization in nonequilibrium systems [3]. Particularly interesting is that these structures open also a simple access for studying the relation between wave and ray optics, quantum and classically trajectories, respectively, in billiard problems [4,5], where the reflective boundaries are created by refractive index steps determining the size of the active aperture.…”