From coherent to incoherent hexagonal patterns in semiconductor resonators

Abstract

We find that hexagonal structures forming in semiconductor resonators can range from coherent patterns to arrangements of loosely bound spatial solitons, which can be individually switched. Such incoherent arrangements are stabilized by gradient forces, as evidenced by the stability of hexagonal structures with single-or multiple-soliton defects. We interpret the experimental observations by numerical simulations based on a model for a large aperture semiconductor microresonator.PACS 42.65.Sf, 42.65.Pc, 47.54.+r Pattern formation in the form of hexagonal structures was predicted years ago for resonators containing a reactive nonlinearity [1]. We have recently given the first proof of the phenomenon using semiconductor microresonators in the dispersive limit [2]. This kind of pattern formation was regarded as an important precursor of optical soliton formation, the latter being of technical importance for all-optical information processing [3]. We showed the existence of these bright and dark spatial solitons recently [4,5].Our finding, that individual bright spots of the hexagonal patterns can for certain parameters be "switched off" without apparent effects for the rest of the hexagonal pattern [2], caused a debate about whether such individually switchable "pixels" in a hexagonal pattern have soliton properties and more in general about the nature of these hexagonal patterns. In this article we clarify these questions by interpreting our experimental observations using numerics on a semiconductor resonator model [6].For completeness we repeat shortly the experimental arrangement: Light of wavelength near the semiconductor band edge (850 nm), generated by a continuous Ti:Al 2 0 3 -laser, irradiates an area of 50-100 µm diameter of the semiconductor resonator sample, with intensity of up to 3 kW/cm 2 . The sample is a quantum-well stack between Bragg mirrors of 99.7 % reflectivity [7]. The optical resonator length is about 3 µm so that a Fresnel number of several 100 is excited, sufficient for complex structure to form. The light is admitted to the sample for durations of a few µs (through a mechanical chopper, to limit thermal phenomena) repeated every ms.As the substrate, on which the resonator sample is grown, is opaque at the wavelength used, all observations are done in reflection. Either by taking ns-snapshots of the illuminated area, or by following the reflected intensity in particular points of the illuminated area as a function of time, using a fast photodiode. Details are given in [2,5].

Transverse Patterns in Nonlinear Optical Resonators

“…Patterns with hexagonal symmetry are also frequently found in such resonators [134,135]. Both types of pattern are familiar in hydrodynamic systems, such as systems showing Rayleigh-Bénard convection.…”

Spatial Semiconductor-Resonator Solitons

“…These observations of local switching indicate that these hexagonal patterns are not coherent pattern: the individual spots are rather independent, even at this dense packing where the spot distance is about the spot size. These experimental findings can be understood in the frame of the model (1) [27]. Fig.…”

Spatial resonator solitons

“…The individual spots are spatial solitons: they are independent, even at this dense packing where the spot distance is about the spot size. These experimental findings can be understood in the frame of the model (1) [8] . FIG.…”

“…We note that the transition from the coherent low intensity pattern to the incoherent higher intensity structure proceeds through stripe patterns as shown in FIG. 18 (b) [8]. For the intensity of FIG.…”

“…A simple periodic pattern such as a hexagonal field structure in the cross section of a nonlinear resonator can disintegrate into spatial resonator solitons [8]. A closer examination of these structures shows many common traits with biological structures.…”