Regenerative oscillations, spatial-temporal single pulses and static inhomogeneous structures in optically bistable semiconductors

Balkarei, Yu. I.; Grigor'yants, A V; Rzhanov, Yuri; Elinson, M. I.

doi:10.1016/0030-4018(88)90054-5

Cited by 30 publications

(12 citation statements)

References 12 publications

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“…Hopf bifurcations have been found to induce oscillations in pulse solutions to a homogeneous reaction-diffusion system on a bounded domain [3,19,27,35] and in front solutions to a homogeneous reaction-diffusion system in which symmetry has been broken [15]. However, evidence from [5,33] indicates that the generation of edge oscillations in the Fabry-Perot interferometer is a genuinely inhomogeneous phenomenon.…”

Section: J E Rubinmentioning

confidence: 99%

Stability, bifurcations and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system

Rubin

1999

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We consider a class of inhomogeneous systems of reaction-diffusion equations that includes a model for cavity dynamics in the semiconductor Fabry–Pérot interferometer. By adapting topological and geometrical methods, we prove that a standing pulse solution to this system is stable in a certain parameter regime, under the simplification of homogeneous illumination. Moreover, we explain two bifurcation mechanisms which can cause a loss of stability, yielding travelling and standing pulses, respectively. We compute conditions for these bifurcations to persist when inhomogeneity is restored through a certain general perturbation. Under certain of these conditions, a Hopf bifurcation results, producing periodic solutions called edge oscillations. These inhomogeneous bifurcation mechanisms represent new means for the generation of solutions displaying edge oscillations in a reaction-diffusion system. The oscillations produced by each inhomogeneous bifurcation are expected to depend qualitatively on the properties of the corresponding homogeneous bifurcation.

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Section: J E Rubinmentioning

confidence: 99%

Stability, bifurcations and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system

Rubin

1999

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…We assume these conditions are met. Moreover, in this article we restrict ourselves by considering only the homogeneous distributions also in the plane of the semiconductor layer, leaving the transversal effects 4,5 to an additional study. Then, the description of the semiconductor etalon is reduced to the following two rate equations:…”

Section: Model Of a Semiconductor Etalonmentioning

confidence: 99%

“…Note that a considerable difference in the relaxation rates of the competing ONs, resulting in a splitting of the fast and slow stages in the dynamics of the nonlinear system, is a general condition for a discussed kind of regenerative pulsations. [1][2][3][4][5][6][7][8][9] In the fast stage, the response of the semiconductor etalon is determined only by the effective electron temperature T e which, computed as a function of the intensity of the incident light, I i , is shown in Fig. 3͑a͒.…”

Section: Fast Optical Bistabilitymentioning

confidence: 99%

“…1 Although this is quite a common phenomenon, not restricted by any particular type of device nor mechanism of ON, most foregoing studies, [2][3][4][5][6][7] including ours, [4][5][6][7] refer to a semiconductor etalon with electronic and thermal dispersive nonlinearities. In that case, carrier concentration, due to band filling in a narrow band gap semiconductor like InSb [3][4][5][6][7] or weakening of free-exciton resonance in a wide band gap semiconductor like GaAs, 2 and lattice temperature both effect the near absorption edge refractive index, but in opposite manners. The former plays the role of the fast variable responsible for optical bistability, while slow variation of the latter prevents either state from being stable, that ultimately results in the regenerative oscillations.…”

Section: Introductionmentioning

confidence: 99%

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Regenerative pulsations in semiconductor etalon due to competition between carrier generation and heating effects on band filling

Tolstikhin

Grigor'yants

Roer

1997

Journal of Applied Physics

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Competition between carrier concentration and effective temperature effects on the dielectric function of a degenerate semiconductor in a spectral range near its fundamental absorption edge is suggested as a mechanism for regenerative pulsations in a stationary pumped optical etalon. The origin of self-pulsations is similar to that in a bistable etalon with competing concentration and thermal optical nonlinearities, but, due to its purely electronic nature, the proposed mechanism provides a way for a much higher repetition frequency, probably in the GHz range. The model of the phenomenon and modeling examples are all related to a Fabry–Perot resonator filled with the bulk n+-In0.53Ga0.47As as an active medium.

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“…Turing models have been applied to such diverse areas as biology and chemistry [26], ecology [44,31,4,1], semiconductor physics [2], material sciences [51], hydrodynamics [52], astrophysics [34] and even economics [28].…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation of Competing Microorganisms in Sediments

Schmitz

Baurmann

Engelen

et al. 2007

Math. Model. Nat. Phenom.

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Abstract. We present a three species model describing the degradation of substrate by two competing populations of microorganisms in a marine sediment. Considering diffusion to be the main transport process, we obtain a reaction diffusion system (RDS) which we study in terms of spontaneous pattern formation. We find that the conditions for patterns to evolve are likely to be fulfilled in the sediment. Additionally, we present simulations that are consistent with experimental data from the literature. We focus on the interaction between pattern formation and non-uniform forcing, which naturally occurs in our model, since layers closer to the sea water are richer in particular chemicals than deeper layers. We find that heterogeneous forcing has a strong impact on the structures that evolve, leading to the formation of banded structures or even pulses instead of the well-known Turing patterns.

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Regenerative oscillations, spatial-temporal single pulses and static inhomogeneous structures in optically bistable semiconductors

Cited by 30 publications

References 12 publications

Stability, bifurcations and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system

Stability, bifurcations and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system

Regenerative pulsations in semiconductor etalon due to competition between carrier generation and heating effects on band filling

Pattern Formation of Competing Microorganisms in Sediments

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