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Journal of Optics B Quantum and Semiclassical Optics

Modulational instabilities and cavity solitons in semiconductor microcavities

L. A. Lugiato, Lorenzo Spinelli, G. Tissoni, Massimo Brambilla

Published Jan 1, 1999• 14 citations
Publisher

Abstract

We consider a model recently proposed, describing a multiple quantum well semiconductor microcavity driven by a coherent holding beam. We discuss here some general features of stationary modulational instabilities affecting the system. By generalizing a method introduced in a previous paper on two-level atoms in optical cavities, we give a detailed description of the stationary instabilities in the parameter space. The modulational instability can be related to the presence of stable cavity solitons, which have been predicted in this system. Therefore we have a helpful tool to research the best parametric conditions for stable cavity solitons, a very demanding task due to the large number of parameters. Finally, we show that our analysis can be extended to more general models, describing a nonlinear diffusive material inside an optical cavity with a general form of the interaction terms.

DOI
10.1088/1464-4266/1/1/010

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We consider a model recently proposed, describing a multiple quantum well semiconductor microcavity driven by a coherent holding beam. We discuss here some general features of stationary modulational instabilities affecting the system. By generalizing a method introduced in a previous paper on two-level atoms in optical cavities, we give a detailed description of the stationary instabilities in the parameter space. The modulational instability can be related to the presence of stable cavity solitons, which have been predicted in this system. Therefore we have a helpful tool to research the best parametric conditions for stable cavity solitons, a very demanding task due to the large number of parameters. Finally, we show that our analysis can be extended to more general models, describing a nonlinear diffusive material inside an optical cavity with a general form of the interaction terms.
Light propagation in a 2-D array of coupled optical cavities with Kerr nonlinearity driven by a plane holding beam is numerically studied. Optical bistability together with its modulational instability (MI) are investigated, and 2-D discrete cavity solitons are simulated. These simulations revealed the switching on/off of the solitons along with the ability of a proper Gaussian beam (GB) to control their positions. Soliton-soliton and soliton-GB interactions are considered, and finally, all-optical NOR , XNOR, and NAND gates are proposed as realized by this device.
We proposed a formalism enables us to describe accurately the interaction between the electromagnetic field and linear as well as nonlinear polarizations from a quantum well in a microcavity, considering on the same footing either true guided modes or Fabry-Perot quasi-modes. We showed that stable pulses propagating along quantum wells in such a microcavity can be sustained by cavity modes for two kinds of nonlinear mechanisms at different time scales. The first mechanism is ultrafest two-level unharmonicity leading to the self-induced transparency for 2π-pulses. In this case, we could derive soliton velocity as well as other pulse characteristics and compare them to bulk ones. We found pulse energies in the picojoule range. We gave some hint of the advantages of quantum wells and possible ways to flexibly design a system in view of given pulse requirements. The second mechanism is the slower third-order nonlinearity. In this case the linear polarizability of the quantum well giving rise to the so-called vacuum Rabi splitting has to be included and new split models have to be obtained before nonlinearity is taken into account. The obtainmnet of the soliton solution is found to depend critically on the sign and magnitude of the curvature of the new dispersion relation for which suggestive examples are given. In view of experiments, laser pulses for self-induced transparency seem available. For Kerr nonlinearity, the detailed effect of inhomogeneity on splitting and linewidth has to be studied in more detail to evaluate the potential of this mechanisms in novel systems for soliton generation.
We consider a passive optical cavity containing a photonic crystal and a purely absorptive two-level medium. The cavity is driven by a superposition of two coherent beams forming a periodically modulated pump. Using a coupled mode reduction and direct numerical modeling of the full system we demonstrate the existence of bistability between uniformly periodic states, modulational instabilities and localized structures of light. All are found to exist within the conduction band of the photonic material. Moreover, contrary to similar previously found intra-band structures, we show that these localized structures can be truly stationary states.
Summary form only given. Owing to their robustness and potential applications in all-optical information transmission, processing, and storage schemes, there is growing interest in optical solitons. Recently, it was shown that bright solitons can exist in semiconductor Fabry-Perot resonators at accessible power levels. These cavity solitons or soliton pixels may serve as basic units in information storage systems because they can be easily and individually set and erased. In previous studies, it was assumed that the photon energy is near the exciton resonance. For these energy levels and high carrier densities, an effective two-level system approach that relates the complex susceptibility changes linearly to the carrier density is appropriate. If one reduces the photon energy further, many-particle effects come into play, and the linear dependence ceases to hold. In this work, we use an appropriate, phenomenological material model that accounts for all prominent many-particle effects such as exciton formation, screening, gap renormalization, and band filling. It turns out that the diversity of soliton structures is richer than previously demonstrated.
We study the nonlinear dynamics of the interaction of two-level atoms and a selected mode of a high- Q cavity with frequency modulation analytically and numerically. In the absence of modulation, the corresponding semiclassical Heisenberg equations for the expectation values of the collective atomic observables and the field-mode amplitudes allow, in the rotating wave approximation and in the strong-coupling limit, an exact solution with arbitrary detuning. Using this solution, we detect the coherent effect of trapping of the population of atomic levels and of trapping of the number of photons in the cavity. The explanation for this effect lies in the destructive interference of the atomic dipoles and the field mode. The integrable version of the system of equations exhibits a separatrix near which a stochastic layer is formed when modulation is introduced. The width of the layer is found to gradually increase with degree of modulation, and finally it fills the entire energy-permissible volume of the phase space. We show that the rotating wave approximation does not hinder the formation of Hamiltonian chaos in cavity semiclassical electrodynamics. The calculation of the maximum Lyapunov indices of nonlinear (in this approximation) equations of motion as functions of the modulation frequency δ and the frequency of natural Rabi oscillations of the atom-field system, Ω, suggests that Hamiltonian chaos appears first in the area of the fundamental parametric resonance, δ /2Ω≃1. Parametric instability increases with increasing modulation and decreasing detuning from the atom-field resonance, generating at exact resonance new areas of chaos corresponding to multiple parametric resonances. The results of numerical experiments and estimates of the characteristic parameters show that Rydberg atoms placed in a high- Q microwave cavity are possible objects for observing parametric instability and dynamical chaos.