Model For Optical Bistability Research Articles

A mathematical model of optical bistability and the multiplicity of its solutions

Abstract The problem of high-intensity laser pulse interaction with a semiconductor under the condition of the light energy nonlinear absorption is considered. Mathematical model of an optical bistability based on re-normalization of forbidden energy zone of a semiconductor because of the induced electric field is presented. The multiplicity of the problem solutions at the Neumann boundary conditions statement is discussed and ways of its overcoming are proposed. The effective method for the numerical solution of the problem is developed and computer simulation results are presented.

ANALYTICAL MODEL FOR OPTICAL BISTABILITY IN LASER WITH SATURABLE ABSORBER

In this paper, we develop a theoretical model that accurately describes the nonlinear phenomenon of optical bistability in Fabry-Perot laser containing a saturable absorber "LSA". We present an analytical model for optical bistability in a LSA. The physics of optical bistability in a classical optical resonant system such as Fabry-Perot etalon has been well-established, and can be described by simple analytical models. The photon intensities were determined as a function of the pumping rate of the active medium, and we analyzed the linear stability of the stationary solutions obtained.

Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials

Optical bistability at nanoscale is a promising way to realize optical switching, a key component of integrated nanophotonic devices. In this work we present an analytical model for optical bistability in a metal nano-antenna involving Kerr nonlinear medium based on detailed analysis of the correlation between the incident and extinction light intensity under surface plasmon resonance (SPR). The model allows one to construct a clear picture on how the threshold, contrast, and other characteristics of optical bistability are influenced by the nonlinear coefficient, incident light intensity, local field enhancement factor, SPR peak width, and other physical parameters of the nano-antenna. It shows that the key towards low threshold power and high contrast optical bistability in the nanosystem is to reduce the SPR peak width. This can be achieved by reducing the absorption of metal materials or introducing gain media into nanosystems.

A Model for Optical Bistability in a Hybrid Semiconductor Photonic Crystal Structure

A new model for optical bistability in a photonic crystal structure closed to a semiconductor is presented. It is found that increase in the strength of self-interaction can destroy this nonlinear phenomenon whereas a small variation of this interaction from low initial value can control the area of the bistable loop.

Hexagonal patterns in optical bistability.

The mean-field model of optical bistability in a ring cavity is extended to include diffraction in two transverse dimensions. Nonlinear analysis in the neighborhood of the instability of the homogeneous solution indicates the formation of stable hexagonal patterns, and this is confirmed by numerical simulation, with reasonable quantitative agreement. Simulations with higher excitation show defect structures and complex dynamical patterns.

Dynamical equations for optical bistability in multiple quantum well structures

We formulate a model which governs the dynamical evolution of an optically bistable system based on multiple quantum well structures. The electric field is assumed near resonance with an excitonic line. Under conditions of adiabatic elimination of the exciton density, and using commonly adopted expressions for the dielectric susceptibility, the set of equations is shown to be fully equivalent to the well known model for optical bistability in two-level systems with adiabatic elimination of the atomic polarization. This result allows to exploit the extended literature on two-level atom optical bistability, for application to the case of multiple quantum well devices.

Model for optical bistability in GaAs/AlGaAs Fabry–Perot étalons including diffraction, carrier diffusion, and heat conduction

A new model for optical bistability in layered semiconductor Fabry–Perot étalons is presented. The model accounts for diffraction, carrier diffusion, and thermal conduction. Assuming that the spot size and the thickness of the nonlinear layer are smaller than the diffusion length of the carriers, a simplified model is derived that has been used to design bistable AlGaAs étalons with improved thermal properties.

Model of optical bistability in the quantum-well self-electro-optic-effect device

Optical bistability of the multiple-quantum-well self-electro-optic-effect device is studied using a detailed model for a P–I–N photodiode under a constant voltage bias. By solving the Maxwell equations with the experimentally determined absorption function, bistability curves are obtained as functions of the incident frequency and of the bias potential. These results show good agreement with previously reported experimental data.

A model for optical bistability in semiconductors

A theoretical model of the excitation of a semiconductor by laser is considered. The novelty of this work is that, as distinguished from previous works, the effect of electron-hole interactions on optical bistability is included analytically.

Atomic correlations in driven optical systems.

We consider the one-mode quantum-statistical model of optical bistability, and show that atom-atom correlations are negligible in the good-cavity limit, in all effects that can be described by a linearized treatment. In the light of this result, we discuss the concept of ``atomic cooperation'' in quantum optical systems. In the purely absorptive case, the atomic polarization exhibits a squeezing effect which arises both in the good- and in the bad-cavity limit. This phenomenon has the same origin of the squeezing effect in resonance fluorescence.

Asymptotic relations and period doubling bifurcations in a mean-field model of optical bistability

We analyze the domain of instability of a single-mode, mean-field model of optical bistability and propose asymptotic relations that govern the speed of bifurcation of the phase-space trajectories and the critical slowing down in the neighborhood of each bifurcation threshold.

Oscillatory instabilities leading to "optical turbulence" in a bistable ring cavity

A model for optical bistability in a ring cavity which exhibits periodic self-oscillation and period-doubling bifurcations leading to aperiodic behavior---"optical turbulence"---is discussed. For two two-dimensional maps describing cavity dynamics in an adiabatic limit (Ikeda's model), period-doubling sequences are studied numerically and found to be consistent with Feigenbaum's conjecture of universality. In the dispersive limit unstable regions are mapped as a function of round-trip losses and cavity detuning. From analytic expressions for this parameter dependence minimum power requirements for self-oscillation are estimated. A new instability for absorptive systems in a detuned cavity is identified.

Self-pulsing and chaos in a mean-field model of optical bistability

We have discovered and analyzed periodic and chaotic self-pulsing behavior in a single-mode, mean-field model of optical bistability. Our results indicate that one route to chaos taken by this system is a sequence of period doubling bifurcations. With the help of a Poincaré map we have identified the strange attractor that is responsible for the non-periodic self-pulsing.

The relation between the Bonifacio-Lugiato and the Ikeda instabilities in optical bistability

The main purpose of this paper is to show that the Ikeda instability emerges within the framework of the Bonifacio- Lugiato ring cavity model of optical bistability if the operating conditions are such that the cavity transit time is much longer than the atomic relaxation times. We also show that, while the Ikeda instability disappears in the mean field limit (α L ⪡ 1, T ⪡ 1), it can persist for a laser with injected signal.

Derivation of a master equation for optical bistability

We sketch the proof of a rigorous master equation for a model of optical bistability and obtain its Fokker Planck equation in the coherent state representation.