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Annales de Physique

Optical bistability in a laser containing a saturable absorber

Smail Djabi, H. Boudoukha, M. Djabi

Published Jan 1, 2007• 3 citations
Publisher

Abstract

In this work, the theory of optical bistability for the homogeneously broadening of a nonlinear absorber inside Fabry-Perot interferometer is treated. The theoretical influence of the resonator losses on the optical bistability is examined mainly in the cases for which losses depend on both the mode frequency and the density of photons. On the basis of the Rate Equation Approach (REA), we analytically and numerically solved this type of equation for stationary case.

DOI
10.1051/anphys:2008008

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In this work, the theory of optical bistability for the homogeneously broadening of a nonlinear absorber inside Fabry-Perot interferometer is treated. The theoretical influence of the resonator losses on the optical bistability is examined mainly in the cases for which losses depend on both the mode frequency and the density of photons. On the basis of the Rate Equation Approach (REA), we analytically and numerically solved this type of equation for stationary case.
Our work concerns the study of the effect of the optical bistability and multistability in a laser saturable absorber of a Fabry Perot resonator with a homogenous widening. We theoretically studied the influence of the losses of the resonators on the optical bistability by examining mainly the cases where the losses of the resonator depend on the position of the emitted mode of a frequency and the losses of the resonator depend on the density of photons We examined the influence of the physical parameters of laser saturable absorber such as the coefficient of saturation and pumping of the medium active and absorbing on the density of the photons for each loss We showed the effect of the optical bistability and multistability then we analyzed the linear stability of the solutions obtained.
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.
The optical bistability (OB) behavior of single-mode Fabry- Perot lasers containing saturable absorber (LSA) is presented on the basis of the rate equations with allowance for spontaneous emission and spatial hole-burning. Special attention is paid to the case of dominant inhomogeneous broadening in both Lorentzian and Gaussian models. The OB occurrence conditions are clearly displayed in phase diagrams. The influence of the main LSA parameters on OB characteristics as well as on OB curves' stability are investigated in detail. Some practical suggestions for optimizing the bistable operation in LSA are also given.
The characteristics of the mode intensity and conditions for occurrence of optical bistability in a ring laser with a saturable absorber are considered. The rate equation approximation method is used to find analytic expressions for these characteristics. It is shown that changes in such physical parameters as the homogeneous and inhomogeneous broadening, coefficients of relaxation of amplifying and absorbing cells, etc. cause changes in the range of existence of optical bistability or a hysteresis cycle. The influence of inhomogeneous broadening and of spontaneous emission near the lasing threshold on the appearance of optical bistability is demonstrated for the single-mode regime.
A simple mathematical model to describe the action of a saturable absorber in a laser cavity (LSA) was developed. The approach considered here takes in a phenomenological way into account the essential physical processes which makes it possible to determine the principal parameters in a LSA and their influences on the optical bistability. We will study theoretically optical bistability in a trimodale laser containing a saturable absorber in the case that the active medium and absorber show a homogeneous broadening. We determine the densities of photons as function of the pumping of the active medium and analyze the linear stability of the solutions obtained.