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Soviet Journal of Quantum Electronics

Bistability of the soliton amplitude in a ring resonator with nonlinearly absorbing media

Alexander A. Zabolotskii

Published Aug 31, 1986• 0 citations
Publisher

Abstract

Perturbation theory is used in a study of the dynamics of an optical soliton in a ring resonator with a nonlinearly absorbing cell and external pumping. It is shown that the influence of impurity atoms with a saturable transition may give rise to a hysteretic dependence of the soliton amplitude at the exit from the resonator on the amplitude of a monochromatic pump field.

DOI
10.1070/qe1986v016n08abeh007334

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Soviet Journal of Quantum Electronics•Mar 31, 1986•1 citation
Perturbation theory is used in a study of the dynamics of an optical soliton in a ring resonator with a nonlinearly absorbing cell and external pumping. It is shown that the influence of impurity atoms with a saturable transition may give rise to a hysteretic dependence of the soliton amplitude at the exit from the resonator on the amplitude of a monochromatic pump field.
A model of the absorption-induced nonlinear response of an atomic Bose-Einstein condensate driven by a weak resonant laser beam is presented. The model takes into account the slow BEC decay due to spontaneous emission and magnetic-trap loss by binary collisions, as well as compensation of the decay by injection of ground-state atoms into the trap. It is shown that the nonlinear response is much stronger than in other nonlinear optical media. For a BEC interferometer driven by a monochromatic beam, the threshold intensity for hysteretic switching is found, and dissipative spatial solitons are demonstrated.
We formulate a first-principles description of the behavior of a bidirectional ring cavity containing a saturable absorbing medium, and driven by an external coherent field. The setting of interest to this study is an extension of the ordinary optically bistable system, where a ring resonator supports only one of the two possible directions of propagation of the cavity field. In this more general case and in the uniform-field limit, we show that the dynamics of the fields-atoms system is described by an infinite set of coupled equations that can be readily solved by standard numerical means after appropriate truncation of the number of atomic variables. With the help of two different approaches, we find unexpected, long-time stationary solutions such that the forward and backward fields oscillate with different carrier frequencies: the first is based upon the time-dependent equations and the second on a set of nonlinear-algebraic equations describing the steady states. As an added confirmation, we carry out a linear-stability analysis of the unidirectional steady state for the purpose of identifying the conditions under which a backward field can grow from an initial fluctuation. By this approach we also suggest a possible strategy for the experimental observation of stationary, frequency-shifted output fields.
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.