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Soviet Journal of Quantum Electronics

Periodic and chaotic variations of the intensity and polarization of light at the exit from a ring resonator filled with a nonlinear gyrotropic medium

Vladimir Makarov, A. V. Matveeva

Published Jan 31, 1988• 3 citations
Publisher

Abstract

An analysis is made of the amplitude and polarization effects which accompany the propagation of laser radiation in a ring resonator filled with a nonlinear gyrotropic medium. The ranges of the parameters of the radiation, resonator, and medium are found for which there are periodic and chaotic changes in the intensity, degree of ellipticity, and angle of rotation of the polarization ellipse of the output radiation. Analytic expressions are obtained for the frequency of changes in the output characteristics.

DOI
10.1070/qe1988v018n01abeh011204

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Optical bistability in resonators containing a nonlinear gyrotropic isotropic medium is analyzed by studying the dependence of the bifurcation intensity of the incident radiation on its ellipticity. It is found that if the gyrotropy is weak, this dependence may have symmetry-induced singular points or turning points. The stable radiation states in the resonator formed near a singular or turning point differ in respect of the polarization and are due to the evolution of the polarization instability. Bifurcation curves are plotted for a ring resonator containing a medium with a cubic nonlinearity. The form of these curves changes appreciably as the gyrotropy is increased. The change in the resonator transmission accompanying changes in the gyrotropy is studied.
We study the propagation of electromagnetic radiation through a ring-cavity device containing a dispersive nonlinear medium. Under conditions appropriate for introducing the slowly varying envelope approximation and for adiabatically eliminating the atomic variables, we calculate analytical expressions between the steady-state-output intensity and the input-field amplitude for two models of the nonlinear susceptibility, the two-level atomic medium and the Kerr medium. The stability of these curves is determined, with special attention given to changes in the thresholds by varying the return-trip phase shift, the linear absorption, and the reflection coefficients of the mirrors. We investigate the positive-branch instabilities resulting in a pulsing output intensity and calculate the bifurcation rate for the period-doubling hierarchy and the fractal dimension of our two-dimensional maps for the Kerr medium. The convergence of the bifurcation rate to a constant is slow, and we find, as in the publications of Snapp et al. [ Opt. Commun.40, 68 ( 1981)] and Carmichael et al. [ Phys. Rev. A26, 3408 ( 1982)], that this constant is consistent with that found for the class of one-dimensional maps with a quadratic maximum. This universal constant is observed over a large range of fractal dimensions for the chaotic attractor. Discussions of pulse-output bistability, intermittency, and anomalous switching are given.
A theoretical investigation is made of the polarization characteristics of the optical polarization and amplitude multistability of a Fabry?Perot interferometer filled with a nonlinear resonant medium. In the case of linear polarization of the incident radiation it is shown that an amplitude hysteresis differs considerably from a hysteresis predicted by a scalar theory; moreover, the degree of polarization exhibits a hysteresis. A calculation is made of the critical input intensity of elliptically polarized radiation for which the ellipticity at the output rises strongly even when it is negligible at the input.
A theoretical analysis is made of the resonant interaction between a traveling monochromatic light wave of arbitrary intensity and polarization and the 1/21/2 and 10 transitions in gas atoms in a magnetic field. An analysis is made of the influence of atomic collisions and coherence of the Zeeman sublevels of the terms on the structure of nonlinear magnetooptic resonances in the amplitude and polarization characteristics of the wave. Some features of nonlinear magnetooptic resonances for laser excitation of atoms from the ground state are noted. A study is made of the Faraday rotation and self-rotation of the polarization ellipse of the radiation as a function of the detuning of the wave frequency, the saturation parameter, and the optical density of the gas. The stability of the polarization of light in the medium is discussed. It is noted that these laws may be used to analyze and control the radiation characteristics of lasers and amplifiers when the level of saturation of a resonant gaseous medium in a magnetic field is high.