SPIN-RELATED OPTICAL BISTABILITY AND TRISTABILITY

Abstract

This thesis concerns with nonlinear behaviors of spin-related bistable and tristable systems. In recent years there has been a substantial theoretical and experimental effort on optically bistable systems. An optically bistable system is a device which exhibits two distinct states of optical transmission. It has acquired much attention from the aspect of practical application as optical devices and also from the fundamental standpoint since it offers various nonlinear phenomena inherent in systems far from equilibrium. It is shown, in this thesis, that inclusion of light polarization leads to qualitatively new variations of the phenomena. Light polarization is connected to the atomic spins of the medium. So far no works on polarization effects in optical bistability have been made. Here two types of such spin-related optical system are proposed and studied. The first system is a Fabry-Perot cavity filled with atoms with degenerate Zeeman sublevels in the ground state. It is found that for linearly polarized incident light, the high transmission state is doubly degenerate with respect to the output light polarization; one is almost right-circularly polarized (σ+ state) and the other is almost left-circularly polarized (σ- state). In the low transmission state, the output remains linearly polarized (linear state). Therefore the three states coexist and we call the phenomenon optical tristability. In the σ+ (σ-) state, the atomic spins are oriented parallel (antiparallel) to the propagation direction of the incident light, whereas in the linear state, they are random. When we increase the intensity of the linearly polarized incident light, at a critical point, the linear state becomes unstable and a discontinuous transition to the σ+ or σ- state takes place with equal probabilities. The symmetry of the system with respect to the polarization is spontaneously broken. This is a result of a competitive interaction of the σ+ (rightcircularly polarized) and σ- (left-circularly polarized) light beams through optical pumping. Bifurcations which appear when the input intensities of σ+ and σ- components are changed independently are also investigated. It is found that the bifurcation structure can well be understood in context of a butterfly catastrophe. Next the dynamical property of the system is studied. It is shown that when we apply a static magnetic field transversely to the optical axis, self-sustained precession of the spin polarization occurs. Correspondingly, the σ+ and σ- components of the transmitted light are modulated at about the Larmor frequency. It is also shown that a modified Bloch equation which describes the motion of the spin polarization in the cavity can be reduced to the van der Pol equation. The second system we propose uses the same medium as the first one but has no optical cavity. The optical system is composed of a cell containing the atoms, a λ/8 plate, and a mirror. The feedback is realized by the optically induced Faraday effect. The system exhibits a pitchfork bifurcation which breaks the symmetry as the input intensity is increased. Namely, the symmetry breaking is of a supercritical type, whereas in the first system it is of a subcritical type. This system has also two input parameters and a cusp catastrophe appears when they are changed independently. It is also found that in the presence of a transverse magnetic field, self-sustained spin precession takes place. The static behavior of the second system is confirmed experimentally by using Na vapor and a multimode dye laser. Chaotic (or turbulent) phenomena in optical bistability is also investigated. Chaotic oscillation occurs when a delay time in the feedback loop is longer than the response time of the medium as predicted by Ikeda. The delay-induced chaos in a simple and familiar acoustic system is studied experimentally. It is an acoustic analogue of optically bistable systems. The system goes over into chaotic state after some cascades of period-doubling bifurcations as we increase the loop gain. The delay-induced chaos in the second optical system is investigated. Particular attention is paid on the symmetry of the solutions with respect to the polarizations. The output of the system bifurcates in the following way as the input light intensity increases: (1) symmetric steady state, (2) asymmetric steady state, (3) asymmetric periodic oscillation, (4) asymmetric chaos, (5) symmetric chaos. The first bifurcation is a well-known symmetry-breaking transition. It is shown that the last bifurcation through which the symmetry is recovered can be viewed as a crisis of chaos, which has been defined by Grebogi et al. as a sudden change of strange attractor. By changing system parameters, we find three distinct types of the crises in the experiment with an electronic circuit which simulates the differential-difference system equation. Before and after the crises, waveforms characteristic of each type is observed. In a simple two-dimensional-map model, we can find the three types of crises. It is also found that the types of crises are determined by the nature of unstable fixed (or periodic) points which cause the crises by colliding to the chaotic attractors. The symmetry-recovering crises seem to be general phenomena appearing in nonlinear systems with some symmetries.