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Soviet Journal of Quantum Electronics

Conditions of bistability in large-aperture optical systems

Nikolai N Rozanov

Published Oct 31, 1990• 4 citations
Publisher

Abstract

An analysis is made of the limits of validity of a description of large-aperture bistable systems on the basis of a theory of plane waves. The limitations arise because of transverse effects. The results show that instabilities of the transverse structure of the field in nonlinear interferometers can be suppressed effectively by using resonators with an expanding beam. The possibility of a low-threshold bistability in nonlinear reflection systems with two incident beams is discussed.

DOI
10.1070/qe1990v020n10abeh007458

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An analysis is made of the limits of validity of a description of large-aperture bistable systems on the basis of a theory of plane waves. The limitations arise because of transverse effects. The results show that instabilities of the transverse structure of the field in nonlinear interferometers can be suppressed effectively by using resonators with an expanding beam. The possibility of a low-threshold bistability in nonlinear reflection systems with two incident beams is discussed.
Of the Lorenz-type instabilities expected in optical systems, the single-mode instability in optical bistability has been the subject of detailed theoretical and experimental work by our groups. A treatment employing the plane-wave and mean-field limits of the Maxwell-Bloch equations predicts a rich variety of higher-order bifurcations including period doublings and intermittency.1 An extension of this work to include the transverse dependence of the intracavity field reveals no significant qualitative differences between the plane-wave theory and the Gaussian beam theory as regards the stability boundaries obtained from a linearized analysis.2 The instability persists in the presence of a Gaussian transverse profile and the boundaries are not radically modified compared with those obtained from the plane-wave theory. However, numerical integration of the Maxwell-Bloch equations in the single transverse mode approximation does not show the wealth of higher-order dynamic states present in the plane-wave case. An experimental investigation of optical bistability for two-level atoms in a single transverse, single longitudinal mode cavity exhibits limit cycle oscillation with stability boundaries that agree well with the boundaries obtained from the work in Ref. 2. However, for the range of values C < 300, |Δ| < 5, |θ| < 50, X ~ 102, the experimental results do not show the diversity of higher dynamic states expected from the plane-wave theory, in agreement with our numerical results. In addition the measurements support the existence of a single transverse mode oscillation. The sum of our theoretical and experimental work provides a quantitative statement for the role of the transverse effects in optical instabilities.
Specific features of the light-beam transverse structure transformation in the process of four-wave coupling in the Fabry-Perot interferometer with a resonant nonlinearity under conditions of bifurcation of the symmetry breaking and optical bistability are analyzed. The asymmetric regimes of the interaction, characterized by a difference both in the integrated transmission functions of the nonlinear interferometer for two light beams with equal intensities and in the spatial intensity distribution at the exit of the interferometer, are considered.