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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Phase switching in optical subharmonic generation: an alternate bistable operation of a nonlinear Fabry-Perot resonator

Horatiu Totia, Marius Micluta

Published Mar 8, 1995• 0 citations
Publisher

Abstract

In this paper we present a theory of optical subharmonic generation in a nonlinear Fabry-Perot resonator. Our approach, based on classical electrodynamics, leads to a Mathieu-Hill-type equation. This enables us to describe the generation of optical subharmonic oscillation in terms of a general formalism used to account for parametric phenomena, and to outline the possibility of using a nonlinear Fabry-Perot resonator as a memory device able to store the phase of a signal. The oscillation threshold condition is discussed and the rate of amplitude rise at start-up is evaluated.

DOI
10.1117/12.203549

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In this paper we present a theory of optical subharmonic generation in a nonlinear Fabry-Perot resonator. Our approach, based on classical electrodynamics, leads to a Mathieu-Hill-type equation. This enables us to describe the generation of optical subharmonic oscillation in terms of a general formalism used to account for parametric phenomena, and to outline the possibility of using a nonlinear Fabry-Perot resonator as a memory device able to store the phase of a signal. The oscillation threshold condition is discussed and the rate of amplitude rise at start-up is evaluated.
It is well known that n-th order subharmonic oscillations (where n is integer) possess a fundamental property of having n possible and equally probable oscillation phases, each of which corresponding to the same oscillation amplitude.1 It was demonstrated both theoretically and experimentally by this author2 that very high order subharmonics can be excited in passive lump nonlinear systems driven by a sufficiently strong pumping signal. It was also shown that subharmonics can be generated by the optical parametric oscillator.3 In this paper we show that optical subharmonic oscillators may provide a novel kind of optical multistability - specifically, phase multistability of these oscillations, with the same amplitude for each steady state of the phase. This differs drastically from all presently known types of optical bistability, all of which are based on amplitude multistability. The new principle results in a unique property of the system which we call symmetry of the states: all the steady states of the system possess the same stability, noise, etc. characteristics and may be switched from one steady state to another by an external signal of the same small amplitude.
A Fabry-Perot resonator filled with second-order nonlinear optical material is investigated. Attention is devoted to making the resonator act as a nonlinear mirror for ultralow-intensity light signals that can be switched by a control beam at the second-harmonic frequency. The interaction process is an input-phase-independent parametric downconversion. The theoretical problem is solved through implementation of a dummy variable method optimized for a parametric process. Efficient amplification and bistability of low-intensity signals have been found.
The combination of polarization optics and nonlinear optics gives rise to interesting new physical phenomena1. In the work presented here we will focus on planar resonators with a nonlinearity of diffusive nature, such as the nonlinear Fabry-Perot resonator (NLFP). There are two ways to display the role of polarization in the bistable response of such a device. First, in a configuration where the light wave is obliquely incident on the resonator, as the interface's reflectances depend on the polarization state of the incident light. Second, in a configuration where the beam impinges normally on a resonator now filled with an anisotropic material, as a phase shift is induced between the linear Airy resonances of the two polarization eigenmodes. In this paper, two dynamic theories for planar resonators are presented for both configurations mentioned above, for an arbitrary polarization of the incident plane wave.
In this paper we consider the nonlinear Fabry-Perot and its applications to optical signal and image processing. This paper addresses the signal processing aspects of a nonlinear Fabry-Perot interferometer with emphasis on image processing. The device geometry is shown in Figure 1. A thin nonlinear medium, whose refractive index is a function of the light intensity inside the Fabry-Perot is sandwiched between two plane parallel mirrors. The output as a function of input is shown in Fig. 2, for two different values of the difference between the Fabry-Perot low intensity resonance and the incident wavelength. The bistable curve in 2a is the origin of the term optical bistability and makes possible an optical memory, in which the output is a function of the history of the device. The Figure 2b represents a typical nonlinear transfer curve which may be used for signal processing. It can be seen that small changes in the input intensity Ic make large changes in the output intensity.
The aim of present paper is to propose several dynamical models of nonlinear Fabry-Perot resonators. The models are all described by sets of difference-differential (delay-differential) equations involving multiple time delays, and they are extended versions of the difference-differential equations proposed for the ring-type resonators by one of the present authors. We show in detail how these model equations are derived from the Maxwell-Bloch equations, assuming: 1) fast transversal relaxation, 2) weak nonlinearity, and 3) dispersive limit. We propose a hybrid optical bistable device as an analog system of a model equation.