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IEEE Journal of Quantum Electronics

Regenerative oscillation in the nonlinear Fabry-Perot interferometer

J. A. Goldstone, E. Garmire

Published Feb 1, 1983• 14 citations
Publisher

Abstract

We present an analytic and numerical analysis of regenerative oscillation in the lossless nonlinear Fabry-Perot based on a semiclassical model. We show that unstable positive slope regions may exist along all branches of the steady-state transfer curve which lead to regenerative oscillation or to precipitation to lower branches. The stability of these oscillations is analyzed in terms of the dynamic behavior of the nonlinear index. Our analytic expressions for the period, amplitude, waveform, and phase relation of the output intensity and index oscillations are shown to agree with numerical results to better than 10 percent. We investigate the possibility of experimental observation of regenerative oscillation, and show that it may be present under reasonable experimental conditions.

DOI
10.1109/jqe.1983.1071835

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We present an analytic and numerical analysis of regenerative oscillation in the lossless nonlinear Fabry-Perot based on a semiclassical model. We show that unstable positive slope regions may exist along all branches of the steady-state transfer curve which lead to regenerative oscillation or to precipitation to lower branches. The stability of these oscillations is analyzed in terms of the dynamic behavior of the nonlinear index. Our analytic expressions for the period, amplitude, waveform, and phase relation of the output intensity and index oscillations are shown to agree with numerical results to better than 10 percent. We investigate the possibility of experimental observation of regenerative oscillation, and show that it may be present under reasonable experimental conditions.
We present a detailed analysis showing that positive-branch instabilities occur in nonlinear resonators in the Fabry-Pérot (folded) configuration. Responses in the unstable region can be unstable or chaotic, depending on parameter values. Values of the response/round-trip time ratio in excess of unity can still yield instabilities, albeit on progressively higher branches as the ratio increases. The analysis proceeds from the basic optical bistability equations through the Maxwell-Debye equations to an explicit expression for the nonlinear phase shift. Linearization leads to thresholds in good agreement with direct computation. A simple expression for the accessible domain of phase-space is derived. The fundamental oscillation is interpreted as a cavity-resonant sideband instability.
The dynamic properties of a Fabry–Perot interferometer filled with a material exhibiting second-order dispersive nonlinearity are studied both theoretically and experimentally. The response of the medium is described by an intensity dependent phase constant as derived from self-action effects. Considering two relaxation times, that of the material and that of the cavity, the basic relations for the stability analysis and for the numerical calculations are obtained. Bistability and self-pulsing effects are predicted. Moreover, the transient behavior is characterized by anomalous switching properties like overshoot and alternate switching. The corresponding experiments performed on a nonlinear transmission line resonator confirm the theoretical results. In a final discussion, the relations to the field of nonlinear optics are outlined.
We develop equations for the dynamic response of the non-linear Fabry-Perot, including a finite material response time. Our model demonstrates overshoot switching for rapid onset signals. This phenomenon makes possible several new effects: switching below steady-state intensity values, output response determined by input onset characteristics, pulse trains transmitted in four distinct modes including alternate switching, and input phase switching up as well as down. Our model also exhibits critical slowing down which occurs, in general, at unstable equilibrium output intensities. Finally, we include coupled nonlinear cavities and analyze a three-mixror configuration which produces pulsed outputs for appropriate CW inputs.
We consider semiconductor Fabry-Perot interferometer (FBI) where interband free carriers photogeneration and heating due to recombination make a different sign contribution to the refractive index and temperature shift of band edge results in induced absorption. Such situation is realized in a number of semiconductors which demonstrate optical bistability (OB). Using the parameters of InSb /1,2/ we have numerically investigated transformation of steady input-output characteristic IO(Iin) under variation of initial detuning δo of FPI. Different δo leads to the following characteristics: dispersive-absorptive hysteresis of "butterfly"-type /3/; "butterfly"-type hysteresis with unstable regions corresponding to McCall’s regenerative oscillations (RO) /4/; single-valued characteristic with region of RO; as well as characteristic containing region of RO and absorptive OB with sharp decreasing of output intensity IO at forward switching. The limits of changing of input intensity Iin, δo and characteristic thermal time are found, where RO and OB of dispersive and absorptive type are exist.
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.
A simple regenerative fiber amplifier with a nonlinear refractive index is described and analyzed. Using standard equations of operation, we model the circulating intensity within the resonant cavity and determine the nonlinear phase response to changes in this intensity over the entire range of initial cavity detuning. Simple stability criteria are established and described. It is shown that the presence of sufficient nonlinearity leads to stable regions of operation with consistent phase-intensity relationships. Based on these results, the phase of the amplifier output is predicted relative to the injected field for the entire range of initial detuning