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Topical Meeting on Optical Bistability (OB)

The Physical Mechanism of Optical Instabilities

Yaron R. Silberberg, Israel Bar-Joseph

Published Jan 1, 1983• 0 citations
Publisher

Abstract

Nonlinear optical systems can transform a continuous wave input beam, if it is intense enough, into an oscillating light output. The system which has been most thoroughly studied is an optical resonator, usually of the ring type, containing either a Kerr medium1,2 or a two-level medium. Unfortunately, the mathematical approaches of these studies do not lend themselves to a tractable intuitive explanation of the self-pulsation phenomena, and do not identify the physical origin of instabilities. In this paper we consider a different approach, showing that optical instabilities stem from one source, namely, gain generated by four-wave mixing processes. This gain, together with feedback supplied by the resonator, leads to oscillation of sidebands of the input field. The beating between these sidebands and the input field causes the oscillating output intensity. The salient feature of our approach lies in its intuitive appeal, namely, it is possible to predict the behavior of the system for a wide range of parameters. Moreover, our model enables understanding of the system's evolvement beyond the first bifurcation, something usually not possible with the other approaches.

DOI
10.1364/obi.1983.wd1

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Nonlinear optical systems can transform a continuous wave input beam, if it is intense enough, into an oscillating light output. The system which has been most thoroughly studied is an optical resonator, usually of the ring type, containing either a Kerr medium1,2 or a two-level medium. Unfortunately, the mathematical approaches of these studies do not lend themselves to a tractable intuitive explanation of the self-pulsation phenomena, and do not identify the physical origin of instabilities. In this paper we consider a different approach, showing that optical instabilities stem from one source, namely, gain generated by four-wave mixing processes. This gain, together with feedback supplied by the resonator, leads to oscillation of sidebands of the input field. The beating between these sidebands and the input field causes the oscillating output intensity. The salient feature of our approach lies in its intuitive appeal, namely, it is possible to predict the behavior of the system for a wide range of parameters. Moreover, our model enables understanding of the system's evolvement beyond the first bifurcation, something usually not possible with the other approaches.
Two counterpropagating waves in a Kerr medium were shown to exhibit instabilities, which lead to self-oscillations, bifurcations, and chaos.1 These instabilities, as well as self-oscillation phenomena in bistable systems, can be explained by a gain-feedback mechanism.2 Fields at frequencies adjacent to the input pump-wave frequency can be amplified through four-wave-mixing interactions. If feedback is supplied, sidebands at these frequencies can be excited and beat with the pump wave to yield an oscillating output. In a counterpropagating-beam configuration, the feedback is distributed, and it originates from the grating that is formed by the interfering beams.
The dynamical behavior of counterpropagating light waves interacting with a nonlinear medium is studied numerically. It is found that the wave and the medium form a system that becomes unstable under certain conditions and exhibits self-oscillation. Because the interacting medium is modeled by an ensemble of two-level systems, we recognize the self-oscillation frequency as the Rabi-frequency of the constituent systems. The physical mechanisms responsible for this self-oscillation are the gain and the distributed feedback of the combined lightwave-medium system. When the environment changes, in particular when the intensity is increased, this system becomes more unstable and we find that the oscillation exhibits more complex behavior, including quasi-periodic motion and chaos. We analyze the output fields by using Fourier spectra, phase portraits, and autocorrelation functions. In the chaotic regime, the Lyapunov exponents and dimensions are also calculated. A physical interpretation of the quasiperiodic motion is given by an exact calculation of the absorption spectrum of our two-level medium. The negative absorption (gain) peaks are found at the frequencies of the quasi-periodic motions, thus implying that the gain of the combined light-medium system is responsible at least in part for the observed complex behavior. In addition, we investigate the stability of the propagating plane wave when a transverse wave is added to the system as a perturbation. Instabilities are analyzed by linearizing the nonlinear equations which model the lightwave-medium system. The results show that the instability is highly-correlated with the four-wave mixing phase conjugation.
Given one oscillating mode in a laser or an optical bistability cavity, can other modes build up, that is, is single-mode operation unstable? The answer depends on an interplay of spontaneous emission, saturated gain, and four-wave mixing processes that permit one or more sidemodes both to be resonant with cavity modes and to have more gain than loss. We discuss this problem for cavities containing one- or two-photon two-level media subjected to a classical wave of arbitrary intensity and one or two weak quantized sidemodes. While a single sidemode may have gain, two sidemodes symmetrically placed about a strong pump mode can have greater gain due to four-wave mixing contributions sometimes called combination tones. The theory is valid for the buildup of sidemodes from quantum noise until the sidemodes begin to saturate. Subsequent dynamics including chaos must be handled by a theory that allows all modes to saturate. The same physical mechanisms are important in saturation spectroscopy and control the generation of squeezed states in a cavity. However while the instabilities depend on sidemode gain and spontaneous emission, the generation of squeezed states of the vacuum avoids these phenomena, depending solely on quantum combination tones.
The steady-state polarizations of fields counterpropagating in nonlinear Kerr media can exhibit complicated behavior.1 We examine the temporal behavior for the case of an isotropic nonlinear Kerr medium and show that the polarizations are temporally unstable above a certain threshold intensity, even when the input polarizations are linear and parallel to each other. This polarization configuration is known to be spatially stable and is often chosen for the two strong pump waves in phase conjugation by degenerate four-wave mixing. We find that the threshold intensity for the polarization instability is approximately the intensity at which the phase conjugate reflectivity is equal to unity. Depending on the ratio of the two input intensities, this instability just above threshold can manifest itself as an abrupt rotation of the output polarizations to a new steady-state value or as a periodic oscillation of the output polarizations. At higher intensities the polarization can evolve chaotically in time, and depending on the ratio of the transit time through the medium to the response time of the medium the output intensity can fluctuate chaotically as well.
We have developed a theory for nondegenerate oscillations in optical resonators containing an intracavity phase-conjugate element. The phase-conjugate element consists of a nonlinear transparent medium that is pumped externally by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation of an input beam of slightly different frequency occurs because of nondegenerate four-wave mixing. The theory takes into account linear absorption (or gain) in the medium and is applied to study the threshold behavior of phase-conjugate oscillators. For the special case of no conventional mirrors, the phase-conjugate oscillator reduces to an ordinary phase-conjugate mirror, and our general formulation yields the results of previous studies. Our analysis shows that the parametric gain required for oscillation increases (or decreases) as a result of linear absorption (or gain) in the medium, and oscillation can occur at a frequency different from that of the pump beams in the presence of large linear gain (or loss). The effects of linear absorption (or gain) on the filter operation are also examined.
Further theoretical observations and a new analysis of stationary degenerate and nearly degenerate optical wave mixing effects in a Kerr-like nonlinear medium are presented. The effects of phase modulations, beam ratio, intensity, wave mixing angle and frequency differences and other physical and optical parameters in multiwave mixing mediated probe gain and their application in ring oscillation devices are analyzed in detail. New experimental studies of the intensity and the angular dependence of the probe beam amplification and side diffractions in liquid crystal provide further insights into the phenomena.