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International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems

Theory Of An All-Optical AM-FM Modulator

Pierre Meystre, G. Reiner, Ewan M. Wright

Published Jan 1, 1985• 0 citations
Publisher

Abstract

Phase conjugate resonators (PCR) are optical resonators in which (at least) one of the mirrors is a phase-conjugate one (PCM), e.g. a four-wave mixing cell. These systems are of considerable experimental and theoretical interest, specially in view of their potential to eliminate phase distorsions within the resonator1. In recent work2, we discussed a PCR consisting of a Fabry-Perot resonator with one end mirror replaced by a lossless Kerr medium of infinitely fast response time pumped by two counterpropagating beams of same frequency. We described the PCM within the Raman-Nath approximation3, but including fully the effects of pump depletion. The normal mirror was positioned such as to couple the first order scattered field back into the PCM. We found that this system can break into self-oscillations corresponding to the half-axial modes predicted by linear theories1,4. For higher pump intensities, this is followed by a sequence of bifurcations to chaos, with in general the coexistence of several basins of attraction. We also showed5 that the first of this sequence of bifurcations is in general already sufficient to induce a quasi-periodic motion of the intracavity field phase, leading in practice to its complete indetermination.

DOI
10.1364/idlnos.1985.wa5

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Optics Letters•Jul 1, 1985•18 citations
Phase conjugate resonators (PCR) are optical resonators in which (at least) one of the mirrors is a phase-conjugate one (PCM), e.g. a four-wave mixing cell. These systems are of considerable experimental and theoretical interest, specially in view of their potential to eliminate phase distorsions within the resonator1. In recent work2, we discussed a PCR consisting of a Fabry-Perot resonator with one end mirror replaced by a lossless Kerr medium of infinitely fast response time pumped by two counterpropagating beams of same frequency. We described the PCM within the Raman-Nath approximation3, but including fully the effects of pump depletion. The normal mirror was positioned such as to couple the first order scattered field back into the PCM. We found that this system can break into self-oscillations corresponding to the half-axial modes predicted by linear theories1,4. For higher pump intensities, this is followed by a sequence of bifurcations to chaos, with in general the coexistence of several basins of attraction. We also showed5 that the first of this sequence of bifurcations is in general already sufficient to induce a quasi-periodic motion of the intracavity field phase, leading in practice to its complete indetermination.
This paper is the second in a series describing propagation of electromagnetic radiation in phase-conjugate oscillators. We apply the formulation developed in the first paper to study the phase-conjugate resonator (PCR) and the Fabry–Perot cavity with an intracavity phase-conjugate mirror (PCM). Our results show that nondegenerate oscillation occurs in the PCR for large parametric gains and fixed separation between the conventional reflector and the PCM. The bandwidth is considerably reduced from that of a PCM alone. In the phase-conjugate oscillator, oscillation will occur at the pump frequency only if there is no separation between the conventional mirrors and the phase-conjugate element and if the nonlinear medium fills the entire Fabry–Perot cavity.
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.
The exact theory of degenerate four-wave mixing in a Kerr-like medium in the Bragg scattering regime is used to study the reflectivity of phase-conjugate mirrors pumped by intense laser beams. The analysis takes into account pump depletion, nonlinear phase modulation and the relaxation time of the nonlinearity. The steady-state response exhibits multivalued reflectivity, hysteresis and potential bistability; however, the transient response shows that at most one value of the phase-conjugate reflectivity is stable. Periodic or chaotic pulsations are predicted beyond threshold values of pump intensity. The onset of a natural oscillation in the Kerr-like medium is also predicted in the absence of a continuous probe beam; the resulting field amplitude is stable and weakly sensitive upon the presence of external noise.
A mean field theory of nearly-degenerate four-wave mixing is developed for the optical bistability, which has recently been found in a phase-conjugate resonator consisting of a normal mirror and a phase-conjugate mirror under relatively strong pumping. The bistability in transmission of the probe beam occurs as the mirror separation or the probe offset frequency is changed, but for a limited range of probe beam intensity. This behavior is explained as occurring under injection-locked conditions because of combined effects of tilting and broadening, or narrowing of the resonance curves due to nonlinearities in the phase-conjugate reflectivity arising from pump depletion.