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

Wave distortion correction and optical bistability in a nonlinear medium near phase-conjugate mirror

Timo A. Laine, Ari T. Friberg

Published Jul 6, 1999• 0 citations
Publisher

Abstract

Nonlinear optical properties in thin layers are investigated near a phase conjugate mirror. By using a rigorous electromagnetic theory of volume gratings the wave distortion correction by phase conjugation is examined in a nonlinear Kerr medium and Agarwal's theorem is numerically demonstrated. At specific incidence angles guided modes are formed inside the layered structure. When the nonlinearity is increased optical bistability is observed in waveguide resonances. An analytic solution is developed to explain the numerical data.

DOI
10.1117/12.358369

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Nonlinear optical properties in thin layers are investigated near a phase conjugate mirror. By using a rigorous electromagnetic theory of volume gratings the wave distortion correction by phase conjugation is examined in a nonlinear Kerr medium and Agarwal's theorem is numerically demonstrated. At specific incidence angles guided modes are formed inside the layered structure. When the nonlinearity is increased optical bistability is observed in waveguide resonances. An analytic solution is developed to explain the numerical data.
The calculus of variations is applied to electromagnetic fields in a layered nonlinear structure supporting a guided wave. The system also includes a phase-conjugate mirror (PCM). By introducing a variational dimension and using a collection of plane waves as a trial function, we approximate the exact solution of the nonlinear Kerr–Maxwell equation. The formalism is new, and it involves the nonlinear interference of multiple plane waves. A simple analytical expression for the nonlinear field in the presence of the PCM is derived, and the fact that the scattered intensities may become bistable when the angle of incidence is varied is demonstrated. In particular, our theory predicts the angular bistability in the backscattering direction, where the effect of the guided waves is subtle. Our numerical results are also in good agreement with other theoretical approaches and with the experimental data.
A new use of gratings in nonlinear optics is presented, i.e., the realization of bistable components. The device studied here consist of grating couplers ruled on a Kerr nonlinear medium, which use the guided-wave resonance to increase the local field and thus the nonlinearities. The result is that they are intrinsic bistable optical systems with high-speed, low pumping thresholds, and geometry well adapted to optical integration. First, a linear electromagnetic study of the devices is presented. It follows optimizing the grating parameters in order to get the best coupling between the incident beam and the guided mode inside the corrugated waveguide. Then a graphical construction is given that demonstrates the bistable character of the system in nonlinear optics. Next a nonlinear analysis of the devices is rigorously derived from Maxwell equations. It states precisely the predictions of the graphical construction and allows comparison of the effectiveness of the guided-wave resonance with the surface plasmon resonance in order to reduce the threshold of bistability.
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.
This paper is concerned with the interplay between electromagnetic resonances and the phase-matching condition in guided-wave nonlinear optics. Several examples are given: quasi phase-matched second-harmonic generation using a grating with a subwavelength periodicity, cascaded optical bistability, Kerr-type distributed couplers under pulse illumination with duration of the order of the cavity build-up time or shorter, surface plasmon-enhanced stimulated Raman scattering at a grating overcoated by a few monolayers of a Raman active medium.
Recent interest in degenerate four-wave mixing in artificial Kerr media to produce phase conjugate waves has concentrated on the visible and infrared spectra. Attempts to extend this technique to the millimeter wave and microwave spectral regions encounter severe difficulties arising from the requirements of medium nonlinearity and high beam intensities. The former problem may be solved by the use of artificial Kerr media and the latter by confinement in a waveguide. In a single-mode waveguide, however, wavefront perturbations cannot propagate. Phase conjugation therefore reduces in this case to a 1-D conjugation capable only of correcting for longitudinal phase error. Observation of this conjugate wave with a slow response medium is made possible by using a sequential method. The general concept is to first write the nonlinear refractive index grating using counterpropagating pump and probe waves. Subsequently, both waves are turned off, and a pump wave approaching from the opposite side reads (scatters from) the grating to produce the phase conjugate wave.
The authors study analytically and numerically the effect of a periodic perturbation in the index of refraction of a nonlinear optical medium. Using a one-dimensional model for monochromatic waves incident on the medium, they find that near resonance between the perturbation and the modulation of the electric field there can be a significant enhancement of optical bistability in the low intensity regime. In particular, they discuss in detail the case of the primary resonance, which is responsible for the most significant effects, and show how one can optimize the bistability curve for the implementation of an optical switch, based on the information provided by the resonance structure.