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IEEE Journal of Quantum Electronics

Quasi-phase-matched second-harmonic generation by backward propagating interaction

M. Matsumoto, Kazuo Tanaka

Published Apr 1, 1995• 41 citations
Publisher

Abstract

Both static and dynamical analyses of quasi-phase-matched second-harmonic generation by backward propagating interaction, where the second-harmonic wave is generated in reflection, are presented. It is shown that bistability appears in the generated second-harmonic power if the amount of phase mismatch is suitably chosen. The bistability also appears in the output fundamental wave, since the cascaded second-order nonlinear process gives rise to the effective self-modulation of the fundamental wave, which can be applied to all-optical signal processing. The output second-harmonic and fundamental powers can be switched between two bistable states by controlling the intensity or phase of the input fundamental wave.>

DOI
10.1109/3.371945

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Both static and dynamical analyses of quasi-phase-matched second-harmonic generation by backward propagating interaction, where the second-harmonic wave is generated in reflection, are presented. It is shown that bistability appears in the generated second-harmonic power if the amount of phase mismatch is suitably chosen. The bistability also appears in the output fundamental wave, since the cascaded second-order nonlinear process gives rise to the effective self-modulation of the fundamental wave, which can be applied to all-optical signal processing. The output second-harmonic and fundamental powers can be switched between two bistable states by controlling the intensity or phase of the input fundamental wave.>
The effect of saturable absorption on second-harmonic generation in a quasi-phase-matched structure is studied, including both plane-wave and diffractive coupling of the fields and detuning of the pump field from resonance. In the regime of large Fresnel numbers, the main effect of saturable absorption is to suppress the parametric instability, which limits the efficiency of the second-harmonic generation and places a bound on the device length in order to fit sufficient harmonic power. The optical limiting nature of resonance absorption places an upper bound on the gain that quasi-phase-matching can achieve. In the diffractive regime, a variety of output transverse structures may be initiated by modulation of the relative phase and mutual displacement between the input beams of the pump and seeding harmonic signal. In particular, second-harmonic dragging, i.e., the asymmetric interaction between initially overlapping pump and second-harmonic beams propagating at different angles, is observed such that a pump beam can drag a second-harmonic one out a spatial aperture, thereby implementing a colored logical switch with gain.
Cascaded nonlinear phase shifts via second-harmonic generation are theoretically studied for quasi-phase-matched (QPM) structures. Both the effective phase mismatch and the structure itself contribute to the resultant nonlinear phase shift. Depending on the sign of the effective phase mismatch, structural contribution may enhance or depress the nonlinear phase shift. The fundamental wave will experience a nonlinear phase shift even if the effective phase matching is satisfied. By properly designing the effective phase mismatch, QPM structures with large material-based phase mismatch may provide large nonlinear phase shifts before saturation.
The scope of this paper is to revisit the use of quadratic crystals cut for second harmonic generation (SHG) with type II phase-matching in view of all-optical processing of light signal. The investigations on this topic mainly focused in the past years on the possibilities opened by cascading of quadratic nonlinearities in phase-mismatched conditions [1]. The goal of this paper is to remind the reader that various types of optical processing are achievable with sum and difference frequency generation in phase-matched position without the requirement for cascaded nonlinearities. In a first part we will report few examples of the use of difference frequency generation (or down conversion) for signal processing. In a second part we will show that type II SHG with unbalanced fundamental inputs may lead to coherent amplification or transistor like operation.
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.
We theoretically analyze a new class of aperiodic phase mismatch. The phase-matching function that is chosen depends on the calculated second-harmonic amplitude generated in the device during the propagation of the fundamental beam at given input intensity and wavelength. We show that, in such a configuration, the fields evolve toward the eigenmodes of a χ(2) two-wave mixing process. Hence a constant pump and an enhanced nonlinear phase shift that grows linearly with propagation length are obtained. We also discuss the feasibility of this scheme that provides an alternative approach for the realization of optical switching devices or Kerr-effect compensators.