The authors numerically investigate optical bistability in a periodic waveguide in the presence of a quadratic nonlinearity allowing phase-matched second-harmonic generation. The structure is a tuned Bragg coupler for two counterpropagating modes at the fundamental frequency, and is coherently controlled by a seed at the second harmonic.
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.
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 paper is concerned with second harmonic generation in optical resonators like prism or grating couplers when the depletion of the pump field is strong enough so that is can no longer be neglected. This means that we have to take into account the feedback between the signal field at 2(omega) circular frequency and the pump field at (omega) . Two different approaches are developed. The first one is a rigorous electromagnetic analysis based on the numerical integration of nonlinear Maxwell equations at both (omega) and 2(omega) frequencies, incorporated in a root-finding procedure to take the depletion into account. The second is based on a couple mode analysis which leads to a set of coupled mode equations governing the amplitudes of the pump and second harmonic frequency fields. These methods allow to predict that second- harmonic generation in prism or grating couplers can lead to optical bistability. Contrary to the Kerr-like bistability, this new type of bistability occurs not only at one side of the resonance maximum but on both sides provided the absolute value of the offset in the incident angle is above a threshold. The two approaches give numerical results in very good agreement. The coupled mode theory provides analytical predictions of the threshold value and brings physical insight on this new effect.
We deal with second-harmonic generation in chi((2)) nonlinear-optical resonators such as prism or grating couplers. The theoretical study is performed within the framework of a recently developed coupled-mode analysis leading to a set of equations governing the amplitudes of pump and second-harmonic frequency fields. We predict analytically that second-harmonic generation in prism or grating couplers may lead to optical bistability. We believe this to be the first demonstration of such an effect in chi((2)) optical resonators.