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Nonlinear Guided Waves and Their Applications

Optical Bistability by Cascading χ(2) in Prism or Grating Couplers

R. Reinisch, E. Popov, M. Nevière

Published Jan 1, 1995• 0 citations
Publisher

Abstract

The features of second harmonic generation (SHG) in the depleted pump regime are known since the early works of N. Bloembergen et al.[1]. For some years, this kind of SHG has attracted a great deal of interest[2]. The reason is as follows : in the presence of depletion of the fundamental frequency field together with a small phase mismatch, this kind of interaction can lead to a nonlinear (NL) phase shift of several π[2]. There lies the interest of such a process.

DOI
10.1364/nlgw.1995.nfa14

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The features of second harmonic generation (SHG) in the depleted pump regime are known since the early works of N. Bloembergen et al.[1]. For some years, this kind of SHG has attracted a great deal of interest[2]. The reason is as follows : in the presence of depletion of the fundamental frequency field together with a small phase mismatch, this kind of interaction can lead to a nonlinear (NL) phase shift of several π[2]. There lies the interest of such a process.
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.
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.