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Japanese Journal of Applied Physics

Optical Bistability in Periodic Channel Waveguides

Toshihiro Okamoto, Kunihiko Koshimura, Masanobu Haraguchi, Masuo Fukui

Published Feb 1, 1998• 1 citation
Publisher

Abstract

We have derived nonlinear coupled mode equations appropriate for periodic channel waveguides. These equations contain the three different nonlinear coefficients which were not taken into account in the previous analysis provided by Stegeman et al.. [IEEE. J. Quantum Electron. 18 (1982) 1610.] It has been shown that such nonlinear coefficients lower the switching power for optical bistability generated in the periodic channel waveguides. Dependence of the switching power on the waveguide size, waveguide structure and the grating parameters has been numerically obtained for ridge polydiacetylene (PDA-C4UC4) waveguides.

DOI
10.1143/jjap.37.522

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We have derived nonlinear coupled mode equations appropriate for periodic channel waveguides. These equations contain the three different nonlinear coefficients which were not taken into account in the previous analysis provided by Stegeman et al.. [IEEE. J. Quantum Electron. 18 (1982) 1610.] It has been shown that such nonlinear coefficients lower the switching power for optical bistability generated in the periodic channel waveguides. Dependence of the switching power on the waveguide size, waveguide structure and the grating parameters has been numerically obtained for ridge polydiacetylene (PDA-C4UC4) waveguides.
In order to study optical bistability in a non-linear distributed feedback structure (NLDFB), we have generalized previous work. A mono-mode rectangular waveguide is chosen as the basic configuration for the device, although other guides could be considered. The grating, providing the passive feedback mechanism, has a geometry that can be arbitrarily chosen. Linear absorption is taken into account and the non-linearity is taken to be of the Kerr type. The effect of these three perturbations is treated using the Coupled Mode Theory and the Slowly Varying Envelope Approximation, including the radiation modes. Expressions for the coupling constants due to the three fundamental perturbations are derived and we show that new terms arise due to the interplay between the latter. Our model shows that an extra term, causing a shift of the Braggfrequency occurs in the equations. The analytical expressions are integrated numerically with the proper boundary conditions. Overall reflection and transmission properties of the device are displayed as a function of the intensity, the period of the grating, its length and several other device parameters.
Two current goals in the area of optical bistability are (1) to reduce the power required for switching between two states, and (2) to reduce the material volume (and hence power dissipation). An obvious approach is to minimize the cross-sectional area of the beam, for example by using channel waveguides of the type shown in Fig. 1. A grating milled into the surfaces can be used as the distributed feedback mechanism. In this paper we analyze a channel, guided wave, distributed feedback geometry and present numerical results for InSb waveguides.
Multiple-scale analysis is employed for the study of nonlinear wave propagation in periodic layered media. In a first step, wave propagation in each individual layer is modeled by a corresponding equivalent nonlinear transmission line. The multiple-scale analysis is then employed to establish a system of nonlinear equations for the amplitudes of the forward and backward waves in the transmission lines of the model mentioned. This system of nonlinear equations is solved with the aid of a continuation technique for derivation of transmission characteristics of the periodic structure. To study optical bistability, a parameter-switching algorithm is utilized for obtaining the solutions of the system including both stable and unstable ones. For the sake of verification, we have also utilized a nonlinear finite-difference time-domain (NFDTD) method to analyze the wave propagation in the aforementioned structure. While there is an acceptable agreement between the bistability results obtained using our method and the NFDTD, there is a considerable difference between our results and the ones derived using the conventional coupled-mode theory.
Utilizing prism coupling of an argon laser beam into a nonlinear ZnS waveguide we have observed power-dependent optical bistability. We detuned the incidence angle by several linewidths from the optimal low power efficiency case. At this position we observed switching and hysteresis and verified the hysteresis loop to be bistable. The origin of the bistability we tentatively identified as a combination of intensity-dependent absorption and dispersion. Our conditions for bistability were different from those of W. Lukosz et al. in OPTICAL BISTABILITY III (Springer-Verlag, New York, 1986), p. 109.
Previously reported observations of optical bistability in a GaAs/GaAlAs waveguide cavity included whole-sample thermally induced absorptive and refractive bistability [1] and localised (μs) thermally induced absorptive bistability [2]. Other groups have observed refractive bistability due to an optoelectronic mechanism in MQW GaAs/GaAlAs waveguides [3,4]. In this paper we report the observation of bistability due to thermally induced changes in leaky modes within a GaAs/GaAlAs waveguide and discuss the optimisation of optoelectronic nonlinearities in semiconductor guides of this type. A leaky planar waveguide consists of a low index layer bounded by two higher index layers. These exhibit radiative losses, where for the nth order mode the attenuation coefficient is proportional to (n+1)2 [5]. In this investigation the waveguides used were short enough to allow good transmission of the lower order modes.