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Electrical Engineering in Japan

Characteristics of the optical resonator composed of the nonlinear directional coupler

Kiyoshi Kishioka

Published Jan 1, 2004• 1 citation
Publisher

Abstract

This paper describes a simple method of analysis of an optical resonator composed of a nonlinear directional coupler. Assuming the coupler is made in semiconductor-doped glass by the K+-ion diffused technique, the transmission and reflection characteristics are calculated and demonstrated. The parameter dependence of the bistability appearing in the transmitted and reflected light is also presented. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(3): 1–10, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20036

DOI
10.1002/eej.20036

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This paper describes a simple method of analysis of an optical resonator composed of a nonlinear directional coupler. Assuming the coupler is made in semiconductor-doped glass by the K+-ion diffused technique, the transmission and reflection characteristics are calculated and demonstrated. The parameter dependence of the bistability appearing in the transmitted and reflected light is also presented. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(3): 1–10, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20036
In the nonlinear directional coupler, the optical field and the nonlinear material usually interact in a spatially and temporally local fashion and the device exhibits a nonlinear transmission characteristics, but it is not bistable. In this paper, it is shown theoretically that optical bistability in the input optical power is possible for the nonlinear directional coupler if the local phase change of the optical mode propagating through tile coupler is influenced by the excitation over the whole coupler. This condition can be satisfied in a coupler based on biased-pin-diodes comprising coupled asymmetric quantum wells in the i-region, Calculations show that in this configuration, the nonlinear directional coupler can exhibit sharp switching characteristics, low switching optical powers, optical bistability or bifurcation.
We present a method for calculating the dynamic input–output characteristics of a nonlinear fiber ring resonator caused by a change in input intensity. It is based on an original method developed by Bischofberger and Shen [Phys. Rev. A 19, 1169 (1979)] to study a transient nonlinear Fabry–Perot resonator. We treat a double-coupler fiber ring resonator, in which two types of optical bistability (transmission bistability and reflection bistability) are available and present the illustrative numerical results for a few cavity parameters. This analysis will be useful for a future experimental verification of optical bistability in fiber ring resonators and for the design of fiber bistable devices.
We present an analysis of the dynamic behavior of a nonlinear fiber ring resonator when an optical pulse with an arbitrary shape envelope is incident into it through a fiber directional coupler. The transient analysis is based on the extension of a well-known multiple-beam interference method to non-linear transmission problems. The steady-state analyses reported so far predict that the ring resonator exhibits reflection optical bistability in the input-output characteristics under appropriate conditions. But, our transient analysis shows that a nearly periodical oscillation of the transmitted power always takes place at a suitable initial detuning when the resonator has no loss or a small loss. It seems that the present instability is caused by the repetition of accumulation and release of the power in the ring resonator. We can obtain a bistable hysteresis loop by introducing a loss to the directional coupler. The dynamic behavior of bistability in a nonlinear fiber ring resonator with coupler loss is then investigated. It is found that a remarkable undershoot and overshoot occur in the switch-off curve and switch-on curve, respectively.