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IEEE Journal of Quantum Electronics

Dynamic behavior of reflection optical bistability in a nonlinear fiber ring resonator

Kazuhiko Ogusu

Published Jan 1, 1996• 31 citations
Publisher

Abstract

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.

DOI
10.1109/3.535356

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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.
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.
In this paper we demonstrate the dynamic simulation of light traveling in a nonlinear fiber optic ring resonator (FORR) with a single coupler. The mathematical relations describing the nonlinear characteristics of the FORR are derived from light transmission theory in linear optical systems. Optical nonlinear phenomena such as bifurcation and chaos are investigated for optical bistability and the Ikeda instability. It is found that for the Ikeda instability of light inside a FORR, the ring-cavity lifetime is much longer than the Kerr-effect response time of the fiber ring. Transmission curves of bistability and instability are shown as a function of the coupler insertion losses (γ) and the coupling coefficients (κ).
The effect of degenerate two-wave mixing (DTWM) in a general case (i.e., with pump depletion) on a single-mode single-coupler optical fiber ring resonator is studied theoretically. Two all-fiber DTWM schemes are used. It is found that DTWM can bring about (1) a saturation-type transmission curve of the fiber ring resonator and (2) bistability in the output and circulating (resonant) intensities. In addition, the linewidth of the resonant curve of the output intensity differs from that obtained with an undepleted pump beam, and there is a central dip in the same resonant- curve. The condition for the existence of bistability is obtained. The dependence of the bistable characteristics on various parameters of the fibers and the coupler is investigated. Under certain conditions bistability can reduce the linewidth of the resonant curve of the output intensity.
Bistability in the pump beam of one-coupler and two-coupler single-mode optical fiber ring resonators by using two different all-fiber schemes of degenerate two-wave mixing is demonstrated theoretically. The bistable behavior of the pump beam (or the input beam) can be controlled by changing the intensity of either the pump beam or the input beam. Depending on the scheme of the degenerate two-wave mixing and the controlling beam, the bistable hysteresis loop of the pump beam may be a normal type or an inverting type. The dependence of the bistability on some major parameters of the fibers and the couplers is investigated.
In this paper, the transient response of a double coupler fiber ring resonator containing an erbium-doped fiber amplifier (EDFA) in half part of the fiber ring resonator and a quantum dot-doped fiber (QDF) saturable absorber in the other half, is investigated. It is demonstrated that, depending on the device parameters and the input power of the signal and pump, various types of dynamic behaviors (such as bistability, monostability, and regenerative pulsation) can be observed in this intrinsic, optical bistable device. The proposed device can be exploited by optical communication networks to realize all-optical functionalities.
We numerically investigate the transient interaction between optical Kerr bistability and stimulated Brillouin scattering (SBS) when an intense optical pulse is incident in a short fiber ring resonator. An initial phase detuning of the ring resonator and the difference in the phase shift between the pump wave and the created Stokes wave are taken into account in the three-wave SBS model. The ratio of the Brillouin gain coefficient to the nonlinear refractive index of the fiber, which is termed the relative Brillouin gain coefficient, is used as a key parameter for examining the conditions for obtaining optical Kerr bistability in a fiber ring resonator. The numerical results show that optical Kerr bistability cannot be obtained in a ring resonator made from a conventional fused-silica fiber because of the generation of SBS. However, if other fibers with relative Brillouin gain coefficients at least 1 order smaller than that of fused-silica fibers are used, we can suppress SBS and hence obtain optical Kerr bistability. Moreover, we investigate theoretically and experimentally the dynamics of SBS in a fused-silica fiber ring resonator irradiated by a Gaussian pulse. The relaxation and pulsation in the Stokes signal depend strongly on the initial phase detuning of the ring resonator. The experimental results obtained with a single-frequency pulsed YAG laser agree qualitatively with theoretical predictions.