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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Transient Response Of Nonlinear Ring Resonators Using Gaas With Photon Energy Below Band Gap

Steven M. Jensen

Published Aug 27, 1982• 1 citation
Publisher

Abstract

Non-linear ring-resonators are shown to exhibit optical bistability with nanosecond switch times, when using GaAs as a non-linear material and photon energies below band gap. A computer program developed specifically to model the transient response of these devices is used to extract values for the non-linearity and its response time from the observed characteristics.

DOI
10.1117/12.933222

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Non-linear ring-resonators are shown to exhibit optical bistability with nanosecond switch times, when using GaAs as a non-linear material and photon energies below band gap. A computer program developed specifically to model the transient response of these devices is used to extract values for the non-linearity and its response time from the observed characteristics.
Semiconductors exhibit large optical nonlinearities near the band edge because of resonance enhancement. Optical bistability occurs when the optical nonlinearities are coupled with feedback. In bulk GaAs and GaAs–AlGaAs multiple-quantum-well superlattices, the nonlinearity arising from the presence of the free-exciton resonance has produced room-temperature optical bistability with a few milliwatts of power. The formation of biexcitons in CuCl, the saturation of the bound exciton on CdS, and band-filling effects in InSb, InAs, and HgCdTe lead to observation of bistability in these materials. A bistable etalon can be operated in an optical-gate mode to generate optical analogs of electronic gates such as and, or, and nor. It has been demonstrated that a GaAs optical NOR gate responds in ∼1 psec, using only ≲3 pJ of energy. However, because of the carrier lifetime of a few nanoseconds, the repetition rate of the NOR gate is now limited to a few hundred megahertz.
The optically non-linear response of arbitrary planar semiconductor resonators (microresonators) is studied theoretically. We use a versatile approach that takes into account the finite beam width as well as pulse length of the incident light, and incorporates the non-linearity consistently. The intensity-dependent non-linearity of semiconductors is described by appropriate phenomenological models. We show that the propagation characteristic of the leaky waves excited controls the response behaviour of the resonators. Conditions for switching and optical bistability are identified. The effect of various parameters on the response is studied numerically.
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.
Effect of relaxation time on the performance of photonic crystal optical bistable switches based on Kerr nolinearity is discussed. This paper deals with optical pulses with the duration of about 50 ps. In such cases the steady state response of the optical device can be used to approximate the pulse evolution if the nonlinearity is assumed instantaneous, hence analytical solutions such as the coupled mode theory can be used to obtain the time evolution of the electromagnetic fields. However if the relaxation time of the material nonlinear response is also considered, changes in the power levels and in the shape of the hystersis loop is observed. In this case, we use the nonlinear finite difference time domain method (NL-FDTD) to follow the system dynamics and get the bistability hystersis loop. Codes are developed to analyze the instantaneous Kerr materials and the Kerr materials with finite response times. Depending on the material, the relaxation times of the order of 1-10fs should be considered in studying bistability to obtain the right shape of the output pulses. It is observed that the relaxation leads to larger input power and threshold and hence degrades the performance of the switch in pulse shaping.