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Journal of Lightwave Technology

Optical Bistability in a Silicon Waveguide Distributed Bragg Reflector Fabry–Pérot Resonator

Andrew Grieco, Boris A. Slutsky, Dawn T. H. Tan, Steve Zamek, M. Nezhad, Yeshaiahu Fainman

Published May 24, 2012• 41 citations
Publisher

Abstract

We demonstrate optical bistability in a silicon waveguide Fabry-Pérot resonator formed by a pair of distributed Bragg reflectors. In the bistable regime, the output power of the resonator ceases to be uniquely determined by the input power because multiple powers within the cavity satisfy the resonance condition. Pulsating behavior is observed within the resonator output, and is attributed to noise within the experimental setup driving the resonator between the multiple allowed output powers.

DOI
10.1109/jlt.2012.2197731

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We demonstrate optical bistability in a silicon waveguide Fabry-Pérot resonator formed by a pair of distributed Bragg reflectors. In the bistable regime, the output power of the resonator ceases to be uniquely determined by the input power because multiple powers within the cavity satisfy the resonance condition. Pulsating behavior is observed within the resonator output, and is attributed to noise within the experimental setup driving the resonator between the multiple allowed output powers.
We present a theoretical model that describes accurately the nonlinear phenomenon of optical bistability in silicon-waveguide resonators but remains amenable to analytical results. Using this model, we derive a transcendental equation governing the intensity of a continuous wave transmitted through a Fabry-Perot resonator formed using a silicon-on-insulator waveguide. This equation reveals a dual role of free carriers in the formation of optical bistability in silicon. First, it shows that free-carrier absorption results in a saturation of the transmitted intensity. Second, the free-carrier dispersion and the thermo-optic effect may introduce phase shifts far exceeding those resulting from the Kerr effect alone, thus enabling one to achieve optical bistability in ultrashort resonators that are only a few micrometers long. Bistability can occur even when waveguide facets are not coated because natural reflectivity of the silicon- r interface can provide sufficient feedback. We find that it is possible to control the input-output characteristics of silicon-based resonators by changing the free-carrier lifetime using a reverse-biased p-n junction. We show theoretically that such a technique is suitable for realization of electronically assisted optical switching at a fixed input power and it may lead to silicon-based, nanometer-size, optical memories.
Bistability of an optical resonator with distributed Bragg-reflectors is analyzed by using the coupled-mode theory. Hysteresis and nonlinear properties are given as a function of the quantities characterizing the Kerr medium (the quadratic electrooptic coefficient n 2 and the length of the Kerr medium l ) and the propagation characteristics of the corrugated waveguide (the coupling coefficient k and the optical loss in the corrugated waveguide Γ). We show that the optical resonator with distributed Bragg-reflectors has a multi-valued transmission characteristic by the Kerr effect. From the numerical calculations, the up-switching and down-switching power intensities of bistable operation are estimated.
Photonic data transmission and processing require highly efficient all-optical elements for signal amplification, switching and data storage. It could be shown experimentally that semiconductor planar resonators can be envisaged as promising candidates [1]. In particular, optical bistability, that has been shown to exist in these configurations, opens a wide field of applications. Because the operating frequencies are near the band gap of the direct semiconductors used the nonlinearities are giant. Hence the critical power for nonlinear effects to occur is fairly moderate. In view of these advantages it might be worthwhile to study such resonators in a waveguide scheme because it can be included into integrated optics configurations. In planar resonators one has not to worry about the absorption, being extremely large near the gap, because the overall thickness is only a few micrometers and they are usually operated in reflection. The situation appears more involved in waveguides. Usually one prefers to exploit the transmitted signal in order to separate input and output channels. Moreover the efficiency of the distributed Bragg reflectors, surrounding the cavity, is usually some orders of magnitude less than that of conventional planar mirrors requiring rather long reflectors. Because the cavity length exceeds that of planar resonators considerably too one has to guarantee that the overwhelming part of the resonator is essentially transparent for the guided mode. This has of course the consequence that it does not contribute to any resonant nonlinear effect. Hence we propose a resonator that is only loaded by a thin layer of nonlinear but absorbing material (GaAs) in the cavity region (see Fig.1).
A theoretical demonstration of optical bistability in periodic layered media, particularly in long-period GaAs/AlAs superlattices is presented. The proposed structure consists of a periodic multilayer system, as opposed to previously demonstrated nonlinear bistable devices which employed Fabry-Perot etalons. The optical resonance effect which is essential for bistable devices is, in this case, induced by a refractive index modulation. The nonlinear active medium is distributed in the whole structure rather than placed between the two mirrors of a Fabry-Perot cavity. It is shown by a complete calculation of wave propagation in the periodic nonlinear medium that a multiple valued feature appears in the structure's nonlinear reflectivity spectrum. The input/output characteristics of the structure exhibit bistable hysteresis similar to that of a nonlinear Fabry-Perot etalon.>
Dispersive optical bistability in a Fabry-Perot, a distributed feedback (DFB), or a distributed Bragg reflector (DBR), semiconductor laser amplifier has recently attracted much attention, because of its potential in the operation of highly functional optical devices. While the steady-state operation of bistable diode laser amplifiers are well understood, studies of the dynamic properties have been limited to switching time, critical slowing down and output spiking measurements[1-3]. Little attention has been paid to the dynamic frequency chirp which is associated with the turn-on spike at the onset of light injection. Such frequency chirp exists because in dispersive bistability the Fabry-Perot resonance (or the DBR/DFB transmission peak) sweeps through the injected wavelength as a result of alight induced refractive index change. In this paper, we report on a theoretical analysis and the first experimental observation of this dynamic chirp in a Fabry-Perot type nonlinear semiconductor laser amplifier. It is found that the magnitude of the chirp depends on the input power, which in turn is related to critical slowing down.