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arXiv:2201.06272 · Journal of Physics D Applied Physics

Analysis of bistability at the coupling between waveguide and whispering gallery modes of a nonlinear hemicylinder

Henrik A. Parsamyan, Khachik Sahakyan, Khachatur Nerkararyan

Published Jan 10, 2022• 2 citations
arXivHTMLPDF

Abstract

Abstract The optical bistability caused by the coupling between modes of the parallel-plate waveguide and a nonlinear hemicylindrical crystal is studied using theoretical and numerical analysis. In such a system a waveguide channel is parallelly coupled to whispering gallery modes (WGMs) of a hemicylindrical microresonator ensuring bistable behaviour at input intensities of the order of a few MW cm−2. The characteristic minimum switching time of the system (around 30 ps) can be controlled by varying the thickness of the metal layer which couples the waveguide and WGMs. This is conditioned by the change of the quality Q-factor, as well as the coupling coefficient of the resonator. The main advantages of the system are fabrication simplicity, small sizes of the order of 3 µm, integrability with other optical components and the possibility of adjusting the processes by making use of the electro-optical effect.

DOI
10.1088/1361-6463/ac49b8

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Abstract The optical bistability caused by the coupling between modes of the parallel-plate waveguide and a nonlinear hemicylindrical crystal is studied using theoretical and numerical analysis. In such a system a waveguide channel is parallelly coupled to whispering gallery modes (WGMs) of a hemicylindrical microresonator ensuring bistable behaviour at input intensities of the order of a few MW cm−2. The characteristic minimum switching time of the system (around 30 ps) can be controlled by varying the thickness of the metal layer which couples the waveguide and WGMs. This is conditioned by the change of the quality Q-factor, as well as the coupling coefficient of the resonator. The main advantages of the system are fabrication simplicity, small sizes of the order of 3 µm, integrability with other optical components and the possibility of adjusting the processes by making use of the electro-optical effect.
Optical whispering gallery modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago.This phenomenon has a rather general nature, equally applicable to sound and all other waves.It enables resonators of unique properties attractive both in science and engineering.Very high quality factors of optical WGM resonators persisting in a wide wavelength range spanning from radio frequencies to ultraviolet light, their small mode volume, and tunable in-and out-coupling make them exceptionally efficient for nonlinear optical applications.Nonlinear optics facilitates interaction of photons with each other and with other physical systems, and is of prime importance in quantum optics.In this paper we review numerous applications of WGM resonators in nonlinear and quantum optics.We outline the current areas of interest, summarize progress, highlight difficulties, and discuss possible future development trends in these areas.
We analyze the resonant linear and nonlinear transmission through a photonic crystal waveguide side-coupled to a Kerr-nonlinear photonic crystal resonator. First, we extend the standard coupled-mode theory analysis to photonic crystal structures and obtain explicit analytical expressions for the bistability thresholds and transmission coefficients which provide the basis for a detailed understanding of the possibilities associated with these structures. Next, we discuss limitations of standard coupled-mode theory and present an alternative analytical approach based on the effective discrete equations derived using a Green's function method. We find that the discrete nature of the photonic crystal waveguides allows a geometry-driven enhancement of nonlinear effects by shifting the resonator location relative to the waveguide, thus providing an additional control of resonant waveguide transmission and Fano resonances. We further demonstrate that this enhancement may result in the lowering of the bistability threshold and switching power of nonlinear devices by several orders of magnitude. Finally, we show that employing such enhancements is of paramount importance for the design of all-optical devices based on slow-light photonic crystal waveguides.
We designed and manufactured an optical bistability waveguide device based on nonlinear one-dimensional photonic crystal used CdS_xSe_(1-x) doped glass. This kind of semiconductor doped glass has large nonlinear refractive index and nonlinear fast response time. The distribution of refractive index of the nonlinear one-dimensional photonic crystal waveguide satisfies sine function. We obtained the nonlinear photonic crystal waveguide by exposure holography and etching techniques. Length of the photonic crystal waveguide is about 3 mm. The height of the peak-groove of the waveguide is 0.1 μm. According to our design, the center of bandgap of the one-dimensional photonic crystal lies at 514.5 nm while the power density of the incident light, the incident light was reflected by the photonic crystal. When the power density of the incident light increasing, the bandgap is shifting to the direc-tion of short wavelength due to the decreasing of the refractive index with the increasing of the incident power density, so more incident light is transmitted. In experiment, we used an active mode-locking pulse of Ar ion laser as the light source which wavelength is 514.5 nm, repeating frequency is 82 MHz and pulse width is 200 ps. The light beam was coupled into the device by prism with a laser average power of 1.28 W (in the case of nonlinear saturation operation, optimum coupling efficiency is about 6%). Pulse wave forms of incident light and transmitted from sample were recorded in turn by 7 904 oscilloscope. The optical bistability curve of input power density and output one is fitted by computer. We obtained the threshold power density of bistable switch to be 1.60×10~5 W/cm~2 (it is equivalent to average power of 77 mW) and both the rise and fall time are 63 ps. We used the Finite Difference Time Domain Method to obtain the characteristics of the bandgap shift with the incident power density increasing of the nonlinear photonic crystal and calculate the optical bistability curve of this device. In theory, the threshold power density of bistable switch is about 1.40×10~5 W/cm~2 and the switch time is about 50 ps. The theoretical results agree well with the experimental ones. This device is a new and feasible one for optical information process and optical computing in the future.
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).