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Japanese Journal of Applied Physics

Bistability of Optical Resonator with Distributed Bragg-Reflectors by Using the Kerr Effect

Masahiro Okuda, Kiyoshi Onaka

Published May 1, 1977• 30 citations
Publisher

Abstract

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.

DOI
10.1143/jjap.16.769

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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.
The effect of the bleaching property of a saturable absorber and the optical loss in a corrugated waveguide on bistability is analyzed by using the coupled-mode theory. Hysteresis and nonlinear properties are given as a function of the quantities characterizing the saturable absorber (the absorption coefficient Γ 0 , and the length of saturable absorber l ) and the propagation characteristics of the corrugated waveguide (the coupling coefficient k and the optical loss in waveguide Γ). It is clear, by selecting the optimum values of these parameters., that the saturable optical resonator has a bistable property which is useful as an optical gate, an optical amplifier, and an optical memory in integrated optical circuits.
Transient behaviors of a saturable optical resonator with distributed Bragg-reflectors are analyzed in the scheme of time-dependent coupled wave equations. The up and down switching times of the saturable optical resonators are calculated for various values of the optical intensity, the width of incident pulse, and the relaxation time and the length of the saturable absorber. It is shown that the switching time of a saturable resonator has an optimum value for the optical intensity and the width of the incident pulse. Also, the switching time becomes shorter, as increasing the normalized length of the saturable absorber. However, even if the optimum values of the optical intensity and the width of the incident pulse are employed, the switching time is much larger than the transit time in the saturable resonator, because the transmission pulse is constructed by multiple reflections in the reflector.
Optical bistability in a nonlinearly reflective fiber grating through the mode coupling between the LP/sub 01/ and counter propagation LP/sub 02/ modes (i,e., the reflective LP/sub 01//spl rlhar2/LP/sub 02/ mode converter) is investigated by using the coupled-mode theory. Both the transmissive and the reflective properties of this nonlinear device are analyzed, which show that the output-versus-input relation exhibits the optical bistability. The switching power and the bistable hysteresis performances are also discussed. In addition, the comparison between the nonlinearly reflective mode converter (LP/sub 01//spl rlhar2/LP/sub 02/) and the nonlinear fiber Bragg grating reflector (i,e., the LP/sub 01/ and counter-propagation LP/sub 01/ modes) is also presented. It is shown that the former has much lower switching power than the latter.>
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).
Bistable optical systems are of considerable interest to produce high-speed optical signal-processing devices. Among them, those that use a nonlinear optical medium are attractive because they allow the lowest possible switching time. By the use of a suitable electromagnetic resonance, the bistability threshold can be lowered to a reasonnable value, for the incident power. Keeping in mind that a bistable optical system should be well adapted to optical integration in a planar geometry, one is naturally confronted to a corrugated waveguide filled with a nonlinear (Kerr) medium.