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Nonlinear Optics

Distribution and simultaneous local control of the optical hysteresis shape

Mohamed Maafa, Saif A. Al Graiti, Son Kim Pham, Drew N. Maywar

Published Jan 1, 2021• 2 citations
Publisher

Abstract

We experimentally demonstrate the distribution of a bistable optical signal to two locations, and then independently and simultaneously control the hysteresis shape at each location using local sets of linear optical components.
DOI
10.1364/nlo.2021.nf2a.4

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We experimentally demonstrate the control of the hysteresis shape of a bistable optical signal at a location downstream of the nonlinear photonic resonator within which the bistability is generated; this shape control mechanism is performed without any signal sent upstream to the bistable system. The downstream shape-control element consists of a fiber-optic polarization controller and linear polarizer in series, and the nonlinear resonator generates an optical signal whose bistable branches exhibit different states of power and polarization. The diversity of demonstrated hysteresis shapes include the canonical counter-clockwise (CCW) shape (S-shape), the clockwise (CW) shape (inverted S-shape), and butterfly shapes; since all shapes originate from the same bistable signal, all shapes exhibit the same switching input powers. Moreover, the shape-selection process enhances the bistable switching contrast to 20 and 21 dB for the CCW and CW shapes, respectively. The shape-selection technique is demonstrated using a Fabry-Pérot semiconductor optical amplifier, is applicable to other nonlinear photonic resonators, and provides flexibility to future combinational and sequential all-optical signal processing applications.
We provide a mathematical model to elucidate how a linear polarizer can be used to transform the shape of an optical-power hysteresis curve into the canonical counterclockwise (CCW) shape, clockwise (CW) shape, and upward-switching and downward-switching butterfly shapes. This transformation is possible for optical signals whose states of polarization also exhibit hysteresis. Critical to our model is a generalized Malus' law that accounts for elliptical input polarization as well as insertion loss, finite extinction ratio, and pass-axis orientation angle of the linear polarizer. The generalized Malus' law reveals that the transmittivity of the polarizer itself exhibits a bistable hysteresis curve, and this transmittivity acts on the input-power hysteresis curve to produce the variety of output-power shapes. Additionally, we model the optimization of the hysteresis contrast of the CCW and CW shapes, achieving 20 dB or more by using a polarization controller placed upstream of the polarizer. Modeling and experimental validation are carried out using a polarization-varying bistable signal generated by an anisotropic Fabry–Perot semiconductor optical amplifier, and the results are applicable to other nonlinear resonators and means of polarization-varying signal generation. This model can be used for the study, design, and optimization of a variety of sequential and combinational all-optical signal processing applications.