Optical hysteresis shape transformation using linear polarization components

Abstract

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.