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Journal of the Optical Society of America B

Optical hysteresis shape transformation using linear polarization components

Saif A. Al Graiti, Drew N. Maywar

Published Nov 11, 2021• 1 citation
Publisher

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.

DOI
10.1364/josab.439048

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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.
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.
Abstract We demonstrate and elucidate the local selectable inversion of the hysteresis shape of a bistable optical signal after fan-out. This selectability is based on a hysteresis-shape transformation that yields a switching contrast over 20 dB in magnitude for both the inversion clockwise (CW) and the non-inversion counterclockwise (CCW) hysteresis shapes, while maintaining input-switching powers. This behavior leverages an initial signal whose bistability is manifested by its state of polarization; a generalized Malus’ law elucidates how selection is possible by controlling the transmittivity hysteresis through each local polarizer. The concept is demonstrated using a Fabry–Pérot semiconductor optical amplifier to produce the initial bistable polarization-rotating signal, followed by a 1 × 2 fan-out and the realization of all four hysteresis shapes at each location, independent of the other location. This fan-out and selectable inversion behavior is applicable to other nonlinear photonic systems and provides new functionality for parallel optical processing.
We study the simultaneous occurrence of dispersive optical bistability and nonlinear polarization rotation in a nonlinear photonic resonator. The demonstrated bistable hysteresis curves of the Stokes parameters broaden the notion of optical bistability in nonlinear resonators beyond that of the traditional optical-power hysteresis curve. We present a theoretical model to fully understand the polarization hysteresis curves observed in the laboratory and to establish the relevant scaling parameters for bistable action. By optimizing the optical-signal power injected into each polarization mode of the resonator and optimizing the small-signal birefringence of the resonator by selection of the signal wavelength, a polarization rotation of 30% orthogonality was achieved between stable polarization states in the lab. The theoretical and experimental methods reported here are carried out for the case of a Fabry–Perot semiconductor optical amplifier, and are extendable to the investigation of simultaneous occurrence of these phenomena in other nonlinear media (such as Kerr media) and other photonic resonators.
We present what is to our knowledge the first study of optical bistability in Fabry-Perot laser-diode amplifiers that have asymmetric facet reflectivities. When operated in reflection, the light input-light output characteristics exhibit a transition from counterclockwise to clockwise hysteresis by way of an X-shaped or butterfly hysteresis. This transition can be achieved by a change in either the device bias or the phase detuning of the incident light. Our results are in good agreement with calculation.
We have measured optical power and wavelength polarization bistability in a 1550 nm-Vertical Cavity Surface-Emitting Laser (VCSEL) subject to orthogonally-polarized optical injection into the orthogonal polarization of the fundamental transverse mode. Optical bistability with very wide hysteresis cycles, up to four times wider than previously reported results has been measured for both the optical power and wavelength domain. We also report the experimental observation of three different shapes of polarization bistability, anticlockwise, clockwise and X-Shape bistability, all of them with wide hysteresis cycles. This rich variety of behaviour at the important wavelength of 1550 nm offers promise for the use of VCSELs for all-optical signal processing and optical switching/routing applications.
We present experimental measurements of bistable characteristics for the case of a 1.55-/spl mu/m symmetric Fabry-Perot laser amplifier with a particularly rich variety of behavior for reflected signals. Three main forms of hysteresis loops are observed on reflection. The hysteresis loop changes from anticlockwise to clockwise hysteresis in the optical output-input characteristic when the drive current or initial phase detuning is changed. A "butterfly" hysteresis loop is observed experimentally at an optical input power as low as 300 /spl mu/W for a drive current equal to 94% of the lasing threshold. The dependence of the reflective optical bistability on drive current, initial phase detuning, and injected optical pewter has been investigated for the first time in an uncoated 1.55-/spl mu/m amplifier. Measurements of the device voltage shifts on switching reveal hysteresis loops which match those in the corresponding optical powers and which indicate the amount of gain saturation and nonlinear refraction responsible for bistability. An analytical model is used to describe the observed reflective bistability and to give insight into the detailed physical mechanisms responsible.