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Annual Meeting Optical Society of America

Hysteresis effects attributed to free-space diffraction in a passive optical system

D. J. Jones, Donna Kay Bandy

Published Jan 1, 1992• 0 citations
Publisher

Abstract

We investigate the time-dependent behavior of an optically thin passive medium driven by an external coherent signal and show dynamical hysteresis effects in the regimes of large and small Fresnel numbers, positive and negative detuning, and changes in the cavity quality. We attribute shifting and deformation of the bistable loop and spatial hysteresis to free-space diffraction effects that are independent of diffusive and diffractive coupling within the medium. Since radial variation of the bistable loop is not present in the parameter space explored, we suggest that free-space diffraction does not contribute to this effect and adds weight to experimental findings that evidence diffusive coupling as the dominant mechanism for radial variations of the bistable loop.

DOI
10.1364/oam.1992.wq7

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We investigate the time-dependent behavior of an optically thin passive medium driven by an external coherent signal and show dynamical hysteresis effects in the regimes of large and small Fresnel numbers, positive and negative detuning, and changes in the cavity quality. We attribute shifting and deformation of the bistable loop and spatial hysteresis to free-space diffraction effects that are independent of diffusive and diffractive coupling within the medium. Since radial variation of the bistable loop is not present in the parameter space explored, we suggest that free-space diffraction does not contribute to this effect and adds weight to experimental findings that evidence diffusive coupling as the dominant mechanism for radial variations of the bistable loop.
Transverse effects are known to play a central role in nonlinear-optical systems.Since experiments are generally performed with lasers with finite transverse dimensions, the transverse nature of the field must be considered.Experimental evidence, for example, indicates that mechanisms in the form of diffusive and diffractive coupling within the medium, free-space diffraction, or some combination of these, can create transverse structures which are important in optical bistability and self-focusing/defocusing.In particular, transverse coupling is attributed to such phenomena as radial dependence of the switch up times of bistable loops, spatial hysteresis, and the formation of solitary waves in passive systems.The dynamical effects of free-space diffraction in a unidirectional ring cavity containing a thin resonant absorber driven by an external coherent signal is considered.Minimal focusing effects exist in this system by incorporating a thin medium whose width is small compared to the cavity length and Raleigh range.There is no restriction on the medium response time relative to the round trip time; i.e. the time-dependent polarization is not adiabatically eliminated from the equations of motion.Free-space diffraction effects are isolated and diffraction and diffusive coupling within the medium is negligible.In this model where free-space diffraction is the dominant mechanism for changing the field profile in the system, shifting, deformation, and radial variation of the bistable loop and spatial hysteresis is attributed to an inherent dispersion induced by the free-space diffraction.
By incorporating the radial dependence of the field, we explore the dynamical behavior of a passive optical system consisting of two focusing lenses, optically thin passive medium, and two partially transmitting mirrors, where one mirror functions as the entrance port for the external signal, and the second functions as the output coupler. The medium and the free-space diffraction are described by the Maxwell-Bloch equations and Kirchhoff's diffraction integral, respectively. A comparison between confocal resonators and nonconfocal resonators is made, and polarization effects are isolated.
Self-focusing effects in optical bistable hysteresis loops have been observed in a GaAs-GaAlAs superlattice.1 Experimentally, one sees drastic overshooting in the hysteresis loops and changes in the output profile as the imaging lens is translated along the propagation direction, thus imaging different object planes onto a fixed image plane (i.e. aperture). Nearly identical results are found by a one-transverse-dimension numerical simulation of good-cavity bistability in which the output is free-space propagated backwards in space, corresponding to the movement of the imaging lens. These effects arise from a radially-dependent phase shift caused by the excitonic nonlinear refraction and a gaussian beam profile.
A nonlinear oscillator model is used as a prototypical medium for intrinsic optical bistability.1 The phenomenon of intrinsic optical bistability is so named because the medium does not require the optical feedback of a cavity. In this model we retain dispersive effects and introduce a diffractive coupling of the electromagnetic field amplitude. The threshold of the optical bistable device is insensitive to the Fresnel number, which determines the coupling between field amplitudes at different transverse positions.2 This is useful for obtaining reproducible operating characteristics of an array of devices. The medium can be introduced inside a cavity to understand the role of dispersive and diffractive effects in a more fundamental way. The threshold intensity is again insensitive to the Fresnel number. Furthermore, we observe instabilities in the cavity configuration, but no chaotic solutions were found. The periodic instabilities are sensitive functions of the Fresnel number.
We discuss a novel type of optical instability, which leads to the spontaneous formation of a stationary spatial structure, instead of to the onset of oscillations or pulsations. A passive system is contained in an optical cavity, to which we add two lateral mirrors. Under appropriate conditions, diffraction of radiation can induce the onset of a transverse-stripe structure in an initially uniform plane-wave field configuration. In this paper, we consider the case of a homogeneously broadened two-level system. The model on which our analysis is based is derived from the Maxwell-Bloch equations in the paraxial approximation, using the mean-field limit and assuming a large Fresnel number. We show that, with respect to the bistability parameter C, the threshold of the spatial instability coincides with the bistability threshold for absorptive, resonant optical bistability. The spatial instability requires, however, a detuned configuration and can arise both in the absence and presence of bistability. In the latter case, it can occur both in the lower and in the upper branch of the steady-state curve. The instability is caused by competition between different transverse modes, which realize a situation of spatial coexistence, different from the state of temporal coexistence which characterizes the spontaneous oscillations that arise from the previously known multimode instabilities. Finally, we discuss some points relevant for an experimental observation of this phenomenon.