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Journal of Applied Physics

Transverse effects and enhanced dispersive optical bistability in a nonlinear Fabry–Pérot filled with a self-focusing medium

R. Reinisch, Guy Vitrant

Published Jun 1, 1990• 11 citations
Publisher

Abstract

This paper is concerned with transverse effects arising from diffraction in a nonlinear Fabry–Pérot filled with a self-focusing medium. It is shown that the resulting bistable loop is ‘‘enhanced’’ with respect to the plane-wave one. This result contrasts with the self-defocusing case where optical bistability disappears when decreasing the width of the input beam.

DOI
10.1063/1.345102

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Free-Space Diffraction Effects in AN all Optical Passive Driven System

Darlena J. Jones

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.

•Jan 1, 1993•0 citations
This paper is concerned with transverse effects arising from diffraction in a nonlinear Fabry–Pérot filled with a self-focusing medium. It is shown that the resulting bistable loop is ‘‘enhanced’’ with respect to the plane-wave one. This result contrasts with the self-defocusing case where optical bistability disappears when decreasing the width of the input beam.
Bistable operation of an initially detuned Fabry-Perot etalon with a spatially varying transverse input is studied numerically. Non-linear medium propagation effects are accounted for explicitly. Fast Fourier transforms are used to treat beam diffraction, providing a computationally efficient numerical algorithm. Steady state bistable loops are computed for a Fresnel number close to unity, under both self-focusing and defocusing conditions. Beam diffraction causes earlier switch-on in the defocusing case.
A transverse optical bistability would not occur with a plane-wave input; it is characterized by pronounced changes in transverse profiles, but not in total transmission.1 The systems studied here consist of a single feedback mirror and a nonlinear medium (Na vapor) sufficiently thin that diffraction is negligible during the nonlinear radially dependent phase encoding. With the input focused beyond (before) the Na and the mirror center of curvature on the input (output) side of the Na, self-defocusing (self-focusing) optical bistability is seen--but only when the feedback is nonconcentric, i.e., the feedback beam is displaced off-axis relative to the input beam. If cylindrical lenses are used to form an elongated focus in the Na, bistability is still seen. This suggests that one-transverse-dimension (ID) theories may be adequate to describe the system's steady-state and transient behavior. ID numerical simulations with nonconcentric feedback are under way.
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.