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Physical Review Letters

Role of Diffractive Coupling and Self-Focusing or Defocusing in the Dynamical Switching of a Bistable Optical Cavity

Jerome V. Moloney, H. M. Gibbs

Published Jun 7, 1982• 106 citations
Publisher

Abstract

Optical bistability transients have been computed including one transverse Cartesian coordinate. With a Gaussian transverse input profile but weak diffractive coupling, the switchup intensity is radially dependent, and the output requires hundreds of round trips to reach steady state. Strong diffractive coupling results in whole-beam switchup and much faster convergence to steady state.

DOI
10.1103/physrevlett.48.1607

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Optical bistability transients have been computed including one transverse Cartesian coordinate. With a Gaussian transverse input profile but weak diffractive coupling, the switchup intensity is radially dependent, and the output requires hundreds of round trips to reach steady state. Strong diffractive coupling results in whole-beam switchup and much faster convergence to steady state.
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.
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.
Pioneered by Moloney and collaborators [1], transverse effects of nonlinear passive systems in a ring cavity have been the object of extensive study. Analytical investigations with diffractive coupling in one transverse dimension have demonstrated [1] that static and dynamic transverse structures occur in this system. Extension of the mean-field dispersive model developed from optical bistability to include diffraction [2] independently demonstrated qualitatively similar features, again in one transverse dimension. Investigations in two transverse dimensions have been largely confined to numerical studies by the Moloney group [1], showing for gaussian beam illumination ring structures which develop through azimuthal instability to a pattern of spots which typically execute a slow chaotic motion with a progressive loss of symmetries.
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.