Abstract
The ‘ring cavity problem’ of nonlinear laser optics describes the behavior of a laser beam which propagates through a ‘bistable optical cavity’; this is a ring resonator system consisting of a nonlinear dielectric medium (of length ℓ), and several partially transmitting mirrors including an input and an output mirror. During one ring circulation, the propagating laser beam enters the nonlinear medium, emerges, is partially transmitted through the output mirror, is partially fed back around the circuit mirror system to the entry point at the input mirror, and added there to the input pump field beam. The system describes the spatial modulation and filtration of laser beams in order to achieve ‘memory’. The appearance of a wide range of spontaneously emerging spatial coherent structures (‘filaments’) is of practical importance in laser optics where the physical control of these structures has led to new and natural methods for information processing (‘pixel transfer’), as well as a theoretical model of a route to chaos and turbulence; for the physical background see references [3]–[11], [13]–[18].
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Illner, R., Lange, H., Teismann, H. (2002). On some Mathematical Aspects of the Ring Cavity Problem. In: Lorenzi, A., Ruf, B. (eds) Evolution Equations, Semigroups and Functional Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 50. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8221-7_10
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