The Liquid Crystal Light Valve with Optical Feedback: a Case Study in Pattern Formation

Pattern formation in different systems has attracted a growing attention in these last years. In the field of optics, transverse profiles of propagating beams have been investigated since the first studies on interference and diffraction. This initial interest was raised to a new level by the growing importance of nonlinear effects that could be observed with high intensity beams, typically laser light. In an extended nonlinear medium, above a certain threshold, the uniform intensity becomes unstable and the space-time distribution splits into domains that can be correlated on a long range (patterns) or on a short range (localized structures, space-time chaos). The attention has been focussed on two main groups of systems: active and passive systems. Active optical devices are those in which the medium is in an excited state and it can transfer energy to the light field, whereas passive optical devices are those in which the medium is in its ground state. In the case of active optics the systems investigated are large Fresnel number lasers, photorefractive and parametric oscillators. In passive optics, the simplest system one can think of consists of a laser beam propagating in a nonlinear optical medium. A great impulse to systematic investigation of patterns in passive optics was given nonlinear materials contained in optical cavities. A good compromise between simplicity of theoretical treatment and feasibility of experimental