Pattern formation and competition in nonlinear optics

Publisher Summary This chapter focuses on the concept of optical pattern formation. The field of optical pattern formation (OPF) studies the spatial and spatiotemporal phenomena that arise in the structure of electromagnetic field in the planes orthogonal with respect to the direction of propagation. Most theoretical treatments of the interaction between matter and radiation introduce the plane wave approximation—that is, they assume that the electric field is uniform in each transverse plane. However, the field of OPF studies mainly the interaction with nonlinear media, where the phenomena emerge spontaneously as a consequence of an instability; another name that is commonly used to designate OPF is “transverse nonlinear optics.” Historically, the broad interest in OPF emerged as a natural evolution of the previous development of the field of optical instabilities and chaos, when the main attention shifted gradually from purely temporal effects to spatio-temporal phenomena. For both the fields of optical instabilities and OPF, continuous inspiration arose from the formulation of general disciplines as Haken's synergetics or Prigogine's theory of dissipative structures

Optical Pattern Formation

The characteristics features of the field of Transverse Nonlinear Optics are briefly illustrated, as an introduction to this special issue of Chaos, Solitons & Fractals .

Transverse nonlinear optics: Introduction and review

The semiconductor resonator is an example of an optical system where two modulational instabilities with different wave numbers coexist. In the limit of nascent bistability, the dynamics is generically described by a nonvariational real order parameter equation, of which we give a detailed derivation. This considerably simplifies the linear and weakly nonlinear stability analyses. When the two instabilities are close together, we derive normal form equations and put special emphasis on "envelope" branches of solutions. These particular solutions may connect the two instability points or form an isola. On the basis of these rigorous results, we finally discuss the case of distant modulational instabilities, in both one and two transverse dimensions.

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Optical patterns with different wavelengths.

Patterns, fronts and structures in a Liquid-Crystal-Light-Valve with optical feedback

Localized structures in chaotic patterns: From disorder to ordering

Multi-conical instability in the passive ring cavity: linear analysis

Two-dimensional patterns of a passive optical ring cavity with delayed feedback are presented in a case where multiconical emission is predicted by a linear stability analysis. Multiconical emission can indeed be obtained when a diaphragm is inserted inside the cavity. The first cone exhibits hexagonal pattern, only on the defocusing side, while a metastable pentagon is found on the focusing side; multi-cross-rolls are observed on the outer cones. A modified version of the mean field model predicting multiconical emission is discussed.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A. S. Patrascu

Papers

Localized structures in chaotic patterns: From disorder to ordering

Multi-conical instability in the passive ring cavity: linear analysis

Transverse effects in an optical passive system with time delay and feedback