Laser beams that contain phase singularities can be generated with computer-generated holograms, which in the simplest case have the form of spiral Fresnel zone plates.

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Generation of optical phase singularities by computer-generated holograms.

Pattern formation and competition in nonlinear optics

Bistability of the transverse configuration of the optical field is found for a helium–neon laser oscillating in the TEM01* hybrid optical-resonator mode. Optically induced switching between the mirror-symmetric field patterns occurs when a fraction of the spatially rotated output field is reinjected into the laser resonator. These phenomena are described theoretically with laser equations modeling the mutual interaction of the two first-order transverse modes of the optical resonator. The experimentally observed bistability and switching of the field patterns is in full qualitative agreement with the theoretical results.

Bistability and optical switching of spatial patterns in a laser

Beams of light interacting with nonlinear-optical materials naturally form complex transverse profiles. Self-focusing, filamentation, modulational instabilities, spontaneous pattern formation and symmetry breaking, nonlinear waveguiding, and transverse mode excitation are but some of the many phenomena that are observed in lasers, in optical bistability, and in the free interaction of beams. As an introduction to a special issue of the Journal of the Optical Society of America B on transverse effects in nonlinear-optical systems, we provide this overview of history and current work.

Overview of transverse effects in nonlinear-optical systems

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

We investigate the spontaneous emergence of transverse patterns in lasers by using both the standard two-level model and the so-called cubic approximation, which is generally valid in the threshold regions. The stationary intensity configurations fall into two distinct classes. The first includes solutions of the single-mode type with the frequency and spatial structure of one of the transverse resonances. The solutions of the second group involve the simultaneous oscillation of several cavity modes, operating in such a way as to produce a stationary intensity profile. The stationary character of these multimode configurations emerges from the fact that the transverse modes of the resonator lock onto a common frequency during the nonlinear transient. We call this phenomenon cooperative frequency locking.

C. Oldano

Papers

Cooperative frequency locking and stationary spatial structures in lasers