Optical Pattern Formation Research Articles

Bessel function modes and O(2)-symmetry breaking in diffractive optical pattern formation processes

Spontaneous two-dimensional transverse optical pattern formation is investigated in a single feedback mirror experiment using nematic liquid crystals as nonlinear optical media. It is shown that instead of theoretically predicted hexagons assuming plane wave input waves, the observed patterns are more correctly represented by spatial Bessel function modes if the symmetry of finite size laser beams is taken into account.

Chaos, complexity and morphogenesis: Optical-pattern formation and recognition

In 1952 A. Turing introduced the concept of chemical morphogenesis. A medium with at least two interacting and diffusing components (activator and inhibitor) can be subjected to spontaneous pattern formation, with a scale length independent of the boundary conditions, and thus maintained even in the infinite volume limit. This is at variance with pattern formation in fluids (as,e.g., Rayleigh-Benard and Faraday instabilities) where the size is imposed by the boundary geometry. In non-linear optics, patterns emerge from the coupling of a diffractive equation describing electromagnetic propagation with a diffusion equation describing the local modification of the polarizability in a medium. As we adjust an extensive parameter (the so-called Fresnel numberF) corresponding to the optical aspect ratio, we observe a transition from a regime dominated by the boundary constraints to a Turing-type regime dominated by the bulk parameter. This is equivalent to saying that the preminent role is due to the diffractive equation in one case and to the diffusive one in the other. Morphogenesis for lowF arises from the non-linear competition among a small number of degrees of freedom, giving rise to a space-uniform excitation with a low-dimensional dynamics. This gives rise to the different scenarios of chaos. Their properties have been explored in the past decade. In the large-F case, the space-time instabilities rapidly evolve toward complex patterns, not reducible to a few indicators. In the case of two-dimensional fields, global characterization is achieved via the statistics of the topological defects.

Local and global effects of boundaries on optical-pattern formation in Kerr media.

The space-time field evolution in a Kerr slice with single feedback mirror is considered. A full symmetry analysis of the governing equations reveals profound differences between plane-wave and Gaussian-beam excitation. For Gaussian-beam pumping primary bifurcations to a succession of polygonal figures are predicted and confirmed in numerical simulations. Secondary bifurcations are complicated by competition between local and global bifurcations. Chaotic itinerancy and intermittency are among the phenomena observed in the simulations. For broad pump beams, multispot polygons with fivefold symmetry are observed to coexist with sixfold quasilattice patterns, in excellent agreement with the theoretical predictions based on symmetry considerations only

Transition from boundary- to bulk-controlled regimes in optical pattern formation.

By increasing the Fresnel number F of the cavity of a photorefractive oscillator, we report the transition from a boundary-controlled regime, where the size of the transverse patterns scales as 1/ \ensuremath{\surd}F , to a bulk-controlled regime where the pattern size is independent of F. In this new regime, the size corresponds to an intrinsic correlation length imposed by diffusion processes within the material. The wave number spectrum of the emitted field has a sharp cutoff, corresponding to the length scale of bulk correlations. Such a new behavior is explained by the wave number dependence of the gain within the instability region.

Spontaneous optical pattern formation in a nematic liquid crystal with feedback mirror

Spontaneous two dimensional transverse optical pattern formation has been observed in a simple feedback mirror experiment using a hybridly aligned nematic liquid crystal 5CB as a nonlinear optical medium. Grating wave-numbers of the patterns and threshold intensities are investigated as a function of the distance between the nonlinear film and the mirror. Comparison with a theoretical model of the reorientational optical nonlinearity and the present arrangement is presented.

Modulational-induced optical pattern formation in a passive optical-feedback system

Two-dimensional metastable patterns can appear randomly across a broad laser beam profile in a passive optical ring cavity. The instability responsible for pattern formation is primarily modulational in nature, leading to a competitive interaction between strongly saturated solitary-wave ringlike and filamentary spatial structures. The complexity of pattern formation depends sensitively on saturated filament density, which can be conveniently controlled in an optical-feedback arrangement. Our preliminary computational results suggest that the instability domain can be partitioned into two general categories: (1) rapid modulational growth to a single stationary filament or a long-lived metastable pattern involving five filaments growing directly from a shelflike ridge about the central filament or (2) a significantly slower formation of localized filaments forming primarily from a slow modulational growth on fully developed saturated solitary-wave rings. One-dimensional computations with a retarded material response indicate that the general trend of unstable formation should be relatively insensitive to finite retardation effects.