Light Propagation In Liquid Crystals Research Articles

Two-Dimensional Solitons in Nonlocal Media: A Brief Review

This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history in optics and related areas. Some results produced by the work (such as solitons supported by thermal nonlinearity in optical glasses, and orientational nonlinearity, which affects light propagation in liquid crystals) are well known, and have been properly reviewed in the literature, therefore the respective models are outlined in the present review in a brief form. Some other studies, such as those addressing models with fractional diffraction, which is represented by a linear nonlocal operator, have started more recently, therefore it will be relevant to review them in detail when more results will be accumulated; for this reason, the present article provides a short outline of the latter topic. The main part of the article is a summary of results obtained for two-dimensional solitons in specific nonlocal nonlinear models originating in studies of Bose–Einstein condensates (BECs), which are sufficiently mature but have not yet been reviewed previously (some results for three-dimensional solitons are briefly mentioned too). These are, in particular, anisotropic quasi-2D solitons supported by long-range dipole-dipole interactions in a condensate of magnetic atoms and giant vortex solitons (which are stable for high values of the winding number), as well as 2D vortex solitons of the latter type moving with self-acceleration. The vortex solitons are states of a hybrid type, which include matter-wave and electromagnetic-wave components. They are supported, in a binary BEC composed of two different atomic states, by the resonant interaction of the two-component matter waves with a microwave field that couples the two atomic states. The shape, stability, and dynamics of the solitons in such systems are strongly affected by their symmetry. Some other topics are included in the review in a brief form. This review uses the “Harvard style” of referring to the bibliography.

Light Propagation in Confined Nematic Liquid Crystals and Device Applications

Liquid crystals are interesting linear and nonlinear optical materials used to make a wide variety of devices beyond flat panel displays. Liquid crystalline materials can be used either as core or as cladding of switchable/reconfigurable waveguides with either an electrical or an optical control or both. In this paper, materials and main device structures of liquid crystals confined in different waveguide geometries are presented using different substrate materials, such as silicon, soda lime or borosilicate glass and polydimethylsiloxane. Modelling of the behaviour of liquid crystal nanometric molecular reorientation and related refractive index distribution under both low-frequency electric and intense optical fields is reported considering optical anisotropy of liquid crystals. A few examples of integrated optic devices based on waveguides using liquid crystalline materials as core for optical switching and filtering are reviewed. Reported results indicate that low-power control signals represent a significant feature of photonic devices based on light propagation in liquid crystals, with performance, which are competitive with analogous integrated optic devices based on other materials for optical communications and optical sensing systems.

Interplay between multiple scattering and optical nonlinearity in liquid crystals.

We discuss the role played by time-dependent scattering on light propagation in liquid crystals. In the linear regime, the effects of the molecular disorder accumulate in propagation, yielding a monotonic decrease in the beam spatial coherence. In the nonlinear case, despite the disorder-imposed Brownian-like motion to the self-guided waves, self-focusing increases the spatial coherence of the beam by inducing spatial localization. Eventually, a strong enhancement in the beam oscillations occurs when power is strong enough to induce self-steering, i.e., in the non-perturbative regime.

OPTICAL SPATIAL SOLITONS IN LIQUID CRYSTALS

We have worked out the structure of optical spatial solitons in liquid crystals. The optical nonlinearity in these systems can be due to (i) Director reorientation, (ii) Suppression of the director fluctuations, (iii) Change of tilt angle in smectic liquid crystals, and (iv) Thermal indexing. When we considered the combined effect of laser suppression of the director fluctuation and thermal indexing we not only get the usual soliton solutions but also find a kink soliton solution. When both the third and fourth processes are operating we find a soliton solution with the nonlinearity which can continuously change from one type to the other. We have worked out the critical laser power required for the formation of solitons in different cases. We have also addressed ourselves to nonlinear optical effects on light propagation in liquid crystals. In the case of beams with large width for which diffraction can be ignored we find interesting modulation of the beam width in a nematic due to the second and fourth processes.

Lagrangian approach to light propagation in liquid crystals.

A Lagrangian and Hamiltonian formulation of light propagation in layered nematic liquid crystals is presented in the general case of a plane wave for any incidence angle and polarization. The resulting Lagrange or Hamiltonian equations reproduce both Maxwell's equations and the torque equations governing the molcular director equilibrium under light action. The theory includes nonlinear optical effects due to molecular reorientation. The exact formulation is then reduced to a simpler one using the generalized geometric-optics approximation. The corresponding approximate expression for the optical torque is also derived.