Two-color, nonlocal vector solitary waves with angular momentum in nematic liquid crystals

Abstract

The propagation and interaction of two solitary waves with angular momentum in bulk nematic liquid crystals, termed nematicons, have been studied in the nonlocal limit. These two spinning solitary waves are based on two different wavelengths of light and so are referred to as two-color nematicons. Under suitable boundary conditions, the two nematicons can form a bound state in which they spin about each other. This bound state is found to be stable to the emission of diffractive radiation as the nematicons evolve. In addition this bound state shows walk-off due to dispersion. Using an approximate method based on the use of suitable trial functions in an averaged Lagrangian of the two-color nematicon equations, modulation equations for the evolution of the individual nematicons are derived. These modulation equations are extended to include the diffractive radiation shed as the nematicons evolve. Excellent agreement is found between solutions of the modulation equations and full numerical solutions of the nematicon equations. The shed diffractive radiation is found to play a much lesser role in the nonlocal limit than in the local limit

Exact and approximate solutions for optical solitary waves in nematic liquid crystals

“…The variational approximate solutions will be based on a number of different, widely used trial functions in order to determine their absolute and relative accuracies. The details of these variational solutions have been given elsewhere [40,65], so they will only be summarized here. The three trial functions to be used are a hyperbolic secant [40], as this is the profile of the soliton solution of the (1 + 1)-D NLS equation, a Gaussian [35,37,65] and a hyperbolic secant squared, the last based on the exact solution (10).…”

Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

“…These modulation equations do not include loss to diffractive radiation [28,31] as it has been observed experimentally [25] and from theoretical solutions [29] that on the length scales of a typical cell this loss is very small and can be ignored. This point is taken up further in the …”

“…An added complication with studying nematicons is that there is no known exact analytical solitary wave (nematicon) solution of the nematicon equations. Due to this, it has been found that a powerful approximate technique for studying this problem is that based on trial functions in variational formulations of the governing equations [26][27][28][29], this being an extension of modulation theory [30]. This technique is adapted and used in the present work.…”

Vector vortex solitons in nematic liquid crystals

“…3. Using the twocomponent equations re-written in a Lagrangian formulation [14], we employ the trial functions for the vortex, its soliton component and the director angle,…”