Two-color vector-soliton interactions in nematic liquid crystals in the local response regime

The propagation and interaction of two bulk solitary waves, termed nematicons, in a nematic liquid crystal are studied in the local limit. These two nematicons are based on light of two different wavelengths, and so are referred to as two color nematicons. Under suitable boundary conditions the two nematicon beams of different wavelengths can couple, creating a self-localized vector solitary wave. Due to the different diffraction coefficients and indices of refraction for each wavelength, the vector solitary wave shows walk-off. Using a suitable trial function in an averaged Lagrangian formulation of the two color nematicon equations, approximate equations governing the evolution of the two color nematicons are derived. These approximate equations are extended to include the diffractive radiation shed as the nematicons evolve. Excellent agreement is found for the walk-off as given by these approximate equations and by full numerical solutions of the nematicon equations. It is shown that the inclusion of the effect of the shed diffractive radiation is vital in order to obtain this excellent agreement.