Interaction and steering of nematicons
The waveguiding effect of spatial solitary waves in nonlinear optical media has been suggested as a potential basis for future all-optical devices, such as optical interconnects. It has been shown that low power (∼ mW) beams, which can encode information, can be optically steered using external electric fields or through interactions with other beams. This opens up the possibility of creating reconfigurable optical interconnects. Nematic liquid crystals are a potential medium for such future optical interconnects, possessing many advantageous properties, including a “huge” nonlinear response at comparatively low input power levels. Consequently, a thorough understanding of the behaviour of spatial optical solitary waves in nematic liquid crystals, termed nematicons, is needed. The investigation of multiple beam interaction behaviour will form an essential part of this understanding due to the possibility of beam-on-beam control. Here, the interactions of two nematicons of different wavelengths in nematic liquid crystals, and the optical steering of nematicons in dye-doped nematic liquid crystals will be investigated with the aim of achieving a broader understanding of nematicon interaction and steering. The governing equations modelling nematicon interactions are nonintegrable, which means that nematicon collisions are inelastic and radiative losses occur during and after collision. Consequently numerical techniques have been employed to solve these equations. However, to fully understand the physical dynamics of nematicon interactions in a simple manner, an approximate variational method is used here which reduces the infinite-dimensional partial differential equation problem to a finite dynamical system of comparatively simple ordinary differential equations. The resulting ordinary differential equations are modified to include radiative losses due to beam evolution and interaction, and are then quickly solved numerically, in contrast to the original governing partial differential equations. N¨other’s Theorem is applied to find various conservation laws which determine the final steady states, aid in calculating shed radiation and accurately compute the trajectories of nematicons. Solutions of the approximate equations are compared with numerical solutions of the original governing equations to determine the accuracy of the approximation. Excellent agreement is found between full numerical solutions and approximate solutions for each physical situation modelled. Furthermore, the results obtained not only confirm, but explain theoretically, the interaction phenomena observed experimentally. Finally, the relationship between the nature of the nonlinear response of the medium, the trajectories of the beams and radiation shed as the beams evolve is investigated.