Tunable self-focusing and self-steering of nematicons

Nematicons, i.e., optical spatial solitons in nematic liquid crystals (NLC), have been attracting a great deal of attention due to their unique properties such as, for example, excitability at powers of a few hundred μW and the possibility to be electrically and/or optically (by other light beams) bent.[1] In this work we investigate, both experimentally and theoretically, the nematicon behavior for different degrees of nonlinearity, discussing how the latter affects the beam width (self-focusing) and trajectory (self-steering). Having defined the angle between the molecular director n (i.e., the local optic axis) and the beam wavevector k = n₀k₀ z (k₀ is the vacuum wavenumber, n₀ the linear refractive index), the propagation of the extraordinary wave in the plane yz in a homogeneous NLC cell of thickness L across x is ruled by the equivalent 2D model [2,3] equation equation where is the beam magnetic field and is the all-optical perturbation on , with ₀ being the unperturbed , i.e., ₀ = (F = 0). In Eqs. (1-2), D_y is the diffraction coefficient along y, ^(b) the walk-off of the soliton, = [₀/(4K)](n² n ²)[Z₀/(n₀ cos)]², and n _e ² is the nonlinear change in the extraordinary refractive index n_e. Eq. (2) is a reorientational equation which allows to compute the dielectric properties of the medium ( and n_e) once it is known the torque exerted by light on the NLC molecules, whereas (1) determines the beam profile once the n-distribution is known. It is clear from Eq. (2) that the nonlinear response, determined by the optical torque, depends on the initial angle ₀: hence, by changing ₀ it is possible to easily modify the nonlinear response of the sample, the latter feasible via an applied bias in a planar cell with interdigitated comb-like electrodes. [3] In the limit ₀, using Eqs. (1-2) it is possible to define two scalar parameters to investigate self-focusing (ruled by n_e ²) and self-steering (determined by ) versus ₀: a nonlocal Kerr coefficient n₂, given by n₂(₀) = 2sin[2( ₀)]n_e ²(₀) tan, and equation, proportional to the sensitivity of to the light intensity (Fig. 1), respectively. Numerical simulations of Eqs. (1-2) via BPM confirm the soliton behavior versus ₀ (Fig. 1). Figure 1 also shows the corresponding experimental results, with an excellent agreement with the theoretical predictions.