Tunable self-focusing and self-steering of nematicons

Abstract

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 = n 0 k 0 z (k 0 is the vacuum wavenumber, n 0 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 Φ is the beam magnetic field and ψ is the all-optical perturbation on θ, with θ 0 being the unperturbed θ, i.e., θ 0 = Φ (F = 0). In Eqs. (1–2), D y is the diffraction coefficient along y, δ(b) the walk-off of the soliton, γ = [e 0 /(4K)](n ∥ 2 − n ⊥ 2)[Z 0 /(n 0 cosδ)]2, and Δn 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 (δ 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 θ 0 : hence, by changing θ 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 ψ θ ≪ 0 , using Eqs. (1–2) it is possible to define two scalar parameters to investigate self-focusing (ruled by Δn e 2) and self-steering (determined by δ) versus θ 0 : a nonlocal Kerr coefficient n 2 , given by n 2 (θ 0 ) = 2γsin[2(θ 0 −δ)]n e 2(θ 0 ) tanδ, and equation, proportional to the sensitivity of δ to the light intensity (Fig. 1), respectively. Numerical simulations of Eqs. (1–2) via BPM confirm the soliton behavior versus θ 0 (Fig. 1). Figure 1 also shows the corresponding experimental results, with an excellent agreement with the theoretical predictions.