Tunable self-focusing and self-steering of nematicons

摘要

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 n̂ (i.e., the local optic axis) and the beam wavevector k = n0k0 ẑ (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 Φ is the beam magnetic field and ψ is the all-optical perturbation on θ, with θ0 being the unperturbed θ, i.e., θ0 = Φ (F = 0). In Eqs. (1–2), Dy is the diffraction coefficient along y, δ^(b) the walk-off of the soliton, γ = [ε0/(4K)](n∥² − n⊥²)[Z0/(n0 cosδ)]², and Δne² is the nonlinear change in the extraordinary refractive index ne. Eq. (2) is a reorientational equation which allows to compute the dielectric properties of the medium (δ and ne) once it is known the torque exerted by light on the NLC molecules, whereas (1) determines the beam profile once the n̂-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 θ0 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 Δne²) and self-steering (determined by δ) versus θ0: a nonlocal Kerr coefficient n2, given by n2(θ0) = 2γsin[2(θ0−δ)]ne²(θ0) 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 θ0 (Fig. 1). Figure 1 also shows the corresponding experimental results, with an excellent agreement with the theoretical predictions.