Solitons in highly nonlocal nematic liquid crystals: Variational approach

Abstract

We investigate numerically and theoretically solitons in highly nonlocal three-dimensional nematic liquid crystals. We calculate the fundamental soliton profiles using the modified Petviashvili method. We apply the variational method to the widely accepted scalar model of beam propagation in uniaxial nematic liquid crystals and compare the results with numerical simulations. To check the stability of such solutions, we propagate them in the presence of noise. We discover that the presence of any noise induces the fundamental solitons-the so-called nematicons-to breathe. Our results explain the difficulties in experimental observation of steady nematicons.

Variational and accessible soliton approximations to multidimensional solitons in highly nonlocal nonlinear media

“…(2), with zero boundary conditions on a circle of radius d ≫ T , and in the limit of a thick transverse width. We can take these expressions as an approximate solution on a D−dimensional cube, as demonstrated in [9,17] for the two-dimensional case.…”

“…The system of equations of interest consists of the nonlinear Schrödinger equation for the propagation of the optical field E and the diffusion equation for the nonlocal response of the medium θ. This is a fairly general model for nonlinear optical media with diffusive nonlocality, widely used in the literature [1,6,9]. In the local limit, the first term in Eq.…”

“…For the study of VA and AS approximations to the fundamental soliton solutions in a (D+1)-dimensional highly nonlocal medium we adopt the following model of coupled dimensionless equations [1,9]:…”

“…It provides for natural explanation of oscillations seen when, e.g., noise is included into the nonlocal nonlinear models. The noise is inevitable in any real physical system and causes a regular oscillation of soliton parameters with the period well predicted by our VA calculus [9]. It may even destroy solitons [13].…”

“…To include interactions between solitons within boundaries, as well the impact of the finite size of the sample, we developed a variational approach (VA) to solitons in nonlinear media with long-range nonlocality, such as NLCs [9], materials with thermal nonlocality [10], photorefractive crystals [11], and Bose-Einstein condensates [12]. Starting from an appropriate ansatz, this approach delivers a stationary solution for the beam amplitude and width, as well as the period of small oscillations about the stationary state.…”