Finding exact spatial soliton profiles in nematic liquid crystals

Abstract

Abstract:Finding exact analytical soliton profile solutions is only possible for certain types of non-linear media. In most cases one must resort to numerical techniques to find the soliton profile. In this work we present numerical calculations of spatial soliton profiles in nematic liquid crystals. The nonlinearity is governed by the optical-field-induced liquid crystal director reorientation, which is described by a system of coupled nonlinear partial differential equations. The soliton profile is found using an iterative scheme whereby the induced waveguide and mode profiles are calculated alternatively until convergence is achieved. In this way it is also possible to find higher order solitons. The results in this work can be used to accurately design all-optical interconnections with soliton beams.

Solitons in highly nonlocal nematic liquid crystals: Variational approach

“…In many publications semianalytical models were used for soliton profile calculations [17,18]; however, simplified models cannot describe all aspects of the reorientation dynamics. For the more general vectorial model, in which the order parameter in NLC is not constant, steady fundamental soliton profiles were found numerically [19], by including all three components of the optical electric field.…”

Reply to “Comment on ‘Spatial optical solitons in highly nonlocal media”'

“…Thirdly, in biased cells nematicons propagate in a wide linear index well and possess walk-off in the vertical plane (x, z): the model used in [8] does not account for this dynamics, which was addressed later in [11,15]. Reality is far more complex than a single Schrödinger-Poisson equation: (i) in real samples there are interfaces at finite distances, as we discussed in [1]; ii) several nonlinear effects act together, thus models considering only the reorientational response are approximations [50,51]; iii) actual reorientation is driven by a more complicated equation than a single Poisson equation, even in the perturbative regime [38,52]; iv) NLC described by a molecular director field are a simplification of an underlying many body system which is subject to continuous temporal fluctuations [38,53]. The elegant SMM, despite its mathematical simplicity, explains qualitatively nonlinear light propagation, predicting an oscillatory (breathing) behavior qualitatively different from the breather dynamics in a standard NLSE [54][55][56], stability in (2 + 1)D [57] and interaction between solitons [17,58,59].…”

Temporal dynamics of light-written waveguides in unbiased liquid crystals

“…As a matter of fact, the static (or low-frequency [22]) electric field creates a transverse gradient in the refractive index distribution, the maximum being at the center of the cell. The bias-induced inhomogeneity works both as a strongly multimodal waveguide [30] and a potential landscape where the soliton starts to oscillate [31,32]. Such dynamics is strongly affected by spatial walk-off [23] as well, a fundamental ingredient in the propagation of nematicons [21,33] neglected in Ref.…”