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Full-Text Articles in Physics
Reorientational Versus Kerr Dark And Gray Solitary Waves Using Modulation Theory, Prof. Tim Marchant
Reorientational Versus Kerr Dark And Gray Solitary Waves Using Modulation Theory, Prof. Tim Marchant
Tim Marchant
We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrodinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive …
Modulation Analysis Of Boundary Induced Motion Of Optical Solitary Waves In A Nematic Liquid Crystal, Tim Marchant
Modulation Analysis Of Boundary Induced Motion Of Optical Solitary Waves In A Nematic Liquid Crystal, Tim Marchant
Tim Marchant
We consider the motion of a solitary wave, a nematicon, in a finite cell filled with a nematic liquid crystal. A modulation theory is developed to describe the boundary-induced bouncing of a nematicon in a one-dimensional cell and it is found to give predictions in very good agreement with numerical solutions. The boundary-induced motion is then considered numerically for a two-dimensional cell and a simple extension of the modulation theory from one to two space dimensions is then made, with good agreement being found with numerical solutions for the nematicon trajectory. The role of nematicon shape and relative position to …
Mathematical Modelling Of Nematicons And Their Interactions, Prof. Tim Marchant
Mathematical Modelling Of Nematicons And Their Interactions, Prof. Tim Marchant
Tim Marchant
The mathematical modelling of guided wave (nematicon) propagation in liquid crystals is considered. Model equations are derived based on suitable trial functions in an averaged Lagrangian. These equations are used to model nematicon interactions.
Collisionless Shock Resolution In Nematic Liquid Crystals, Tim Marchant
Collisionless Shock Resolution In Nematic Liquid Crystals, Tim Marchant
Tim Marchant
The diffractive resolution on a collisionless shock formed along the spatial profile of a beam in a nematic liquid crystal is considered, this material being an example of a self-focusing, nonlocal medium. It is found that the shock is resolved through the formation of an undular bore structure which persists for experimentally relevant propagation distances due to nonlocality delaying the onset of modulational instability. Both 1+1 and 2+1 dimensional bores with circular symmetry are considered (termed line and circular bores, respectively). A semianalytical solution is developed for the line undular bore, approximating it as a train of uniform solitary waves. …
Nonlocal Validity Of An Asymptotic One-Dimensional Nematicon Solution, Tim Marchant
Nonlocal Validity Of An Asymptotic One-Dimensional Nematicon Solution, Tim Marchant
Tim Marchant
The propagation of coherent, polarized light in a nematic liquid crystal, governed by the nematicon equations, is considered. It is found that in the special case of 1 + 1 dimensions and the highly nonlocal limit, the nematicon equations have an asymptotic bulk solitary wave solution, termed a nematicon, which is given in terms of Bessel functions. This asymptotic solution gives both the ground state and the symmetric and antisymmetric excited states, which have multiple peaks. Numerical simulations of nematicon evolution, for parameters corresponding to experimental scenarios, are presented. It is found, for experimentally reasonable parameter choices, that the validity …
Dipole Soliton Formation In A Nematic Liquid Crystal In The Non-Local Limit, Tim Marchant
Dipole Soliton Formation In A Nematic Liquid Crystal In The Non-Local Limit, Tim Marchant
Tim Marchant
The interaction of two symmetric solitary waves, termed nematicons, in a liquid crystal is considered in the limit of nonlocal response of the liquid crystal. This nonlocal limit is the applicable limit for most experimentally available liquid crystals. In this nonlocal limit, two separate cases for the initial separation of the nematicons are considered, these being large and small separation. Both spinning and nonspinning nematicons are considered. It is found that in the case of large initial separation, the nematicons can form a spinning or nonspinning bound state with a finite steady separation, this being called a nematicon dipole, when …
Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant
Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant
Tim Marchant
Solitary wave interaction for a higher-order version of the nonlinear Schrödinger (NLS) equation is examined. An asymptotic transformation is used to transform a higher-order NLS equation to a higher-order member of the NLS integrable hierarchy, if an algebraic relationship between the higher-order coefficients is satisfied. The transformation is used to derive the higher-order one- and two-soliton solutions; in general, the N-soliton solution can be derived. It is shown that the higher-order collision is asymptotically elastic and analytical expressions are found for the higher-order phase and coordinate shifts. Numerical simulations of the interaction of two higher-order solitary waves are also performed. …