Exact and approximate solutions for optical solitary waves in nematic liquid crystals

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Physica D: Nonlinear Phenomena, ISSN: 0167-2789, Vol: 284, Page: 1-15

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J. Michael L. MacNeil; Noel F. Smyth; Gaetano Assanto
Elsevier BV
Physics and Astronomy; waves; nematic; liquid; solitary; crystals; solutions; approximate; exact; optical; Engineering; Science and Technology Studies
article description
The equations governing optical solitary waves in nonlinear nematic liquid crystals are investigated in both (1+1) and (2+1) dimensions. An isolated exact solitary wave solution is found in (1+1) dimensions and an isolated, exact, radially symmetric solitary wave solution is found in (2+1) dimensions. These exact solutions are used to elucidate what is meant by a nematic liquid crystal to have a nonlocal response and the full role of this nonlocal response in the stability of (2+1) dimensional solitary waves. General, approximate solitary wave solutions in (1+1) and (2+1) dimensions are found using variational methods and they are found to be in excellent agreement with the full numerical solutions. These variational solutions predict that a minimum optical power is required for a solitary wave to exist in (2+1) dimensions, as confirmed by a careful examination of the numerical scheme and its solutions. Finally, nematic liquid crystals subjected to two different external electric fields can support the same solitary wave, exhibiting a new type of bistability.