Chapter 7: Interaction of Nematicons and Nematicon Clusters
Department of Mathematics and Mechanics, IIMAS, Fenomenos Nonlineales y Mecánica, Universidad Nacional Autónoma de México, Mexico D.F., Mexico
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, Scotland, United Kingdom
7.1 Introduction
The theory for modeling and evolution of a single solitary wave in a nematic liquid crystal, a nematicon, has been described in Chapter 3. One of the key concepts discussed in that chapter was that of the nonlocal response of the nematic medium. This nonlocal response means that the perturbation due to the optical beam on the nematic extends far beyond the waist of the optical beam itself. Although an important effect for a single nematicon, it stops the catastrophic collapse that occurs in the case of a local two-dimensional optical solitary wave [1], it becomes vital when the interaction of multiple nematicons is studied. The nonlocal perturbation of the nematic means that two optical beams can interact through the nematic even though they appear to be well separated. Indeed, the interaction between two or more nematicons will be found to have a close connection with the action at a distance of Newtonian gravitation [2].
A primary motivation for the study of the interaction of nematicons is that this interaction can be used as the basis for all-optical routing and logic ...
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