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On Tight-Binding Approximations in Optical Lattices

Authors


Christopher W. Curtis, Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA; e-mail: christopher.w.curtis@colorado.edu

Abstract

The validity of using the tight-binding approximation for the nonlinear Schrödinger equations with a two-dimensional optical lattice is considered. This work provides a rigorous foundation for a technique based on “orbital” functions that is central to solid-state physics and nonlinear optics. Simple and honeycomb lattices are addressed, and it is therefore shown that the use of tight-binding approximations is justified in complicated situations.

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