Discrete diffraction and shape-invariant beams in optical waveguide arrays

Abstract

General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws describing beam spreading, beam decay and discrete far-field patterns in homogeneous arrays are derived using the method of moments and the steepest descend method. In curved arrays, the method of moments is extended to describe evolution of global beam parameters. A family of beams which propagate in curved arrays maintaining their functional shape -referred to as discrete Bessel beams- is also introduced. Propagation of discrete Bessel beams in waveguide arrays is simply described by the evolution of a complex $q$ parameter similar to the complex $q$ parameter used for Gaussian beams in continuous lensguide media. A few applications of the $q$ parameter formalism are discussed, including beam collimation and polygonal optical Bloch oscillations. \

14 pages, 5 figures

References in corpus (5)

• Observation of two-dimensional surface solitons in anisotropic waveguide arrays
• Diffraction-managed solitons and nonlinear beam diffusion in modulated arrays of optical waveguides
• Broadband diffraction management and self-collimation of white light in photonic lattices
• Defect-free surface states in modulated photonic lattices
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Cited by in corpus (2)

• Maryland model in optical waveguide lattices
• Controlling the path of discretized light in waveguide lattices