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.

Quantum Entanglement in Coupled Lossy Waveguides Using SU(2) and SU(1, 1) Thermo-Algebras

“…For coupled waveguides without damping, special attention has been given to the time evolution of the NOON states as inputs and we have shown that as we increase the photon number, the entanglement of the NOON states survives with time, thus making them extremely suitable for quantum information. The solution for damped systems was obtained by transforming the master equation to a Schrodinger type equation and applying the disentanglement formulae for SU (2) and SU(1, 1). Our work extends that of Rai et al [4], as it gives the exact solution for the master equation, and, in addition shows how the entanglement behaves for input thermal states.…”

“…Thus, the problem of solving master equation is reduced to solving a Schrodinger like equation. Symmetries associated with the Hamiltonian (such as SU (2) and SU(1, 1) symmetries) can be exploited to solve the master equation. This makes the study of entanglement in lossy systems very tractable.…”

Quantum interference in photonic lattices with defects

“…In addition to the defect modes, the input beams also excite Bloch-Floquet modes of the periodic array, which are dispersive waves, i.e., they diffract as the propagation distance z increases and tend to delocalize light over the various waveguides of the lattice [25]. Therefore, after an initial transient, the light that remains trapped near the defect region arises from the initially excited localized modes.…”

Supermodes of a double-ring fibre array with symmetric coupling

“…At present, the physics of one-and two-dimensional infinite fibre arrays has been studied in detail in a number of works [2][3][4]. This is partially explained by a novel phenomenon of discrete diffraction, which takes place in waveguide arrays [5,6]. Some interesting results have been obtained for the curved [7] and nonlinear [8,9] waveguide arrays.…”