Optical waveguide Hamiltonians leading to step-2 difference equations

We examine the evolution of an N-point signal produced and sensed at finite arrays of points transverse to a planar waveguide, within the framework of the finite quantization of geometric optics. In contradistinction to the common mechanical Hamiltonians (kinetic plus potential energy terms) the cla...

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Vydané v:Journal of physics. Conference series Ročník 284; číslo 1; s. 012051 - 8
Hlavní autori: Rueda-Paz, Juvenal, Wolf, Kurt Bernardo
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Bristol IOP Publishing 01.03.2011
Predmet:
Arrays
Difference equations
Eigenvalues
Eigenvectors
Evolution
Geometrical optics
Hamiltonian functions
Mathematical analysis
Mathematical models
Optical waveguides
Oscillators
Physics
Planar waveguides
Potential energy
Refractivity
ISSN:1742-6596, 1742-6588, 1742-6596
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Shrnutí:We examine the evolution of an N-point signal produced and sensed at finite arrays of points transverse to a planar waveguide, within the framework of the finite quantization of geometric optics. In contradistinction to the common mechanical Hamiltonians (kinetic plus potential energy terms) the classical waveguide Hamiltonian is the square root of a difference of squares of the refractive index profile minus the optical momentum. The finitely quantized model requires the solution of the square eigenvalue and eigenfunction problem which leads to a step-two difference equation that contains two solutions and two signs of energy. We find the proper linear combinations to fit the Kravchuk functions of the finite oscillator model.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/284/1/012051