International Journal of Theoretical Physics

, Volume 44, Issue 1, pp 95–125 | Cite as

Wavelength-Dependent Modifications in Helmholtz Optics

Article

Abstract

The Helmholtz wave equation is linearized using the Feshbach–Villars procedure used for linearizing the Klein–Gordon equation, based on the close algebraic analogy between the Helmholtz equation and the Klein–Gordon equation for a spin-0 particle. The Foldy–Wouthuysen iterative diagonalization technique is then applied to the linearized Helmholtz equation to obtain a Hamiltonian description for a system with varying refractive index. The Hamiltonian has a wavelength-dependent part absent in the traditional descriptions. Besides reproducing all the traditional quasi-paraxial terms, our method leads to additional contributions dependent on the wavelength. Applied to the axially symmetric graded-index fiber, this method results in wavelength-dependent modifications of the paraxial behavior and the aberration coefficients to all orders. Explicit expression for the modified aberration coefficients to the third order are presented. Sixth- and eighth-order Hamiltonians are also presented.

KEY WORDS

Scalar wave optics Helmholtz equation wavelength-dependent effects beam propagation Hamiltonian description aberrations graded-index fiber mathematical methods of optics Feshbach–Villars linearization Foldy–Wouthuysen transformation 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Middle East College of Information Technology (MECIT), Technowledge CorridorKnowledge Oasis MuscatMuscatSultanate of Oman

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