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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 4 — Apr. 1, 2007
  • pp: 1189–1200

Set of modes for the description of wave propagation through slabs with a transverse variation of the refractive index

B. J. Hoenders, M. Bertolotti, and R. Uitham  »View Author Affiliations

JOSA A, Vol. 24, Issue 4, pp. 1189-1200 (2007)

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The scattering of electromagnetic waves by a slab whose refractive index is changing along its boundary planes is exactly calculated in a closed analytical form. The key feature of the calculation is the introduction of a new set of modes. As a specific example, we calculate the reflected and transmitted fields generated by the interaction of an incoming plane wave with an N-layered medium, the layers of which are perpendicular to the boundary planes of a slab.

© 2007 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(050.1970) Diffraction and gratings : Diffractive optics
(120.2440) Instrumentation, measurement, and metrology : Filters
(230.1950) Optical devices : Diffraction gratings
(260.1960) Physical optics : Diffraction theory

ToC Category:
Physical Optics

Original Manuscript: August 30, 2006
Manuscript Accepted: October 25, 2006
Published: March 14, 2007

B. J. Hoenders, M. Bertolotti, and R. Uitham, "Set of modes for the description of wave propagation through slabs with a transverse variation of the refractive index," J. Opt. Soc. Am. A 24, 1189-1200 (2007)

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  5. We would like to stress the point that Eqs. obtained above for the spectral densities are very similar to those obtained in the case of a slab composed of a medium with constant index of refraction: The modes Ej(rm,f), j=1...4 are then the plane waves eif?r with appropriate values for the refractive index, and taking the Fourier transform of Eqs. leads to the well-known set of inhomogeneous linear algebraic equations for the unknown amplitudes of the plane waves inside and outside the slab.
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  16. We recall that this, e.g., is the case if one calculates the scattering and transmission of an incoming wave by a slab.

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