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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • 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)
http://dx.doi.org/10.1364/JOSAA.24.001189


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Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-4-1189


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References

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  2. V. D. Kupradze, Randwertaufgaben der Schwingungstheorie und Integralgleichungen (Deutscher Verlag der Wissenschaften, 1956).
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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.
  6. P. Yeh, Optical Waves in Layered Media, Wiley Series in Pure and Applied Optics (Wiley, 1988).
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  9. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), Chap. 3.2.
  10. D. G. Stavenga, S. Foletti, G. Palasantzas, and K. Arikawa, "Light on the moth-eye corneal nipple array of butterflies," Proc. R. Soc. London, Ser. B 273, 661-667 (2006). [CrossRef]
  11. E. Hilb, "Über Reihenentwicklungen, welche aus speziellen Randwertproblemen bei gewöhnlichen linearen inhomogenen Differentialgleichungen entspringen," J.f.Math 140, 207-229 (1913).
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  13. S. Hassani, Mathematical Physics, (Springer, 1999), Chap. 20, pp. 553-582.
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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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