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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: Franco Gori
  • Vol. 31, Iss. 4 — Apr. 1, 2014
  • pp: 808–817

Hypersingularity, electromagnetic edge condition, and an analytic hyperbolic wedge model

Lifeng Li  »View Author Affiliations


JOSA A, Vol. 31, Issue 4, pp. 808-817 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000808


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Abstract

It is insufficient to consider that hypersingularity is unphysical solely based on energy considerations. With a proper combination of the two degenerate hypersingular modes, the energy-flux edge condition is satisfied. A hyperbolic wedge model is presented that is much simpler than the previous model for the purpose of studying singular characteristics of the edge fields. This model not only reproduces the sharp edge model as the wedge becomes infinitely sharp but also naturally shows how the two degenerate hypersingular modes of the sharp edge model should be combined. In an incidental study of the effect of rounding edges on numerical computation, I show that the converged results for rounded edges do not converge to a fixed value when the radius of curvature tends to zero, if the corresponding sharp edge supports hypersingularity. I also prove that introducing a small amount of absorption loss for the purpose of improving numerical convergence is effective only when the ratio of the real parts of the permittivities of the two media forming the wedge is close to −1. Finally I remark on the possible illposedness of the hypersingularity problem without imposition of the edge condition.

© 2014 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1950) Diffraction and gratings : Diffraction gratings
(050.2770) Diffraction and gratings : Gratings
(290.0290) Scattering : Scattering
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

History
Original Manuscript: December 19, 2013
Manuscript Accepted: February 14, 2014
Published: March 27, 2014

Citation
Lifeng Li, "Hypersingularity, electromagnetic edge condition, and an analytic hyperbolic wedge model," J. Opt. Soc. Am. A 31, 808-817 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-4-808

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