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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 4 — Feb. 19, 2007
  • pp: 1783–1793

Stage number and refractive index dependence of the quality factor of the localized electromagnetic eigenmodes in the Menger sponge fractal

Kazuaki Sakoda  »View Author Affiliations

Optics Express, Vol. 15, Issue 4, pp. 1783-1793 (2007)

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The eigenfrequency and quality factor of the localized electromagnetic modes of the dielectric Menger sponge fractal were investigated theoretically for stage number 1 to 4 with a dielectric constant of 2.8 to 12.0 in the normalized frequency range of ωa/2πc = 0.4 to 1.6, where a is the size of the Menger sponge and c is the light speed in free space. It was found that the quality factor of the eigenmode is larger on average when the spatially averaged dielectric constant of the fractal structure is larger, which is consistent with the mechanism of the usual refractive index confinement. Particularly the largest quality factor of 1720 was found for stage 1. These features imply that the fractal nature is irrelevant to the localization in this frequency range. The theoretical results are compared with previous experimental observation and the reason for their discrepancy is discussed.

© 2007 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(260.1180) Physical optics : Crystal optics
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Physical Optics

Original Manuscript: November 27, 2006
Revised Manuscript: January 28, 2007
Manuscript Accepted: January 28, 2007
Published: February 19, 2007

Kazuaki Sakoda, "Stage number and refractive index dependence of the quality factor of the localized electromagnetic eigenmodes in the Menger sponge fractal," Opt. Express 15, 1783-1793 (2007)

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