Stage number and refractive index dependence of the quality factor of the localized electromagnetic eigenmodes in the Menger sponge fractal.
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 omegaa/2 pic = 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.
Sakoda
Kazuaki
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