Physics – Classical Physics
Scientific paper
1999-03-26
J. Phys.: Condens. Matter 11, 2503 - 2512 (1999)
Physics
Classical Physics
14 pages, 3 figs., RevTex. For more info look at http://www.amolf.nl/external/wwwlab/atoms/theory/index.html
Scientific paper
10.1088/0953-8984/11/12/005
For the case of a simple face-centered-cubic photonic crystal of homogeneous dielectric spheres, we examine to what extent single-sphere Mie resonance frequencies are related to band gaps and whether the width of a gap can be enlarged due to nearby resonances. Contrary to some suggestions, no spectacular effects may be expected. When the dielectric constant of the spheres $\epsilon_s$ is greater than the dielectric constant $\epsilon_b$ of the background medium, then for any filling fraction $f$ there exists a critical $\epsilon_c$ above which the lowest lying Mie resonance frequency falls inside the lowest stop gap in the (111) crystal direction, close to its midgap frequency. If $\epsilon_s <\epsilon_b$, the correspondence between Mie resonances and both the (111) stop gap and a full gap does not follow such a regular pattern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by $\approx 5%$.
Moroz Alexander
Tip Adriaan
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