Converging lower bounds to the photonic-bandgap edges

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Series titleProceedings of SPIE--the International Society for Optical Engineering; no. 4655
ConferencePhotonic bandgap materials and devices, January 23rd to 25th 2002, San Jose California
Subjectphotonic band gap; lower bounds; intermediate problems
AbstractA photonic band gap is determined by its boundaries, which are frequently computed by the Rayleigh-Ritz method, with the plane wave or the finite element basis functions. This method produces a sequence of upper bounds. Since there are no error estimates available on these approximations, the extent of the band gap is not accurately determined, particularly as this method is also known to suffer from a poor rate of convergence for the cases of interest. We adopt the method of intermediate problems to develop a procedure to calculate the lower bounds to the photonic band gap edges. The lower and the upper bounds supplement each other to determine a band gap with arbitrary accuracy, which is essential for designing the photonic band gap material. Computation of the lower bounds requires only slightly more effort than the upper bounds to produce the approximations with comparable accuracy. An alternative method to determine upper bounds is also developed in the process.
AffiliationNRC Industrial Materials Institute; National Research Council Canada
Peer reviewedYes
NPARC number21272977
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Record identifierd4697726-ebf2-459f-bdc2-23dd7e9894b6
Record created2014-12-03
Record modified2016-05-09
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