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Gralak B, de Dood M, Tayeb G, et al. Theoretical study of photonic band gaps in woodpile crystals. Phys Rev E Stat Nonlin Soft Matter Phys. 2003;67(6):066601doi: 10.1103/PhysRevE.67.066601.
Gralak, B., de Dood, M., Tayeb, G., Enoch, S., & Maystre, D. (2003). Theoretical study of photonic band gaps in woodpile crystals. Physical review. E, Statistical, nonlinear, and soft matter physics, 67(6), 066601. https://doi.org/10.1103/PhysRevE.67.066601
Gralak, Boris, et al. "Theoretical study of photonic band gaps in woodpile crystals." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 67,6 (2003): 066601. doi: https://doi.org/10.1103/PhysRevE.67.066601
Gralak B, de Dood M, Tayeb G, Enoch S, Maystre D. Theoretical study of photonic band gaps in woodpile crystals. Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jun;67(6):066601. doi: 10.1103/PhysRevE.67.066601. Epub 2003 Jun 04. PMID: 16241362.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jun;67(6):066601. doi: 10.1103/PhysRevE.67.066601. Epub 2003 Jun 04.

Theoretical study of photonic band gaps in woodpile crystals.

Physical review. E, Statistical, nonlinear, and soft matter physics

Boris Gralak, Michiel de Dood, Gérard Tayeb, Stefan Enoch, Daniel Maystre

Affiliations

  1. FOM-Institute for Atomic and Molecular Physics, Amsterdam, The Netherlands. [email protected]

PMID: 16241362 DOI: 10.1103/PhysRevE.67.066601

Abstract

We investigate numerically the existence of photonic band gaps in woodpile crystals. We present a numerical method specifically developed to solve Maxwell's equations in such photonic structures. It is based upon a rigorous mathematical formulation and leads to a considerable improvement of the convergence speed as compared to other existing numerical methods. We tested our method by comparing the calculated reflectivity with measurements on an actual sample, i.e., a silicon woodpile photonic crystal designed for 1.5 microm wavelength. Excellent agreement is obtained, provided the main structural imperfections of the sample are taken into account. We show that the existence of photonic band gaps in woodpile crystals requires an index contrast higher than 2.05 +/- 0.01. The effects of imperfections of such structures with an index contrast equal to 2.25 are also investigated. Thus, the relative band gap width falls from 3.5% to 2.2% with structurals imperfection similar to those of the sample.

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