Photonic bandgap analysis based on the dynamical diffraction theory and its application to multilayer structures

Vito Mocella; Luca De Stefano; Luigi Moretti; Ivo Rendina

doi:10.1117/12.545747

15 September 2004 Photonic bandgap analysis based on the dynamical diffraction theory and its application to multilayer structures

Vito Mocella, Luca De Stefano, Luigi Moretti, Ivo Rendina

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Proceedings Volume 5450, Photonic Crystal Materials and Nanostructures; (2004) https://doi.org/10.1117/12.545747
Event: Photonics Europe, 2004, Strasbourg, France

Abstract

Photonic band gap Crystals (PhC) are usually analyzed using the analogy between photon propagation in artificial periodic structures and electron wave propagation in real crystals. The forbidden band of photons is regarded as equivalent to the energy gap that electrons experience in crystals because of the periodic potential. On the other hand, electron propagation and electromagnetic wave diffraction in periodic solids, respectively developed into band-theory and Dynamical Diffraction Theory (DDT), are formally identical. It appears therefore natural to perform an analysis of the features of an electromagnetic phenomenon, as the PBG, in analogy to the most direct antecedent electromagnetic theory, the DDT, that historically has also represented the direct reference for the derivation of the band-theory of electrons. In this communication, we introduce an analysis of the features of PhCs in analogy with the DDT, underlining the differences between DDT classical application to the x-ray diffraction from real crystals and that from artificial crystals at optical wavelengths. In particular, the high contrast of material refractive indices in PhC makes inapplicable some approximations generally used in x-ray diffraction analysis. Moreover, we discuss in which cases DDT has to be generalized in order to overcome such limitations. The theoretical derivation carried out is validated by the good agreement with the experimental results obtained for very simple 1D photonic crystals, such as porous silicon multilayers and silicon nitride multilayers. The generalization of the proposed approach to the case of 2D and 3D photonic crystals is also discussed.

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Vito Mocella, Luca De Stefano, Luigi Moretti, and Ivo Rendina "Photonic bandgap analysis based on the dynamical diffraction theory and its application to multilayer structures", Proc. SPIE 5450, Photonic Crystal Materials and Nanostructures, (15 September 2004); https://doi.org/10.1117/12.545747

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KEYWORDS

Photonic crystals

Crystals

Diffraction

X-ray diffraction

Refractive index

X-rays

Wave propagation

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