Finite size scaling of density of states in photonic bandgap crystals

The famous vanishing of the density of states (DOS) in a band gap, be it photonic or electronic, pertains to the infinite-crystal limit. In contrast, all experiments and device applications refer to finite crystals, which raises the question: Upon increasing the linear size \(L\) of a crystal, how f...

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Bibliographic Details
Published in:arXiv.org 2018-05
Main Authors: Shakeeb Bin Hasan, Mosk, Allard P, Vos, Willem L, Lagendijk, Ad
Format: Article
Language:English
Subjects:
Band gap
Crystals
Density of states
Dependence
Photonic band gaps
Photonic crystals
Online Access:Get full text
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Summary:The famous vanishing of the density of states (DOS) in a band gap, be it photonic or electronic, pertains to the infinite-crystal limit. In contrast, all experiments and device applications refer to finite crystals, which raises the question: Upon increasing the linear size \(L\) of a crystal, how fast does the DOS approach the infinite-crystal limit? We present a theory for finite crystals that includes Bloch-mode broadening due to the presence of crystal boundaries. Our results demonstrate that the DOS for frequencies inside a band gap has a \(1/L\) scale dependence for crystals in one, two and three dimensions.
ISSN:2331-8422
DOI:10.48550/arxiv.1701.01743