Finite size scaling of density of states in photonic bandgap crystals

Abstract

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.

References in corpus (3)

• Signature of a three-dimensional photonic band gap observed on silicon inverse woodpile photonic crystals
• Local density of optical states in the band gap of a finite photonic crystal
• Reflectivity calculated for a 3D silicon photonic band gap crystal with finite support

Cited by in corpus (17)

• Classical antennae, quantum emitters, and densities of optical states
• Finite-Size Effects on Periodic Arrays of Nanostructures
• The local density of optical states in the 3D band gap of a finite photonic crystal
• "Cartesian light": unconventional propagation of light in a 3D superlattice of coupled cavities within a 3D photonic band gap
• Experimental probe of a complete 3D photonic band gap
• Light transport through amorphous photonic materials with localization and bandgap regimes
• Reflectivity of Finite 3D GaAs Photonic Band Gap Crystals
• Localization of light in a three-dimensional disordered crystal of atoms
• Hyperuniformity and wave localization in pinwheel scattering arrays
• Finite-size scaling of the density of states inside band gaps of ideal and disordered photonic crystals
• Enhanced Absorption in thin and ultrathin silicon films by 3D photonic band gap back reflectors
• Aperiodic bandgap structures for enhanced quantum two-photon sources
• Spontaneous emission rate and the density of states inside a one dimensional photonic crystal
• Discrepant transport characteristics under Anderson localization at the two limits of disorder
• Non-utopian optical properties computed of a tomographically reconstructed real photonic nanostructure
• Dispersion of backward-propagating waves in a surface defect on a 3D photonic band gap crystal
• Sensing the position of a single scatterer in an opaque medium by mutual scattering