The local density of optical states in the 3D band gap of a finite photonic crystal

Abstract

A three-dimensional (3D) photonic band gap crystal is an ideal tool to completely inhibit the local density of optical states (LDOS) at every position in the crystal throughout the band gap. This notion, however, pertains to ideal infinite crystals, whereas any real crystal device is necessarily finite. This raises the question as to how the LDOS in the gap depends on the position and orientation inside a finite-size crystal. Therefore, we employ rigorous numerical calculations using finite-difference time-domain (FDTD) simulations of 3D silicon inverse woodpile crystals filled with air or with toluene, as previously studied in experiments. We find that the LDOS versus position decreases exponentially into the bulk of the crystal. From the dependence on dipole orientation, we infer that the characteristic LDOS decay length ${\ell }_{\rho }$ is mostly related to far-field dipolar radiation effects, whereas the prefactor is mostly related to near-field dipolar effects. The LDOS decay length has a remarkably similar magnitude as the Bragg length for directional transport, which suggests that the LDOS in the crystal is dominated by vacuum states that tunnel from the closest interface towards the position of interest. Our work leads to design rules for applications of 3D photonic band gaps in emission control and lighting, quantum information processing, and in photovoltaics.

11 pages, 8 figures, Typo in abstract corrected

References in corpus (5)

• Classical antennae, quantum emitters, and densities of optical states
• The role of fabrication deviations on the photonic band gap of 3D inverse woodpile nanostructures
• Electromagnetic Wave Source Conditions
• Reflectivity of Finite 3D GaAs Photonic Band Gap Crystals
• Finite-size scaling of the density of states inside band gaps of ideal and disordered photonic crystals

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• Spatially shaping waves to penetrate deep inside a forbidden gap
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• Polaritonic cylinders as multifunctional metamaterials: Single scattering and effective medium description
• Enhanced Absorption in thin and ultrathin silicon films by 3D photonic band gap back reflectors
• Optical Properties of Chiral Three-Dimensional Photonic Crystals made from Semiconductors
• Dispersion of backward-propagating waves in a surface defect on a 3D photonic band gap crystal