Three-dimensional photonic band gap cavity with finite support: Enhanced energy density and optical absorption

Abstract

We study numerically the transport and storage of light in a three-dimensional (3D) photonic band gap crystal doped by a single embedded resonant cavity. The crystal has finite support since it is surrounded by vacuum, as in experiments. Therefore, we employ the finite element method to model the diamond-like inverse woodpile crystal that consists of two orthogonal arrays of pores in a high-index dielectric such as silicon and that has experimentally been realized by CMOS-compatible methods. A point defect that functions as the resonant cavity is formed in the proximal region of two selected orthogonal pores with a radius smaller than the ones in the bulk of the crystal. We present a field-field cross-correlation method to identify resonances in the finite-support crystal with defect states that appear in the 3D photonic band gap of the infinite crystal. Out of five observed angle-independent cavity resonances, one is s-polarized and four are p-polarized for light incident in the X or Z directions. It is remarkable that quality factors up to Q = 1000 appear in such thin structures (only three unit cells), which is attributed to the relatively small Bragg length of the perfect crystal. We find that the optical energy density is remarkably enhanced at the cavity resonances by up to 2400× the incident energy density in vacuum or up to 1200× the energy density of the equivalent effective medium. We find that an inverse woodpile photonic band gap cavity with a suitably adapted lattice parameter reveals substantial absorption in the visible range. Below the 3D photonic band gap, Fano resonances arise due to interference between the discrete fundamental cavity mode and the continuum light scattered by the photonic crystal. We argue that the five eigenstates of our 3D photonic band gap cavity have quadrupolar symmetry, in analogy to d-like orbitals of transition metals. We conclude that inverse woodpile cavities offer interesting perspectives for applications in optical sensing and photovoltaics. arXiv:1808.05607v1 [physics.optics]

Cartesian light: Unconventional propagation of light in a three-dimensional superlattice of coupled cavities within a three-dimensional photonic band gap

“…2(b) reveals that these bands have nonzero bandwidths, indicating that cavity resonances in the M x M y M z = 3 × 3 × 3 superlattice are coupled, as is investigated in this paper. Our results agree well with a simultaneous investigation of a single cavity in an inverse woodpile crystal with finite support, studied by other numerical methods [50]. Notably, Ref.…”

“…This hybrid combination allows one to explore light-matter interactions deep inside the band gap that are well shielded from any perturbing vacuum fluctuations by the surrounding 3D photonic band gap [70]. Indeed, recent parallel work has pointed out that with inverse woodpile cavities one can observe a substantially enhanced optical absorption at the cavity locations, which offers favorable opportunities for tiny optical sensors [50]. In the presence of two-level Cs atoms, we anticipate hybrid dispersion effects much beyond those observed before in weakly interacting opals [71].…”

“…Near the intersection region of the two smaller pores, the light is confined in all three directions to within a mode volume as small as V mode = λ 3 , where λ is the free-space wavelength [49]. Supercell band structures revealed up to five resonances within the band gap of the perfect crystal, depending on the defect pore radius r [49], that have quadrupolar symmetry [50]. The best confinement occurs for a defect radius r /r = 0.5 that is also considered here.…”

“…Notably, Ref. [50] also reports that the first two bands are nearly degenerate. Based on the occurrence of five cavity bands, on degeneracies between bands, and on the field distribution (reported in Ref.…”

“…Based on the occurrence of five cavity bands, on degeneracies between bands, and on the field distribution (reported in Ref. [49]), it has been concluded that the resonances of the inverse woodpile cavity have quadrupolar symmetry and are the optical analogs of d-orbitals in solid-state physics [50]. Therefore, it is naively expected that neighboring cavities couple in diagonal directions.…”