Observation of light propagation through a three-dimensional cavity superlattice in a 3D photonic band gap

TL;DR

This work demonstrates experimental observation of light propagating as discretized hops between resonant cavities embedded in a 3D photonic band gap. By fabricating 3D inverse woodpile silicon crystals with a periodic cavity superlattice, and using plane-wave expansion theory to predict defect bands, the authors show Cartesian light bands in the in-gap region and confirm 3D hopping through position-resolved reflectivity and lateral scattering measurements. The results include reproducible in-gap scattering peaks across multiple cavities, evidencing genuine 3D coupling and light transport, with potential implications for 3D photonic networks and 3D Anderson localization of light. This constitutes the first experimental observation of 3D discretized light transport in a cavity superlattice and points toward future 3D quantum photonic network applications using wavefront control.

Abstract

We experimentally investigate unusual light propagation inside a three-dimensional (3D) superlattice of resonant cavities that are confined within a 3D photonic band gap. Therefore, we fabricated 3D diamond-like photonic crystals from silicon with a broad 3D band gap in the near-infrared and doped them with a periodic array of point defects. In position-resolved reflectivity and scattering microscopy, we observe narrow spectral features that match well with superlattice bands in band structures computed with the plane wave expansion. The cavities are coupled in all three dimensions when they are closely spaced and uncoupled when they are further apart. The superlattice bands correspond to light that hops in high symmetry directions in 3D - so-called Cartesian Light - that opens applications in 3D photonic networks, 3D Anderson localization of light, and future 3D quantum photonic networks.

Figures (12)

• Figure 1: Schematic of a few possible paths for waves (yellow) hopping in Cartesian directions in a 3D cavity superlattice. At the end of their Cartesian journey, waves may exit from a different crystal surface (top) than where they entered (right). Each cavity is shown as a red sphere and the surrounding (photonic band gap) crystal as the 3D mesh with blue spheres as unit cells.
• Figure 2: Scanning electron micrograph of a 3D cavity superlattice embedded in a 3D photonic band gap crystal made of silicon, viewed in the (X,Z)-direction. The inverse woodpile crystal has lattice constants $a=0.68~\mathrm{\mu m}$ in the Y-direction and $c=0.48~\mathrm{\mu m}$ in the X, Z-directions. The designed pore radius is $r = 0.16~\mathrm{\mu m}$ for the main nanopores and $r'=r/2=0.08~\mathrm{\mu m}$ for the defect pores. The superlattice of the point defects has the unit cell with dimensions $5c, 5a, 5c$. The excess silicon at the intersections of these defect pores inside the material form point defects, constituting the superlattice of 3D cavities.
• Figure 3: (a,b) Measured reflectivity (blue dots) and lateral scattering (red triangles, right ordinate) spectra of the cavity superlattice SL5 on a defect and in between two defects ($X = 2.5~\mathrm{\mu m}$), collected with s-polarization (E-field $\perp$ X-directed pores). The broad reflectivity peaks correspond to the band gaps of the crystal at the particular location, as indicated by the yellow regions that match very well with theory. In (a), the lateral scattering peak at $6900~\mathrm{cm^{-1}}$ within the band gap (cyan highlight) corresponds to a reflectivity trough and a Cartesian band in the band structures. (c) Photonic band structure of a cavity superlattice in an inverse woodpile crystal, rotated for comparison with measured spectra, with frequency and wave vector reduced by the lattice parameter $a$, and with $\epsilon = 12.1$ typical of Si. Crystal pores have a relative radius $r/a = 0.22$ and defect pores $r' = r/2$. The yellow region between $a/\lambda = 0.44$ and $0.502$ is the 3D photonic band gap of the superlattice crystal, and the allowed bands outside the band gap are shown as dark grey areas. The cavity superlattice sustains two types of bands inside the band gap: flat bands typical of Cartesian light in the lower half of the gap (colored bands), and other bands in the upper half of the gap (black bands). (d) Photonic band structure of an inverse woodpile photonic crystal with $r/a=0.22$ without cavities. The yellow region between $a/\lambda = 0.44$ and $0.56$ is the unperturbed 3D band gap.
• Figure 4: Camera images of the front surface of superlattice SL3 for cross-polarized light taken at two different frequencies. Left: at $\omega = 7386~\mathrm{cm^{-1}} = \omega_{\rm{SL}}$, i.e. at the center of the superlattice peak. Right: at $7174~\mathrm{cm^{-1}}$, outside the superlattice peak. The surface of the crystal is illuminated by a separate LED to reveal rectangular XY crystal surface. On top left of each figure, the white bar on the top left indicates scale of $5~\mu$m
• Figure 5: Lower edges (red upright triangles) and upper edges (blue downward triangles) of the position-dependent photonic gap versus $Y$, obtained from reflectivity measurements on two crystals with a cavity superlattice with different lattice spacings. Frequency of the peak inside the stopband obtained from lateral scattering measurements are shown by green circles on each panel. Below each plot the SEM image of the surface of the crystals are stitched with same scale for reference for the reader. The magenta dashed lines trace the positions of the defect pores.