High-Q surface-defect photonics on three-dimensional photonic crystals: realizing the projected $Q>100{,}000$, controlling surface disorder, and efficient external coupling via the surface-mode gap

Ishizaki and Noda (Nature 460, 367–370, 2009) demonstrated that the surface of a three-dimensional (3D) photonic crystal — where the 3D periodicity terminates — supports two-dimensional surface states, a designable surface-mode gap, and localized surface-defect nanocavities, reaching quality factors $Q\approx 9{,}000$ on an eight-layer GaAs woodpile structure, with a theoretical projection that increasing the number of stacked layers beyond eight could yield $Q>100{,}000$. The best experimentally demonstrated surface-defect quality factor remains $Q\approx 40{,}000$ (2013); the loss mechanisms arising from fabrication-induced disorder and surface scattering have been quantified only theoretically (2013); and efficient external coupling exploiting the surface-mode gap has been shown only numerically (2015). The problem — experimentally realizing the theoretically projected high-$Q$ performance of surface-defect modes on 3D photonic crystals, identifying and controlling the disorder and surface-mode leakage channels that limit it, and demonstrating practical efficient coupling between external fields and surface or interior modes — remains open.

Background

A photonic crystal is a dielectric material whose refractive index varies periodically on the scale of the wavelength of light, so that, by analogy with electrons in a crystalline solid, certain frequency ranges — photonic bandgaps — forbid light from propagating. In a three-dimensional (3D) photonic crystal with a complete bandgap, no electromagnetic mode can propagate in any direction, which makes such crystals attractive building blocks for guiding, confining, and manipulating photons in optical circuits. A standard realization is the woodpile (stacked-stripe) structure: alternating layers of parallel dielectric rods, each layer rotated 90° and shifted by half a period relative to the layer two below; Noda, Tomoda, Yamamoto and Chutinan (Science 289, 604, 2000) fabricated woodpile crystals of GaAs with a complete bandgap at near-infrared wavelengths by a wafer-fusion and stacking technique. The conventional route to photon manipulation in these crystals embeds artificial defects (missing or modified rods) and light emitters inside the bulk, creating waveguides and nanocavities in the crystal interior; for example, Aoki, Guimard, Nishioka, Nomura, Iwamoto and Arakawa (Nature Photonics 2, 688, 2008) coupled quantum-dot emission to an interior 3D-photonic-crystal nanocavity. Modes at the surface, where the 3D periodicity terminates, had been studied mainly theoretically — Meade, Brommer, Rappe and Joannopoulos (Physical Review B 44, 10961, 1991) predicted electromagnetic Bloch waves localized at a photonic-crystal surface — and were largely regarded as parasitic perturbations of interior defect modes.

Ishizaki and Noda (Nature 460, 367–370, 2009) showed experimentally that the surface of a 3D photonic crystal can itself be used as an accessible two-dimensional photonic subsystem. Using an eight-layer GaAs woodpile (lattice constant $a=500$ nm, rod width and thickness $200$ nm) with a complete bandgap over roughly 1300–1600 nm, they excited surface states by evanescent coupling through a prism (the optical analog of the Otto/Kretschmann surface-plasmon configuration: total internal reflection in a prism of index 1.5 separated from the crystal by a submicrometer air gap produces an evanescent field with a controlled in-plane wavevector $k_{//}$, which is necessary because surface modes below the air light-line cannot be excited or radiate into free space), mapped the surface-state dispersion, observed surface-guided propagation with an estimated $1/e$ length of about 385 µm (the distance over which the surface-guided light intensity decays to $1/e$ of its initial value), and opened a surface-mode gap — an in-plane bandgap for surface states — by modifying the top layer from a striped to a crossed-rod geometry. Introducing a designed surface defect (a partially widened surface rod) produced localized resonant modes with quality factors up to about 9,000, the highest reported at the time for 3D photonic crystal nanocavities; the quality factor $Q=\lambda_0/\Delta\lambda_0$ measures the photon lifetime of the resonance as the ratio of the central wavelength to the resonance linewidth. Their numerical and theoretical analysis indicated that increasing the number of stacked layers beyond eight — which suppresses leakage of the surface mode through the finite crystal into the substrate — could raise $Q$ above 100,000. The paper also noted scattered light from unintended surface imperfections (a signature of surface scattering by fabrication disorder) and proposed that the absorption-free dielectric surface, and coupling schemes exploiting the surface-mode gap, could enable efficient access to embedded interior waveguides and cavities and new sensing and light–matter-interaction modalities.

Problem Statement

On the platform established by Ishizaki and Noda (2009) — localized surface-defect modes formed in a surface-mode gap on a woodpile-type 3D photonic crystal with a complete photonic bandgap — the open problem, in the generality stated by the source, is to bring surface-defect photonics on 3D photonic crystals to their theoretically projected performance and to make the surface a fully functional, externally accessible two-dimensional photonic layer. Concretely: (i) experimentally realize surface-defect modes with the projected quality factors exceeding 100,000, versus the measured $Q\approx 9{,}000$ (eight layers, 2009) and $Q\approx 40{,}000$ (advanced defect designs, 2013), and establish which loss channels (radiation, leakage through the finite stack, scattering by fabrication-induced surface disorder) actually limit the measured $Q$; (ii) identify, quantify, and control the surface irregularities and fabrication-induced disorder that scatter surface-guided light and reduce $Q$, down to the few-nanometer pattern-fidelity level that theory identifies as decisive (reference 3 quantifies this as a pattern-fluctuation standard deviation of $\sigma\approx 2$ nm); and (iii) demonstrate practical, efficient coupling that exploits the surface-mode gap to route light between an external medium and surface or embedded interior waveguides and cavities without loss to undesirable surface channels, reaching the coupling efficiency predicted numerically for a surface-mode-gap structure — $\approx 90\%$, versus $\approx 60\%$ without the gap (reference 4) — opening the systematic use of these absorption-free surfaces for light–matter interaction and sensing. These three directions are the components of one objective — quantitative, loss-controlled command of photons at the surface of 3D photonic crystals.

References

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