Two regimes of confinement in photonic nanocavities: bulk confinement versus lightning rods

Abstract

We present a theoretical study of dielectric bowtie cavities and show that they are governed by two essentially different confinement regimes. The first is confinement inside the bulk dielectric and the second is a local lightning-rod regime where the field is locally enhanced at sharp corners and may yield a vanishing mode volume without necessarily enhancing the mode inside the bulk dielectric. We show that while the bulk regime is reminiscent of the confinement in conventional nanocavities, the most commonly used definition of the mode volume gauges in fact the lightning-rod effect when applied to ultra-compact cavities, such as bowties. Distinguishing between these two regimes will be crucial for future research on nanocavities, and our insights show how to obtain strongly enhanced light-matter interaction over large bandwidths.

Nanometer-scale photon confinement in topology-optimized dielectric cavities

“…The procedure for measuring the fabrication constraints is detailed in Supplementary Section 2 . This ensures that the optimization is protected from local lightning-rod effects at the surface and instead achieves robust confinement inside the dielectric bowtie 24 . Our devices are based on 240 nm crystalline (100) silicon membranes ( n = 3.48) suspended in air, patterned with electron-beam lithography, dry etching, and selective vapor-phase hydrofluoric acid etching.…”

“…Experimental demonstrations of dielectric confinement of light below the diffraction limit have been reported before 34 but the claimed mode volumes in these preliminary experiments were later shown 24 to be underestimated by at least one order of magnitude due to numerical errors and inconsistencies. Another issue with previous experiments is that they employed a V-groove whose tip enhances the optical intensity by a lightning-rod surface effect that falls off exponentially inside the dielectric and does not provide subdiffraction confinement away from the surface.…”

“…Third, the presence of material discontinuities in few-nanometer devices makes the numerical modeling of bowtie cavities very challenging, requiring a very small mesh size 23 . Even the smallest discontinuity in the outline of the geometry implies a mode volume of zero 24 . Such numerical artefacts arise from the well-known electric-field divergences at sharp tips and corners 5 , 9 , 23 , 32 , 33 .…”

“…Such numerical artefacts arise from the well-known electric-field divergences at sharp tips and corners 5 , 9 , 23 , 32 , 33 . This also implies that the commonly used definition of the mode volume, which normalizes to the maximum, is not generally applicable to DBCs because it gauges unintended lightning-rod surface effects rather than the effect of confining light inside the material 24 .…”

“…This means that lightning-rod surface effects are particularly sensitive to numerical artefacts and we therefore evaluate and report the mode volume in the center of our silicon bridges as devised in ref. 24 . This quantity is robust against surface effects such as non-vertical sidewalls as shown explicitly in Supplementary Section 1 , and it is the relevant quantity describing enhanced spontaneous emission from embedded emitters such as defect centers 35 .…”