A systematic design approach for one-dimensional and crossed photonic nanobeam cavities for quantum dot integration

Abstract

We present a systematic workflow for the design of one-dimensional photonic crystal nanobeam cavities with non-zero cavity lengths. By simultaneously optimizing the lattice periodicity, air-hole geometry, and cavity length, our approach enables precise control of optical confinement while mitigating radiative losses and linewidth broadening effects. The method is further extended to the design of crossed nanobeam cavities with both matching and mismatched resonance frequencies. This strategy significantly reduces the need for extensive parameter sweeps, providing an efficient route toward optimized cavity designs for integrated quantum photonic applications. Moreover, the resulting structures are inherently compatible with the integration of single-photon emitters.

Figures (8)

• Figure 1: Nanobeam cavity design: Symmetric 1D photonic crystal nanobeam cavity that incorporates a finite cavity length $l_{cavity}$, a mirror region and a taper region where the holes are tapered from small to big in order to maximize the coupling between the Bloch mode and the waveguide mode.
• Figure 2: Schematic illustration of a typical photonic bandstructure in the first half of the Brillouin zone.The dashed black line denotes the light line, separating radiative modes from modes confined to the structure; the dielectric (red) and air (blue) bands lie below it. The star and triangle mark the modes at the Brillouin zone edge, and the orange line indicates the midgap frequency that defines the center of the photonic bandgap.
• Figure 3: Variations of the (TE) dielectric and air bands as a function of the lattice constant ($a$) and filling fraction ($F$). The warm colormap represents the dielectric band, while the cool colormap represents the air band. The gray plane at $321$THz indicates the bandgap region, with intersections with the dielectric and air bands shown as black lines.
• Figure 4: Map of $\gamma$ at the target frequency of $321$ THz, obtained using the model of $\gamma$Quan2010Quan2011 over the bandgap area of Fig.\ref{['fig:3Dbands']}. The color bar indicates the value of $\gamma$ across the parameter map. The dashed white lines denote the threshold at which the hole size exceeds the waveguide width. The green and orange lines illustrate how design strategies based solely on the lattice periodicity Ohta2011 or the air-hole geometry Quan2010Quan2011 would appear on the $\gamma$ map. Red segments of the outer contour indicate intersections with the dielectric band, while blue segments indicate intersections with the air band.
• Figure 5: (a) Cavity resonance frequency versus cavity length $l$, obtained by extending the dielectric region at the cavity center between the two central holes and sweeping its length from $0$ nm to $600$ nm. The targeted frequency $f_\text{targeted}=321$,THz is indicated by the grey dashed line. Resonances at the target frequency occur for cavity lengths of approximately $100$ nm (green dot) and $450$ nm (red dot). (b) $E_y$-field profile for a cavity length of $100$ nm and $450$ nm. Black lines denote the structure outlines of the waveguide and the holes.