Slow-wave effect and mode-profile matching in photonic crystal microcavities

Physical mechanisms involved in the light confinement in photonic crystal slab microcavities are investigated. We first present a full three-dimensional numerical study of these microcavities. Then, to gain physical insight into the confinement mechanisms, we develop a Fabry-Perot model. This model provides accurate predictions and sheds new light on the physics of light confinement. We clearly identify two mechanisms to enhance the $Q$ factor of these microcavities. The first one consists of improving the mode-profile matching at the cavity terminations and the second one of using a slow wave in the cavity.

Figure 1

Schematic top view of the investigated microcavities formed by filling $N$ holes in the $\Gamma K$ direction of a two-dimensional PC structure composed of a triangular lattice of air holes (lattice constant $a=0.42\mu \mathrm{m}$) etched into a silicon slab. The picture holds for a cavity with three missing holes $(N=3)$. The slab thickness is $0.6a$ and the air holes radii $0.29a$. The hole displacement at the cavity edges is denoted by $d$. Planes $P$ and $P^{\prime }$ are used as phase references for the modal reflectivity used in the Fabry-Perot model.

Figure 2

Comparison between experimental data (squares), calculation data (circles), and FP model predictions (solid curves). (a), (b), and (c) $Q$-enhancement for $N=1$, 2, and 3, respectively. In (a), the FP model predictions do not show up for $d⩽0.1a$. For small $d$’s, the resonance wavelength is beneath $1.5\mu \mathrm{m}$ and the Bloch mode of the single-line-defect PC waveguide leaks in the air clads. (d) Resonance wavelength redshift for $N=3$.

Figure 3

The total-phase delay ${\Phi }_T\left(\lambda \right)$ has been represented for $d∕a=0$, 0.05, 0.1, 0.15, and 0.25 and for $N=3$. The phase matching occurs for ${\Phi }_T\left({\lambda }_0\right)=4\pi$ (dashed horizontal line). Inset: dispersion diagram of the fundamental Bloch mode (solid curve). The dashed lines correspond to the resonance wavelengths for the above-mentioned values of $d$. From top to bottom, $d$ increases.

Figure 4

(a), (b), and (c) Effect of the holes shift on the main physical parameters involved in Eq. (2) for $N=3$. (d) ${\mid r\left(\lambda \right)\mid }^2$ for two mirrors with $d=0$ (dashed-dotted curve) and $d=0.18a$ (solid curve). The arrows indicate the reflectivity change for the three cavities. From left to right, $N=1$, 2, and 3.