Discrete quality-factor control in a side-coupled photonic crystal microcavity: evanescent Bloch tunnelling and the finite-cell correction

Abstract

A point-defect cavity side-coupled to a line-defect waveguide in a two-dimensional photonic crystal of silicon rods in water is studied with plane-wave expansion and finite-difference time-domain computations. The defect-rod radius tunes the resonance continuously within the band gap, as first-order perturbation theory predicts, whereas the quality factor changes in discrete steps set by the number of lattice rows between cavity and guide; displacing the defect rod by up to a tenth of a period changes it by less than 7 percent. Each added row multiplies the quality factor by a factor that follows, without an adjustable parameter, from the decay of the evanescent Bloch channel of the bulk crystal that is phase-matched to the guided mode; the channel at zero wavevector along the guide predicts little more than half that factor. Two biases of a finite computational domain, leakage across the cladding and a standing wave set up by reflections at the ends of the truncated guide, lower the per-row factor and change the quality factor by up to a factor of two if left uncorrected. Scaled to 1550 nm the design gives a sensitivity of 634 nm per refractive index unit, which perturbation theory reproduces, and the linewidth agrees with that of a transmission spectrum normalized to a cavity-free reference. Absorption by water caps the quality factor near 9200 and limits the useful number of barrier rows. The guided mode lies inside the light cone, so a slab of finite height needs a different guide.

arXiv comment26 pages, 7 figures, 5 tables. Data, code and supplementary material: doi:10.5281/zenodo.22912910