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

Abstract

A point-defect microcavity side-coupled to a W1 waveguide in a two-dimensional photonic crystal of silicon rods immersed in an aqueous analyte is studied by plane-wave expansion and finite-difference time-domain computation. The resonance moves continuously through the transverse-magnetic band gap with the square of the radius of the defect rod, as first-order perturbation theory predicts for the dielectric area restored to the lattice site. The quality factor is set instead by the separation between cavity and waveguide, counted in lattice rows: each added row multiplies it by 7.10 at the reference defect radius, whereas moving the defect rod by up to a tenth of a lattice period changes it by less than 7 per cent. The per-row factor follows, at two defect radii and with no adjustable parameter, from the decay of the slowest evanescent Bloch channel of the crystal at the wavevector of the guided mode. Two checks are needed before such values can be trusted in a finite cell: convergence in cladding thickness and removal of the reflections from the waveguide ends. Without them the per-row factor comes out too low and the quality factor wrong by up to a factor of two. Scaled to 1550 nm the design gives a sensitivity of 634 nm per refractive index unit, which perturbation theory reproduces, and a Fano fit to an independently normalised transmission spectrum confirms the linewidth. The absorption of water at this wavelength lowers the quality factor of the reference geometry by a third and caps it near 9200, which limits the benefit of adding further rows.