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.
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BibTeX
@misc{oguz2026discrete,
title = {{Discrete quality-factor control in a side-coupled photonic crystal microcavity: evanescent Bloch tunnelling and the finite-cell correction}},
author = {Hasan Oguz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.31952},
eprint = {2609.31952},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31952},
}
RIS
TY - UNPB
TI - Discrete quality-factor control in a side-coupled photonic crystal microcavity: evanescent Bloch tunnelling and the finite-cell correction
AU - Hasan Oguz
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2609.31952
UR - https://arxiv.org/abs/2609.31952
AB - 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.
ER -