Interaction of whispering gallery modes in integrated optical microring or microdisk circuits: hybrid coupled mode theory model

Ellen F. Franchimon; Kirankumar R. Hiremath; Remco Stoffer; Manfred Hammer

doi:10.1364/JOSAB.30.001048

Journal of the Optical Society of America B
Vol. 30,
Issue 4,
pp. 1048-1057
(2013)
•https://doi.org/10.1364/JOSAB.30.001048

Interaction of whispering gallery modes in integrated optical microring or microdisk circuits: hybrid coupled mode theory model

Ellen F. Franchimon, Kirankumar R. Hiremath, Remco Stoffer, and Manfred Hammer

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Ellen F. Franchimon, Kirankumar R. Hiremath, Remco Stoffer, and Manfred Hammer, "Interaction of whispering gallery modes in integrated optical microring or microdisk circuits: hybrid coupled mode theory model," J. Opt. Soc. Am. B 30, 1048-1057 (2013)

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- Integrated Optics
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About this Article
History
- Original Manuscript: December 7, 2012
- Revised Manuscript: February 14, 2013
- Manuscript Accepted: February 14, 2013
- Published: March 29, 2013

Abstract

Whispering gallery modes supported by open circular dielectric cavities are embedded into a nonparametric two-dimensional frequency domain hybrid coupled mode theory framework. Regular aggregates of these cavities, including straight access channels, are investigated. The model enables convenient studies of the guided wave scattering process, the response of the circuit to guided wave excitation. Transmission resonances can be characterized directly in terms of resonance frequency and linewidth by computing supermodes of the entire composite circuits, comprising both cavities and bus waveguides. Examples of single ring and disk filters, a coupled-resonator optical waveguide, and a three-cavity photonic molecule in a reflector configuration allow the approach to be assessed.

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Ring	$λ_{r} / μm$	$Q$	$Δ λ / μm$	Fig.	Disk	$λ_{r} / μm$	$Q$	$Δ λ / μm$	Fig.
WGM(0, 39)	1.56373	$1.1 \cdot 10^{5}$	$1.4 \cdot 10^{- 5}$	1(c)	WGM(0, 40)	1.56514	$8.2 \cdot 10^{5}$	$1.9 \cdot 10^{- 6}$	6(a)
pert.	1.56516				pert.	1.56579
${(tr)}_{BM}$	$1.5621 x$			5(a)	(tr)	$1.5645 x$			6(b)
${(tr)}_{WGM (0, 39)}$	$1.5622 x$			5(b)	${(sm)}_{ud .}$	1.56454	$6.7 \cdot 10^{2}$	$2.3 \cdot 10^{- 3}$	6(c)
$(tr)_{WGM (0, 37 - 41)}$	$1.5622 x$			5(c)	WGM(1, 35)	1.57444	$1.7 \cdot 10^{3}$	$9.3 \cdot 10^{- 4}$	6(d)
${(sm)}_{ud .}$	1.56219	$4.3 \cdot 10^{2}$	$3.7 \cdot 10^{- 3}$	5(d)	pert.	1.57904
${(sm)}_{bd ., even}$	1.56223	$4.5 \cdot 10^{2}$	$3.5 \cdot 10^{- 3}$	5(e)	(tr)	$1.5730 x$			6(e)
${(sm)}_{bd ., odd}$	1.56215	$4.0 \cdot 10^{2}$	$3.9 \cdot 10^{- 3}$	5(f)	${(sm)}_{ud .}$	1.57320	$1.1 \cdot 10^{3}$	$1.4 \cdot 10^{- 3}$	6(f)

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Journal of the Optical Society of America B