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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 17 — Aug. 22, 2005
  • pp: 6354–6375

Vertically-stacked multi-ring resonator

M. Sumetsky  »View Author Affiliations

Optics Express, Vol. 13, Issue 17, pp. 6354-6375 (2005)

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A vertically-stacked multi-ring resonator (VMR), which is a sequence of ring resonators stacked on top of each other, is investigated. The light in the VMR propagates horizontally in the plane of rings and at the same time propagates vertically between the adjacent rings due to evanescent coupling. If fabricated, the VMR may be advantageous compared to the conventional planar arrangement of coupled rings due to its dramatic compactness and more flexible transmission characteristics. In this paper, the uniform VMR, which consists of N rings coupled to the input and output waveguides, is studied. The uniform VMR is a 3D version of a coupled resonator optical waveguide (CROW). Closed analytical expressions for the transmission amplitudes and eigenvalues are obtained by solving coupled wave equations. In the approximation considered, it is shown that, in contrast to the conventional planar ring CROW, a VMR can possess eigenmodes even when interring coupling as well as coupling between rings and waveguides is strong. For the isolated VMR, the eigenvalues of the propagation constant are shown to change linearly with the interring coupling coefficient. The resonance transmission near the VMR eigenvalues is investigated. The dispersion relation of a VMR with an infinite number of rings is found. For weak coupling, the VMR dispersion relation is similar to that of a planar ring CROW (leading, however, to a much smaller group velocity), while for stronger coupling, a VMR does not possess bandgaps.

© 2005 Optical Society of America

OCIS Codes
(060.2340) Fiber optics and optical communications : Fiber optics components
(190.0190) Nonlinear optics : Nonlinear optics
(230.5750) Optical devices : Resonators
(230.7370) Optical devices : Waveguides
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Research Papers

Original Manuscript: July 8, 2005
Revised Manuscript: August 4, 2005
Published: August 22, 2005

M. Sumetsky, "Vertically-stacked multi-ring resonator," Opt. Express 13, 6354-6375 (2005)

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