Chains of coupled square dielectric optical microcavities

Hammer, Manfred

doi:10.1007/s11082-009-9268-3

Cited by 6 publications

(4 citation statements)

References 33 publications

(40 reference statements)

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“…on fields with complex frequency and integer angular wavenumber. Similar to [17], the HCMT template would then include the bus modes with their varying amplitudes, together with a series of whispering gallery modes of the cavity that fall in the wavelength interval of interest, each multiplied by a single variable coefficient. Implementation and evaluation of that approach is under way.…”

Section: Discussionmentioning

confidence: 99%

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HCMT models of optical microring-resonator circuits

Hammer

2010

J. Opt. Soc. Am. B

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Circuits of dielectric integrated optical microring resonators are addressed through a 2-D hybrid analytical / numerical coupled mode theory (HCMT) model. Analytical modes of all straight and curved cores form templates for the optical fields of the entire circuits. Our variational technique then generates solutions for the amplitude functions in their natural Cartesian and polar coordinates, discretized by 1-D finite elements. Bidirectional wave propagation through all channels and pronounced reflections can be taken into account. The series of examples includes rings coupled in parallel, rows of cavities (coupled resonator optical waveguides, CROWs) of varying length, a triangular photonic molecule, and a resonator with a slit ring to illustrate the role of intra-cavity reflections.

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Section: Discussionmentioning

confidence: 99%

“…As an alternative we propose to apply the Hybrid analytical / numerical Coupled Mode Theory (HCMT) formalism of [16,17]. The approach can treat directly the full resonator circuits, i.e.…”

Section: Introductionmentioning

confidence: 99%

HCMT models of optical microring-resonator circuits

Hammer

2010

J. Opt. Soc. Am. B

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“…Instead, one resorts to numerical means. The respective "hybrid" analytical/numerical CMT variant (HCMT) was introduced in [16], at first applied to circuits with rectangular refractive index distributions, including the crossings of perpendicular waveguide channels, waveguide Bragg gratings and related filters, and systems of coupled square microcavities [16,17]. References [18,19] report on HCMT models of a series of micro-ring or -disk circuits.…”

Section: Introductionmentioning

confidence: 99%

Hybrid coupled-mode modeling in 3D: perturbed and coupled channels, and waveguide crossings

2017

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The 3D implementation of a hybrid analytical/numerical variant of the coupled-mode theory is discussed. Eigenmodes of the constituting dielectric channels are computed numerically. The frequency-domain coupled-mode models then combine these into fully vectorial approximations for the optical electromagnetic fields of the composite structure. Following a discretization of amplitude functions by 1D finite elements, procedures from the realm of finite-element numerics are applied to establish systems of linear equations for the thendiscrete modal amplitudes. Examples substantiate the functioning of the technique and allow for some numerical assessment. The full 3D simulations are highly efficient in memory consumption, moderately demanding in computational time, and, in regimes of low radiative losses, sufficiently accurate for practical design. Our results include the perturbation of guided modes by changes of the refractive indices, the interaction of waves in parallel, horizontally or vertically coupled straight waveguides, and a series of crossings of potentially overlapping channels with fairly arbitrary relative positions and orientations.

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“…By now, a large variety of implementations has been achieved [1,[5][6][7][8][9][10][11]. Naturally, also the extension to more than one cavity has been suggested, for example, as chains of coupled ring or disc resonators [12,13], of defects in photonic crystal hosts [14,15], of coupled resonator spheres [16][17][18], or of coupled square resonators on a grid [19].…”

Section: Introductionmentioning

confidence: 99%

Pathway interference in a loop array of three coupled microresonators

2011

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A system of three coupled toroidal microresonators arranged in a loop configuration is studied. This setup allows light entering the resonator setup from a tapered fiber to evolve along a variety of different pathways before leaving again through the fiber. In particular, the loop configuration of the resonators allows for an evolution which we term roundtrip process, in which the light evolves from one resonator sequentially through all others back to the initial one. This process renders the optical properties of the system sensitive to the phases of all coupling and scattering constants in the system. We analyze the transmission and reflection spectra, and interpret them in terms of interference between the various possible evolution pathways through the resonator system. In particular, we focus on the phase dependence of the optical properties. Finally, we discuss possible applications for this phase sensitivity induced by the roundtrip process, such as the measurement of the position of a nanoparticle close to one of the resonators, and the measurement of changes in the refractive index between two resonators. Our analytical results for the applications are supported by proof-of-principle calculations based on finite-difference-time-domain solution of Maxwell's equations in two dimensions on a grid.

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Chains of coupled square dielectric optical microcavities

Cited by 6 publications

References 33 publications

HCMT models of optical microring-resonator circuits

HCMT models of optical microring-resonator circuits

Hybrid coupled-mode modeling in 3D: perturbed and coupled channels, and waveguide crossings

Pathway interference in a loop array of three coupled microresonators

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