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

M. Hammer, S. Alhaddad, J. Förstner, Journal of the Optical Society of America B 34 (2017) 613–624.

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Abstract
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, pro- cedures from the realm of finite-element numerics are applied to establish systems of linear equations for the then- discrete 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 com- putational 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.
Publishing Year
Journal Title
Journal of the Optical Society of America B
Volume
34
Issue
3
Page
613-624
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Hammer M, Alhaddad S, Förstner J. Hybrid coupled-mode modeling in 3D: perturbed and coupled channels, and waveguide crossings. Journal of the Optical Society of America B. 2017;34(3):613-624. doi:10.1364/josab.34.000613
Hammer, M., Alhaddad, S., & Förstner, J. (2017). Hybrid coupled-mode modeling in 3D: perturbed and coupled channels, and waveguide crossings. Journal of the Optical Society of America B, 34(3), 613–624. https://doi.org/10.1364/josab.34.000613
@article{Hammer_Alhaddad_Förstner_2017, title={Hybrid coupled-mode modeling in 3D: perturbed and coupled channels, and waveguide crossings}, volume={34}, DOI={10.1364/josab.34.000613}, number={3}, journal={Journal of the Optical Society of America B}, publisher={The Optical Society}, author={Hammer, Manfred and Alhaddad, Samer and Förstner, Jens}, year={2017}, pages={613–624} }
Hammer, Manfred, Samer Alhaddad, and Jens Förstner. “Hybrid Coupled-Mode Modeling in 3D: Perturbed and Coupled Channels, and Waveguide Crossings.” Journal of the Optical Society of America B 34, no. 3 (2017): 613–24. https://doi.org/10.1364/josab.34.000613.
M. Hammer, S. Alhaddad, and J. Förstner, “Hybrid coupled-mode modeling in 3D: perturbed and coupled channels, and waveguide crossings,” Journal of the Optical Society of America B, vol. 34, no. 3, pp. 613–624, 2017.
Hammer, Manfred, et al. “Hybrid Coupled-Mode Modeling in 3D: Perturbed and Coupled Channels, and Waveguide Crossings.” Journal of the Optical Society of America B, vol. 34, no. 3, The Optical Society, 2017, pp. 613–24, doi:10.1364/josab.34.000613.
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