Coupling coefficients for photonic crystal waveguides

Michaelis, Dirk; Peschel, Ulf; Waechter, Christoph A.; Braeuer, Andreas H.

doi:10.1117/12.478331

Cited by 5 publications

(6 citation statements)

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“…A necessary requirement for the Bloch-ABC is an orthogonality relation between different Bloch eigenmodes of a PC, PC waveguide or metamaterial. An orthognality relation for Bloch eigenmodes has previously been presented in several papers [14][15][16][17][18] . Here we generalize this orthogonality relation to work with eigenmodes of lossy (and active) crystals, as well as crystals made up of anisotropic and bianisotropic materials.…”

Section: Discussionmentioning

confidence: 99%

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Absorbing boundary condition for Bloch–Floquet eigenmodes

Fietz¹

2013

J. Opt. Soc. Am. B

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We present an absorbing boundary condition for electromagnetic frequency domain simulations of photonic crystals and metamaterials. This boundary condition can simultaneously absorb multiple Bloch-Floquet eigenmodes of a periodic crystal, including both propagating and evanescent modes. The photonic crystal or metamaterial in question can include lossy, active, anisotropic and even bi-anisotropic inclusions. The absorbing boundary condition is dependent on an orthogonality condition for Bloch-Floquet eigenmodes, a generalized version of which is presented here. We test this absorbing boundary condition numerically and present the results.

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Section: Discussionmentioning

confidence: 99%

“…The orthogonality relation that we use is a generalization (see Appendix A for the derivation) of that presented in Refs. [14][15][16][17][18] , generalized to work with lossy PCs…”

Section: Bloch Absorbing Boundary Conditionmentioning

confidence: 99%

Absorbing boundary condition for Bloch–Floquet eigenmodes

Fietz¹

2013

J. Opt. Soc. Am. B

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“…A detailed description of the underlying modelling scheme has been given elsewhere, [14,15], therefore a short repetition of the basics is presented here, only. If light propagation from a low index contrast telecom fibre to a high NA monomode or PC waveguide is considered, it is intuitively clear that scalar approximation and simple ray optics will fail when the mode field diameter shall be squeezed down to about one vacuum wavelength or less.…”

Section: Modelling and Lens Designmentioning

confidence: 99%

“…In the homogeneous medium adjacent to the dummy plane the intended narrow field distribution in the coupling plane is calculated by ASP with a single propagation step. In the coupling plane, the coupling efficiency from the focal field to the intended guided mode can be calculated, [14],…”

Section: Modelling and Lens Designmentioning

confidence: 99%

Fiber-chip coupling with silicon microlenses

Waechter

Benkenstein

Hoefer

et al. 2005

Integrated Optics: Devices, Materials, and Technologies IX

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Direct coupling from fibres to waveguides requires field matching to achieve high coupling efficiency. 3D on-chip tapers are well suited in principle, but practicability may depend on materials and geometrical structures used for the waveguide chip, especially when photonic crystal defect waveguides are involved. To adapt the spot size of the fibre mode to that of a waveguide with high index contrast, silicon micro-lenses can be used advantageously. Although positioning requires finer resolution with small foci this can be accomplished by state-of-the-art micro-positioning equipment. A theoretical description of the hybrid coupling concept and corresponding numerical results are presented, where the design covers the range from free-space ray-trace to FDTD at the chip-level. Experimental results for the characterisation of the optimised aspheric silicon micro-lenses are reported as well.

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“…Even such a simulation procedure with adapted numerical methods for each part of the propagation requires a considerable computation time. To speed up the simulation process for system optimisation remarkably, the FDTDsimulation can be replaced by a formula for the coupling efficiency to a conventional high-index or a PhC-waveguide 91 validity of this approximation should be checked at least for the final result of an optimisation by FDTD. Nevertheless, Eq.…”

Section: Specific Applications and Requirementsmentioning

confidence: 99%