Abstract
To detach large vectorial full-wave electromagnetic scattering problems from the specific, dissimilar bases that are typically associated with the optical waveguiding structures comprising an optical interface, we propose and demonstrate the expansion of wavefields in a single universal Wilson basis. We construct a Wilson basis by following the derivation in the paper by Daubechies, Jaffard and Journé. This basis features exponentially decaying basis functions in both the spatial and spectral domain. The strong localization in phase-space, with basis functions that strongly resemble wavefields, allow for efficient expansions of high-frequency electromagnetic fields. In a Wilson basis, the interface scattering problem is effectively separated from the physical configuration. For the evaluation of multiple, laterally displaced interface configurations, one may reuse electromagnetic fields in the Wilson basis, because the translation operator is sparse and diagonally dominant. We consider actual reflection-transmission problems comprising optical fibers and homogeneous media in the Wilson basis framework in a companion paper. There, the localization in the spectral domain aids the conversion of the numerical scheme to generate electromagnetic fields in homogeneous media due to Wilson-basis discretized electromagnetic sources. In this paper, we review the Wilson basis construction, demonstrate the expansion of modal electromagnetic fields in an optical fiber, and complex-source beams that are tilted with respect to the optical axis. Even for largely tilted beams (up to 60°), despite being highly oscillatory in the cross-sectional plane, the fields are well represented by a finite number of higher-order Wilson basis functions.
Highlights
Passive optical networks for indoor applications typically rely on multi-mode optical fibers to facilitate high-bandwidth communication over distances up to several hundred meters (IEEE 2010)
To detach large vectorial full-wave electromagnetic scattering problems from the specific, dissimilar bases that are typically associated with the optical waveguiding structures comprising an optical interface, we propose and demonstrate the expansion of wavefields in a single universal Wilson basis
We have evaluated the integrals in Eq (16), and visualize the power density distributions due to the projections of displaced Wilson basis functions w‘;nðx À xdÞ onto the nondisplaced counterparts w‘0;n0 ðxÞ in Figs. 4 and 5
Summary
Passive optical networks for indoor applications typically rely on multi-mode optical fibers to facilitate high-bandwidth communication over distances up to several hundred meters (IEEE 2010). The ability to tailor the basis functions to the physical size of the optical wavefields and match to the spatial frequencies allows for a high degree of flexibility Another example of combining global and local formulations is a beam-based phasespace source representation (Arnold 2002). 3, we show that spatial field translations may be achieved directly in the Wilson basis with a sparse, diagonally dominant operator This is an appealing feature, and useful for the evaluation of electromagnetically large reflection-transmission problems consisting of optical fibers with different but finite lateral alignment configurations. The convergence of spectal convolution integrals of dyadic Green’s functions for electromagnetic field evaluation due to Wilson-basis discretized source distributions benefit from the spectral localization of the Wilson basis This allows to extend to interfaces consisting of homogeneous half-spaces or homogeneous slabs. It shows that including only a few levels of higher-order basis functions are already sufficient to accurately represent modal electromagnetic fields in the Wilson basis
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
