A power-in-bucket model enabled designs of nanostructure-enhanced waveguides for highly efficient wide-angle light couplings

Well-designed nanostructures on fiber facets can boost wide-angle light coupling and thus gain considerable attention because of the potential for intensive applications. However, previous theories commonly concentrate on the configurations of the bare waveguide, lacking full consideration of structure-assisted couplings. Here, a power-in-bucket (PIB) model is introduced to explore the coupling behavior of structure-modified waveguides. The analytical model investigates two representative coupling scenarios,including Gaussian beam and plane wave excitation. The PIB-computed coefficient {\eta} enhancements agree well with the experimental values, especially for the multiple-mode fibers under large-angle illuminations. Using PIB to optimize the beam-fiber parameters, we show that at the incidence angle of 37 degree, {\eta} could increase from 0.3320 to 0.5102 by the identical ring gratings. Overall, the proposed model provides a useful account of the mechanism of grating-aided light couplings. These findings would be of great help in designing structure-enhanced probes for wide-angle broadband light collection applications.