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

TL;DR

The paper introduces a power-in-bucket (PIB) model to analyze and optimize light coupling into structure-modified optical fibers under wide-angle illumination. By decomposing coupling into two parameters, $T_{beam}$ and $T_{NA}$, the PIB framework yields a simple, intensity-based coefficient $\eta_{pib}=T_{beam}\cdot T_{NA}$ that applies to both Gaussian-beam and plane-wave excitations, for bare and grating-enhanced waveguides. The authors demonstrate that ring-like gratings can significantly boost coupling efficiency, achieving $\eta$ up to $0.5102$ at $\theta=37^{\circ}$ (from $0.3320$) in a two-parameter optimization that favors higher fiber NA and larger core radius. The model aligns well with experiments across multiple wavelengths (e.g., 1550 nm and 650 nm) and suggests a practical design route for broadband, wide-angle light collection in fiber-based probes and interconnects. Overall, the PIB framework provides a fast, analytical tool to guide the construction of high-performance, structure-enhanced fiber couplers for applications such as Raman spectroscopy and fiber–chip interconnections.

Abstract

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 η 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, η 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.

Figures (4)

• Figure 1: The power-in-bucket (PIB) model for waveguide coupling behavior analysis. (a) A sketch illustrating that a focused Gaussian beam is incident on the end face of an optical fiber at an angle of $\theta$. (b-c) Two sketches correspond to PIB-related parameters of power ratios of $T_{beam}$ and $T_{NA}$, respectively. (d) A diagram comparing the coupling efficiency using the PIB model (orange line) and the rigorous small-angle-approximated model (light gray line), respectively. The black dots indicate the measured data of the bare single-mode fiber 28 (SMF-28).
• Figure 2: Boosting Gaussian beam-illuminated coupling efficiency using structure-enhanced waveguides. (a) The diagram of a ring-like grating patterned on the fiber facet. (b) A 2D model showing that the gratings split incoming Gaussian light into several diffraction orders, and the additional light can be coupled into the waveguide. (c-d) Wide-angle coupling coefficient enhancement using the polymer ring grating at a wavelength of 1550 nm and 650 nm, respectively. The black dots represent the measured efficiencies using grating-integrated SMF-28.
• Figure 3: Coupling efficiencies improvement of the grating-fiber under plane wave excitation. (a-b) A sketch along with the 2D model mimicking a plane wave incident on the grating-printed fiber endface. The coupling efficiency comparison between a bare SMF-28 fiber (c) and the grating-enabled one (d). The orange line and black dots originate from the PIB calculations and measurements, respectively.
• Figure 4: Further improving coupling efficiency $\eta$ by modifying beam and waveguide property. The grating (same as Fig. \ref{['fig-gaussian']}) is excited under $\theta = 37^{\circ}$ incidence light ($\lambda$ = 1550 nm) for both graph. (a) $\eta$-vs-$w_0$. The NA of fiber is fixed at 0.1084 with $w_1 = 5.055~\mu m$, while $NA_{beam}$ and half-width $w_0$ are tuned. (b) $\eta$-vs-$w_1$. The beam is arranged as $NA_{beam}$ = 0.1080 and $w_0=4.54 \mu m$. Six types of $NA_{fiber}$ along with increased radii $w_1$ are selected to examine their influence on $\eta$.