# Controlling branching angle of waveguide splitters based on GRIN lenses

## TL;DR

This paper explores the use of gradient index lenses like GMFE and Eaton lenses to control the branching angles of waveguide splitters, enabling wider angles than traditional Y-junctions through ray-tracing and finite element analysis.

## Contribution

It introduces a novel approach using GRIN lenses to achieve wide-angle waveguide splitters, including a 90° splitter with Eaton lenses, expanding design possibilities.

## Key findings

- GMFE lenses enable splitting angles of 25°, 45°, and 65°
- Eaton lens facilitates a 90° splitter design
- Performance verified by ray-tracing and finite element simulations

## Abstract

Designing beam splitting structures with wide branching angles is of great significance. The branching angle of conventional Y-junctions is limited. In this paper, we investigate the possibility of utilizing gradient index (GRIN) lenses with two focal points such as the generalized Maxwell's fisheye (GMFE) and Eaton lenses in controlling the branching angle of power splitters. The GMFE lens can provide a wide range of branching angles, however, we present only splitting angles of 25$^\circ$, 45$^\circ$, and 65$^\circ$. Furthermore, we propose a 90$^\circ$ splitter structure by employing the Eaton lens. We evaluate the performance of the proposed power splitters by ray-tracing and full-wave finite element method. While GRIN lenses provide a broad range of splitting angles, they require isotropic metamaterials to implement high refractive indices at the center of these lenses.