Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach

TL;DR

This paper introduces a 2.5D finite element method for accurately modeling light emission from dipolar emitters coupled to waveguides, significantly reducing computational costs while maintaining high accuracy, applicable to various waveguide geometries.

Contribution

The paper presents a novel 2.5D FEM approach that decomposes 3D waveguide-emitter systems into independent 2D problems, enabling efficient and precise emission rate calculations for complex waveguide structures.

Findings

High accuracy in emission rate predictions compared to 3D models

Effective modeling of multi-mode and multi-core waveguides

Capability to include dipole orientation effects, enabling unidirectional mode excitation

Abstract

We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be decomposed into a series of independent 2D problems (2.5D), which reduces the computational cost. Moreover, the reduced 2D problems can be extremely accurate, compared to its 3D counterpart. Our method can precisely quantify the total emission rates, as well as the fraction of emission rates into different modal channels for waveguides with arbitrary cross-sections. We compare our method with dyadic Green's function for the light emission in single mode metallic nanowire, which yields an excellent agreement. This method is applied in multi-mode waveguides, as well as multi-core waveguides. We further show that our method has the full capability of including dipole orientations, as illustrated via a rotating dipole, which leads to unidirectional excitation of guide modes. The 2.5D Finite Element Method (FEM) approach proposed here can be applied for various waveguides, thus it is useful to interface single-photon single-emitter in nano-structures, as well as for other scenarios involving coupled waveguide-emitters.