# Numerical and Experimental Study of Mode Coupling Due to Localised Few-Mode Fibre Bragg Gratings and a Spatial Mode Multiplexer

## TL;DR

This paper studies how adding a spatial mode multiplexer can simplify the use of few-mode fibre Bragg gratings in sensing applications.

## Contribution

The paper introduces a novel multiplexing technique based on transverse location and modal content in few-mode fibres.

## Key findings

- A spatial mode multiplexer slightly simplifies the transmission spectrum of few-mode FBGs.
- Modal filtering after reflection enables WDM monitoring of FM-FBGs.
- A new multiplexing approach based on transverse location and initial modal coupling is reported.

## Abstract

Mode conversion effects in Fibre Bragg Gratings (FBGs) are widely exploited in applications such as sensing and fibre lasers. However, when FBGs are inscribed into Few-mode optical Fibres (FMFs), the mode interactions become highly complex due to the increased number of guided modes, rendering their practical use difficult. In this study, we investigate whether the addition of a spatial mode multiplexer, used to selectively excite specific fibre modes, can simplify the interpretation and utility of few-mode FBGs (FM-FBGs). We focus on point-by-point (PbP)-inscribed FBGs, localised with respect to the transverse cross-section of the fibre core, and study their interaction with a range of Hermitian Gauss input modes. We present a comprehensive numerical study supported by experimental validation, examining the mechanisms of mode coupling induced by localised FBGs and its implications, with a focus on sensing applications. Our results show that the introduction of a spatial mode multiplexer leads to slight simplification of the FBG transmission spectrum. Nevertheless, significant simplification of the reflection spectrum is achievable after modal filtering occurs as the reflected light re-traverses the spatial mode multiplexer, potentially enabling WDM monitoring of FM-FBGs. Notably, we report a novel approach to multiplexing FBGs based on their transverse location within the fibre core and the modal content initially coupled into the fibre. To the best of our knowledge, this multiplexing technique is yet to be reported.