# Spectral Characteristics and Displacement Sensing of U-Shaped Single-Mode–Multimode–Single-Mode Fiber Structure

## TL;DR

This paper introduces a U-shaped fiber structure that improves micro-displacement sensing by combining interference effects for better sensitivity and linearity.

## Contribution

The novel U-shaped SMS fiber structure combines MMI and MZI effects to achieve high sensitivity and linearity in micro-displacement sensing.

## Key findings

- The U-shaped SMS fiber structure achieves an average sensitivity of 5.41 pm/μm with 99.62% linearity over a 5 mm range.
- The maximum sensitivity reaches 34.46 pm/μm with a minimum detectable displacement of ~5.804 nm.
- The structure shows a uniform spectral drift pattern across micro-displacement ranges of 50 μm, 500 μm, and 5 mm.

## Abstract

The U-shaped fiber configuration represents the elementary form of micro-displacement sensing, characterized by its exceptional freedom and flexibility. The study proposes the U-shaped bent single-mode–multimode–single-mode (SMS) fiber structure that integrates the multimode interference (MMI) effect for enhanced mode dispersion and the Mach–Zönder interference (MZI) effect for spectral sensitivity improvement. The transmission spectral properties of the U-shaped SMS fiber structure with a bent radius over 1 cm are experimentally measured as the change in displacement varied within the range of 5 mm in this work. As the radius decreases, the spectrum shows redshift, which is related to the central wavelength of the peak or dips—a smaller wavelength results in a stronger redshift for the same displacement change. The average sensitivity of micro-displacement measurement within a range of 5 mm is 5.41 pm/μm, and the linearity is 99.62%. The maximum sensitivity of U-shaped SMS fiber structure is 34.46 pm/μm, with the minimum displacement change of approximately 5.804 nm. The transmission spectral properties of the U-shaped SMS fiber structure within the ranges of 50 μm, 500 μm, and 5 mm are experimentally measured in this work. This experiment observed a relatively uniform spectral drift pattern in a large range of micro-displacement sensing. The measurement range is limited by the limited spectral range of the light source and the discontinuous variation in the effective refractive index. This provides an experimental reference for further understanding the characteristics of U-shaped fiber structures and applying its application in micro-displacement sensing.