# An Axial Force Sensor Based on a Long-Period Fiber Grating with Dual-Peak Resonance

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## Abstract

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## 1. Introduction

_{2}laser. A maximum force sensitivity of 41.24 nm/N can be achieved at the bending radius of 1.14 mm. A similar structure was used in a phase-shifted LPFG for force sensing [15]. Gabriela S. B. et al. [16] presented an LPFG fabricated in a polymer microstructure fiber using transverse periodic loading combined with fiber heating for force sensing. The results showed that the sensor has a linear response to force with a sensitivity of −1.39 nm/N. It is obvious that the above technologies can improve force sensitivity by damaging the mechanical structure of the optical fiber, but inevitably they make the optical fiber sensing head very fragile.

## 2. Working Principle

_{11}is the self-coupling coefficient of the fiber core mode. σ

_{22}is the mutual coupling coefficient of the cladding mode. $\delta =\frac{1}{2}\left({\beta}_{co}-{\beta}_{cl}\right)-\frac{\pi}{\Lambda}=2\pi {n}_{eff}^{co}\left(\frac{1}{\lambda}-\frac{1}{{\lambda}_{B}}\right)$, where λ

_{B}is the central wavelength of the grating.

^{−4}, the grating period is 188.5 μm, and the grating length is 3 cm. The transmission spectrum (black line) and energy distribution map (spot map) of the 19th cladding mode are obtained by simulation, as shown in Figure 4. The position of the dual peaks and the losses correspond to the results in Figure 2 and Figure 3, indicating that the simulation results are correct. The above parameters will be used to analyze the LPFG axial force sensing.

_{2}= P (P = F/s, where s is the cross-sectional area of the fiber). According to Hooke’s law, the strain in each direction can be expressed as [23]

_{11}and p

_{12}are the elongation coefficients (Pockels coefficients) of the fiber core and cladding, respectively. For quartz fibers, p

_{11}= 0.113 and p

_{12}= 0.252. In single-mode fibers, the longitudinal electric field is much smaller than the transverse electric field. Therefore, it is mainly the transverse refractive index n

_{it}that plays a role in the fiber core mode. Figure 5a–c simulates the relationship between the transmission spectrum, as well as the position of the dual peaks and their losses for different sizes of axial forces. It can be seen that as the force increases, the resonant peak at the short wavelength is red-shifted, while the resonance peak at the long wavelength is blue-shifted, i.e., the two peaks move closer and closer to the central wavelength. Additionally, the dual-peak loss decreases as the axial force increases. Figure 5d shows the scatter plot and fitted curve of the wavelength difference between the two resonance peaks. The sensitivity of this LPFG axial force sensor is given as −14.95 nm/N and the linearity of the fitted curve is 0.997, showing a good linear relationship.

## 3. Experiments and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic diagram of (

**a**) fiber structure and (

**b**) the experiment setup for axial force measurement.

**Figure 5.**Simulation results; (

**a**) Transmission spectrum of LPFG for different sizes of axial force; (

**b**) the relationship between the variation in two resonant peak losses for different sizes of axial force; (

**c**) relationships between the wavelengths of the two resonant peaks for different sizes of axial force; (

**d**) scatter plot and fitted curve of the wavelength difference between the two resonant peaks for different sizes of axial force.

**Figure 7.**Experiment results; (

**a**) Transmission spectrum of LPFG for different sizes of axial force; (

**b**) the relationship between the variation in two resonant peak losses for different sizes of axial force; (

**c**) relationships between the wavelengths of the two resonant peaks for different sizes of axial force; (

**d**) scatter plot and fitted curve of the wavelength difference between the two resonant peaks for different sizes of axial force.

Structure | Axial Force Sensitivity | Range | Fabricated Method | Ref. |
---|---|---|---|---|

Half-etched FBG | 1.96 nm/N | 0.20–2.50 N | Chemical corrosion with hydrofluoric acid | [10] |

Microfiber-tapered FBG | 3146 nm/N | 0–0.0062 N | Focused ion beam machining | [11] |

Microbend LPFG | 41.24 nm/N | 0–1.90 N | Inserting a microbend at the edge | [14] |

LPFG fabricated in a polymer microstructure fiber | 1.39 nm/N | 0–16 N | Transverse periodic loading combined with fiber heating | [16] |

Dual-peak LPFG | 14.047 nm/N | 0.490–4.508 N | UV laser | Our work |

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**MDPI and ACS Style**

Luo, W.; Wang, Y.; Ling, Q.; Guan, Z.; Chen, D.; Wu, Q.
An Axial Force Sensor Based on a Long-Period Fiber Grating with Dual-Peak Resonance. *Photonics* **2023**, *10*, 591.
https://doi.org/10.3390/photonics10050591

**AMA Style**

Luo W, Wang Y, Ling Q, Guan Z, Chen D, Wu Q.
An Axial Force Sensor Based on a Long-Period Fiber Grating with Dual-Peak Resonance. *Photonics*. 2023; 10(5):591.
https://doi.org/10.3390/photonics10050591

**Chicago/Turabian Style**

Luo, Weixuan, Ying Wang, Qiang Ling, Zuguang Guan, Daru Chen, and Qiong Wu.
2023. "An Axial Force Sensor Based on a Long-Period Fiber Grating with Dual-Peak Resonance" *Photonics* 10, no. 5: 591.
https://doi.org/10.3390/photonics10050591