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17 pages, 1206 KiB

Open AccessArticle

Polar Decomposition of Jones Matrix and Mueller Matrix of Coherent Rayleigh Backscattering in Single-Mode Fibers

by Hui Dong, Hailiang Zhang and Dora Juan Juan Hu

Sensors 2024, 24(6), 1760; https://doi.org/10.3390/s24061760 - 8 Mar 2024

Viewed by 489

The Jones matrix and the Mueller matrix of the coherent Rayleigh backscattering (RB) in single-mode fibers (SMFs) have been derived recently. It has been shown that both matrices depict two polarization effects—birefringence and polarization-dependent loss (PDL)—although the SMF under investigation is purely birefringent, [...] Read more.

The Jones matrix and the Mueller matrix of the coherent Rayleigh backscattering (RB) in single-mode fibers (SMFs) have been derived recently. It has been shown that both matrices depict two polarization effects—birefringence and polarization-dependent loss (PDL)—although the SMF under investigation is purely birefringent, having no PDL. In this paper, we aim to perform a theoretical analysis of both matrices using polar decomposition. The derived sub-Jones/Mueller matrices, representing birefringence and PDL, respectively, can be used to investigate the polarization properties of the coherent RB. As an application of the theoretical results, we use the derived formulas to investigate the polarization properties of the optical signals in phase-sensitive optical time-domain reflectometry (φ-OTDR). For the first time, to our knowledge, by using the derived birefringence–Jones matrix, the common optical phase of the optical signal in φ-OTDR is obtained as the function of the forward phase and birefringence distributions. By using the derived PDL–Mueller matrix, the optical intensity of the optical signal in φ-OTDR is obtained as the function of the forward phase and birefringence distributions as well as the input state of polarization (SOP). Further theoretical predictions show that, in φ-OTDR, the common optical phase depends on only the local birefringence in the first half of the fiber section, which is occupied by the sensing pulse, irrelevant of the input SOP. However, the intensity of the φ-OTDR signal is not a local parameter, which depends on the input SOP and the birefringence distribution along the entire fiber section before the optical pulse. Moreover, the PDL measured in φ-OTDR is theoretically proven to be a local parameter, which is determined by the local birefringence and local optical phase distributions. Full article

(This article belongs to the Special Issue Distributed and Single-Point Fiber Optic Sensors: Applications and Technology)

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13 pages, 3265 KiB

Open AccessArticle

Fabry–Perot Cavity Optimization for Absolute Strain Sensing Using Finite Element Analysis

by João M. B. Pereira, Paula M. P. Gouvea, Arthur M. B. Braga, Isabel C. S. Carvalho and Antonio C. Bruno

Sensors 2023, 23(21), 8785; https://doi.org/10.3390/s23218785 - 28 Oct 2023

Viewed by 708

Abstract

The finite element method (FEM) was used to investigate the optical–mechanical behavior of a Fabry–Perot Interferometer (FPI) composed of a capillary segment spliced between two sections of standard optical fiber. The developed FEM model was validated by comparing it with theory and with [...] Read more.

The finite element method (FEM) was used to investigate the optical–mechanical behavior of a Fabry–Perot Interferometer (FPI) composed of a capillary segment spliced between two sections of standard optical fiber. The developed FEM model was validated by comparing it with theory and with previously published experimental data. The model was then used to show that the absolute strain on the host substrate is usually smaller than the strain measurement obtained with the sensor. Finally, the FEM model was used to propose a cavity geometry that can be produced with repeatability and that yields the correct absolute strain experienced by the host substrate, without requiring previous strain calibration. Full article

(This article belongs to the Special Issue Distributed and Single-Point Fiber Optic Sensors: Applications and Technology)

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13 pages, 2717 KiB

Open AccessArticle

Polarization Properties of Coherently Superposed Rayleigh Backscattered Light in Single-Mode Fibers

by Hui Dong, Hailiang Zhang and Dora Juan Juan Hu

Sensors 2023, 23(18), 7769; https://doi.org/10.3390/s23187769 - 8 Sep 2023

Cited by 1 | Viewed by 886

Abstract

The properties of the state of polarization (SOP) and the degree of polarization (DOP) of Rayleigh backscattered light (RBL) in single-mode fibers (SMF) are investigated theoretically and experimentally when the incident probe is a perfectly coherent continuous-wave (CW) light. It is concluded that [...] Read more.

The properties of the state of polarization (SOP) and the degree of polarization (DOP) of Rayleigh backscattered light (RBL) in single-mode fibers (SMF) are investigated theoretically and experimentally when the incident probe is a perfectly coherent continuous-wave (CW) light. It is concluded that the instantaneous DOP of the coherently superposed RBL is always 100%, and the instantaneous SOP is determined by the distributions of the birefringence and the optical phase along the SMF. Therefore, the instantaneous SOP of the coherently superposed RBL does not have a constant relationship with the SOP of the incident CW probe. Furthermore, the instantaneous SOP varies randomly with time because the optical phase is very sensitive to ambient temperature and vibration even in the lab environment. Further theoretical derivation and experimental verification demonstrate, for the first time, that the temporally averaged SOP of the coherently superposed RBL has a simple constant relationship with the SOP of the incident CW probe, and the temporally averaged DOP is 1/3 in an SMF with low and randomly distributed birefringence. The derived formulas and obtained findings can be used to enhance the modelling and improve the performances of phase-sensitive optical time-domain reflectometry and other Rayleigh backscattering based fiber-optic sensors. Full article

(This article belongs to the Special Issue Distributed and Single-Point Fiber Optic Sensors: Applications and Technology)

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7 pages, 1871 KiB

Open AccessCommunication

Fs-Laser Fabricated Miniature Fabry–Perot Interferometer in a No-Core Fiber for High-Temperature Applications

by Chen Zhu, Osamah Alsalman and Jie Huang

Sensors 2023, 23(18), 7754; https://doi.org/10.3390/s23187754 - 8 Sep 2023

Cited by 3 | Viewed by 1047

Abstract

This paper reports a fiber in-line Fabry–Perot interferometer (FPI) fabricated in a no-core fiber using the direct femtosecond laser writing technique for high-temperature sensing applications. Two in-line reflectors are directly inscribed in a no-core fiber to construct a low-finesse FPI. Fringe visibility greater [...] Read more.

This paper reports a fiber in-line Fabry–Perot interferometer (FPI) fabricated in a no-core fiber using the direct femtosecond laser writing technique for high-temperature sensing applications. Two in-line reflectors are directly inscribed in a no-core fiber to construct a low-finesse FPI. Fringe visibility greater than 10 dB is obtained from the reflection spectra of the fabricated no-core fiber FPIs. Temperature responses of a prototype no-core fiber FPI are characterized up to 1000 °C. The proposed configuration is compact and easy to fabricate, making it attractive for sensing applications in high-temperature harsh environments. Full article

(This article belongs to the Special Issue Distributed and Single-Point Fiber Optic Sensors: Applications and Technology)

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14 pages, 9457 KiB

Open AccessArticle

Measurement of the Acoustic Relaxation Absorption Spectrum of CO₂ Using a Distributed Bragg Reflector Fiber Laser

by Kun Shen, Jixian Yuan, Min Li, Xiaoyan Wen and Haifei Lu

Sensors 2023, 23(10), 4740; https://doi.org/10.3390/s23104740 - 14 May 2023

Cited by 1 | Viewed by 1048

Abstract

Reconstruction of the acoustic relaxation absorption curve is a powerful approach to ultrasonic gas sensing, but it requires knowledge of a series of ultrasonic absorptions at various frequencies around the effective relaxation frequency. An ultrasonic transducer is the most widely deployed sensor for [...] Read more.

Reconstruction of the acoustic relaxation absorption curve is a powerful approach to ultrasonic gas sensing, but it requires knowledge of a series of ultrasonic absorptions at various frequencies around the effective relaxation frequency. An ultrasonic transducer is the most widely deployed sensor for ultrasonic wave propagation measurement and works only at a fixed frequency or in a specific environment like water, so a large number of ultrasonic transducers operating at various frequencies are required to recover an acoustic absorption curve with a relative large bandwidth, which cannot suit large-scale practical applications. This paper proposes a wideband ultrasonic sensor using a distributed Bragg reflector (DBR) fiber laser for gas concentration detection through acoustic relaxation absorption curve reconstruction. With a relative wide and flat frequency response, the DBR fiber laser sensor measures and restores a full acoustic relaxation absorption spectrum of CO₂ using a decompression gas chamber between 0.1 and 1 atm to accommodate the main molecular relaxation processes, and interrogates with a non-equilibrium Mach-Zehnder interferometer (NE-MZI) to gain a sound pressure sensitivity of −45.4 dB. The measurement error of the acoustic relaxation absorption spectrum is less than 1.32%. Full article

(This article belongs to the Special Issue Distributed and Single-Point Fiber Optic Sensors: Applications and Technology)

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13 pages, 1407 KiB

Open AccessArticle

A Machine Learning Specklegram Wavemeter (MaSWave) Based on a Short Section of Multimode Fiber as the Dispersive Element

by Ogbole C. Inalegwu, Rex E. Gerald II and Jie Huang

Sensors 2023, 23(10), 4574; https://doi.org/10.3390/s23104574 - 9 May 2023

Cited by 2 | Viewed by 1443

Abstract

Wavemeters are very important for precise and accurate measurements of both pulses and continuous-wave optical sources. Conventional wavemeters employ gratings, prisms, and other wavelength-sensitive devices in their design. Here, we report a simple and low-cost wavemeter based on a section of multimode fiber [...] Read more.

Wavemeters are very important for precise and accurate measurements of both pulses and continuous-wave optical sources. Conventional wavemeters employ gratings, prisms, and other wavelength-sensitive devices in their design. Here, we report a simple and low-cost wavemeter based on a section of multimode fiber (MMF). The concept is to correlate the multimodal interference pattern (i.e., speckle patterns or specklegrams) at the end face of an MMF with the wavelength of the input light source. Through a series of experiments, specklegrams from the end face of an MMF as captured by a CCD camera (acting as a low-cost interrogation unit) were analyzed using a convolutional neural network (CNN) model. The developed machine learning specklegram wavemeter (MaSWave) can accurately map specklegrams of wavelengths up to 1 pm resolution when employing a 0.1 m long MMF. Moreover, the CNN was trained with several categories of image datasets (from 10 nm to 1 pm wavelength shifts). In addition, analysis for different step-index and graded-index MMF types was carried out. The work shows how further robustness to the effects of environmental changes (mainly vibrations and temperature changes) can be achieved at the expense of decreased wavelength shift resolution, by employing a shorter length MMF section (e.g., 0.02 m long MMF). In summary, this work demonstrates how a machine learning model can be used for the analysis of specklegrams in the design of a wavemeter. Full article

(This article belongs to the Special Issue Distributed and Single-Point Fiber Optic Sensors: Applications and Technology)

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12 pages, 3648 KiB

Open AccessCommunication

A Fabry–Perot Sensor with Cascaded Polymer Films Based on Vernier Effect for Simultaneous Measurement of Relative Humidity and Temperature

by Teng Zhang, Qun Han, Zhizhuang Liang, Junfeng Jiang and Zhenzhou Cheng

Sensors 2023, 23(5), 2800; https://doi.org/10.3390/s23052800 - 3 Mar 2023

Cited by 3 | Viewed by 1938

Abstract

In this paper, fiber sensor based on Vernier effect for simultaneous measurement of relative humidity (RH) and temperature is proposed. The sensor is fabricated by coating two kinds of ultraviolet (UV) glue with different refractive indexes (RI) and thicknesses on the end face [...] Read more.

In this paper, fiber sensor based on Vernier effect for simultaneous measurement of relative humidity (RH) and temperature is proposed. The sensor is fabricated by coating two kinds of ultraviolet (UV) glue with different refractive indexes (RI) and thicknesses on the end face of a fiber patch cord. The thicknesses of two films are controlled to generate the Vernier effect. The inner film is formed by a cured lower-RI UV glue. The exterior film is formed by a cured higher-RI UV glue, of which thickness is much thinner than the inner film. Through the analysis of the Fast Fourier Transform (FFT) of the reflective spectrum, the Vernier effect is formed by the inner lower-RI polymer cavity and the cavity composed of both polymer films. By calibrating the RH and temperature response of two peaks on the envelope of the reflection spectrum, simultaneous measurements of RH and temperature are realized by solving a set of quadratic equations. Experimental results show that the highest RH and temperature sensitivities of the sensor are 387.3 pm/%RH (in 20%RH to 90%RH) and −533.0 pm/°C (in 15 °C to 40 °C), respectively. The sensor has merits of low cost, simple fabrication, and high sensitivity, which makes it very attractive for applications that need to simultaneously monitor these two parameters. Full article

(This article belongs to the Special Issue Distributed and Single-Point Fiber Optic Sensors: Applications and Technology)

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17 pages, 6072 KiB

Open AccessArticle

Monitoring Epoxy Coated Steel under Combined Mechanical Loads and Corrosion Using Fiber Bragg Grating Sensors

by Luyang Xu, Dawei Zhang, Ying Huang, Shuomang Shi, Hong Pan and Yi Bao

Sensors 2022, 22(20), 8034; https://doi.org/10.3390/s22208034 - 21 Oct 2022

Cited by 10 | Viewed by 1592

Abstract

Fiber Bragg grating (FBG) sensors have been applied to assess strains, stresses, loads, corrosion, and temperature for structural health monitoring (SHM) of steel infrastructure, such as buildings, bridges, and pipelines. Since a single FBG sensor measures a particular parameter at a local spot, [...] Read more.

Fiber Bragg grating (FBG) sensors have been applied to assess strains, stresses, loads, corrosion, and temperature for structural health monitoring (SHM) of steel infrastructure, such as buildings, bridges, and pipelines. Since a single FBG sensor measures a particular parameter at a local spot, it is challenging to detect different types of anomalies and interactions of anomalies. This paper presents an approach to assess interactive anomalies caused by mechanical loading and corrosion on epoxy coated steel substrates using FBG sensors in real time. Experiments were performed by comparing the monitored center wavelength changes in the conditions with loading only, corrosion only, and simultaneous loading and corrosion. The theoretical and experimental results indicated that there were significant interactive influences between loading and corrosion for steel substrates. Loading accelerated the progress of corrosion for the epoxy coated steel substrate, especially when delamination in the epoxy coating was noticed. Through the real-time monitoring from the FBG sensors, the interactions between the anomalies induced by the loading and corrosion can be quantitatively evaluated through the corrosion depth and the loading contact length. These fundamental understandings of the interactions of different anomalies on steel structures can provide valuable information to engineers for better management of steel structures. Full article

(This article belongs to the Special Issue Distributed and Single-Point Fiber Optic Sensors: Applications and Technology)

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15 pages, 6548 KiB

Open AccessArticle

Highly Sensitive Strain Sensor by Utilizing a Tunable Air Reflector and the Vernier Effect

by Farhan Mumtaz, Muhammad Roman, Bohong Zhang, Lashari Ghulam Abbas, Muhammad Aqueel Ashraf, Yutang Dai and Jie Huang

Sensors 2022, 22(19), 7557; https://doi.org/10.3390/s22197557 - 6 Oct 2022

Cited by 10 | Viewed by 1578

Abstract

A highly sensitive strain sensor based on tunable cascaded Fabry–Perot interferometers (FPIs) is proposed and experimentally demonstrated. Cascaded FPIs consist of a sensing FPI and a reference FPI, which effectively generate the Vernier effect (VE). The sensing FPI comprises a hollow core fiber [...] Read more.

A highly sensitive strain sensor based on tunable cascaded Fabry–Perot interferometers (FPIs) is proposed and experimentally demonstrated. Cascaded FPIs consist of a sensing FPI and a reference FPI, which effectively generate the Vernier effect (VE). The sensing FPI comprises a hollow core fiber (HCF) segment sandwiched between single-mode fibers (SMFs), and the reference FPI consists of a tunable air reflector, which is constituted by a computer-programable fiber holding block to adjust the desired cavity length. The simulation results predict the dispersion characteristics of modes carried by HCF. The sensor’s parameters are designed to correspond to a narrow bandwidth range, i.e., 1530 nm to 1610 nm. The experimental results demonstrate that the proposed sensor exhibits optimum strain sensitivity of 23.9 pm/με, 17.54 pm/με, and 14.11 pm/με cascaded with the reference FPI of 375 μm, 365 μm, and 355 μm in cavity length, which is 13.73, 10.08, and 8.10 times higher than the single sensing FPI with a strain sensitivity of 1.74 pm/με, respectively. The strain sensitivity of the sensor can be further enhanced by extending the source bandwidth. The proposed sensor exhibits ultra-low temperature sensitivity of 0.49 pm/°C for a temperature range of 25 °C to 135 °C, providing good isolation for eliminating temperature–strain cross-talk. The sensor is robust, cost-effective, easy to manufacture, repeatable, and shows a highly linear and stable response for strain sensing. Based on the sensor’s performance, it may be a good candidate for high-resolution strain sensing. Full article

(This article belongs to the Special Issue Distributed and Single-Point Fiber Optic Sensors: Applications and Technology)

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