OPTO-MECHANICAL FIBER OPTIC SENSORS

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2 OPTO-MECHANICAL FIBER OPTIC SENSORS

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4 OPTO-MECHANICAL FIBER OPTIC SENSORS Research, Technology, and Applications in Mechanical Sensing Edited by HAMID ALEMOHAMMAD

5 Butterworth-Heinemann is an imprint of Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright Ó 2018 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: For information on all Butterworth-Heinemann publications visit our website at Publisher: Mara E. Conner Acquisition Editor: Sonnini R. Yura Editorial Project Manager: Ana Claudia A. Garcia Production Project Manager: Mohanapriyan Rajendran Designer: Greg Harris Typeset by TNQ Books and Journals

6 CONTENTS List of Contributors xi Biography xiii Preface xv Chapter 1 Opto-Mechanical Modeling of Fiber Bragg Grating Sensors Hamid Alemohammad 1.1 Fiber Bragg Gratings Opto-Mechanical Properties of Optical Fibers Fiber Bragg Gratings With Structurally and Thermally Induced Index Changes Light Propagation in Optical Fibers With Induced Optical Anisotropy Coupled-Mode Theory Derivation of Coupled-Mode Theory for Fiber Bragg Gratings With Uniform Grating Coupled-Mode Theory for Superstructure Fiber Bragg Gratings Appendices References Chapter 2 Superstructure Fiber Bragg Grating Sensors for Multiparameter Sensing Hamid Alemohammad 2.1 Superstructure Fiber Bragg Gratings With Periodic On-Fiber Films Opto-Mechanical Modeling Simulation Results

7 vi CONTENTS 2.4 Geometrical Features of Fabricated Superstructure Fiber Bragg Gratings With On-Fiber Films Measurement Test Rig Optical Response Analysis References Chapter 3 Flat-Cladding Fiber Bragg Grating Sensors for Large Strain Amplitude Fatigue Tests Xija Gu 3.1 Introduction Experiments Sensor Validation Results Application in the Fatigue Test of a Friction StireWelded Aluminum Alloy Application in Asymmetric Fatigue Deformation of a Magnesium Alloy Conclusions References Chapter 4 Fiber Bragg Grating Strain Sensor for Microstructure in Situ Strain Measurement and Real-Time Failure Detection Hua Lu, Xija Gu 4.1 Introduction Fiber Bragg Grating Basics and Sensor Fabrication Comparison of Cantilever Strain Measured by a Fiber Bragg Grating Sensor and a Strain Gauge Printed Circuit Board Assembly Test Sample Preparation for Bend Testing Strain Gauge A and Fiber Bragg Grating Sensor Installation on Assembly Packages

8 CONTENTS vii 4.6 Comparison of Ball Grid Array Substrate Strain Results by Fiber Bragg Grating Sensor Array and Finite Element Analysis Modeling Four-Point Bending System and Test Setup Dye-and-Pry Failure Visual Inspection Test Results and Discussion Conclusions References Chapter 5 Distributed Brillouin Sensing Using Polymer Optical Fibers Yosuke Mizuno, Neisei Hayashi, Kentaro Nakamura 5.1 Introduction Characterization of Brillouin Scattering in Polymer Optical Fibers Distributed Measurement Polymer Optical Fiber Fuse Conclusion References Chapter 6 Femtosecond Laser-Inscribed Fiber Bragg Gratings for Sensing Applications Stephen J. Mihailov 6.1 Introduction The Fiber Bragg Grating The Fiber Bragg Grating Sensor Femtosecond Laser-Induced Bragg Gratings Applications of Femtosecond Laser-Induced Fiber Bragg Gratings for Sensing Conclusions References

9 viii CONTENTS Chapter 7 Innovative Fiber Bragg Grating Sensors for Highly Demanding Applications: Considerations, Concepts, and Designs Lun-Kai Cheng, Peter Martijn Toet 7.1 Introduction Fiber Bragg Grating Sensor System High-Demand Fiber Bragg Grating Sensor System Performance Fiber Bragg GratingeBased Sensors for Dedicated Operational Conditions Fiber Bragg GratingeBased Sensors for Special Physical Parameters Acknowledgments References Chapter 8 Fiber Optic Sensors in the Oil and Gas Industry: Current and Future Applications Christopher Baldwin 8.1 Introduction Breakdown of the Oil and Gas Industry Thermal Monitoring Pressure Monitoring in the Downhole Environment Flow Monitoring Seismic Monitoring Acoustic Monitoring Future Directions References Further Reading

10 CONTENTS ix Chapter 9 Aerospace Applications of Optical Fiber Mechanical Sensors Craig Lopatin 9.1 Introduction and Background Measurements for Flight Control Overview Concluding Remarks References Further Reading Chapter 10 Fiber Optical Sensors in Biomechanics Antonio B. Lobo Ribeiro, Paulo Roriz 10.1 Introduction Why Fiber Optical Sensors in Biomechanics? Applications in Biomechanics of Rigid Bodies Applications in Biomechanics of Deformable Bodies Applications in Biomechanics of Fluids Final Remarks References Chapter 11 Fiber Optic Sensors for Biomedical Applications Daniele Tosi, Sven Poeggel, Iulian Iordachita, Emiliano Schena 11.1 Introduction Biomedical Fiber Optic Sensor Systems Optical Fiber Sensors for Diagnostics Optical Fiber Sensors for Robotic Microsurgery Smart Textiles and Wearable Sensors References Index

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12 LIST OF CONTRIBUTORS Hamid Alemohammad AOMS Technologies Inc., Toronto, ON, Canada Christopher Baldwin Weatherford, Laurel, MD, United States Lun-Kai Cheng TNO, Delft, The Netherlands Xija Gu Ryerson University, Toronto, ON, Canada Neisei Hayashi Tokyo Institute of Technology, Yokohama, Japan Iulian Iordachita Johns Hopkins University, Baltimore, MD, United States Antonio B. Lobo Ribeiro University Fernando Pessoa, Porto, Portugal Craig Lopatin Technion-Israel Institute of Technology, Haifa, Israel Hua Lu Ryerson University, Toronto, ON, Canada Stephen J. Mihailov National Research Council of Canada, Ottawa, ON, Canada Yosuke Mizuno Tokyo Institute of Technology, Yokohama, Japan Kentaro Nakamura Tokyo Institute of Technology, Yokohama, Japan Sven Poeggel University of Limerick, Limerick, Ireland

13 xii LIST OF CONTRIBUTORS Paulo Roriz University Institute of Maia (ISMAI), Maia, Portugal; INESC TEC, Porto, Portugal; LABIOMEP, Porto Biomechanics Laboratory, Porto, Portugal; CIDESD-ISMAI, CIDESD, Maia, Portugal Emiliano Schena Università Campus Bio-Medico di Roma, Rome, Italy Peter Martijn Toet TNO, Delft, The Netherlands Daniele Tosi Nazarbayev University, Astana, Kazakhstan

14 BIOGRAPHY Hamid Alemohammad, PhD, PEng, is the cofounder and CEO of AOMS Technologies Inc. Dr. Alemohammad has PhD in Mechanical Engineering from the University of Waterloo in Ontario, Canada. He is specialized in industrial and academic research on fiber optic sensors along with the commercialization of fiber optic sensor technologies for harsh environment and industrial sensing applications.

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16 PREFACE The 1960s was a turning point for the fiber optic industry following the breakthrough discovery by Charles Kao (2009 Nobel Prize Laureate in Physics) and George Hockham from Standard Telecommunication Laboratories in England on reducing the loss in glass fibers by removing impurities. In the following decade, the work conducted by scientists at Corning and Bell Laboratories resulted in the development of a scalable mass production process for the manufacturing of low-loss optical fibers, which are now widely deployed to transmit voice and data over long distances. Optical fibers, which are a commodity for the telecommunications industry, have found their way into the sensing industry. In the early days, fiber optic sensor technology was adopted only by the oil and gas and defense sectors, because of the relatively high cost of the technology. However, thanks to new advancements in the development of low-cost optoelectronic systems, the technology is finding niche markets in other industry sectors including biomedical, environmental, transportation, structural health monitoring, and process industries. The industrial adoption of fiber optic sensors stems from unique features and technical capabilities unmatched by electronic sensors; these features include low-loss remote sensing, the ability to work in harsh environments, immunity to electromagnetic interference, small size, and capability of integrated and distributed sensing. The numbers of patents and scholarly articles published in the area of fiber optic sensing, new companies commercializing state-of-art fiber optic sensor technologies, and research and development (R&D) investments by renowned research centers indicate the global growth of this technology. According to the market research report Fiber Optic Sensors: Global Markets published by BCC Research in 2017, the global market size for fiber optic sensors is projected to reach $3.2 billion by 2021 from $2.0 billion in 2016 with a 5-year compound annual growth rate of around 10%. The world-class research on specialty optical fiber sensors (i.e., polymer fibers, photonic crystal fibers, femtosecond written fiber

17 xvi PREFACE Bragg gratings, etc.) and the development of low-cost and affordable optical fiber sensor interrogators are the primary drivers for the adoption of the technology and emergence of new use cases for fiber optic sensing. This book relays state-of-the-art research results and prospective advances in the field of fiber optic sensing with emphasis on opto-mechanical sensing applications. It is a consolidated collection of contributions by researchers in academia, research centers, and industrial R&D departments. The book aims at agglomerating recent research into one single source that is accessible to a wide range of audience. It provides a reference source for R&D engineers, scientists, application engineers, and technical managers in industries relevant to test and measurement and for university faculty members, postdoctoral fellows, and graduate students practicing research in various engineering and applied science disciplines. Hamid Alemohammad AOMS Technologies, Inc. Toronto, Canada

18 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS Yosuke Mizuno, Neisei Hayashi, Kentaro Nakamura Tokyo Institute of Technology, Yokohama, Japan 5.1 Introduction Polymer (or plastic) optical fibers (POFs) [1,2], which provide extremely easy and cost-effective connections compared to other standard glass fibers, are sufficiently flexible to withstand a large strain of several tens of percent [3,4]. Therefore, despite their higher loss compared to that of silica glass fibers, POFs have been utilized in medium-range communication applications such as home networks and automobiles [5] as well as in highstrain monitoring applications [3,6]. On the other hand, Brillouin scattering in optical fibers [7,8], which is one of the most significant nonlinear effects, has been extensively studied. Its applications include a variety of useful devices and systems, such as optical amplifiers [7], lasers [7,9], optical comb generators [9], microwave signal processors [10], slow light generators [11], phase conjugators [12], fiber-core aligners [13], tunable delay lines [14], optical memories [15], and distributed strain and temperature sensors [16e20]. As of this writing, Brillouin scattering has been studied not only for silica fibers but also for some specialty glass fibers including tellurite fibers [21,22], As 2 Se 3 chalcogenide fibers [23,24], bismuth oxide fibers [25,26], photonic crystal fibers [27,28], and multicore fibers [29]. However, until our first observation [30], no experimental reports had been provided on Brillouin scattering in POFs, which adds a variety of advantages of POFs over the conventional application field of Brillouin scattering. Here we focus on the sensing applications of Brillouin scattering. In addition to their high flexibility, one attractive feature of POF-based sensors is a unique function called a memory effect [31], with which the information on the applied large strain can be stored owing to their plastic deformation. Based on this Opto-Mechanical Fiber Optic Sensors. Copyright 2018 Elsevier Inc. All rights reserved. 97

19 98 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS effect, we have created a novel concept: we need not always put expensive analyzers at the ends of the sensing fibers; after earthquakes, an officer has only to go round with a single analyzer. With this concept, the application range of fiber optic sensing technology, which has been limited to only large-scale civil structures owing to its high cost, can be extended to smaller-scale multifamily residences and individual houses. A memory effect regarding temperature has also been reported [32,33]. This chapter reviews current knowledge of Brillouin scattering in POFs and its application to distributed measurement. In Section 5.2, we first present the fundamental properties of Brillouin scattering in POFs at 1.55 mm, such as the Brillouin frequency shift (BFS), Brillouin linewidth, Brillouin gain coefficient, and Brillouin threshold power [30]. For sensing applications, we also describe the BFS dependence on strain and temperature in POFs, including a BFS hopping phenomenon [34e36]. Furthermore, some methods for enhancing the Brillouin signal are detailed [37,38]. Then in Section 5.3, we present the first demonstration of truly distributed strain and temperature sensing with a high spatial resolution in POFs using a correlation-domain technique. The performance limitation of POF-based sensing systems is fully discussed [39]. Section 5.4 deals with a so-called POF fuse phenomenon, the fundamental properties of which need to be well investigated to perform distributed Brillouin measurement with a signal-to-noise ratio (SNR) that is as high as possible [40e42]. Finally, Section 5.5 summarizes this chapter, and an outlook on future work is given. 5.2 Characterization of Brillouin Scattering in Polymer Optical Fibers Here we present the unique characteristics of Brillouin scattering in POFs. In addition to the fundamental properties, the BFS dependence on strain (from small strain of <1.0% to large strain of 60%) and temperature is clarified. Induction of stimulated scattering and employment of POFs with smaller cores are also described as promising methods for enhancing the Brillouin signal in POFs Fundamental Properties In this section, we describe the first observation of Brillouin scattering in POFs and present its fundamental properties, such as BFS, Brillouin linewidth, Brillouin gain coefficient, and Brillouin threshold power [30].

20 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS Brillouin Scattering in Optical Fibers When a light beam is injected into an optical fiber, it interacts with acoustic phonons and generates backscattered light called Stokes light. This phenomenon is called spontaneous Brillouin scattering. Because the phonons decay exponentially, the backscattered Brillouin light spectrum, also known as the Brillouin gain spectrum (BGS), takes the shape of a Lorentzian function with a bandwidth of several tens of megahertz. The frequency at which the peak power is obtained in the BGS is downshifted by several gigahertz from the incident light frequency, and the amount of this frequency shift is known as the BFS. In optical fibers, the BFS n B is given as [7] n B ¼ 2nv A l p ¼ 2n l p sffiffiffi E ; (5.1) r where n is the refractive index, v A the acoustic velocity in the fiber, l p the wavelength of the incident pump light, E Young s modulus, and r the density. If tensile strain is applied or the temperature is changed in a standard silica single-mode optical fiber (SMF), the BFS moves to a higher frequency in proportion to the applied strain (þ580 MHz/%) [43] and the temperature change (þ1.18 MHz/K) [44]. In some specialty fibers, such as tellurite glass fibers, it is known that the BFS moves to a lower frequency with increasing applied strain ( 230 MHz/%) [22] and temperature ( 1.14 MHz/K) [26]. In both cases, we can derive the strain amplitude and temperature change by measuring the BFS in the fiber Experimental Setup A standard POF composed of polymethyl methacrylate (PMMA) [2] is optimally designed for visible light transmission at 650 nm, with a propagation loss of w150 db/km. However, its loss at telecommunication wavelength is so high (>> db/km) that the Brillouin signal cannot be detected. In the meantime, to observe Brillouin scattering in a PMMA-based POF at 650 nm, we need to prepare all the necessary optical devices at this wavelength, which is not easy. Therefore, we use a perfluorinated graded-index (PFGI) POF [1,45] instead of a PMMA-based POF. It consists of a core (120 mm diameter), cladding, and overcladding (750 mm diameter) encased in polyvinyl chloride. The core and cladding layers are composed of doped and undoped poly(perfluoro-butenylvinyl ether), respectively. The refractive index at the center of the core is 1.356, whereas that of the cladding layer is 1.342; these values do not depend strongly on

21 100 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS the optical wavelength [45]. The numerical aperture (NA) is The polycarbonate reinforcement overcladding reduces microbending losses and increases the load-bearing capability. The propagation loss is relatively low (w250 db/km; comparable to that of a PMMA POF at 650 nm) even at 1.55 mm, and inexpensive optical amplifiers can be used to boost the optical power. Fig. 5.1A depicts the experimental setup for investigating the Brillouin scattering properties in the POF. For BGS measurement with a high resolution, we employed so-called self-heterodyne detection [20]. All the optical paths except the POF itself were composed of silica SMFs. A distributed-feedback laser diode (DFB-LD) at mm was employed as a light source, and its output was divided into two light beams with an optical coupler. Figure 5.1 (A) Experimental setup for investigating the Brillouin scattering properties in perfluorinated graded-index (PFGI) polymer optical fibers (POFs). BFS, Brillouin frequency shift; DAQ, data acquisition; DC, direct current; DFB-LD, distributed feedback laser diode; EDFA, erbium-doped fiber amplifier; ESA, electrical spectrum analyzer; PC, polarization controller; PD, photodiode. (B) Brillouin gain spectrum in the 100-m-long POF at 20-dBm pump power. The inset shows its magnified view around the peak. BGS, Brillouin gain spectrum. (C) Relative power of the Stokes light backscattered from the 100-m-long POF plotted as a function of pump power.

22 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 101 One of the beams was, after passing a polarization controller (PC), directly used as the reference light of the heterodyne detection. The other beam was amplified with an erbium-doped fiber amplifier (EDFA) and injected into the POF as the pump light. Then, the optical beat signal between the backscattered Stokes light and the reference light was converted to an electrical signal with a photodiode (PD). Finally, the signal was amplified by 23 db with an electrical preamplifier and monitored with an electrical spectrum analyzer (ESA). We optically coupled the silica SMF and the POF using a butt coupling technique [46]. Because the core diameters are largely different (8 mm for SMF versus 120 mm for POF), a large optical loss is expected when light travels from the POF into the SMF. However, this loss contributes only to the attenuation of the Stokes light once generated in the POF, and it was measured to be approximately 12 db. On the other hand, when light travels from the SMF into the POF, the loss was less than 0.2 db, which is sufficiently low to investigate the Brillouin scattering properties in the POF Brillouin Gain Spectrum The BGS was observed when the 100-m-long PFGI POF was pumped at 20 dbm (Fig. 5.1B). The peak corresponding to the BFS was observed at 2.83 GHz, which is about four times lower than that of standard silica fibers. This allows the use of a PD and an ESA that are less expensive with a lower bandwidth. The acoustic velocity v A can be calculated using the BFS n B as in Eq. (5.1). With n of 1.35 and l p of mm, v A in this POF was calculated to be 1627 m/s, which is much lower than that of standard bulk PMMA, w2700 m/s [47]. By Lorentzian fitting, the 3-dB Brillouin linewidth Dn B was measured to be 105 MHz, which is three to five times broader than that of silica fibers [48], resulting in deterioration of the sensitivity of time-domain sensors [17]. Fig. 5.1C shows the dependence of the relative Stokes power on pump power. The Stokes power is generally known to grow exponentially at the Brillouin threshold power P th and then reaches saturation, which indicates the transition from spontaneous to stimulated Brillouin scattering (SBS). Although a rough estimation of P th is often performed using this kind of figure [7,21,23,48,49], saturation of the Stokes power is not observed in Fig. 5.1C. Therefore, P th of this POF appears to be much higher than 30 dbm (¼1 W). The detailed estimation of P th is provided later in this section.

23 102 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS We subsequently evaluated the Brillouin gain coefficient g B. Using the acoustic velocity v A and the Brillouin linewidth Dn B, g B is given by [49] g B ¼ 2pn7 p 2 12 cl 2 p rv ADn B ; (5.2) where p 12 is the longitudinal elastooptic coefficient and c the light velocity. Because the accurate values of p 12 and r are not known for perfluorinated PMMA, we used the values of standard PMMA [50] in this calculation. Using the measured values of v A ¼ 1627 m/s and Dn B ¼ 105 MHz, along with n ¼ 1.35, p 12 ¼ 0.297, l p ¼ mm, and r ¼ kg/m 3, g B was calculated to be m/w, which is close to that of silica fibers (3e m/w) [7]. Owing to the multimode nature of the POF, the actual g B value may be larger than this value. Finally, we estimated the Brillouin threshold power P th.an alternative way to calculate g B is to use the following equation [51]: g B ¼ 21bA eff KP th L eff ; (5.3) where A eff is the effective cross-sectional area, and L eff is the effective length defined as L eff ¼½1 expð alþš=a. (5.4) Here, a is the propagation loss and L is the fiber length. For multimode fibers, a correction factor b is needed [52], which can be treated as 2 when the NA is approximately 0.2. K is a constant that depends on the polarization properties of the fiber [49,53] and is 1 if the polarization is maintained and otherwise. Then, using the values of g B ¼ m/w, b ¼ 2 [52], A eff ¼ 209 mm 2 [54], K ¼ 0.667, a ¼ 0.056/m, and L ¼ 100 m, P th can be calculated to be 24 W. This value is valid compared to the theoretical values of w10 W (L ¼ 300 m) [54] or w100 W (L ¼ 100 m) [55]. Because P th is in proportion to b A eff in Eq. (5.3), P th can be reduced to a moderate power level by using POFs with smaller core diameters (refer to Section 5.2.4) Strain and Temperature Dependence In this section, we present the BFS dependence on relatively small strain (<1.0%) and low temperature (<80 C) in the POF, and clarify that Brillouin scattering in POFs can be utilized to

24 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 103 develop highly sensitive temperature sensors with reduced strain sensitivity [36]. We also show that this BFS dependence is probably caused by the dependence of Young s modulus on strain and temperature in the POF Experiments We used a 5-m-long PFGI POF with the same physical properties as those used in the previous experiments. The experimental setup for investigating the BFS dependence on strain and temperature in the POF is basically the same as that described in Section The Brillouin signal generated in the 1-m-long SMF between the circulator and the POF is included in the Stokes light, but it has no influence on the BGS measurement, because the BFS in the SMF is typically 11 GHz, about four times higher than that in the POF. The whole length of the POF was fixed using epoxy glue onto a translation stage, to which different strains were applied. Temperature was adjusted with a heater along the whole length of the POF. Fig. 5.2A shows the strain dependence of the BGS in the POF. The pump power was 19 dbm, and strains of 0.2%, 0.4%, 0.6%, 0.8%, and 1.0% were applied. As the applied strain increased, the BGS shifted toward lower frequency. Fig. 5.2B shows the strain dependence of the BFS. The slope was almost linear, and its coefficient was MHz/%. While the negative sign is the same as for tellurite glass fibers [22], the absolute value was approximately one-fifthofthatofastandardsilicasmf(þ580 MHz/%) [43].Next, Fig. 5.2C shows the temperature dependence of the BGS in the POF. The pump power was 23 dbm, and the temperature was controlled from 30 Cupto80 C with a step of 10 C. As temperature increased, the BGS also shifted toward lower frequency. The Stokes power at high temperature over 40 C was lower than that at 30 C by about 0.7 db, probably because of the nonuniform temperature distribution of the heater. Fig. 5.2D shows the temperature dependence of the BFS, and its coefficient was 4.09 MHz/K. Although the negative sign is also the same as for tellurite glass fibers [26], the absolute value was about 3.5 times as large as that of an SMF (þ1.18 MHz/K) [44]. The larger temperature coefficient leads to sensitivity enhancement of the temperature measurement, whereas the smaller strain coefficient means that PFGI POF-based Brillouin sensors are less susceptible to the applied strain. Therefore, the Brillouin scattering in the PFGI POF can be potentially utilized to implement highly sensitive temperature sensors with low strain sensitivity.

25 104 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS Figure 5.2 (A) Brillouin gain spectrum (BGS) dependence on strain in the polymer optical fiber (POF). (B) Brillouin frequency shift (BFS) plotted as a function of strain. (C) BGS dependence on temperature in the POF. (D) BFS versus temperature. (E) Youngs modulus of polymethyl methacrylate (PMMA) bulk versus temperature. (F) Density of PMMA bulk versus temperature. Plotted using the data reported in the literature: Saneyoshi J, Kikuchi Y, Nomoto O. Handbook of ultrasonic technology. Nikkan Kogyo; 1978 [chapter 5].

26 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS Discussion The origins of the BFS dependence on strain and temperature in the PFGI POF are discussed. The strain coefficient of the normalized BFS is given, by differentiating Eq. (5.1) with respect to strain, as 1 vn B n B vε ¼ 1 vn n vε þ 1 ve 2E vε þ 1 2r Here the following two equations hold true [43]: vr : (5.5) vε 1 vn n vε ¼ n2p 12 kðp 11 þ p 12 Þ ; (5.6) 2 1 r vr vε 1 2k ¼ ; (5.7) 2 where p 11 and p 12 are the elastooptic coefficients, and k is the Poisson ratio. As their values in PFGI POFs are unknown, we used the values for bulk PMMA: p 11 ¼ 0.3 [56], p 12 ¼ [56], and k ¼ 0.34 [57]. Then the first and the third terms in Eq. (5.5) were calculated to be and þ0.16, respectively. Although the second term is reported to drastically vary depending both on the method for applying strain and on the fabrication quality of the fiber, we used 5.75 as the second term, which is the value reported for a standard PMMA-based POF [58]. Compared to its absolute value, the first and the third terms are negligibly small. Then the theoretical strain coefficient was calculated to be MHz/%. Considering that each term in Eq. (5.5) was estimated using the values of PMMA, this value is in moderate agreement with the experimental value of MHz/%. Thus, the strain dependence of the BFS appears to originate from the dependence of Young s modulus on strain in the PFGI POF. Next, we discuss the BFS dependence on temperature in the same manner. The temperature coefficient of the normalized BFS is expressed as 1 vn B n B vt ¼ 1 vn n vt þ 1 ve 2E vt þ 1 2r vr. (5.8) vt The first term can be assumed to be , which is the value reported for a standard PMMA-based POF [50]. To estimate the second and the third terms, we plotted Young s modulus and the density of bulk PMMA at various temperatures using the data in the literature [59] (Fig. 5.2E and F). Using their slopes ( GPa/K and kg/m 3 /K), along with E w 6GPaandr ¼ kg/m 3,

27 106 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS the second and the third terms were calculated to be and þ , respectively. Then the theoretical temperature coefficient was calculated to be 6.72 MHz/K, which is in rough agreement with the experimental value of 4.09 MHz/K. Thus, the temperature dependence of the BFS also seems to originate from the large negative dependence of Young s modulus on temperature inthepfgipof.notethatthebfsdependenceontemperatureina POF with a 50-mm core diameter has also been investigated in a wider temperature range [60] Induction of Stimulated Brillouin Scattering In this section, we describe the observation of SBS in a POF with pumpeprobe technique [38]. The BGS is detected with an extremely high SNR, even with a 1-m-long POF, scrambled polarization state, and no averaging. We also investigate the BGS dependence on probe power and temperature, and confirm that SBS in a POF measured with this technique can be utilized to develop high-accuracy temperature sensors as well Motivation and Principle The Brillouin scattering in POFs observed in the previous experimental setup (Fig. 5.1A) was not stimulated but spontaneous, because the Brillouin threshold of POFs was estimated to be as high as tens of watts (refer to Section ). Consequently, the power of the reflected Stokes light was so low that we had to face the following four problems: (1) a POF longer than several meters was required, (2) the polarization state had to be optimized, (3) averaging of the spectral data had to be conducted several tens of times, and (4) the SNR of the BGS was extremely low, even when (1), (2), and (3) were cleared. To implement practical Brillouin sensors and other systems using POFs, these problems need to be resolved. One solution is to employ the so-called pumpeprobe technique. As described in Section , when the pump power is higher than the Brillouin threshold, a transition to SBS occurs, leading to drastic enhancement of the Stokes light. On the other hand, when probe light at the same frequency as the Stokes light is also injected into the other end of the fiber, SBS is induced even when the power of the pump light is much lower than the Brillouin threshold, because the probe light itself acts as a seed of stimulated scattering [61]. This technique, called the pumpe probe technique, has been used to develop Brillouin systems with a high SNR [62].

28 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS Experimental Setup The fiber under test was a 1-m-long PFGI POF with a core diameter of 120 mm (see Section for details). The experimental setup is schematically shown in Fig. 5.3A, and it is similar to that of Brillouin optical correlation-domain analysis (BOCDA) [18,62e64]. The light beam from a 1.55-mm three-electrode LD was divided into two. One was used as the pump light, after being chopped with an intensity modulator for lock-in detection and being amplified with an EDFA. The other was used as the probe light, after passing two EDFAs, a single-sideband modulator (SSBM), and a polarization scrambler (PSCR). The SSBM was employed with a microwave generator and a proper DC bias control to suppress the carrier (pump) and the anti-stokes component of the two first-order sidebands and to maintain a stable frequency downshift from the pump light. This frequency downshift was swept from 2.5 to 3.5 GHz with a period of 300 ms to obtain the BGS of the POF, which is observed approximately at 2.8 GHz. The suppression ratio of the other frequency components was kepthigherthan25 db(fig. 5.3B). The PSCR, which can modulate the polarization state at 1 MHz, was inserted to suppress the polarization-dependent fluctuations of the signal. The POF and the silica SMFs were butt-coupled with the gaps filled with index Figure 5.3 (A) Experimental setup for observing stimulated Brillouin scattering in the polymer optical fiber (POF) with a pumpeprobe technique. BFS, Brillouin frequency shift; DAQ, data acquisition; DC, direct current; EDFA, erbium-doped fiber amplifier; FG, function generator; FUT, fiber under test; IM, intensity modulator; LD, laser diode; LI-A, lock-in amplifier; MG, microwave generator; OSC, oscilloscope; PD, photodiode; PSCR, polarization scrambler; SSBM, single-sideband modulator; VOA, variable optical attenuator. (B) Optical spectrum of the SSBM output measured when the frequency of the MG was set to 2.83 GHz.

29 108 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS matching oil (n ¼ 1.46) to minimize the Fresnel reflection. The Stokes light was adjusted in power with a variable optical attenuator, and converted to an electrical signal with a 125-MHz PD. After passing a lock-in amplifier (LI-A) with a chopping frequency of MHz and a time constant of 10 ms, the electrical signal was observed as a BGS with an oscilloscope synchronized with the frequency sweep of the SSBM Experimental Results Fig. 5.4A shows the BGS measured without averaging when the pump power and the probe power were 23 and 22 dbm, respectively. The power was normalized so that the peak power was 1.0. Although the POF length was only 1 m and the polarization state was scrambled, the BGS was observed with a much higher SNR than that in Section The BFS was 2.86 GHz, which is slightly higher than the value of 2.83 GHz obtained in Section This discrepancy seems to originate from the difference Figure 5.4 (A) Brillouin gain spectrum (BGS) in the polymer optical fiber observed without averaging. (B) BGS dependence on probe power. (C) BGS dependence on temperature. (D) Brillouin frequency shift dependence on temperature.

30 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 109 in temperature and the time constant of the LI-A, which is not sufficiently short. The 3-dB bandwidth of the BGS measured in this experiment was about 160 MHz, but further research is needed on the bandwidth because it is also dependent on the time constant of the LI-A (when the time constant was shorter than 10 ms, the BGS was distorted). Fig. 5.4B shows the dependence of the BGS on probe power when the pump power was fixed at 23 dbm. The probe power was reduced from 22 down to 6 dbm, and averaging was conducted 30 times for the observable readout when the Stokes power was very low. As the probe power decreased, the Stokes power also decreased, which proves that this BGS is caused by the interaction between the pump light and the probe light, i.e., SBS. The dependence of the BGS on temperature was also measured (Fig. 5.4C). The pump power and the probe power were 23 and 22 dbm, respectively, and averaging was conducted 30 times. The temperature was set to 20 C, 40 C, and 60 C. With increasing temperature, the BGS shifted toward lower frequency. Fig. 5.4D shows the temperature dependence of the BFS. The slope of 4.05 MHz/K is in good agreement with the value obtained in Section , which confirms that the BGS in a POF observed with the pumpeprobe technique can be applied to high-sensitivity temperature sensing. Note that the SBS in a POF has also been detected with a lock-in-free pumpeprobe technique [65] Influence of Core Diameter and Fiber Length As described in Section , the power of the spontaneous Brillouin Stokes light generated in the PFGI POFs with a 120-mm core diameter was low, and it needs to be enhanced for detailed investigations of the BGS including the linewidth narrowing effect. Because the BGS observed with the pumpeprobe technique described in Section is easily influenced by the time constant of lock-in detection, detailed evaluation of its linewidth was not feasible. Another approach to enhance the Stokes signal is to make use of POFs with core diameters smaller than 120 mm. In this section, by characterizing the BGS in POFs with a 62.5-mm core diameter, we investigate the influence of the core diameter and the fiber length on the Brillouin properties, and observe the Brillouin linewidth narrowing effect [37].

31 110 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS Figure 5.5 (A) Brillouin gain spectrum dependence on pump power P in. PFGI-POF, perfluorinated graded-index polymer optical fiber. (B) Relative Stokes power plotted as a function of pump power; comparison between POFs with and 120-mm core diameters Effects of Small Core Diameters Fig. 5.5A shows the measured BGS of a 5-m-long PFGI POF with 62.5-mm core at pump power P in of 5, 10, 15, and 20 dbm. The polarization state optimized for P in of 20 dbm was employed for all the measurements. The center frequency of the BGS, i.e., BFS, was approximately 2.81 GHz, which is slightly lower than the value of 2.83 GHz obtained in Section because of the difference in room temperature. Even when P in was as low as 5 dbm, small but clear BGS was observed. Fig. 5.5B shows the P in dependence of the relative Stokes power, when 5-m-long POFs with core diameters of 62.5 and 120 mm were employed. The reference power was set to about 63 dbm, which is the Stokes power when P in is sufficiently low. The dependence curve of the POF with the 62.5-mm core was about 10 db lower in pump power than that with the 120-mm core, which indicates that, even at the same pump power, we can largely enhance the Stokes signal by using a POF with a smaller core diameter. One of the reasons for the 10-dB curve shift is the difference in Brillouin threshold power P th. By substituting into Eqs. (5.3) and (5.4) the values of b ¼ 2 [52], K ¼ [7], g B ¼ m/ W [30], a ¼ 0.056/m (¼250 db/km), and L ¼ 5m, P th of the POF with the 120-mm core (A eff ¼ 209 mm 2 [54]) was calculated to be 97.7 W. On the other hand, P th of the PFGI POF with the 62.5-mm core (A eff ¼ mm 2 ) was calculated to be 53.3 W, which is lower than 97.7 W by 2.6 db. Thus, the curve shift observed in Fig. 5.5B can be partially explained by the difference in P th, but its amount of 10 db is much larger than the calculated value.

32 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 111 Another reason for the curve shift is the improvement of optical coupling efficiency at the butt coupling when the Stokes light generated in the POF propagates back and is injected into the SMF. Although, owing to the unstable core alignment and the rough surface of the POF, it is difficult to measure the coupling loss accurately, we confirmed that the loss with the POF with the 62.5-mm core was several decibels lower than that with the 120-mm core. This fact, along with the difference in internal structure designed by different manufacturers, moderately explains the 10-dB curve shift Effects of Long Fiber Length According to Eqs. (5.3) and (5.4), to employ long POFs is another way to reduce P th and to enhance the Stokes signal. Fig. 5.6A shows the measured BGS of 80- and 200-m-long POFs with a 62.5-mm core at P in of 5, 10, 15, and 20 dbm. Much larger Stokes signals (w7 db higher at P in of 20 dbm) compared to those of the 5-m-long POF (Fig. 5.5A) were observed. There was, however, almost no difference between the BGS of the 80-m-long POF and that of the 200-m-long POF, only a slight discrepancy of the BFS caused by the room-temperature difference. This means that the incident light is considerably attenuated after propagation for 80 m in the POF. To estimate this effect quantitatively, the effective POF length L eff was plotted as a function of actual length L (Fig. 5.6B), where L eff gradually approaches 18 m (P th w 13 W) with increasing L. Thus, we proved that employing a POF longer than w50 m is not an effective way to enhance the Stokes signal at 1.55 mm. According to Eqs. (5.3) and (5.4), as the core diameter decreases, the Brillouin threshold P th also becomes lower. When P in is higher than P th, SBS is induced and consequently the Stokes signal is exponentially enhanced [7]. Here, under the rough assumption that the multimode nature, NA, refractive index, and loss do not change with core diameters, we calculated P th of a 50-m-long POF with a 10-mm core diameter (hypothetical; A eff ¼ 17.4 mm 2 ) to be 2.22 W (¼33.5 dbm). This value is more than 1 order of magnitude higher than the pump power of several tens to hundreds of milliwatts commonly used in BGS characterization in silica SMFs [48]. Even when the POF is treated as an SMF [i.e., b ¼ 1 [7] but A eff becomes larger [66] in Eq. (5.3)], this difference cannot be compensated for. Thus, it seems to be difficult to reduce P th of POFs down to the same level as that of long silica SMFs by decreasing the core diameter, which is due to the limited effective length of 18 m associated with the high propagation loss at 1.55 mm.

33 112 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS Brillouin Linewidth Narrowing Effect Although the Brillouin linewidth of a POF is reported to be 105 MHz at P in of 20 dbm (refer to Section ), detailed investigations were difficult because the Stokes power was extremely low. Here, by making use of the enhanced Stokes power, we investigated the Brillouin linewidth dependence on P in. Fig. 5.6C shows the measured BGS of the 200-m-long PFGI POF with a 62.5-mm core at P in of 14.5, 17.5, and 23.5 dbm, where the Stokes power is normalized so that the maximum power is 0 db. Fig. 5.6D shows the Brillouin linewidth dependence on P in. From these figures, we can see that, with the increasing P in, the 3-dB linewidth of the BGS decreases, but that its slope gradually Figure 5.6 (A) Brillouin gain spectrum (BGS) dependence on pump power P in ; comparison between the 80-m-long perfluorinated graded-index polymer optical fiber (PFGI-POF) (solid line) and the 200-m-long POF (dotted line). (B) Calculated effective fiber length versus fiber length. (C) Normalized BGS at pump powers of 14.5, 17.5, and 23.5 dbm. (D) Brillouin linewidth versus pump power.

34 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 113 becomes small. This behavior agrees well with the experiment and theory of the linewidth narrowing effect in silica-based SMFs [48] Brillouin Frequency Shift Dependence on Large Strain In Section 5.2.2, the BGS (and BFS) dependence on relatively small strain (<1.0%) in a POF was presented. In this section, we investigate the BGS dependence on larger strain of up to 60% in a POF, and observe a nonmonotonic behavior [35] caused by a BFS hopping phenomenon [34] Experimental Setup We employed a 0.6-m-long PFGI POF with a 50-mm core diameter. Instead of the standard experimental setup based on selfheterodyne detection described in Section , we used a newly developed Fresnel-assisted setup [67], which can detect the BGS in POFs with a higher SNR. Large strain was applied to the POF with two computer-controlled motorized stages at room temperature of 20 C Experimental Results First, we measured the BGS dependence on large strain of up to 60% in the POF (Fig. 5.7A). The pump power was 26 dbm, and the strain rate was 200 mm/s. The Brillouin peak observed at w2.8 GHz in the absence of strain shifted to lower frequency at <2.3% strain, and then shifted to a higher frequency; its peak power gradually reduced with increasing strain (>10%), whereas an additional peak appeared at w3.2 GHz when the strain was >7.3%. At 31% strain, the power of the two peaks was almost the same, and at 60% strain, the initial peak almost disappeared (note that the peak at w2.85 GHz originated from the w3-cmlong unstrained POF section near the connector). The BFS of the two peaks were then plotted as a function of strain (Fig. 5.7B). The dependence of the initial peak showed a nonmonotonic behavior (>20%, the BFS cannot be accurately measured). The BFS of the newly appeared peak was almost constant, independent of the applied strain, in this range. Next, Fig. 5.7C shows side views of the POF in the presence of w7.3% strain. Several sections were slimmed down in a stepwise manner, and with increasing strain, the slimmed sections grew longer (i.e., spread along the POF), while their outer diameter was maintained. This explains the independence of the BFS from

35 114 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS Figure 5.7 (A) Brillouin gain spectrum dependence on large strain. (B) Brillouin frequency shift (BFS) dependence on large strain. The BFS of the initial peak was not accurately measured at strains of >20% (gray). (C) Side views of the slim-down process of the polymer optical fiber (POF); taken every 4 s. (D) Cross-sectional view of the slimmed-down POF. (E) Measured stressestrain curve of the POF. large strain (>7.3%). The core diameter of the slimmed-down POF was estimated to be 0.84 times that of the unstrained POF from a cross-sectional view (Fig. 5.7D). This phenomenon is probably caused by the yielding of the overcladding layer made up of polycarbonate, and not by the core or cladding layers. The upper yield point of w8.0% [68] agrees with the strain at which the POF was slimmed down (according to the specification sheet, the upper yield point of the core and cladding materials is approximately 20%). This abrupt change in the core diameter seems to have induced the change in the acoustic velocity, therefore resulting in the BFS hopping. Further, the unstable stressestrain curve of the POF in the range from w10% to 60% (see Fig. 5.7E) can also be explained by this phenomenon. Finally, after the whole length of the POF was slimmed down at 60% strain, its BGS and BFS dependence on strain and temperature

36 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 115 Figure 5.8 (A) Brillouin gain spectrum (BGS) dependence on strain. (B) Brillouin frequency shift (BFS) dependence on strain. (C) BGS dependence on temperature. (D) BFS dependence on temperature. was investigated after the strain was released (Fig. 5.8AeD). The BFS dependence coefficients were 65.6 MHz/% and 4.04 MHz/K (Fig. 5.8B and D), which are 0.5 times [36] and 1.3 times [60] the values of an unstrained POF. This result indicates that even more highly sensitive temperature sensing with lower strain sensitivity is feasible by exploiting the Brillouin signals in the slimmeddown POFs. 5.3 Distributed Measurement In this section, we present the first demonstration of truly distributed strain/temperature sensing with a high spatial resolution in POFs based on Brillouin optical correlation-domain reflectometry

37 116 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS (BOCDR) [39]. The performance limitation of this system is also discussed Motivation Low-resolution distributed temperature sensing in a POF has been demonstrated [69] based on Brillouin optical frequencydomain analysis (BOFDA) [16]. They detected a 4-m-long heated section located at one end of a 20-m-long POF, but the spatial resolution and SNR were not sufficiently high for practical use; the relatively high cost of the devices, such as a vector network analyzer and a microwave generator, is also a problem. Although a 3-cm spatial resolution has been obtained by BOFDA [70] in a silica SMF, such a high resolution has not been achieved in a POF, not only because of the high propagation loss, but also because of the weak Brillouin signal resulting from its large core diameter and multimode nature. Employing Brillouin optical time-domain analysis (BOTDA) to acquire the BGS distribution has also been experimentally shown to be extremely difficult [71]. In this section, we report on the first demonstration of distributed strain and temperature sensing with a centimeter-order spatial resolution in a POF based on BOCDR [20], which is highly cost-effective. A 10-cm-long heated section located away from both ends of a 1.3-m-long POF is successfully detected with a theoretical spatial resolution of 7.4 cm and a sampling rate of 3.3 Hz per measured point (corresponding to a measurement time of w1 min, if the number of measured points is 200). We also discuss how the characteristics of POFs (BFS, Brillouin bandwidth, propagation loss, etc.) affect the sensing performance of BOCDR Principle Several distributed measurement techniques based on Brillouin scattering in optical fibers have been proposed so far, which are classified into two categories: reflectometry and analysis. In reflectometry, based on spontaneous Brillouin scattering, a light beam is injected into only one end of the fiber, whereas in analysis, based on SBS, two light beams are injected into both ends of the fiber. Analysis systems proposed so far include BOTDA [17,71e73], BOFDA [16,69,70], and BOCDA [18,63,74], in which a relatively large signal and thus a high SNR can be obtained. Two-end access is, however, less convenient, because the system does not work completely when the fiber has even one breakage

38 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 117 point. Moreover, expensive devices are often required to prepare so-called probe light to induce SBS. In contrast, even though the signal is weak, reflectometry such as Brillouin optical timedomain reflectometry [19,75,76] and BOCDR [20,77,78] can resolve these problems. As the interface between a silica SMF and a POF is easily damaged by injecting short optical pulses with high peak power [79], here we focus on BOCDR. First proposed in 2008 [20], BOCDR has been used as a promising distributed sensing technique with one-end accessibility, a high spatial resolution, a high sampling rate (i.e., fast measurement speed), and cost efficiency. Its operating principle is based on the correlation control of continuous light waves [81]; namely, the pump light and the reference light in a standard self-heterodyne scheme for analyzing Brillouin signals (refer to Section ) are sinusoidally frequency modulated at f m, producing periodical correlation peaks in the fiber to be measured. The measurement range d m is determined by their interval, which is inversely proportional to f m as d m ¼ c 2nf m ; (5.9) where c is the velocity of light in a vacuum and n is the refractive index of the fiber core. By sweeping f m, the correlation peak, i.e., the sensing position, can be scanned along the fiber to acquire the BGS or BFS distribution. According to theory [78], whenf m is lower than the Brillouin bandwidth Dn B, the spatial resolution Dz is given Dz ¼ cdn B 2pnf m Df ; (5.10) where Df is the modulation amplitude of the optical frequency. Considering that f m higher than Dn B does not contribute to the enhancement of Dz [78], and that Df is practically limited to half of the BFS n B of the fiber because of the Rayleigh noise [20,78], the limitation of the spatial resolution Dz min is given by Dz min ¼ c pnn B. (5.11) The number of effective sensing points N R, which can be regarded as an evaluation parameter of the system, is given by the ratio of d m to Dz, as N R ¼ d m Dz ¼ pdf Dn B. (5.12)

39 118 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS To obtain higher N R, Df needs to be raised but it should be lower than n B /2; N R is thus limited to N Rmax ¼ pn B 2Dn B. (5.13) Experimental Setup PFGI POFs with a 50-mm core diameter were employed as the fibers under test (see Section for details). The schematic setup of BOCDR for distributed measurement in a POF (Fig. 5.9A) is basically the same as the basic configuration [20]. All the optical paths except the POF were silica SMFs. A DFB- LD at 1.55 mm with 1-MHz linewidth was used as a light source, and its output frequency was sinusoidally modulated by direct Figure 5.9 (A) Schematic setup of Brillouin optical correlation-domain reflectometry. AC, alternating current; DC, direct current; EDFA, erbium-doped fiber amplifier; ESA, electrical spectrum analyzer; FG, function generator; PC, polarization controller; PD, photodiode; POF, polymer optical fiber. (B) Structure of the POF under test (Expt. 1). (C) Brillouin frequency shift (BFS) distribution obtained when the 50-cm-long section of the POF was strained. (D) BFS distribution obtained when the 50-cm-long section of the POF was heated.

40 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 119 modulation of the driving current. Its output was divided into two light beams with a coupler. One was directly used as the reference light of heterodyne detection, after passing through a 1-km-long delay fiber, to adjust the correlation peak order, and an EDFA to enhance the beat signal. The other beam was amplified with another EDFA, and injected into the POF as the pump light (incident power: 27 dbm). The optical beat signal between the Stokes light and the reference light was then converted to an electrical signal with a PD, which was finally monitored with an ESA with a 300-kHz frequency resolution. Polarization state was optimized with a PC at the beginning of each distributed measurement so that the Rayleigh noise was minimal [80] Experimental Results First, we demonstrate distributed strain and temperature sensing with a moderate spatial resolution but with a high SNR. The modulation frequency f m was swept from to MHz, corresponding to the measurement range d m of 9.5 m according to Eq. (5.9). The modulation amplitude Df was set to 0.9 GHz, resulting in the theoretical spatial resolution Dz of 34 cm from Eq. (5.10) (the Brillouin bandwidth Dn B is w100 MHz in a POF). Their ratio N R was 28. The 56th correlation peak was used. The overall sampling rate of single-location measurement was 3.3 Hz. Fig. 5.9B shows the structure of a 2-m-long POF to be measured, in which strains of <1.2% [within the elastic region (refer to Section 5.2.5)] were applied to a 50-cm-long section fixed on a translation stage, or the same section was heated up to 65 C (sufficiently lower than the glass transition temperature [82]). One end of the POF was butt-coupled to a silica SMF (second port of the circulator) via an SC connector, and the other end was cut at 8 degrees to suppress the Fresnel reflection. The room temperature was 18 C. The measured BFS distribution when strain was applied is shown in Fig. 5.9C. The measurement time was approximately 1 min (200 points), which can be set shorter by reducing the measured points. The 50-cm-long strain-applied section was successfully detected. The BFS shifted to lower frequency with increasing strain with a proportionality constant of MHz/ %, which was moderately consistent with that in Section ( MHz/%). The BFS changed even along the strain-free sections by about 10 MHz, which indicates that the strain measurement error was 0.09%. The measured BFS distribution when temperature was changed is also shown in Fig. 5.9D, where the 50-cm-long heated section was clearly detected. The measurement time was also about 1 min. The proportionality constant of

41 120 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS temperature dependence was 3.27 MHz/ C, which is in good agreement with a previous result ( 3.2 MHz/% [60]). The temperature measurement error was evaluated to be w3.1 C. Next, we demonstrate distributed temperature sensing with a centimeter-order spatial resolution. The modulation configurations of the light source were f m ¼ e MHz and Df ¼ 0.9 GHz, corresponding to d m of 2.1 m and Dz of 7.4 cm (N R ¼ 28). Fig. 5.10A shows the structure of a 1.3-m-long POF employed, of which a 10-cm-long section was heated to 40 C. Fig. 5.10B shows the measured distribution of normalized BGS along the POF, and Fig. 5.10C shows the BGS examples at unheated and heated positions (relative positions of 67 and 104 cm, respectively). Fig. 5.10D shows the BFS distribution corresponding to Fig. 5.10B. The measurement time was approximately 40 s (130 points). The BFS clearly downshifted at the 10-cm-long heated section. The amount of the BFS shift was approximately 26 MHz, which agrees well with the actual temperature (40 C). Figure 5.10 (A) Structure of the polymer optical fiber (POF) under test (Expt. 2). (B) Normalized Brillouin gain spectrum (BGS) distribution. (C) Examples of BGS [Z 1 at 67 cm (room temperature); Z 2 at 104 cm (heated)]. (D) Brillouin frequency shift distribution obtained with a centimeter-order resolution.

42 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 121 The gradual BFS changes at the relative positions of w90 and w115 cm were probably caused by the overlap of two broad BGSs (Dn B w 100 MHz) from the sections with and without the temperature changed Discussion Finally,wecomparetheperformancesofPOF-basedBOCDR with those of silica SMF-based BOCDR. First, according to Eq. (5.11), the highest spatial resolution Dz min theoretically achievable in POF-based BOCDR (n B w 2.8 GHz; n w 1.35) is calculated to be 23 mm, which is approximately 1/4 of that in SMF-based BOCDR (n B w 10.8 GHz; n w 1.46). However, a weak Brillouin signal in a POF, leading to a low SNR, practically limits the spatial resolution, as shown in the aforementioned experiment. Next, according to Eq. (5.13), the maximal number of effective sensing points N Rmax of POF-based BOCDR (Dn B w 100 MHz) is calculated to be 44, which is w1/13 of that of SMF-based BOCDR (Dn B w 30 MHz). This problem can be mitigated by employing so-called temporal-gating [83] and double-modulation schemes [84]. Note that the measurement range d m itself is limited not only by its trade-off relation to Dz but also by the high propagation loss (250 db/km at 1.55 mm) of the POF. Currently, the practical limitation of d m is several tens of meters (depending on Dz, incidentpower,andmany other parameters); we believe it can be elongated to several hundreds of meters by using shorter pump wavelengths at which the propagation loss is much lower (for instance, w10 db/km loss is reported at 0.98 mm [1]). As for the sampling rate of single-location measurements, 3.3 Hz demonstrated in the experiment is restricted by the speed of signal acquisition from theesaviaageneralpurposeinterfacebus,whichmightbe further enhanced by use of faster data acquisition methods that have been implemented in SMF-based BOCDR [77] and BOCDA [64]. Asforcostefficiency, a simplified configuration of BOCDR has been developed and demonstrated using POFs [85]. Highly accurate discriminative sensing of strain and temperature [86] usingpofsisanotherimportantproblemtobe tackled. 5.4 Polymer Optical Fiber Fuse As detailed in Section , the SNR of Brillouin measurement in POFs is not sufficiently high because of the weak Brillouin

43 122 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS signal that originates from their large core diameter and multimode nature. One method for mitigating this problem is to employ higher-power incident light, but power that is too high will induce damage or burning at the butt-coupled interfaces and a so-called optical fiber fuse phenomenon. In this section, we describe the fundamental properties of POF fuse [40e42] Motivation and Principle Fiber fuse is the continuous self-destruction of a fiber by propagating light [87e89]. High-power light propagating through the fiber results in local heating and the creation of an optical discharge that is then captured in the fiber core and travels back along the fiber toward the light source, consuming the light energy and leaving a train of voids [90]. While fiber fuse propagation is stunningly beautiful [91], the fiber cannot be used after the passage of the fuse. This effect is now regarded as one of the critical factors limiting the maximal optical power that can be delivered [92,93]. The fuse properties must be well characterized so that all possible measures are taken to avoid the creation of a fiber fuse. The fuse properties in various glass fibers, including standard silica SMFs [87,88,90,91,94e96], microstructured fibers [97], fluoride fibers [98], chalcogenide fibers [98], erbium-doped fibers [99], photonic crystal fibers [100], and hole-assisted fibers [100], are well documented. The fiber fuse is reported to be typically induced at an input optical power of one to several watts (one to several megawatts per square centimeter) and to have a propagation velocity of one to several meters per second. These properties differ according to the type of glass fiber; the threshold power, for instance, is reported to be much higher in photonic crystal and hole-assisted fibers than in silica SMFs [100], and nonlinear saturation of the fuse velocity has been observed in erbium-doped fibers [99]. However, no reports detailing similar properties of POFs had been provided until our first observation, despite their pressing need. In this section, we characterize the POF fuse and discuss its unique properties. The propagation velocity of the bright spot is 1 to 2 orders of magnitude slower than that in standard silica SMFs. The threshold power density is 1/180 of the reported value for silica SMFs. We find that, after the passage of the fuse, an oscillatory continuous curve is formed in the POF. We also show that the POF fuse can be easily terminated by local elastic deformation of the waveguide structure, and that, by spectral measurement, the bright spot is not a plasma but an optical discharge, the temperature of which is w3600 K.

44 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS Fundamental Characterization A PFGI POF with a 50-mm core diameter was used (see Section for other parameters). Fig. 5.11A depicts the experimental setup, in which 7-dBm (5-mW) output light from a 1.55-mmDFB- LD was amplified by an EDFA to up to 23 dbm (200 mw) and injected into a 15-m-long POF. Two optical isolators were Figure 5.11 (A) Schematic of the experimental setup. The silica single-mode fibers (SMFs) are indicated by blue lines (gray lines in print versions). EDFA, erbium-doped fiber amplifier; POF, polymer optical fiber. (B) Composite photograph of the fiber fuse propagating along the POF; photographs were taken at 1-s intervals. The light was injected from the right-hand side, and the fuse propagated from the left-hand side. The fiber arrangement was that of the literature [90] to allow a direct comparison between the POF and the silica SMF. (C) Magnified view of the propagating fuse. The light was injected from the left-hand side. (D) Propagation velocity of the fiber fuse in a POF measured at 1.55 mm as a function of the maximum power density in the core. Measured data are shown as blue circles (dark gray circles in print versions), and the red line (light gray line in print versions) is a linear fit. The slope of the line is 1590 mm/s/mw$cm 2, and the threshold intensity is 6.6 kw/cm 2. (E) Propagation velocity of the fiber fuse as a function of the power density. The measured data for the silica SMF at 1.48 mm are shown as green circles (gray circles in print versions), and the green line (gray line in print versions) is a linear fit (slope of 11.7 mm/s/mw$cm 2 ); the theoretical threshold power density [95] is 1.16 MW/cm 2. The blue line (light gray line in print versions) is a theoretical prediction [95] for the silica SMF at 1.55 mm (slope of 9.41 mm/s/mw cm 2 ). The data in (D) is also reproduced for comparison. (E) Data extracted from the literature: Atkins RM, Simpkins PG, Yablon AD. Track of a fiber fuse: a Rayleigh instability in optical waveguides. Optics Letters 2003;28:974e76.

45 124 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS inserted to protect the laser and EDFA from reflected or backscattered light. The end of the silica SMF fitted with an FC connector was connected to one end of the POF fitted with an SC connector via an FC/SC adaptor. We confirmed that the fiber fuse can be initiated in the same way as in glass fibers [87,88,90,91,94e100] by external stimuli such as heating, bending, or bringing the fiber output end into contact with an absorbent material. For the demonstration discussed here, we used a POF end that was surface polished roughly with 0.5-mm alumina powder. From observations of the propagation of the fuse along the POF (Fig. 5.11B), the propagation velocity was calculated to be approximately 24 mm/s, which is extremely slow in comparison to Todoroki s [91] result for a silica SMF. The optical power of the propagating light was calculated, using the measured power of the injected light, the coupling loss at the SMF/POF interface, and the propagation loss in the POF, to be approximately 75 mw, corresponding to a maximal power density of 7.6 kw/cm 2 (refer to the next paragraph for the calculation method). A magnified view of the fuse propagation along a straight portion of the POF is shown in Fig. 5.11C (70.5 mw, 22.8 mm/s). Here, we derive an equation for the maximal power density I in the core when light with a certain power P is injected into the graded-index (GI) POF. We consider a refractive index in the core that takes a parabolic profile [1]. Under the assumption that all modes propagate with equal attenuation without coupling, the optical power profile is given, in the same way as the refractive index profile, by [101] r g pðrþ ¼pð0Þ 1 ; (5.14) R where r is the radial distance from the core center, R is the core radius, and g is the refractive index profile coefficient. Consequently, the maximal power density I can be calculated as P I ¼ lim r/0 pr 2 R 2p dq R r 0 0 R 2p dq R R 0 0 r g 1 rdr R r g 1 rdr R ¼ P g þ 2 pr 2 g z 2P pr 2 ; (5.15) where we assumed g z 2 in the GI POF [1]. Eq. (5.15) indicates that the maximal power density in the GI POF with an incident power P is equal to the average power density in a step-index POF of the

46 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 125 same core diameter with twice the incident power. For instance, for P ¼ 75 mw and R ¼ 25 mm, I is calculated to be 7.6 kw/cm 2. We found that the fuse propagation velocity in the POF, measured at 1.55 mm, had an almost linear dependence on the maximal power density with a slope of 1590 mm/s/mw cm 2 (Fig. 5.11D). The power density at which the fuse ceased, i.e., the threshold power density, was 6.6 kw/cm 2 at a propagation velocity of 21.9 mm/s. Comparing these results with those of silica SMFs (Fig. 5.11E; results [94] at 1.48 mm and the theoretical line [95] at 1.55 mm) revealed that at 1.55 mm the slope in the POF data (corresponding to the efficiency of the velocity control) was 170 times as steep as that in the silica SMF (9.41 mm/s/mw$cm 2 ), and the threshold power density of the POF was 180 times lower than that of the silica SMF (w1.2 MW/cm 2 ). The minimal propagation velocity achieved at 1.55 mm was 11 times as low as that experimentally obtained in a silica SMF at 1.48 mm (250 mm/s) [96] Microscopic Observation Digital micrographs taken after the passage of the fuse disclose the extent of the damage to the fiber. The fuse was initially triggered by exploiting the rough surface at the end of the POF (Fig. 5.12A) and was verified to be induced at the center of the core, which supports the assumption in our calculation that the maximal power density in the fiber cross section affects the fuse induction and can be used to determine the threshold power density. The passage of the fuse (Fig. 5.12B) appeared as a continuous black carbonized curve that oscillated periodically along the length of the POF, which is considerably different from the bulletshaped voids observed in glass SMFs. The oscillation period was approximately 1300 mm, which is in general agreement with the theoretical oscillation period of the ray [102]. Fig. 5.12C shows the position where the fuse ceased after the incident optical power was reduced to below the threshold; because the fuse remained at this point for several seconds, it melted a relatively large area of the POF, which resulted in the observed bending. Optical propagation loss in the POF after the passage of the fuse was measured for incremental cutbacks from 30 to 20 cm (Fig. 5.12D) and a fixed input power of 10 dbm (10 mw) at 1.55 mm. A loss of 1.4 db/cm indicates that, unlike silica SMFs, light can propagate through the POF for several tens of centimeters after the passage of the fuse. We believe this is because undamaged regions remain in the core and cladding layers, as these diameters are relatively large, which is a unique characteristic of POFs. Yet this propagation loss is somewhat significant for communication

47 Figure 5.12 (A) Digital micrograph of the polymer optical fiber (POF) end at which the fuse was initiated by exploiting the rough surface. (B) Path of the fuse in the POF. (C) Point at which the fuse was terminated by decreasing the input optical power. (D) Output power dependence on the cut-back length. The open circles are measured points, and the solid line is a linear fit. (E) Image of the fuse termination in the POF at the position of a nickel ring. (F) Emission spectra of the bright spot of the POF fuse, an incandescent light bulb, and background (sunlight). The red circles (dark gray in print versions) indicate some characteristic peaks of the POF fuse spectrum.

48 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 127 applications, and so once the fuse is induced, it is crucial to stop the propagation as soon as possible. Several methods for terminating fiber fuses have been developed for glass fibers [100,103e105], and these are in principle also applicable to POFs. One method is to thin the outer diameter of the fiber at a certain position while maintaining the core diameter [104]; this can reduce the internal pressure and arrest the propagating fuse via deformation. In silica SMFs, this structure is fabricated using hydrofluoric acid as an etchant [104], but in a POF, chloroform could be used to etch the overcladding layer [82]. An even easier method, which we present here, is to pressure-bond a small metal ring around the fiber; this method is applicable only to POFs with an extremely high flexibility. The optical power of the particular propagating mode that provides the bright spot with energy is decreased below the threshold by deformation, and the propagating fuse is thus terminated. The resulting induced optical loss is negligibly low, and an image of the fuse termination at the position of the ring (Fig. 5.12E) shows that bending did not occur. Once the ring is detached, the polymer material will return to the original configuration (elastic deformation) Spectral Analysis Fig. 5.12F shows the measured emission spectrum of the bright spot propagating along the POF (w300 mw incident power). Its comparison with the blackbody-like spectra of an incandescent light bulb and background (i.e., sunlight) shows that, although the POF fuse spectrum has some characteristic peaks, all three spectra are similar. This would indicate that the bright spot of the POF fuse originates not so much from plasma emission as from thermal radiation, because if the bright spot mainly consisted of plasma, the emission spectrum would generally contain some line-shaped components [106,107]. This result may raise doubts as to whether the fast-propagating fuse in glass fibers should be referred to as plasma, as this conclusion has been reached without convincing evidence (the emission spectra that have so far been reported [108e110] do not provide completely clear evidence of the fuse being composed mainly of plasma). Spectra theoretically calculated using Planck s law indicate that the temperature of the bright spot is w3600k, which can also be verified using Wien s displacement law Discussion Fiber fuse in glass multimode fibers (MMFs) has also been reported; the shape of the molten area corresponds to a

49 128 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS summation of the optical paths of all the propagating modes [111,112]. By stark contrast, the entire cross section of the core and cladding of a POF seems to melt (see Fig. 5.12B), partly because of their low glass transition temperature of <108 C and partly because of the relatively slow fuse propagation velocity; and the boundary between the molten and the solid areas of the fiber cannot be observed. In the molten area of the POF, the bright spot travels only along the optical path of a particular propagating mode (that with the highest energy) that provides the bright spot directly with energy. The GI profile may be destroyed by high temperature, but the observed oscillating damage curve suggests that its time constant is longer than the fuse propagation velocity. We point out here that the bright spot probably originates from the carbide. Once carbide is generated at high temperature (>500 C), it absorbs the light and heats the neighboring polymer above the decomposition temperature, resulting in its growth along the optical path. This behavior is analogous to metal particle manipulation by laser irradiation in glass [113], i.e., carbide serves as an equivalent to the metal particle that moves, emitting bright visible light and melting the surrounding glass by photothermal conversion. This interpretation supports the result that POF fuse is not a plasma but an optical discharge. The oscillatory carbonized curve indicating the passage of the POF fuse is thus formed. It is noteworthy that, unlike the case for a silica MMF, light and electric current can simultaneously propagate through the POF after the passage of the fuse, because the generated continuous carbonized curve is electrically conductive. The optical propagation loss of approximately 1.4 db/cm (Fig. 5.12D) is too high for telecommunication but sufficiently low for not so long (centimeter-order) light propagation. This feature will provide a possible scheme for a long photoelectric interaction length, and the optical absorption (or electric current/resistance) might be controlled by adjusting the electric current (or optical power) propagating along the POF, which will be useful in developing various optical/electrical devices. 5.5 Conclusion We have reviewed some unique characteristics of Brillouin scattering in PFGI POFs, and demonstrated POF-based distributed Brillouin sensing of strain and temperature. In Section 5.2, the BFS in the POFs was measured to be w2.8 GHz at 1.55 mm, which showed

50 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 129 negative dependence on strain and temperature. The measured dependence coefficients of 122 MHz/% and 4.1 MHz/K were respectively 0.2 and 3.5 times the values in silica glass fibers, which suggests that the Brillouin scattering in POFs is applicable to highly sensitive temperature sensing with low strain sensitivity. We also presented a nonmonotonic BFS dependence on large strain caused by a BFS hopping phenomenon. Furthermore, enhancement of Brillouin signal was demonstrated by induction of SBS and employment of a POF with a smaller core diameter. In Section 5.3, POF-based distributed Brillouin sensing was demonstrated using BOCDR. Strain and temperature distributions were successfully detected with a high SNR and a high spatial resolution. The performance limitation of the POF-based system was compared with that of glass fiberebased systems. In Section 5.4,we described the fundamental properties of a POF fuse phenomenon, which should be avoided to perform POF-based Brillouin sensing. The POF fuse propagation velocity was 21.9 mm/s, which was 1e2 orders of magnitude slower than that in standard silica fibers. The threshold power density was 1/180 of the value for silica fibers. We also found that a unique oscillatory continuous carbonized curve is formed after the passage of the fuse, which can be terminated easily. In addition, its engineering applications were discussed. Thus, prior efforts in Brillouin scattering in POFs have already achieved substantial progress toward establishing a framework for practical distributed strain and temperature sensing. The key to practical applications is the improvement of the sensing performance, such as the spatial resolution,measurementrange,samplingrate,snr,measurementstability, and system cost, as well as the assignment of new functions, such as the strain and thermal memory and discriminative sensing of strain and temperature. References [1] Koike Y, Asai M. The future of plastic optical fiber. NPG Asia Materials 2009;1:22e8. [2] Kuzyk MG. Polymer fiber optics: materials, physics, and applications. CRC Press; [3] Husdi IR, Nakamura K, Ueha S. Sensing characteristics of plastic optical fibres measured by optical time-domain reflectometry. Measurement Science and Technology 2004;15:1553e9. [4] Ujihara H, Hayashi N, Tabaru M, et al. Measurement of large-strain dependence of optical propagation loss in perfluorinated polymer fibers for use in seismic diagnosis. IEICE Electronics Express 2014;11: [5] Mollers I, Jager D, Gaudino R, et al. Plastic optical fiber technology for reliable home networking e overview and results of the EU project POF- ALL. IEEE Communications Magazine 2009;47:58e68.

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55 134 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS [81] Hotate K, He Z. Synthesis of optical-coherence function and its applications in distributed and multiplexed optical sensing. Journal of Lightwave Technology 2006;24:2541e57. [82] Gravina R, Testa G, Bernini R. Perfluorinated plastic optical fiber tapers for evanescent wave sensing. Sensors 2009;9:10423e33. [83] Mizuno Y, He Z, Hotate K. Measurement range enlargement in Brillouin optical correlation-domain reflectometry based on temporal gating scheme. Optics Express 2009;17:9040e6. [84] Mizuno Y, He Z, Hotate K. Measurement range enlargement in Brillouin optical correlation-domain reflectometry based on double-modulation scheme. Optics Express 2010;18:5926e33. [85] Hayashi N, Mizuno Y, Nakamura K. Simplified Brillouin optical correlation-domain reflectometry using polymer optical fiber. IEEE Photonics Journal 2015;7: [86] Zou W, He Z, Hotate K. One-laser-based generation/detection of Brillouin dynamic grating and its application to distributed discrimination of strain and temperature. Optics Express 2011;19:2363e70. [87] Kashyap R. The fiber fuse e from a curious effect to a critical issue: a 25th year retrospective. Optics Express 2013;21:6422e41. [88] Kashyap R, Blow KJ. Observation of catastrophic self-propelled selffocusing in optical fibres. Electronics Letters 1988;24:47e9. [89] Todoroki S. Fiber fuse: light-induced continuous breakdown of silica glass optical fiber. Springer; [90] Todoroki S. Origin of periodic void formation during fiber fuse. Optics Express 2005;13:6381e9. [91] Todoroki S. Fiber fuse propagation behaviour. In: Yasin M, Harun SW, Arof H, editors. Selected topics on optical fiber technology. InTech; p. 551e70. [92] Jinno M, Miyamoto Y, Hibino Y. Networks: optical-transport networks in Nature Photonics 2007;1:157e9. [93] Morioka T, Awaji Y, Ryf R, et al. Enhancing optical communications with brand new fibers. IEEE Communications Magazine 2012;50:s31e42. [94] Atkins RM, Simpkins PG, Yablon AD. Track of a fiber fuse: a Rayleigh instability in optical waveguides. Optics Letters 2003;28:974e6. [95] Shuto Y, Yanagi S, Asakawa S, et al. Fiber fuse phenomenon in step-index single-mode optical fibers. IEEE Journal of Quantum Electronics 2004;40: 1113e21. [96] Todoroki S. Fiber fuse propagation modes for typical single-mode fibers. In: Proceedings of optical fiber communication/national fiber optic engineers conference, JW2A.11; [97] Dianov EM, Bufetov IA, Frolov AA, et al. Fiber fuse effect in microstructured fibers. IEEE Photonics Technology Letters 2004;16:180e1. [98] Dianov EM, Bufetov IA, Frolov AA, et al. Catastrophic destruction of fluoride and chalcogenide optical fibers. Electronics Letters 2002;38: 783e4. [99] Domingues F, Frias AR, Antunes P, et al. Observation of fuse effect discharge zone nonlinear velocity regime in erbium-doped fibres. Electronics Letters 2012;48:1295e6. [100] Hanzawa N, Kurokawa K, Tsujikawa K, et al. Suppression of fiber fuse propagation in hole-assisted fiber and photonic crystal fiber. Journal of Lightwave Technology 2010;28:2115e20. [101] Gloge D, Marcatili EAJ. Multimode theory of graded-core fibers. Bell System Technical Journal 1973;52:1563e78.

56 Chapter 5 DISTRIBUTED BRILLOUIN SENSING USING POLYMER OPTICAL FIBERS 135 [102] Agrawal GP. Fiber-optic communication systems. Wiley; [103] Abedin KS, Nakazawa M, Miyazaki T. Backreflected radiation due to a propagating fiber fuse. Optics Express 2009;17:6525e31. [104] Dianov EM, Bufetov IA, Frolov AA. Destruction of silica fiber cladding by the fuse effect. Optics Letters 2004;29:1852e4. [105] Hand DP, Birks TA. Single-mode tapers as fibre fuse damage circuitbreakers. Electronics Letters 1989;25:33e4. [106] Tachibana K. Current status of microplasma research. IEEJ Transactions on Electrical and Electronic Engineering 2006;1:145e55. [107] Tendero C, Tixier C, Tristant P, et al. Atmospheric pressure plasmas: a review. Spectrochimica Acta Part B 2006;61:2e30. [108] Dianov EM, Fortov VE, Bufetov IA, et al. High-speed photography, spectra, and temperature of optical discharge in silica-based fibers. IEEE Photonics Technology Letters 2006;18:752e4. [109] Hand DP, Russell PStJ. Solitary thermal shock waves and optical damage in optical fibers: the fiber fuse. Optics Letters 1988;13:767e9. [110] Todoroki S. In-situ observation of fiber-fuse propagation. Japanese Journal of Applied Physics 2005;44:4022e4. [111] Bufetov IA, Frolov AA, Shubin AV, et al. Propagation of an optical discharge through optical fibres upon interference of modes. Quantum Electronics 2008;38:441e4. [112] Davis DD, Mettler SC, DiGiovanni DJ. Experimental data on the fiber fuse. Proceedings of SPIE 1995;2714:202e10. [113] Hidai H, Yamazaki T, Itoh S, et al. Metal particle manipulation by laser irradiation in borosilicate glass. Optics Express 2010;18:20313e20.

57 INDEX Note: Page numbers followed by f indicate figures, t indicate tables. Accelerometers bending beam concept, 199 fiber optic hydrophone, 200 massespring system, 199, 200f Acoustic monitoring hydraulic fracture monitoring, 232 pipeline intrusion detection, 231e232 slugging, 232 Aerospace applications, optical fiber mechanical sensors accelerometers, 255 aircraft design, 244e245 aircraft industry, 248e249 antenna, 240 BOCDA, 251 Bulldog light aircraft, 250e251 cantilever beam theory, 256 CVM, 253 damage, 245e246, 252e253 data mining, 248 design and test phases, 248 D-fiber, 242 embedding fibers, 258e259 ESA, 241e242 fail-safe philosophy, 244e245 fatigue failures, 245e246 fiber cavity etalons, 241 flight control, measurements for measuring acceleration, 243e244 MEMS, 243e244 roles, 244 SHM, 244 ultrasonic system, 244 Fourier transform, 254 g-loads, 250e251 graphite epoxy composite, 240 grating sensors, 258 interrogation methods, 254 Ko theory, 247e248 long-period gratings, 249e250 matched grating approach, 257 NASA, 246 NDE, 238 NDI, 237 optical fiber Bragg grating sensors, advantages of, 239 optical spectrum analyzer, 257 Pak notes, 252 palladium-coated Bragg grating fibers, 242 photodetector, 257 photogrammetry, 252 piezoelectric sensors and actuators, 246e247 POF sensor, 249 radial vibration, 250 Rayleigh scattering, 254 safe-life philosophy, 245 shape reconstruction methods, 253 SHM, stages of, 239 smart structures, 241e242 SNR, 256 solar sails, 243 strain data, 246, 259 structural transfer functions, 247 surface-mounted sensors, 253 tangential vibrations, 250 threat factor, 257e258 truss structure, 240e241 vibrations, 256 wing-tip displacement, 247 Bending plate hydrophone design, 199 BGS. See Brillouin gain spectrum (BGS) Biomechanics, fiber optical sensors adhesion to biological tissues, 268 body fluids, 264 Camino pressure sensors, 282e283 human body liquids, 282e283 intraarticular pressure, 284e286 intramuscular/ intracompartmental pressure, 283e284 intravascular and intracardiac, 282e283 deformable bodies, 264 biomechanical materials testing, 275e277 body structure, 275e277 bone cements, 278 force prediction, 280 FORP system, 281e282 macrobending technology, 281e282 SGs, 277e278 stainless steel bone plates, 279, 279f traumatic head and dental injuries, 278 electrical conductivity, 267 geometrical versatility, 268 immunity to electromagnetic interference, 267 inertness and biocompatibility, 265e267 light source, 265

58 336 INDEX Biomechanics, fiber optical sensors (Continued) pertinent physical parameters, 268 quantitative discipline, 264 remote operation and sensing, 267 rigid bodies, 263e264 assessing body kinematics, 269 concept of, 268e269 data stations, 269e270 electric goniometers and torsiometers, 273e274 EMG systems, 271 force platform, 271 FOV, 269e270 high natural frequency platforms, 271 MEMS-based IMU, 275 MoCap optical systems, hardware components of, 269e270 multiplexed FBG arrays, 273 passive retroreflective markers, 269e270 pedobarograph, 273 pressure mapping devices, 272e273 SHAPE TAPE, 274e275 shear stress, 272e273 three-dimensional MoCap systems, 271 small dimensions and light weight, 267 thermal expansion and thermal conductivity, 267 Biomedical fiber optic sensor systems biophysical parameters, 302e303 cardiovascular diagnostics FFR, 315e316, 315f gastroenterology, 316e317 IAB counterpulsation therapy, 314e315, 314f MEMSs, 315e316 urology, 317e318 diagnostic technologies, 312e314 fiber bragg grating, 308e311 FPI EFPI, 304e305, 307e308 fabrication technique, 305e306 FP cavity, 304e305 nanothick silver diaphragm, 306e307 standard multimode fiber, 305e306 standard single-mode fiber, 305e306 metrologic, 301 physical, 301 pressure-sensing applications, 303 robotic microsurgery calibration, 327 clinical use, 327 optical fiber diameter, 326e327 optical fiber materials, 327 retinal microsurgery, 319e325 tool-shaft force feedback, 325e326 VRS, 318e319 smart textiles and wearable sensors, 327e330 system, 302 Birefringence, 7 Birefringent refractive index change (Type II), 148 Bladder outlet obstruction (BOO), 317 BOCDA. See Brillouin optical correlation domain analysis (BOCDA) Body fluids, biomechanics of, 264 Camino pressure sensors, 282e283 human body liquids, 282e283 intraarticular pressure, 284e286 intramuscular/ intracompartmental pressure, 283e284 intravascular and intracardiac, 282e283 Bragg wavelength sensitivity, different film thicknesses axial force, 34e36, 36t temperature, 36e38, 38t Bragg wavelength, 1, 77e78 Brillouin frequency shift (BFS), 98 Brillouin gain spectrum (BGS), 99, 101e102 Brillouin light spectrum, 99 Brillouin optical correlation domain analysis (BOCDA), 251 Brillouin optical correlationdomain reflectometry (BOCDR), 115e116 Brillouin optical frequencydomain analysis (BOFDA), 116 Brillouin scattering, 97, 128e129 BFS dependence, large strain experimental results, 113e115 experimental setup, 113 core diameter and fiber length, influence of Brillouin linewidth narrowing effect, 112e113 long fiber length, 111 small core diameters, effects of, 110e111 fundamental properties BGS, 101e102 experimental setup, 99e101 optical fiber, 99 induction of experimental results, 108e109 experimental setup, 107e108 motivation and principle, 106 strain and temperature dependence BFS, 105 experiments, 103 PMMA, 105 strain coefficient, 105

59 INDEX 337 theoretical temperature coefficient, 105e106 Brittle fracture, 93 Cantilever test, 88 Cardiovascular diagnostics FFR, 315e316, 315f gastroenterology, 316e317 IAB counterpulsation therapy, 314e315, 314f MEMSs, 315e316 urology, 317e318 Coefficient of thermal expansion (CTE), 223 Comparative vacuum monitoring (CVM), 252e253 Coupled-mode theory, 12 first-order differential equations, 16e17 forward and backward modes, 12, 13f optical fiber gratings, 23e25 phase matching, 15e16 superstructure FBGs exponential components for, 18 Fourier series, 18 Gaussian/cosine grating profile, 18 periodic variations, 17 phase matching conditions, 18e19 reflection spectrum, 19, 19f resonance wavelengths, 18e19 CVM. See Comparative vacuum monitoring (CVM) Cyclic steam stimulation (CSS), 214e215 Data mining, 248 DBR. See Distributed Bragg reflector (DBR) Deformable bodies, biomechanics of, 264 biomechanical materials testing, 275e277 body structure, 275e277 bone cements, 278 force prediction, 280 FORP system, 281e282 macrobending technology, 281e282 SGs, 277e278 stainless steel bone plates, 279, 279f traumatic head and dental injuries, 278 Degree of freedom (DOF), 320 DFB. See Distributed feedback (DFB) Different pressure sensitivity, 189 Distributed acoustic sensing (DAS), 211, 229 Distributed Bragg reflector (DBR), 164e165 Distributed feedback (DFB), 164e165, 199 Distributed pressure-sensing (DPS), 191e192 Distributed temperature sensing (DTS), 181, 211 Distributed-feedback laser diode (DFB-LD), 100e101 Drawdown, 224 D-shape fiber, 162 Ductile fracture, 92e93 Dye-and-pry failure visual inspection, 87e88, 95e96 EDFA. See Erbium-doped fiber amplifier (EDFA) Electric strain gauge, 78e79 Electrical spectrum analyzer (ESA), 100e101 Electromyography (EMG), 271 Enhanced oil recovery (EOR), 214e215 Erbium-doped fiber amplifier (EDFA), 100e101 European Space Agency (ESA), 241e242 FabryePerot (FP), 284 FabryePerot interferometry (FPI), 303e304 EFPI, 304e305, 307e308 fabrication technique, 305e306 FP cavity, 304e305 nanothick silver diaphragm, 306e307 standard multimode fiber, 305e306 standard single-mode fiber, 305e306 Failure map, 90fe91f, 92e93 Failure-onset PCB strain, 94e95 Fatigue test aluminum alloy, 52e55 friction stirewelded aluminum alloy cyclic hardening/softening, 61e62 microhardness profile, 60e61, 61f motivation, 56e57 NZ, 60 plastic deformation, 62e63 plastic strain amplitudes, 59, 59f sample preparations, 57e59 TMAZ, 60 magnesium alloy, 55e56 FBGs. See Fiber bragg gratings (FBGs) Femtosecond laser-induced Bragg gratings active sensing, 164e165 bulk interferometers, 148e150 chemical sensing, 162e164 energy deposition, 143e144 energy transfer, 143e144 free electron plasma formation avalanche ionization process, 144e146 conduction band electrons, 144e146 critical plasma density, 144e146

60 338 INDEX Femtosecond laser-induced Bragg gratings (Continued) electron density, 144e146 seed electrons, 144e146 subpicosecond pulses, 146 transparent dielectric materials, 144 fs-ir laser systems, 143e144 harsh environments, multiparameter sensing in, 159e161 high pressure, 161e162 high radiation, 158e159 high-sensitivity strain measurements, 164e167 high temperature FabryePerot structures, 156e157 fs-ir laser/phase mask approach, 155e156 gas turbine monitoring, 157e158 inhomogeneous combustion, 157e158 metallic coatings, 155 SFBGs, 157 silica single-mode fibers, 154e155 silica-based optical fibers, 156e157 stainless steel tubing/ ceramic alumina tubing, 155 type I and type II gratings, 153e154 volume Bragg gratings, 157 induced index change, regimes of birefringent refractive index change (Type II), 148 type I/smooth refractive index change, 146e147 void formation, 148 phase mask Bragg resonance, 150e151 Fourier components, 150e151 nonsinusoidal modulated gratings, 150e151 phase mask order walk-off, 151 traditional UV lasereinduced gratings, 150 point-by-point grating inscription, 151e152 Fiber Bragg grating (FBG) strain sensors basics and sensor fabrication Bragg wavelength, 77e78 electric strain gauge, 78e79 Hooke s law, 78e79 laser beam, 78 object deformation, 78e79 phase mask method, 78 polyimide coating, 78 reflection spectra, 80, 80f BGA, 83e84 cantilever strain, 80e81 capabilities, 95 different mechanical properties, 76e77 dye-and-pry failure visual inspection, 87e88, 95e96 FEA, 84, 85t four-point bending system and test setup mechanical test parameters, 86 PCB deflection, 86e87 5-V trigger signal, 87 microstructures, 75e76 pad crater, 76e77 PCBA, 75e76, 81e82 strain distribution pattern, 83e84, 84f strain gauges, 77, 82 test results brittle fracture, 93 cantilever test, 88 crosshead dwelling, 89e90 ductile fracture, 92e93 general strain release, 93e95 pad craters, 88e89 strain and load curves, 89e90 Fiber Bragg gratings (FBGs), 303e304 Bragg wavelength (lb), 1 core refractive index, 139 coupled-mode theory. See Coupled-mode theory damage-like process, 140 grating structure, 138e139 femtosecond laser-induced Bragg gratings applications of, 152e167 bulk interferometers, 148e150 energy deposition, 143e144 energy transfer, 143e144 free electron plasma formation, 144e146 fs-ir laser systems, 143e144 induced index change, regimes of, 146e148 phase mask, 150e151 point-by-point grating inscription, 151e152 high-intensity portions, 139 hydrogen gas, 141 laser-induced damage, 140 phase mask approach, 140 photosensitivity, 141 remnant index modulation, 141 sensor Bragg gratingebased sensor system, 141e142, 142f smart skin sensor, 142e143 telecommunications industry, 141e142 thermooptic effect, 142e143 spectral response, 1 structurally and thermally induced index changes birefringence, 7 transverse strain components, 5 temperature-dependent decay, 140 UV photon absorption process, 140 Fiber cavity etalons, 241 Fiber optical respiratory plethysmography (FORP) technique, 281e282

61 INDEX 339 Fiber optic sensors (FOSs) acoustic monitoring hydraulic fracture monitoring, 232 pipeline intrusion detection, 231e232 slugging, 232 advantages, 232e233 biomechanics. See Biomechanics, fiber optical sensors biomedical applications. See Biomedical fiber optic sensor systems downhole environment, pressure monitoring in Bragg gratingebased sensors, 222e223 CTE, 223 drawdown, 224 FabryePerot-based sensors, 222e223 interference testing, 226 lift monitoring, 224e226 pressure and temperature, 225 pressure transient analysis, 224 SAGD applications, 226 zonal monitoring, 225e226 flow monitoring injection monitoring, 228e229 interferometric flowmeter, 227e228 production monitoring, 229 multiparameter sensing, 232e233 oil and gas industry categories, 212e213 CO 2, 215 CSS, 214e215 downstream sector, 212e213 hydraulic fracturing, 215 hydrocarbon production processes, 212e213 SAGD, 214e215 seismic monitoring microseismic monitoring, 230e231 seismic surface arrays, 231 VSP, 230 thermal monitoring downhole thermal monitoring applications, 217e219 pipeline monitoring, 216e217 SAGD Optimization, 221e222 Field of view (FOV), 268 Finite element analysis (FEA), 20, 84, 278 Flat-cladding fiber Bragg grating sensors experiments, 51e52 fatigue test of aluminum alloy, 52e55 friction stirewelded aluminum alloy, 56e64 magnesium alloy, 55e56 fiber optic sensors, 49e50 large strain amplitudes, 49e50 magnesium alloy of, asymmetric fatigue deformation AZ31 extruded, stressestrain hysteresis loops of, 66e68, 70e71 motivation, 64e65 plastic strain amplitude, 68e70 sample preparations, 65e66 Flip-chip ball grid array (FC-BGA), 75e76 Flow monitoring injection monitoring, 228e229 interferometric flowmeter, 227e228 production monitoring, 229 Flowmeter hot-wire anemometry-based FBG flow sensor, 203e204 vortex flowmeter, 201e203 FP. See FabryePerot (FP) Fractional flow reserve (FFR), 315e316 Friction stir welding (FSW), 56e57 Ground reaction force (GRFz), 272f Heat-affected zone (HAZ), 57 High-pressure high-temperature (HPHT), 191e192 High-pressure sensors commercial bending plate type, 191e192 enhanced side-hole fiber pressure sensor, 191 mechanical transducer (plate, tube), 189e190 second fiber Bragg grating temperature sensor, 187e188 sensor design concepts, 187 spliceless distributed pressure sensing, 192e193 using common-mode configuration, 188e189 Hooke s law, 78e79 Hydraulic fracture monitoring, 232 Hydrogen, 184e185 Hydrogen gas, 141 Hydrogen loading, 141 Hydrophone bending plate hydrophone design, 199 frequency response, 197 mandrel type, 196, 196f piston design, 197e199 Inertial measurement units (IMU), 275 Injection monitoring, 228e229 Innovative fiber Bragg grating sensors Bragg wavelength, 176 coupled-wave theory, 176 dedicated operational conditions cryogenic temperature, 183 DTS system, 181 fiber optic sensors, 181 high operational pressure, 183e184 high temperature, 182e183

62 340 INDEX Innovative fiber Bragg grating sensors (Continued) hydrogen, 184e185 low stiffness fiber, 185 radiation, 184 vacuum, 184 high-end performance, critical properties/characteristics of dedicated interrogators, development of, 180e181 high sensitivity, 178e179 high-speed measurement, 179 large number of sensors, 179e180 large-scale sensor network system, 175e176 nonstandard applications, 177 physical parameters, 177e178 accelerometer, 199e201 flowmeter, 201e204 high-pressure sensors, 186e193 hydrophone, 196e199 miniaturized pressure sensor, 193e196 primary sensing parameters, 177 reflection wavelength, 176 revolutionary developments, 175 standard specifications, 177 Interference testing, 226 Interferometric flowmeter, 227e228 Intervertebral disc (IVD), 281 Intraarticular pressure (IAP), 284e286 KarhuneneLoeve transform (KLT), 305e306 Large strain amplitude fatigue tests aluminum alloy, 52e55 friction stirewelded aluminum alloy cyclic hardening/softening, 61e62 microhardness profile, 60e61, 61f motivation, 56e57 NZ, 60 plastic deformation, 62e63 plastic strain amplitudes, 59, 59f sample preparations, 57e59 TMAZ, 60 magnesium alloy, 55e56 Lift monitoring, 224e226 Low stiffness fiber, 185 Low-cycle fatigu (LCF) tests, 56e57 Measurement test rig, 38e39 Mechanical transducer (plate, tube), 189e190 Microelectromechanical systems (MEMS), 243e244, 275 Microseismic monitoring, 229e231 Minimal detectable strain (MDS), 164 Multimode fibers (MMFs), 127e128 Nondestructive evaluation (NDE), 238 Nondestructive inspection (NDI), 237 Nucleus pulposus (NP), 285 Nugget zone (NZ), 57 Numerical aperture (NA), 99e100 Optical fiber sensors, roles, 244 Optical path difference (OPD), 197e198 Optical spectrum analyzer (OSA), 78e79 Opto-mechanical modeling periodic on-fiber films, 31e32 stressestrainetemperature relations, 30e31 structural modeling, 29 Pad crater, 76e77 Partial differential equations (PDEs), 10e11 PbP. See Point-by-point (PbP) PCBA. See Printed circuit board assembly (PCBA) Perfluorinated graded-index (PFGI), 99e100 Periodic on-fiber films, 27e28 Phase matching condition, 15e16 Photodiode (PD), 100e101 Photosensitivity, 141 Physical parameters, 177e178 accelerometers bending beam concept, 199 fiber optic hydrophone, 200 massespring system, 199, 200f flowmeter hot-wire anemometry-based FBG flow sensor, 203e204 vortex flowmeter, 201e203 miniaturized pressure sensor, 193e196 high-pressure sensors commercial bending plate type, 191e192 enhanced side-hole fiber pressure sensor, 191 mechanical transducer (plate, tube), 189e190 second fiber Bragg grating temperature sensor, 187e188 sensor design concepts, 187 spliceless distributed pressure sensing, 192e193 using common-mode configuration, 188e189 hydrophone bending plate hydrophone design, 199 frequency response, 197 mandrel type, 196, 196f piston design, 197e199 Pipeline intrusion detection, 231e232 Piston design, 197e199

63 INDEX 341 Plastic strain amplitude cyclic hardening, 68e69 stress amplitude, 70 PMMA. See Polymethyl methacrylate (PMMA) Pockels photoelastic constant, 2e5 Point-by-point (PbP), 151e152 Polymer/plastic optical fibers (POFs), 185, 249 Brillouin scattering, 97, 128e129 BFS dependence, large strain, 113e115 core diameter and fiber length, influence of, 109e113 fundamental properties, 98e102 induction of, 106e109 strain and temperature dependence, 102e106 concept, 97e98 distributed measurement double-modulation schemes, 121 experimental results, 119e121 experimental setup, 118e119 motivation, 116 principle, 116e118 SMF-based BOCDR, 121 temporal-gating, 121 memory effect, 97e98 POF fuse carbide, 128 electric current, 128 fundamental characterization, 123e125 GI profile, 127e128 microscopic observation, 125e127 MMFs, 127e128 motivation and principle, 122 spectral analysis, 127 Polymethyl methacrylate (PMMA), 99e100, 185 Pressure transient analysis, 224 Pressure/temperature (P/T), 211 Printed circuit board assembly (PCBA), 75e76 Production monitoring, 229 Pumpeprobe technique, 106 Radiation, 184 Radiation-hard fibers, 184 Refractive index distribution, 189 Riccati ordinary differential equation (ODE), 31e32 Rigid bodies, biomechanics of, 263e264 assessing body kinematics, 269 concept of, 268e269 data stations, 269e270 electric goniometers and torsiometers, 273e274 EMG systems, 271 force platform, 271 FOV, 269e270 high natural frequency platforms, 271 MEMS-based IMU, 275 MoCap optical systems, hardware components of, 269e270 multiplexed FBG arrays, 273 passive retroreflective markers, 269e270 pedobarograph, 273 pressure mapping devices, 272e273 SHAPE TAPE, 274e275 shear stress, 272e273 three-dimensional MoCap systems, 271 Robotic microsurgery calibration, 327 clinical use, 327 optical fiber diameter, 326e327 optical fiber materials, 327 retinal microsurgery 3-DOF force-sensing pick instrument, 323e325 2-DOF force-sensing tool, 320 tool-tip force feedback, 319e320 transverse force calculation, 320e322 two degrees of freedom motorized microforceps, 322e323 tool-shaft force feedback, 325e326 VRS, 318e319 Sapphire fiber (SFBGs), 157 SBS. See Stimulated Brillouin scattering (SBS) Seismic monitoring microseismic monitoring, 230e231 seismic surface arrays, 231 VSP, 230 Seismic surface arrays, 231 Self-heterodyne detection, 100e101 SGs. See Strain gauges (SGs) SHM. See Structural health monitoring (SHM) Signal-to-noise ratio (SNR), 98, 256 Single-mode fiber (SMF-28), 80 Steam-assisted gravity drainage (SAGD), 214e215 Stimulated Brillouin scattering (SBS), 101 Stokes power, 110 Strain gauges (SGs), 77, 82, 264 Structural health monitoring (SHM), 239 Superstructure fiber Bragg gratings (SFBGs), 17 measurement test rig, 38e39 geometrical features, 38 optical response analysis strain and temperature, simultaneous measurement of, 44e46 structural loading, 41e43 temperature variations, 39e41 opto-mechanical modeling

64 342 INDEX Superstructure fiber Bragg gratings (SFBGs) (Continued) periodic on-fiber films, 31e32 stressestrainetemperature relations, 30e31 structural modeling, 29 periodic on-fiber films, 27e28 simulation results different film thicknesses, axial force for, 34e36, 35f, 36t on-fiber silver coatings, 32e34, 34f optical constants, 32, 32t reflection spectra, 34e38, 34f temperature for different film thicknesses, 36e38, 38t Theory and opto-mechanical modeling of fiber Bragg gratings (FBGs) Bragg wavelength (lb), 1 coupled-mode theory, 12 first-order differential equations, 16e17 forward and backward modes, 12, 13f optical fiber gratings, 23e25 phase matching, 15e16 SFBGs, 17e19 FEA Cartesian coordinates, 20 linear nonuniform axial strain, 21e23, 21f modeling parameters, 21e23 PDEs, 20 refraction, effective mode index of, 21e23, 22f triangular quadratic element, 20, 21f light propagation in optical fibers anisotropy, 8 boundary condition, 11 Cartesian coordinates, 8, 8f Maxwell s equations, 8 PDE, 10e11 optical fibers, opto-mechanical properties of dielectric material, 2e5, 2f isotropic material, 2e5 photoelastic and thermooptic effects, 2e5 spectral response, 1, 2f structurally and thermally induced index changes birefringence, 7 transverse strain components, 5 Thermal monitoring downhole thermal monitoring applications gas entry, 218 gas lift optimization, 219 injection monitoring, 219 liquid flow, 217e218 wax buildup, 219 pipeline monitoring leak detection, 216e217 temperature and strain, Brillouin monitoring of, 217 SAGD optimization, 221e222 Thermomechanical-affected zone (TMAZ), 57, 60 Time domain multiplexing (TDM), 180 Type I/smooth refractive index change, 146e147 color center defects, 147 Ge-doped silica, 146e147 hydrogen loading process, 147 micro-raman spectroscopy, 146e147 Vacuum, 184 Vertical seismic profile (VSP), 230 Vitreoretinal surgery (VRS), 318e319 Void formation, 148 Vortex flowmeter, 201e203 Wavelength division multiplexing (WDM), 211e212 Wavelength domain multiplexing (WDM), 179 Zonal monitoring, 225e226

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