A FIBER-OPTIC HYDROACOUSTIC PRESSURE SENSOR BASED ON INTERMODE INTERFERENCE
Subject and Purpose. The use of the two-mode operation of an optical fi ber in fiber-optic sensors simplifies the interferometerdesign and enhances the reliability of sensing. Methods and Methodology. The mechanism behind the appearance of intermode phase shifts of the light modes Lp01 and Lp11 unde...
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Видавничий дім «Академперіодика»
2025
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Radio physics and radio astronomy| id |
rpra-journalorgua-article-1485 |
|---|---|
| record_format |
ojs |
| institution |
Radio physics and radio astronomy |
| baseUrl_str |
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| datestamp_date |
2025-12-17T12:39:55Z |
| collection |
OJS |
| language |
Ukrainian |
| topic |
optical fiber fiber-optic sensor intermode interference phase-acoustic sensitivity pressure |
| spellingShingle |
optical fiber fiber-optic sensor intermode interference phase-acoustic sensitivity pressure Linchevskyi, I. V. Chursanova, M. V. A FIBER-OPTIC HYDROACOUSTIC PRESSURE SENSOR BASED ON INTERMODE INTERFERENCE |
| topic_facet |
optical fiber fiber-optic sensor intermode interference phase-acoustic sensitivity pressure волоконний світловод волоконно-оптичний датчик міжмодова інтерференція фазоакустична чутливість тиск |
| format |
Article |
| author |
Linchevskyi, I. V. Chursanova, M. V. |
| author_facet |
Linchevskyi, I. V. Chursanova, M. V. |
| author_sort |
Linchevskyi, I. V. |
| title |
A FIBER-OPTIC HYDROACOUSTIC PRESSURE SENSOR BASED ON INTERMODE INTERFERENCE |
| title_short |
A FIBER-OPTIC HYDROACOUSTIC PRESSURE SENSOR BASED ON INTERMODE INTERFERENCE |
| title_full |
A FIBER-OPTIC HYDROACOUSTIC PRESSURE SENSOR BASED ON INTERMODE INTERFERENCE |
| title_fullStr |
A FIBER-OPTIC HYDROACOUSTIC PRESSURE SENSOR BASED ON INTERMODE INTERFERENCE |
| title_full_unstemmed |
A FIBER-OPTIC HYDROACOUSTIC PRESSURE SENSOR BASED ON INTERMODE INTERFERENCE |
| title_sort |
fiber-optic hydroacoustic pressure sensor based on intermode interference |
| title_alt |
ВОЛОКОННО-ОПТИЧНИЙ ДАТЧИК ГІДРОАКУСТИЧНОГО ТИСКУ НА МІЖМОДОВІЙ ІНТЕРФЕРЕНЦІЇ |
| description |
Subject and Purpose. The use of the two-mode operation of an optical fi ber in fiber-optic sensors simplifies the interferometerdesign and enhances the reliability of sensing. Methods and Methodology. The mechanism behind the appearance of intermode phase shifts of the light modes Lp01 and Lp11 under various types of optical fiber deformation is examined. A mathematical model of a hydroacoustic sensor based on a two-mode optical fiber is proposed and experimentally validated. The intermode phase-acoustic sensitivity of the optical fiber to hydroacoustic pressure is evaluated for the Lp01 and Lp11 modes. A segment of a multimode optical fiber is fusion-spliced to the output of the two-mode fiber. This method creates conditions for the interference of the Lp01 and Lp11 modes and increases the modulation depth of the light flux at its output.Results. The heart of a hydroacoustic pressure-sensitive element in this research is an optical fiber with a core diameter of 18 μm and a numerical aperture of 0.0592. With the use of a 0.86 μm laser, propagation conditions are created for the two modes, Lp01 and Lp11 . The alteration of the mode content when a mode mixer is installed at the input of the optical fiber has been studied. For the fiber-optic sensor with a signal-to-noise ratio of 1:1 at the photodetector output and a frequency bandwidth of 100 Hz, the minimum detectable acoustic pressure inside the sensitive element is 55 Pa, and the intermode phase-acoustic sensitivity is 5.2*10-9 Pa.Conclusions. It has been shown that the two-mode operation of the optical fiber enables the development of interferometric fiber-optic sensors that are sensitive to mechanical deformations of the fiber. These sensors are characterized by a simpler design compared to traditional fiber-optic sensors based on Mach–Zehnder interferometers. It has been demonstratez that using a single-mode optical fiber with a reduced optical radiation wavelength ensures propagation conditions for the two lowest-order modes of the fiber.Keywords: optical fiber, fiber-optic sensor, intermode interference, phase-acoustic sensitivity, pressureManuscript submitted 25.07.2025Radio phys. radio astron. 2025, 30(4): 276-284REFERENCES1. Culshaw, B., Kersey, A., 2008. Fiber-optic sensing: A historical perspective. J. Lightwave Technol., 26(9), pp. 1064—1078. DOI: https://doi.org/10.1109/JLT.0082.9219152. Miliou, A., 2021. In-fiber interferometric-based sensors: overview and recent advances. Photonics, 8(7), 265. DOI: https://doi.org/10.3390/photonics80702653. Li, X., Chen, N., Zhou, X., Gong, P., Wang, S., Zhang, Y., Zhao, Y., 2021. A review of specialty fiber biosensors based on interferometer configuration. J. Biophotonics, 14(6), e202100068. DOI: https://doi.org/10.1002/jbio.2021000684. Wu, Q., Qu, Y., Liu, J., Yuan, J., Wan, S.-P., Wu, T., He, X.-D., Liu, B., Liu, D., Ma, Y., Semenova, Y., Wang, P., Xin, X., Farrell, G., 2021. Singlemode-Multimode-Singlemode fiber structures for sensing applications — A review. IEEE Sens. J., 21(11), pp. 12734—12751. DOI: https://doi.org/10.1109/JSEN.2020.30399125. Sadeque, M.S.B., Chowdhury, H.K., Rafique, M., Durmuş, M.A., Ahmed, M.K., Hasan, M.M., Erbaş, A., Sarpkaya, İ., Inci, F., Ordu, M., 2023. Hydrogel-integrated optical fiber sensors and their applications: A comprehensive review. J. Mater. Chem. C, 11, pp. 9383—9424. DOI: https://doi.org/10.1039/D3TC01206A6. Morshed, A.H.E., 2024. Multimode interference sensors for static and dynamic monitoring. In: S.W. Harun (ed.) Optical technologies for advancing communication, sensing, and computing systems. Intech Open. DOI: https://doi.org/10.5772/intechopen.10083407. Zhuang, F., Li, Y., Guo, T., Yang, Q., Luo, Y., Wang, J., Wang, Sh., 2025. Review on in-situ marine monitoring using physical and chemical optical fiber sensors. Photonic Sens., 15, P. 250230. DOI: https://doi.org/10.1007/s13320-024-0731-38. Vali, V., Shorthill, R.W., 1976. Fiber ring interferometer. Appl. Opt., 15(5), pp. 1099—1100. DOI: https://doi.org/10.1364/AO.15.0010999. Giallorenzi, T.G., Bucaro, J.A., Dandridge, A., Sigel, G.H., Cole, J.H., Rashleigh, S.C., Priest, R.G., 1982. Optical fiber sensor technology. IEEE Trans. Microw. Theory Tech., 30(4), pp. 472—511. DOI: https://doi.org/10.1109/JQE.1982.107156610. Engholm, M., Hammarling, K., Andersson, H., Sandberg, M., Nilsson, H.E., 2019. A bio-compatible fiber optic pH sensor based on a thin core interferometric technique. Photonics, 6(1), 11. DOI: https://doi.org/10.3390/photonics601001111. Liu, Z., Li, G., Zhang, A., Zhou, G., Huang, X., 2021. Ultra-sensitive optical fiber sensor based on intermodal interference and temperature calibration for trace detection of copper (II) ions. Opt. Express, 29(15), pp. 22992—23005. DOI: https://doi.org/10.1364/OE.43468712. Noman, A.A., Dash, J.N., Cheng, X., Tam, H.Y., Yu, C., 2022. Mach-Zehnder interferometer based fiber-optic nitrate sensor. Opt. Express, 30(21), pp. 38966—38974. DOI: https://doi.org/10.1364/OE.46894413. Yang, M., Zhu, Y., Ren, J., 2024. Hourglass-shaped fiber-optic Mach-Zehnder interferometer for pressure sensing. Opt. Fiber Technol., 84, 103746. DOI: https://doi.org/10.1016/j.yofte.2024.10374614. Wang, W., Pei, Y., Ye, L., Song, K., 2020. High-sensitivity cuboid interferometric fiber-optic hydrophone based on planar rectangular fi lm sensing. Sensors, 20(22), 6422. DOI: https://doi.org/10.3390/s2022642215. Dass, S., Jha, R., 2021. Underwater low acoustic frequency detection based on in-line Mach–Zehnder interferometer. J. Opt. Soc. Am. B: Opt. Phys., 38(2), pp. 570—575. DOI: https://doi.org/10.1364/JOSAB.41044016. May-Arrioja, D.A., Ruiz-Perez, V.I., Bustos-Terrones, Y., Basurto-Pensado, M.A., 2016. Fiber optic pressure sensor using a conformal polymer on multimode interference device. IEEE Sens. J., 16(7), pp. 1956—1961. DOI: https://doi.org/10.1109/JSEN.2015.251036017. Li, Y., Jiang, Y., Tang, N., Wang, G., Tao, J., Zhang, G., Ge, Q., Zhang, N., Wu, X., 2023. Fiber optic temperature and strain sensor using dual Mach–Zehnder interferometers. Appl. Opt., 62(8), pp. 1977—1983. DOI: https://doi.org/10.1364/AO.48041418. Yi, D., Liu, F., Geng, Y., Li, X., Hong, X., 2021. High-sensitivity and large-range fiber optic temperature sensor based on PDMS-coated Mach-Zehnder interferometer combined with FBG. Opt. Express, 29(12), pp. 18624—18633. DOI: https://doi.org/10.1364/OE.42838419. Bian, C., Cheng, Y., Zhu, W., Tong, R., Hu, M., Gang, T., 2020. A novel optical fiber Mach-Zehnder interferometer based on the calcium alginate hydrogel film for humidity sensing. IEEE Sens. J., 20(11), pp. 5759—5765. DOI: https://doi.org/10.1109/JSEN.2020.297329020. Bhardwaj, V., Singh, V.K., 2016. Fabrication and characterization of cascaded tapered Mach-Zehnder interferometer for refractive index sensing. Sens. Actuators A Phys., 244, pp. 30—34. DOI: https://doi.org/10.1016/j.sna.2016.04.00821. Unger, H.-G., 1977. Planar optical waveguides and fi bers. Oxford engineering science series. Vol. 5. New York : Clarendon Press. |
| publisher |
Видавничий дім «Академперіодика» |
| publishDate |
2025 |
| url |
http://rpra-journal.org.ua/index.php/ra/article/view/1485 |
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rpra-journalorgua-article-14852025-12-17T12:39:55Z A FIBER-OPTIC HYDROACOUSTIC PRESSURE SENSOR BASED ON INTERMODE INTERFERENCE ВОЛОКОННО-ОПТИЧНИЙ ДАТЧИК ГІДРОАКУСТИЧНОГО ТИСКУ НА МІЖМОДОВІЙ ІНТЕРФЕРЕНЦІЇ Linchevskyi, I. V. Chursanova, M. V. optical fiber; fiber-optic sensor; intermode interference; phase-acoustic sensitivity; pressure волоконний світловод; волоконно-оптичний датчик; міжмодова інтерференція; фазоакустична чутливість; тиск Subject and Purpose. The use of the two-mode operation of an optical fi ber in fiber-optic sensors simplifies the interferometerdesign and enhances the reliability of sensing. Methods and Methodology. The mechanism behind the appearance of intermode phase shifts of the light modes Lp01 and Lp11 under various types of optical fiber deformation is examined. A mathematical model of a hydroacoustic sensor based on a two-mode optical fiber is proposed and experimentally validated. The intermode phase-acoustic sensitivity of the optical fiber to hydroacoustic pressure is evaluated for the Lp01 and Lp11 modes. A segment of a multimode optical fiber is fusion-spliced to the output of the two-mode fiber. This method creates conditions for the interference of the Lp01 and Lp11 modes and increases the modulation depth of the light flux at its output.Results. The heart of a hydroacoustic pressure-sensitive element in this research is an optical fiber with a core diameter of 18 μm and a numerical aperture of 0.0592. With the use of a 0.86 μm laser, propagation conditions are created for the two modes, Lp01 and Lp11 . The alteration of the mode content when a mode mixer is installed at the input of the optical fiber has been studied. For the fiber-optic sensor with a signal-to-noise ratio of 1:1 at the photodetector output and a frequency bandwidth of 100 Hz, the minimum detectable acoustic pressure inside the sensitive element is 55 Pa, and the intermode phase-acoustic sensitivity is 5.2*10-9 Pa.Conclusions. It has been shown that the two-mode operation of the optical fiber enables the development of interferometric fiber-optic sensors that are sensitive to mechanical deformations of the fiber. These sensors are characterized by a simpler design compared to traditional fiber-optic sensors based on Mach–Zehnder interferometers. It has been demonstratez that using a single-mode optical fiber with a reduced optical radiation wavelength ensures propagation conditions for the two lowest-order modes of the fiber.Keywords: optical fiber, fiber-optic sensor, intermode interference, phase-acoustic sensitivity, pressureManuscript submitted 25.07.2025Radio phys. radio astron. 2025, 30(4): 276-284REFERENCES1. Culshaw, B., Kersey, A., 2008. Fiber-optic sensing: A historical perspective. J. Lightwave Technol., 26(9), pp. 1064—1078. DOI: https://doi.org/10.1109/JLT.0082.9219152. Miliou, A., 2021. In-fiber interferometric-based sensors: overview and recent advances. Photonics, 8(7), 265. DOI: https://doi.org/10.3390/photonics80702653. Li, X., Chen, N., Zhou, X., Gong, P., Wang, S., Zhang, Y., Zhao, Y., 2021. A review of specialty fiber biosensors based on interferometer configuration. J. Biophotonics, 14(6), e202100068. DOI: https://doi.org/10.1002/jbio.2021000684. Wu, Q., Qu, Y., Liu, J., Yuan, J., Wan, S.-P., Wu, T., He, X.-D., Liu, B., Liu, D., Ma, Y., Semenova, Y., Wang, P., Xin, X., Farrell, G., 2021. Singlemode-Multimode-Singlemode fiber structures for sensing applications — A review. IEEE Sens. J., 21(11), pp. 12734—12751. DOI: https://doi.org/10.1109/JSEN.2020.30399125. Sadeque, M.S.B., Chowdhury, H.K., Rafique, M., Durmuş, M.A., Ahmed, M.K., Hasan, M.M., Erbaş, A., Sarpkaya, İ., Inci, F., Ordu, M., 2023. Hydrogel-integrated optical fiber sensors and their applications: A comprehensive review. J. Mater. Chem. C, 11, pp. 9383—9424. DOI: https://doi.org/10.1039/D3TC01206A6. Morshed, A.H.E., 2024. Multimode interference sensors for static and dynamic monitoring. In: S.W. Harun (ed.) Optical technologies for advancing communication, sensing, and computing systems. Intech Open. DOI: https://doi.org/10.5772/intechopen.10083407. Zhuang, F., Li, Y., Guo, T., Yang, Q., Luo, Y., Wang, J., Wang, Sh., 2025. Review on in-situ marine monitoring using physical and chemical optical fiber sensors. Photonic Sens., 15, P. 250230. DOI: https://doi.org/10.1007/s13320-024-0731-38. Vali, V., Shorthill, R.W., 1976. Fiber ring interferometer. Appl. Opt., 15(5), pp. 1099—1100. DOI: https://doi.org/10.1364/AO.15.0010999. Giallorenzi, T.G., Bucaro, J.A., Dandridge, A., Sigel, G.H., Cole, J.H., Rashleigh, S.C., Priest, R.G., 1982. Optical fiber sensor technology. IEEE Trans. Microw. Theory Tech., 30(4), pp. 472—511. DOI: https://doi.org/10.1109/JQE.1982.107156610. Engholm, M., Hammarling, K., Andersson, H., Sandberg, M., Nilsson, H.E., 2019. A bio-compatible fiber optic pH sensor based on a thin core interferometric technique. Photonics, 6(1), 11. DOI: https://doi.org/10.3390/photonics601001111. Liu, Z., Li, G., Zhang, A., Zhou, G., Huang, X., 2021. Ultra-sensitive optical fiber sensor based on intermodal interference and temperature calibration for trace detection of copper (II) ions. Opt. Express, 29(15), pp. 22992—23005. DOI: https://doi.org/10.1364/OE.43468712. Noman, A.A., Dash, J.N., Cheng, X., Tam, H.Y., Yu, C., 2022. Mach-Zehnder interferometer based fiber-optic nitrate sensor. Opt. Express, 30(21), pp. 38966—38974. DOI: https://doi.org/10.1364/OE.46894413. Yang, M., Zhu, Y., Ren, J., 2024. Hourglass-shaped fiber-optic Mach-Zehnder interferometer for pressure sensing. Opt. Fiber Technol., 84, 103746. DOI: https://doi.org/10.1016/j.yofte.2024.10374614. Wang, W., Pei, Y., Ye, L., Song, K., 2020. High-sensitivity cuboid interferometric fiber-optic hydrophone based on planar rectangular fi lm sensing. Sensors, 20(22), 6422. DOI: https://doi.org/10.3390/s2022642215. Dass, S., Jha, R., 2021. Underwater low acoustic frequency detection based on in-line Mach–Zehnder interferometer. J. Opt. Soc. Am. B: Opt. Phys., 38(2), pp. 570—575. DOI: https://doi.org/10.1364/JOSAB.41044016. May-Arrioja, D.A., Ruiz-Perez, V.I., Bustos-Terrones, Y., Basurto-Pensado, M.A., 2016. Fiber optic pressure sensor using a conformal polymer on multimode interference device. IEEE Sens. J., 16(7), pp. 1956—1961. DOI: https://doi.org/10.1109/JSEN.2015.251036017. Li, Y., Jiang, Y., Tang, N., Wang, G., Tao, J., Zhang, G., Ge, Q., Zhang, N., Wu, X., 2023. Fiber optic temperature and strain sensor using dual Mach–Zehnder interferometers. Appl. Opt., 62(8), pp. 1977—1983. DOI: https://doi.org/10.1364/AO.48041418. Yi, D., Liu, F., Geng, Y., Li, X., Hong, X., 2021. High-sensitivity and large-range fiber optic temperature sensor based on PDMS-coated Mach-Zehnder interferometer combined with FBG. Opt. Express, 29(12), pp. 18624—18633. DOI: https://doi.org/10.1364/OE.42838419. Bian, C., Cheng, Y., Zhu, W., Tong, R., Hu, M., Gang, T., 2020. A novel optical fiber Mach-Zehnder interferometer based on the calcium alginate hydrogel film for humidity sensing. IEEE Sens. J., 20(11), pp. 5759—5765. DOI: https://doi.org/10.1109/JSEN.2020.297329020. Bhardwaj, V., Singh, V.K., 2016. Fabrication and characterization of cascaded tapered Mach-Zehnder interferometer for refractive index sensing. Sens. Actuators A Phys., 244, pp. 30—34. DOI: https://doi.org/10.1016/j.sna.2016.04.00821. Unger, H.-G., 1977. Planar optical waveguides and fi bers. Oxford engineering science series. Vol. 5. New York : Clarendon Press. Предмет і мета роботи. Використання двомодового режиму роботи волоконного світловоду у волоконно-оптичних датчиках дозволяє спростити конструкцію інтерферометра та збільшити надійність датчика.Методи та методологія. Розглянуто механізм появи міжмодового фазового зсуву для Lp01 і Lp11 мод при різних типах деформації волоконного світловоду. Наведено математичну модель гідроакустичного датчика на двомодовому світловоді та результати його експериментального дослідження. Розраховано міжмодову фазоакустичну чутливість волоконного світловоду до гідроакустичного тиску для мод Lp01 і Lp11. Використання відрізка багатомодового волоконного світловоду, привареного до виходу двомодового світловоду, забезпечує умови інтерференції Lp01 і Lp11 мод і підвищує глибину модуляції світлового потоку на його виході.Результати. Базовим волоконним світловодом для створення чутливого до гідроакустичного тиску елементу слугував світловод із радіусом осердя 9 мкм і числовою апертурою 0.0592. За допомогою використання лазера з довжиною хвилі 0.86 мкм отримано умови для поширення двох мод Lp01 і Lp11. Наведено результати зміни модового складу за наявності змішувача мод на вході світловоду. Для волоконно-оптичного датчика при співвідношенні сигнал/шум одиниця на виході фотоприймача та ширині смуги частот на рівні 100 Гц було зареєстровано мінімальний акустичний тиск всередині чутливого елементу 55 Па, а міжмодова фазоакустична чутливість склала 5.2*10-9 Па.Висновки. Показано, що використання двомодового режиму роботи волоконного світловоду дозволяє створювати інтерферометричні волоконно-оптичні датчики, чутливі до механічних деформацій світловоду. Для таких датчиків характерна простота конструкції в порівнянні з класичними волоконно-оптичними датчиками на базі інтерферометра Маха‒Цендера. Продемонстровано, що використання одномодового волоконного світловоду з пониженням довжини хвилі оптичного випромінювання дозволяє отримати умови для забезпечення поширення перших двох мод світловоду найнижчого порядку.Ключові слова: волоконний світловод, волоконно-оптичний датчик, міжмодова інтерференція, фазоакустична чутливість, тискСтаття надійшла до редакції 25.07.2025Radio phys. radio astron. 2025, 30(4): 276-284БІБЛІОГРАФІЧНИЙ СПИСОК1. Culshaw B., Kersey A. Fiber-optic sensing: A historical perspective. J. Lightwave Technol. 2008. Vol. 26, Iss. 9. P. 1064—1078. DOI: 10.1109/JLT.0082.9219152. Miliou A. In-fiber interferometric-based sensors: overview and recent advances. Photonics. 2021. Vol. 8, Iss. 7. 265. DOI: 10.3390/photonics80702653. Li X., Chen N., Zhou X., Gong P., Wang S., Zhang Y., Zhao Y. A review of specialty fi ber biosensors based on interferometer configuration. J. Biophotonics. 2021. Vol. 14, Iss. 6. e202100068. DOI: 10.1002/jbio.2021000684. Wu Q., Qu Y., Liu J., Yuan J., Wan S.-P., Wu T., He X.-D., Liu B., Liu D., Ma Y., Semenova Y., Wang P., Xin X., Farrell G. Singlemode-Multimode-Singlemode fiber structures for sensing applications — A review. IEEE Sens. J. 2021. Vol. 21, Iss. 11.P. 12734—12751. DOI: 10.1109/JSEN.2020.30399125. Sadeque M. S. B., Chowdhury H. K., Rafique M., Durmuş M. A., Ahmed M. K., Hasan M. M., Erbaş A., Sarpkaya İ., Inci F., Ordu M. Hydrogel-integrated optical fiber sensors and their applications: A comprehensive review. J. Mater. Chem. C. 2023. Vol. 11. P. 9383—9424. DOI: 10.1039/D3TC01206A6. Morshed A.H.E. Multimode interference sensors for static and dynamic monitoring. Optical technologies for advancing communication, sensing, and computing systems. S.W. Harun (ed.), Intech Open, 2024. DOI: 10.5772/intechopen.10083407. Zhuang F., Li Y., Guo T., Yang Q., Luo Y., Wang J., Wang Sh. Review on in-situ marine monitoring using physical and chemical optical fiber sensors. Photonic Sens. 2025. Vol. 15. P. 250230. DOI: https://doi.org/10.1007/s13320-024-0731-38. Vali V., Shorthill R.W. Fiber ring interferometer. Appl. Opt. 1976. Vol. 15, Iss. 5. P. 1099—1100. DOI: 10.1364/AO.15.0010999. Giallorenzi T.G., Bucaro J.A., Dandridge A., Sigel G.H., Cole J.H., Rashleigh S.C., Priest R.G. Optical fiber sensor technology. IEEE Trans. Microw. Theory Tech. 1982. Vol. 30, Iss. 4. P. 472—511. DOI: 10.1109/JQE.1982.107156610. Engholm M., Hammarling K., Andersson H., Sandberg M., Nilsson H.E. A bio-compatible fiber optic pH sensor based on a thin core interferometric technique. Photonics. 2019. Vol. 6, Iss. 1. 11. DOI: 10.3390/photonics601001111. Liu Z., Li G., Zhang A., Zhou G., Huang X. Ultra-sensitive optical fiber sensor based on intermodal interference and temperature calibration for trace detection of copper (II) ions. Opt. Express. 2021. Vol. 29, Iss. 15. P. 22992—23005. DOI:10.1364/OE.43468712. Noman A.A., Dash J.N., Cheng X., Tam H.Y., Yu C. 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Planar optical waveguides and fibers. Oxford engineering science series. Vol. 5. New York: Clarendon Press, 1977. 751p. Видавничий дім «Академперіодика» 2025-12-08 Article Article application/pdf http://rpra-journal.org.ua/index.php/ra/article/view/1485 10.15407/rpra30.04.276 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 30, No 4 (2025); 276 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 30, No 4 (2025); 276 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 30, No 4 (2025); 276 2415-7007 1027-9636 10.15407/rpra30.04 uk http://rpra-journal.org.ua/index.php/ra/article/view/1485/pdf Copyright (c) 2025 RADIO PHYSICS AND RADIO ASTRONOMY |