{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T12:56:06Z","timestamp":1774097766407,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2019,12,9]],"date-time":"2019-12-09T00:00:00Z","timestamp":1575849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["POCI-01-0145-FEDER-029724"],"award-info":[{"award-number":["POCI-01-0145-FEDER-029724"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/CTM\/50025\/2013"],"award-info":[{"award-number":["UID\/CTM\/50025\/2013"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BD\/129428\/2017"],"award-info":[{"award-number":["SFRH\/BD\/129428\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BPD\/124549\/2016"],"award-info":[{"award-number":["SFRH\/BPD\/124549\/2016"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001664","name":"Leibniz-Gemeinschaft","doi-asserted-by":"publisher","award":["Open Access Fund"],"award-info":[{"award-number":["Open Access Fund"]}],"id":[{"id":"10.13039\/501100001664","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The optical Vernier effect magnifies the sensing capabilities of an interferometer, allowing for unprecedented sensitivities and resolutions to be achieved. Just like a caliper uses two different scales to achieve higher resolution measurements, the optical Vernier effect is based on the overlap in the responses of two interferometers with slightly detuned interference signals. Here, we present a novel approach in detail, which introduces optical harmonics to the Vernier effect through Fabry\u2013Perot interferometers, where the two interferometers can have very different frequencies in the interferometric pattern. We demonstrate not only a considerable enhancement compared to current methods, but also better control of the sensitivity magnification factor, which scales up with the order of the harmonics, allowing us to surpass the limits of the conventional Vernier effect as used today. In addition, this novel concept opens also new ways of dimensioning the sensing structures, together with improved fabrication tolerances.<\/jats:p>","DOI":"10.3390\/s19245431","type":"journal-article","created":{"date-parts":[[2019,12,9]],"date-time":"2019-12-09T11:22:51Z","timestamp":1575890571000},"page":"5431","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":173,"title":["Optical Harmonic Vernier Effect: A New Tool for High Performance Interferometric Fiber Sensors"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3512-3687","authenticated-orcid":false,"given":"Andr\u00e9 D.","family":"Gomes","sequence":"first","affiliation":[{"name":"Leibniz Institute of Photonic Technology (Leibniz-IPHT), Albert-Einstein-Strasse 9, 07745 Jena, Germany"},{"name":"INESC TEC and Department of Physics and Astronomy, Faculty of Sciences, University of Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1170-7530","authenticated-orcid":false,"given":"Marta S.","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Leibniz Institute of Photonic Technology (Leibniz-IPHT), Albert-Einstein-Strasse 9, 07745 Jena, Germany"},{"name":"i3N and Department of Physics, University of Aveiro, Campus Universit\u00e1rio de Santiago, 3810-193 Aveiro, Portugal"}]},{"given":"J\u00f6rg","family":"Bierlich","sequence":"additional","affiliation":[{"name":"Leibniz Institute of Photonic Technology (Leibniz-IPHT), Albert-Einstein-Strasse 9, 07745 Jena, Germany"}]},{"given":"Jens","family":"Kobelke","sequence":"additional","affiliation":[{"name":"Leibniz Institute of Photonic Technology (Leibniz-IPHT), Albert-Einstein-Strasse 9, 07745 Jena, Germany"}]},{"given":"Manfred","family":"Rothhardt","sequence":"additional","affiliation":[{"name":"Leibniz Institute of Photonic Technology (Leibniz-IPHT), Albert-Einstein-Strasse 9, 07745 Jena, Germany"}]},{"given":"Hartmut","family":"Bartelt","sequence":"additional","affiliation":[{"name":"Leibniz Institute of Photonic Technology (Leibniz-IPHT), Albert-Einstein-Strasse 9, 07745 Jena, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7680-1056","authenticated-orcid":false,"given":"Orlando","family":"Fraz\u00e3o","sequence":"additional","affiliation":[{"name":"INESC TEC and Department of Physics and Astronomy, Faculty of Sciences, University of Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.sna.2019.03.011","article-title":"Ultrasensitive refractive index sensor based on parallel-connected dual Fabry-Perot interferometers with Vernier effect","volume":"290","author":"Yao","year":"2019","journal-title":"Sens. Actuators A Phys."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chen, P., Dai, Y., Zhang, D., Wen, X., and Yang, M. (2018). Cascaded-cavity Fabry-Perot interferometric gas pressure sensor based on Vernier effect. Sensors, 18.","DOI":"10.3390\/s18113677"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4891","DOI":"10.1364\/OL.40.004891","article-title":"Ultra-high sensitivity Fabry\u2013Perot interferometer gas refractive index fiber sensor based on photonic crystal fiber and Vernier effect","volume":"40","author":"Quan","year":"2015","journal-title":"Opt. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"17239","DOI":"10.1364\/OE.27.017239","article-title":"Ultrasensitive strain sensor based on Vernier-effect improved parallel structured fiber-optic Fabry-Perot interferometer","volume":"27","author":"Nan","year":"2019","journal-title":"Opt. Express"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gomes, A.D., Becker, M., Dellith, J., Zibaii, M.I., Latifi, H., Rothhardt, M., Bartelt, H., and Fraz\u00e3o, O. (2019). Multimode Fabry\u2013Perot Interferometer Probe Based on Vernier Effect for Enhanced Temperature Sensing. Sensors, 19.","DOI":"10.3390\/s19030453"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"19581","DOI":"10.1364\/OE.22.019581","article-title":"Cascaded fiber-optic Fabry-Perot interferometers with Vernier effect for highly sensitive measurement of axial strain and magnetic field","volume":"22","author":"Zhang","year":"2014","journal-title":"Opt. Express"},{"key":"ref_7","first-page":"1","article-title":"Simplified hollow-core fiber-based Fabry\u2013Perot interferometer with modified Vernier effect for highly sensitive high-temperature measurement","volume":"7","author":"Zhang","year":"2015","journal-title":"IEEE Photonics J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5351","DOI":"10.1109\/JLT.2016.2615054","article-title":"Highly sensitive airflow sensor based on Fabry\u2013Perot interferometer and Vernier effect","volume":"34","author":"Zhao","year":"2016","journal-title":"J. Light. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"33290","DOI":"10.1364\/OE.25.033290","article-title":"Sensitivity-enhanced temperature sensor by hybrid cascaded configuration of a Sagnac loop and a F-P cavity","volume":"25","author":"Yang","year":"2017","journal-title":"Opt. Express"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JPHOT.2018.2883994","article-title":"Ultrasensitive temperature sensor with cascaded fiber optic Fabry\u2013Perot interferometers based on Vernier effect","volume":"10","author":"Zhang","year":"2018","journal-title":"IEEE Photonics J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5043","DOI":"10.1364\/AO.57.005043","article-title":"Cylinder-type fiber-optic Vernier probe based on cascaded Fabry\u2013Perot interferometers with a controlled FSR ratio","volume":"57","author":"Kong","year":"2018","journal-title":"Appl. Opt."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.optcom.2017.12.012","article-title":"Optical cascaded Fabry\u2013Perot interferometer hydrogen sensor based on vernier effect","volume":"414","author":"Li","year":"2018","journal-title":"Opt. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"28763","DOI":"10.1364\/OE.26.028763","article-title":"Ultra-highly sensitive gas pressure sensor based on dual side-hole fiber interferometers with Vernier effect","volume":"26","author":"Lin","year":"2018","journal-title":"Opt. Express"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1109\/LPT.2019.2900388","article-title":"Highly sensitive Fabry\u2013Perot demodulation based on coarse wavelength sampling and Vernier effect","volume":"31","author":"Wu","year":"2019","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.sna.2018.11.042","article-title":"Relative humidity sensor based on Vernier effect with GQDs-PVA un-fully filled in hollow core fiber","volume":"285","author":"Zhao","year":"2019","journal-title":"Sens. Actuators A Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"105591","DOI":"10.1016\/j.optlastec.2019.105591","article-title":"High-sensitivity strain sensor implemented by hybrid cascaded interferometers and the Vernier-effect","volume":"119","author":"Liu","year":"2019","journal-title":"Opt. Laser Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2148","DOI":"10.1109\/JSEN.2018.2884889","article-title":"Highly sensitive vector curvature sensor based on two juxtaposed fiber Michelson interferometers with Vernier-like effect","volume":"19","author":"Zhang","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9556","DOI":"10.1038\/s41598-019-45909-2","article-title":"Optical fibre Fabry-P\u00e9rot interferometer based on inline microcavities for salinity and temperature sensing","volume":"9","author":"Flores","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4858","DOI":"10.1364\/AO.58.004858","article-title":"Highly sensitive PDMS-filled Fabry\u2013Perot interferometer temperature sensor based on the Vernier effect","volume":"58","author":"Hou","year":"2019","journal-title":"Appl. Opt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4935","DOI":"10.1109\/JLT.2019.2926066","article-title":"Ultra-sensitive strain sensor based on femtosecond laser inscribed in-fiber reflection mirrors and vernier effect","volume":"37","author":"Deng","year":"2019","journal-title":"J. Light. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6204","DOI":"10.1364\/AO.58.006204","article-title":"Vernier effect of two cascaded in-fiber Mach-Zehnder interferometers based on a spherical-shaped structure","volume":"58","author":"Xie","year":"2019","journal-title":"Appl. Opt."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2587","DOI":"10.1364\/JOSAB.36.002587","article-title":"Digital sensor based on multicavity fiber interferometers","volume":"36","author":"Ullah","year":"2019","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"080601","DOI":"10.3788\/COL201917.080601","article-title":"Vernier effect of fiber interferometer based on cascaded PANDA polarization maintaining fiber","volume":"17","author":"Liu","year":"2019","journal-title":"Chinese Opt. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4833","DOI":"10.1364\/OL.44.004833","article-title":"Highly sensitive fiber optic temperature and strain sensor based on an intrinsic Fabry\u2013Perot interferometer fabricated by a femtosecond laser","volume":"44","author":"Antunes","year":"2019","journal-title":"Opt. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Hu, J., Shao, L., Lang, T., Gu, G., Zhang, X., Liu, Y., Song, X., Song, Z., Feng, J., and Buczynski, R. (2019). Dual Mach-Zehnder interferometer based on side-hole fiber for high-sensitivity refractive index sensing. IEEE Photonics J., 1.","DOI":"10.1109\/JPHOT.2019.2948087"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Su, H., Zhang, Y., Zhao, Y., Ma, K., Qi, K., Guo, Y., and Zhu, F. (2019). Parallel double-FPIs temperature sensor based on suspended-core microstructured optical fiber. IEEE Photonics Technol. Lett., 1.","DOI":"10.1109\/LPT.2019.2944143"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Tian, J., Li, Z., Sun, Y., and Yao, Y. (2019). High-sensitivity fiber-optic strain sensor based on the Vernier effect and separated Fabry\u2014Perot interferometers. J. Light. Technol., 1.","DOI":"10.1109\/JLT.2019.2936174"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"120297","DOI":"10.1109\/ACCESS.2019.2933561","article-title":"A transverse load sensor with ultra-sensitivity employing Vernier-effect improved parallel-structured fiber-optic Fabry-Perot interferometer","volume":"7","author":"Wu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"105679","DOI":"10.1016\/j.optlastec.2019.105679","article-title":"Bending sensor with parallel fiber Michelson interferometers based on Vernier-like effect","volume":"120","author":"Zhang","year":"2019","journal-title":"Opt. Laser Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.optlastec.2019.04.043","article-title":"Demodulation method of Fabry-Perot sensor by cascading a traditional Mach-Zehnder interferometer","volume":"118","author":"Ying","year":"2019","journal-title":"Opt. Laser Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"163181","DOI":"10.1016\/j.ijleo.2019.163181","article-title":"High-sensitive all-fiber Fabry-Perot interferometer gas refractive index sensor based on lateral offset splicing and Vernier effect","volume":"196","author":"Yang","year":"2019","journal-title":"Optik (Stuttg)."},{"key":"ref_32","unstructured":"Born, M., and Wolf, E. (1999). Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Cambridge University Press."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/24\/5431\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:40:50Z","timestamp":1760190050000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/24\/5431"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,9]]},"references-count":32,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["s19245431"],"URL":"https:\/\/doi.org\/10.3390\/s19245431","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,9]]}}}