{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T23:55:09Z","timestamp":1768262109065,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2021,7,21]],"date-time":"2021-07-21T00:00:00Z","timestamp":1626825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Institute of Rangsit University","award":["21\/2563"],"award-info":[{"award-number":["21\/2563"]}]},{"DOI":"10.13039\/501100004192","name":"National Science and Technology Development Agency","doi-asserted-by":"publisher","award":["SCAC02561-7556-TH"],"award-info":[{"award-number":["SCAC02561-7556-TH"]}],"id":[{"id":"10.13039\/501100004192","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We have recently reported in our previous work that one-dimensional dielectric grating can provide an open structure for Fabry\u2013Perot mode excitation. The grating gaps allow the sample refractive index to fill up the grating spaces enabling the sample to perturb the Fabry\u2013Perot mode resonant condition. Thus, the grating structure can be utilized as a refractive index sensor and provides convenient sample access from the open end of the grating with an enhanced figure of merit compared to the other thin-film technologies. Here, we demonstrate that 2D grating structures, such as rectangular pillars and circular pillars, can further enhance refractive index sensing performance. The refractive index theory for rectangular pillars and circular pillars are proposed and validated with rigorous coupled wave theory. An effective refractive index theory is proposed to simplify the 2D grating computation and accurately predict the Fabry\u2013Perot mode positions. The 2D gratings have more grating space leading to a higher resonant condition perturbation and sensitivity. They also provide narrower Fabry\u2013Perot mode reflectance dips leading to a 4.5 times figure of merit enhancement than the Fabry\u2013Perot modes excited in the 1D grating. The performance comparison for thin-film technologies for refractive index sensing is also presented and discussed.<\/jats:p>","DOI":"10.3390\/s21154958","type":"journal-article","created":{"date-parts":[[2021,7,22]],"date-time":"2021-07-22T22:37:14Z","timestamp":1626993434000},"page":"4958","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fabry\u2013Perot Resonance in 2D Dielectric Grating for Figure of Merit Enhancement in Refractive Index Sensing"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9105-8627","authenticated-orcid":false,"given":"Suejit","family":"Pechprasarn","sequence":"first","affiliation":[{"name":"College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1459-8133","authenticated-orcid":false,"given":"Suvicha","family":"Sasivimolkul","sequence":"additional","affiliation":[{"name":"College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8195-1841","authenticated-orcid":false,"given":"Phitsini","family":"Suvarnaphaet","sequence":"additional","affiliation":[{"name":"College of Biomedical Engineering, Rangsit University, Pathum Thani 12000, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Pongruengkiat, W., and Pechprasarn, S. (2017). Whispering-gallery mode resonators for detecting cancer. Sensors, 17.","DOI":"10.3390\/s17092095"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"19517","DOI":"10.1364\/OE.24.019517","article-title":"Grating-coupled Otto configuration for hybridized surface phonon polariton excitation for local refractive index sensitivity enhancement","volume":"24","author":"Pechprasarn","year":"2016","journal-title":"Opt. Express"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"785","DOI":"10.3390\/s110100785","article-title":"Optical microspherical resonators for biomedical sensing","volume":"11","author":"Soria","year":"2011","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1109\/JSTQE.2016.2596259","article-title":"Dispersion enhanced critically coupled ring resonator for wide range refractive index sensing","volume":"23","author":"Chandran","year":"2016","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5797","DOI":"10.1364\/OL.43.005797","article-title":"Optical detection of ultrasound by lateral shearing interference of a transparent PDMS thin film","volume":"43","author":"Learkthanakhachon","year":"2018","journal-title":"Opt. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Sukkasem, C., Sasivimolkul, S., Suvarnaphaet, P., and Pechprasarn, S. (2021). Analysis of Embedded Optical Interferometry in Transparent Elastic Grating for Optical Detection of Ultrasonic Waves. Sensors, 21.","DOI":"10.3390\/s21082787"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Pechprasarn, S., Sukkasem, C., and Suvarnaphaet, P. (2021). Analysis of Dielectric Waveguide Grating and Fabry\u2013Perot Modes in Elastic Grating in Optical Detection of Ultrasound. Sensors, 21.","DOI":"10.3390\/s21124081"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3453","DOI":"10.1364\/AO.57.003453","article-title":"Adjustable microscopic measurement of nanogap waveguide and plasmonic structures","volume":"57","author":"Shen","year":"2018","journal-title":"Appl. Opt."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1021\/ac2029024","article-title":"High-Q optical sensors for chemical and biological analysis","volume":"84","author":"Luchansky","year":"2012","journal-title":"Anal. Chem."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1512","DOI":"10.1016\/j.ijleo.2018.01.047","article-title":"Thin films based one-dimensional photonic crystal for refractive index sensing","volume":"158","author":"Peng","year":"2018","journal-title":"Optik"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1080\/09500340.2018.1427290","article-title":"Hybrid plasmonic waveguide-assisted Metal\u2013Insulator\u2013Metal ring resonator for refractive index sensing","volume":"65","author":"Butt","year":"2018","journal-title":"J. Mod. Opt."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2038","DOI":"10.1109\/3.641320","article-title":"Resonant grating waveguide structures","volume":"33","author":"Rosenblatt","year":"1997","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10628","DOI":"10.1109\/JSEN.2021.3063136","article-title":"Analysis of Open Grating-Based Fabry\u2013P\u00e9rot Resonance Structures With Potential Applications for Ultrasensitive Refractive Index Sensing","volume":"21","author":"Sasivimolkul","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Somekh, M.G., and Pechprasarn, S. (2017). Surface plasmon, surface wave, and enhanced evanescent wave microscopy. Handbook of Photonics for Biomedical Engineering, Springer.","DOI":"10.1007\/978-94-007-5052-4_20"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Suvarnaphaet, P., and Pechprasarn, S. (2018). Quantitative Cross-Platform Performance Comparison between Different Detection Mechanisms in Surface Plasmon Sensors for Voltage Sensing. Sensors, 18.","DOI":"10.3390\/s18093136"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"075401","DOI":"10.1088\/1361-6501\/ab7def","article-title":"Defocus leakage radiation microscopy for single shot surface plasmon measurement","volume":"31","author":"Chow","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"L23","DOI":"10.1088\/0963-9659\/7\/1\/004","article-title":"An integrated optical Bragg-reflector used as a chemo-optical sensor","volume":"7","author":"Veldhuis","year":"1998","journal-title":"Pure Appl. Opt. J. Eur. Opt. Soc. Part A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"151122","DOI":"10.1063\/1.1904716","article-title":"Highly sensitive fiber Bragg grating refractive index sensors","volume":"86","author":"Liang","year":"2005","journal-title":"Appl. Phys. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-018-26424-2","article-title":"Application of confocal surface wave microscope to self-calibrated attenuation coefficient measurement by Goos-H\u00e4nchen phase shift modulation","volume":"8","author":"Pechprasarn","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.sna.2009.01.026","article-title":"Process and material properties of polydimethylsiloxane (PDMS) for Optical MEMS","volume":"151","author":"Schneider","year":"2009","journal-title":"Sens. Actuators A Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4370","DOI":"10.1103\/PhysRevB.6.4370","article-title":"Optical constants of the noble metals","volume":"6","author":"Johnson","year":"1972","journal-title":"Phys. Rev. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6661","DOI":"10.1364\/AO.38.006661","article-title":"Optical and thermal characterization of albumin protein solders","volume":"38","author":"McNally","year":"1999","journal-title":"Appl. Opt."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"19185","DOI":"10.1364\/OE.25.019185","article-title":"Ultra-multiband absorption enhancement of graphene in a metal-dielectric-graphene sandwich structure covering terahertz to mid-infrared regime","volume":"25","author":"Wang","year":"2017","journal-title":"Opt. Express"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Buchmann, J., Zhang, E., Scharfenorth, C., Spannekrebs, B., Villringer, C., and Laufer, J. (2016, January 13\u201314). Evaluation of Fabry-Perot Polymer Film Sensors Made Using Hard Dielectric Mirror Deposition. Proceedings of the SPIE BiOS 2016, San Francisco, CA, USA.","DOI":"10.1117\/12.2234698"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1364\/AO.47.000561","article-title":"Backward-mode multiwavelength photoacoustic scanner using a planar Fabry-Perot polymer film ultrasound sensor for high-resolution three-dimensional imaging of biological tissues","volume":"47","author":"Zhang","year":"2008","journal-title":"Appl. Opt."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1364\/OL.35.000399","article-title":"Optical fiber refractometer based on cladding-mode Bragg grating","volume":"35","author":"Han","year":"2010","journal-title":"Opt. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1577","DOI":"10.1364\/JOSAA.15.001577","article-title":"Effective medium theory of two-dimensional subwavelength gratings in the non-quasi-static limit","volume":"15","author":"Kikuta","year":"1998","journal-title":"JOSA A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2063","DOI":"10.1080\/09500349608232871","article-title":"On the effective medium theory of subwavelength periodic structures","volume":"43","author":"Lalanne","year":"1996","journal-title":"J. Mod. Opt."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"585","DOI":"10.12693\/APhysPolA.116.585","article-title":"Dispersion properties of optical polymers","volume":"116","author":"Sultanova","year":"2009","journal-title":"Acta Phys. Pol. Ser. A Gen. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2758","DOI":"10.1364\/JOSAA.14.002758","article-title":"New formulation of the Fourier modal method for crossed surface-relief gratings","volume":"14","author":"Li","year":"1997","journal-title":"JOSA"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1744","DOI":"10.1364\/BOE.5.001744","article-title":"Detection limits of confocal surface plasmon microscopy","volume":"5","author":"Pechprasarn","year":"2014","journal-title":"Biomed. Opt. Express"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1109\/JQE.1973.1077767","article-title":"Coupled-mode theory for guided-wave optics","volume":"9","author":"Yariv","year":"1973","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1364\/JOSA.64.000274","article-title":"Metal-clad planar dielectric waveguide for integrated optics","volume":"64","author":"Polky","year":"1974","journal-title":"JOSA"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"15039","DOI":"10.1364\/OE.18.015039","article-title":"Theory of plasmonic Fabry-Perot nanolasers","volume":"18","author":"Chang","year":"2010","journal-title":"Opt. Express"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"11281","DOI":"10.1109\/JSEN.2019.2933320","article-title":"A General Description of the Performance of Surface Plasmon Sensors Using a Transmission Line Resonant Circuit Model","volume":"19","author":"Shen","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1980","DOI":"10.1364\/AO.23.001980","article-title":"Refractive properties of magnesium fluoride","volume":"23","author":"Dodge","year":"1984","journal-title":"Appl. Opt."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"9108","DOI":"10.1364\/AO.54.009108","article-title":"Universal dispersion model for characterization of optical thin films over a wide spectral range: Application to hafnia","volume":"54","author":"Franta","year":"2015","journal-title":"Appl. Opt."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/15\/4958\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:32:52Z","timestamp":1760164372000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/15\/4958"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,21]]},"references-count":37,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["s21154958"],"URL":"https:\/\/doi.org\/10.3390\/s21154958","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,21]]}}}