{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T18:57:48Z","timestamp":1773946668554,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,6,26]],"date-time":"2018-06-26T00:00:00Z","timestamp":1529971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002851","name":"China Academy of Engineering Physics","doi-asserted-by":"publisher","award":["JCKY2016212A506-0502"],"award-info":[{"award-number":["JCKY2016212A506-0502"]}],"id":[{"id":"10.13039\/501100002851","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&amp;D Program of China","award":["2017YFB0503100"],"award-info":[{"award-number":["2017YFB0503100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Optical coupling between subwavelength grating pairs allows for the precise measurement of lateral or vertical displacement of grating elements and gives rise to different types of displacement and inertial sensors. In this paper, we demonstrate a design for a nano-optomechanical accelerometer based on a subwavelength grating pair that can be easily fabricated by a single Silicon-on-insulator (SOI) chip. The parameters of the subwavelength grating pair-based optical readout, including period, duty cycle, thickness of grating and metal film, and the distance of the air gap, were optimized by combining a genetic algorithm and rigorous coupled wavelength analysis (RCWA) to obtain the optimal sensitivity to the displacement of suspended grating element and the acceleration. A corresponding mechanical design was also completed to meet the highly sensitive acceleration measurement requirement while considering the mechanical cross-axis sensitivity, dynamic range, bandwidth, and fabrication feasibility. This device was verified by both RCWA and finite-different-time-domain methods, and a tolerance analysis was also completed to confirm that it is able to achieve the extremely high optical displacement sensitivity of 1.8%\/nm, acceleration-displacement sensitivity of 1.56 nm\/mg, and acceleration measurement sensitivity of more than 2.5%\/mg, which is almost one order of magnitude higher than any reported counterparts. This work enables a single SOI-based high performance accelerometer, and provides a theoretical basis and fabrication guides for the design.<\/jats:p>","DOI":"10.3390\/s18072036","type":"journal-article","created":{"date-parts":[[2018,6,26]],"date-time":"2018-06-26T10:40:50Z","timestamp":1530009650000},"page":"2036","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Single Chip-Based Nano-Optomechanical Accelerometer Based on Subwavelength Grating Pair and Rotated Serpentine Springs"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4195-7602","authenticated-orcid":false,"given":"Qianbo","family":"Lu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Jian","family":"Bai","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Kaiwei","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Peiwen","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Weidong","family":"Fang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China"}]},{"given":"Chen","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1038\/nphoton.2012.245","article-title":"A high-resolution microchip optomechanical accelerometer","volume":"6","author":"Krause","year":"2012","journal-title":"Nat. Photonics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.sna.2012.05.014","article-title":"Novel piezoresistive high-g accelerometer geometry with very high sensitivity-bandwidth product","volume":"182","author":"Kuells","year":"2012","journal-title":"Sens. Actuators A Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1109\/JMEMS.2014.2304840","article-title":"Design and experimental evaluation of a low-noise backplate for a grating-based optical interferometric sensor","volume":"23","author":"Kim","year":"2014","journal-title":"J. Microelectromech. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"065001","DOI":"10.1063\/1.4921903","article-title":"High resolution quartz flexure accelerometer based on laser self-mixing interferometry","volume":"86","author":"Wang","year":"2015","journal-title":"Rev. Sci. Instrum."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3316","DOI":"10.1063\/1.126637","article-title":"High-resolution micromachined interferometric accelerometer","volume":"76","author":"Cooper","year":"2000","journal-title":"Appl. Phys. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/JMEMS.2007.910243","article-title":"Micromachined accelerometers with optical interferometric read-out and integrated electrostatic actuation","volume":"17","author":"Hall","year":"2008","journal-title":"J. Microelectromech. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2618","DOI":"10.1088\/0960-1317\/16\/12\/015","article-title":"Design and characterization of a micromachined Fabry\u2013Perot vibration sensor for high-temperature applications","volume":"16","author":"Nieva","year":"2006","journal-title":"J. Micromech. Microeng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1464","DOI":"10.1109\/JMEMS.2012.2211577","article-title":"Design and demonstration of an in-plane silicon-on-insulator optical MEMS Fabry\u2013P\u00e9rot-based accelerometer integrated with channel waveguides","volume":"21","author":"Zandi","year":"2012","journal-title":"J. Microelectromech. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.sna.2008.03.017","article-title":"In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor","volume":"145\u2013146","author":"Krishnamoorthy","year":"2008","journal-title":"Sens. Actuators A Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1007\/s00340-011-4712-z","article-title":"Verification of evanescent coupling from subwavelength grating pairs","volume":"105","author":"Rogers","year":"2011","journal-title":"Appl. Phys. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1364\/OL.29.001182","article-title":"Experimental demonstration of a laterally deformable optical nanoelectromechanical system grating transducer","volume":"29","author":"Keeler","year":"2004","journal-title":"Opt. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1636","DOI":"10.1364\/OL.28.001636","article-title":"Laterally deformable nanomechanical zeroth-order gratings anomalous diffraction studied by rigorous coupled-wave analysis","volume":"28","author":"Carr","year":"2003","journal-title":"Opt. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1117\/12.532340","article-title":"Measurement of a laterally deformable optical MEMS grating transducer","volume":"Volume 5346","author":"Carr","year":"2004","journal-title":"MOEMS and Miniaturized Systems IV"},{"key":"ref_14","first-page":"306","article-title":"Laterally deformable optical NEMS grating transducers for inertial sensing applications","volume":"Volume 5592","author":"Keeler","year":"2004","journal-title":"Nanofabrication: Technologies, Devices and Applications"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1109\/LPT.2014.2312796","article-title":"Design of out-of-plane MOEMS accelerometer with subwavelength gratings","volume":"26","author":"Yao","year":"2014","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.optcom.2015.04.007","article-title":"Tolerance analysis and optimization of a lateral deformable NEMS zeroth-order gratings","volume":"355","author":"Wang","year":"2015","journal-title":"Opt. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1109\/LPT.2003.821258","article-title":"Ultrabroadband mirror using low-index cladded subwavelength grating","volume":"16","author":"Mateus","year":"2004","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1364\/OE.15.001222","article-title":"Nano electro-mechanical optoelectronic tunable VCSEL","volume":"15","author":"Huang","year":"2007","journal-title":"Opt. Express"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1038\/nphoton.2008.3","article-title":"A nanoelectromechanical tunable laser","volume":"2","author":"Huang","year":"2008","journal-title":"Nat. Photonics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1088\/0960-1317\/15\/4\/010","article-title":"Analysis, simulation and relative performances of two kinds of serpentine springs","volume":"15","author":"Barillaro","year":"2005","journal-title":"J. Micromech. Microeng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Gere, J.M. (1991). Mechanics of Materials, Chapman and Hall. [3rd ed.].","DOI":"10.1007\/978-1-4899-3124-5"},{"key":"ref_22","unstructured":"Mason, W.P. (1958). Physical Acoustics and the Properties of Solids, Van Nostrand."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1063\/1.1713863","article-title":"Young\u2019s modulus, shear modulus, and Poisson\u2019s ratio in silicon and germanium","volume":"36","author":"Wortman","year":"1965","journal-title":"J. Appl. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1107\/S1600577514004962","article-title":"Anisotropic elasticity of silicon and its application to the modelling of X-ray optics","volume":"21","author":"Zhang","year":"2014","journal-title":"J. Synchrotron Radiat."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9094","DOI":"10.1364\/OE.24.009094","article-title":"Minimizing cross-axis sensitivity in grating-based optomechanical accelerometers","volume":"24","author":"Lu","year":"2016","journal-title":"Opt. Express"},{"key":"ref_26","unstructured":"Rogers, A.A.A. (2011). Evanescent Wave Coupling Using Different Subwavelength Gratings for a MEMS Accelerometer. [Ph.D. Thesis, University of South Florida]."},{"key":"ref_27","first-page":"1","article-title":"Critical Review: Adhesion in surface micromechanical structures","volume":"15","author":"Maboudian","year":"1997","journal-title":"J. Vac. Sci. Technol. B Microelectron. Nanometer Struct."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/84.232594","article-title":"Mechanical stability and adhesion of microstructures","volume":"2","author":"Mastranelo","year":"1993","journal-title":"J. Microelectromech. Syst."},{"key":"ref_29","unstructured":"Alley, R.L., Cuan, G.J., Howe, R.T., and Komvopoulos, K. (1992, January 22\u201325). The effect of release-etch processing on surface microstructure stiction. Proceedings of the 1992 5th Technical Digest Solid-State Sensor and Actuator Workshop, Hilton Head Island, SC, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5840","DOI":"10.1063\/1.346957","article-title":"Micromechanical fracture strength of silicon","volume":"68","author":"Ericson","year":"1990","journal-title":"J. Appl. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1109\/JMEMS.2017.2693341","article-title":"Design, optimization, and realization of a high-performance MOEMS accelerometer from a double-device-layer SOI wafer","volume":"26","author":"Lu","year":"2017","journal-title":"J. Microelectromech. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/JMEMS.2002.1007396","article-title":"Sub-10 cm 3 Interferometric accelerometer with nano-g resolution","volume":"11","author":"Loh","year":"2002","journal-title":"J. Microelectromech. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/S0169-4332(00)00352-4","article-title":"Electron beam lithography: Resolution limits and applications","volume":"164","author":"Vieu","year":"2000","journal-title":"Appl. Surf. Sci."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/7\/2036\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:10:10Z","timestamp":1760195410000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/7\/2036"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,26]]},"references-count":33,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2018,7]]}},"alternative-id":["s18072036"],"URL":"https:\/\/doi.org\/10.3390\/s18072036","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,26]]}}}