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This work proposed a design method of two-dimensional subwavelength grating filter based on a series feedback neural network, which can realize forward simulation and backward design. It was programed in Python to study the filtering characteristics of two-dimensional subwavelength grating in the range of 0.4\u20130.7 \u00b5m. The shape, height, period, duty cycle, and waveguide layer height of two-dimensional subwavelength grating were taken into consideration. The dataset, containing 46,080 groups of data, was generated through numerical simulation of rigorous coupled-wave analysis (RCWA). The optimal network was five layers, 128 \u00d7 512 \u00d7 512 \u00d7 128 \u00d7 61 nodes, and 64 batch size. The loss function of the series feedback neural network is as low as 0.024. Meanwhile, it solves the problem of non-convergence of the network reverse design due to the non-uniqueness of data. The series feedback neural network can give the geometrical structure parameters of two-dimensional subwavelength grating within 1.12 s, and the correlation between the design results and the theoretical spectrum is greater than 0.65, which belongs to a strong correlation. This study provides a new method for the design of two-dimensional subwavelength grating, which is quicker and more accurate compared with the traditional method.<\/jats:p>","DOI":"10.3390\/s22207758","type":"journal-article","created":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T01:44:13Z","timestamp":1665711853000},"page":"7758","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Design Method of Two-Dimensional Subwavelength Grating Filter Based on Deep Learning Series Feedback Neural Network"],"prefix":"10.3390","volume":"22","author":[{"given":"Jun-Hua","family":"Guo","sequence":"first","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ying-Li","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuai-Shuai","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chang-Long","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7088-250X","authenticated-orcid":false,"given":"Hai-Feng","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1894","DOI":"10.1109\/TBME.2020.3029148","article-title":"Portable automatic microring resonator system using a subwavelength grating metamaterial waveguide for high-sensitivity real-time optical-biosensing applications","volume":"68","author":"Soni","year":"2020","journal-title":"IEEE Trans. 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