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Comput."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this article, we consider the band structure calculations of three-dimensional (3D) anisotropic photonic crystals (PhCs), especially those with nonorthogonal Bravais lattices. By directly working with the intrinsic coordinate system with [Formula: see text] as the basis and the covariant formulation of Maxwell\u2019s equations, the approach proposed here treats nonorthogonal and orthogonal Bravais lattices in an equal and unified manner and trivially incorporates the Bloch condition in the discretization. Yee\u2019s scheme does not require the coordinate system or mesh to be orthogonal, and assisted by linear interpolation, this scheme can handle anisotropic media, by which the frequency domain Maxwell\u2019s equations are discretized into a standard eigenvalue problem (SEP). With an alternative understanding of null-space deflation techniques, this SEP is transformed into several equivalent null-space free SEPs, whose smallest few positive eigenvalues and associated eigenvectors are calculated by an iterative eigensolver of the inner-outer type. Comparison with other methods for band structure calculations of 3D anisotropic and isotropic PhCs is made to demonstrate the effectiveness and strength of our present approach.<\/jats:p>","DOI":"10.1137\/22m1507863","type":"journal-article","created":{"date-parts":[[2023,7,7]],"date-time":"2023-07-07T06:25:01Z","timestamp":1688711101000},"page":"B440-B466","source":"Crossref","is-referenced-by-count":4,"title":["Band Structure Calculations of Three-Dimensional Anisotropic Photonic Crystals in the Oblique Coordinate System"],"prefix":"10.1137","volume":"45","author":[{"given":"Heng","family":"Tian","sequence":"first","affiliation":[{"name":"College of Chemistry and Environmental Engineering, Sichuan University of Science and Engineering, Zigong 643000, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7671-0063","authenticated-orcid":true,"given":"Tiexiang","family":"Li","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematics and Shing-Tung Yau Center, Southeast University, Nanjing 211189; Nanjing Center for Applied Mathematics, Nanjing 211135, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xing-Long","family":"Lyu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Shing-Tung Yau Center, Southeast University, Nanjing 211189; Nanjing Center for Applied Mathematics, Nanjing 211135, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wen-Wei","family":"Lin","sequence":"additional","affiliation":[{"name":"Nanjing Center for Applied Mathematics, Nanjing 211135, People\u2019s Republic of China; Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,7]]},"reference":[{"key":"ref1","unstructured":"COMSOL, COMSOL multiphysics\u00ae v 5.5.0, 2020, http:\/\/www.comsol.com."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5800"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"S.H. 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