{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T07:40:08Z","timestamp":1696578008829},"reference-count":13,"publisher":"American Geophysical Union (AGU)","issue":"8","license":[{"start":{"date-parts":[[2016,8,8]],"date-time":"2016-08-08T00:00:00Z","timestamp":1470614400000},"content-version":"vor","delay-in-days":7,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA 9550-16-C-0017"],"award-info":[{"award-number":["FA 9550-16-C-0017"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Radio Science"],"published-print":{"date-parts":[[2016,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Electric quadrupolar continua satisfying a physically reasonable constitutive relation supports both an evanescent and a propagating eigenmode. Thus, three interface boundary conditions, two plus an \u201cadditional boundary condition\u201d (ABC), are required to obtain a unique solution to a plane wave incident from free space upon an electric quadrupolar half\u2010space. By generalizing the constitutive relation to hold within the transition layer between the free space and the quadrupolar continuum, we derive these three boundary conditions directly from Maxwell's differential equations. The three boundary conditions are used to determine the unique solution to the boundary value problem of an electric quadrupolar slab. Numerical computations show that for long wavelengths, two previous boundary conditions, derived under the assumption that the electric quadrupolarization contains negligible effective delta functions in the transition layer, produce an accurate solution by neglecting the evanescent eigenmode, that is, by assuming it decays within the transition layer. It appears that the general method used to derive the electric quadrupolar ABC can be applied to obtain the boundary conditions for any other realizable constitutive relation in a Maxwellian multipole continuum.<\/jats:p>","DOI":"10.1002\/2016rs006066","type":"journal-article","created":{"date-parts":[[2016,7,26]],"date-time":"2016-07-26T09:56:47Z","timestamp":1469527007000},"page":"1312-1321","source":"Crossref","is-referenced-by-count":5,"title":["Additional boundary condition for electric quadrupolar continua derived from Maxwell's differential equations"],"prefix":"10.1029","volume":"51","author":[{"given":"A. D.","family":"Yaghjian","sequence":"first","affiliation":[{"name":"Electromagnetics Research Consultant  Concord Massachusetts USA"}]},{"given":"M. G.","family":"Silveirinha","sequence":"additional","affiliation":[{"name":"Instituto Superior T\u00e9cnico \u2010 University of Lisbon  Lisbon Portugal"},{"name":"Instituto de Telecomunicac\u00f5es  Lisbon Portugal"}]}],"member":"13","published-online":{"date-parts":[[2016,8,8]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.2007.908368"},{"key":"e_1_2_6_3_1","article-title":"Guided propagation along quadrupolar chains of plasmonic nanoparticles","volume":"79","author":"Al\u00f9 A.","year":"2014","journal-title":"Phys. Rev. B"},{"key":"e_1_2_6_4_1","doi-asserted-by":"crossref","unstructured":"Cho D. J. F.Wang X.Zhang andY. R.Shen(2008) Contribution of electric quadrupole resonance in optical metamaterials 78 121101.","DOI":"10.1103\/PhysRevB.78.121101"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/adma.201205076"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.124597"},{"key":"e_1_2_6_7_1","volume-title":"Multipole Theory in Electromagnetism","author":"Raab R. E.","year":"2005"},{"key":"e_1_2_6_8_1","article-title":"Electromagnetic boundary conditions in multipole theory","volume":"54","author":"Raab R. E.","year":"2013","journal-title":"Math. Phys."},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.2528\/PIERB09021107"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/16\/8\/083042"},{"key":"e_1_2_6_11_1","article-title":"Local constitutive parameters of metamaterials from an effective\u2010medium perspective","author":"Simovski C. 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