{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T20:35:42Z","timestamp":1767904542012,"version":"3.49.0"},"reference-count":14,"publisher":"AIP Publishing","issue":"4","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2006,2,15]]},"abstract":"<jats:p>A possible realization of isotropic artificial backward-wave materials is theoretically analyzed. An improved mixing rule for the effective permittivity of a composite material consisting of two sets of resonant dielectric spheres in a homogeneous background is presented. The equations are validated using the Mie theory and numerical simulations. The effect of a statistical distribution of sphere sizes on the increase of losses in the operating frequency band is discussed and some examples are shown.<\/jats:p>","DOI":"10.1063\/1.2173309","type":"journal-article","created":{"date-parts":[[2006,3,3]],"date-time":"2006-03-03T23:08:02Z","timestamp":1141427282000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":140,"title":["Modeling of isotropic backward-wave materials composed of resonant spheres"],"prefix":"10.1063","volume":"99","author":[{"given":"L.","family":"Jylh\u00e4","sequence":"first","affiliation":[{"name":"Helsinki University of Technology Electromagnetics Laboratory, , P.O. Box 3000, FI-02015 TKK, Finland"}]},{"given":"I.","family":"Kolmakov","sequence":"additional","affiliation":[{"name":"Helsinki University of Technology Radio Laboratory\u2215SMARAD, , FI-02015 TKK, Finland and Microwave Microelectronics Laboratory, , Prof. Popov 5, 197376 St. Petersburg, Russia"},{"name":"Electrotechnical University Radio Laboratory\u2215SMARAD, , FI-02015 TKK, Finland and Microwave Microelectronics Laboratory, , Prof. Popov 5, 197376 St. Petersburg, Russia"}]},{"given":"S.","family":"Maslovski","sequence":"additional","affiliation":[{"name":"Helsinki University of Technology Radio Laboratory\u2215SMARAD, , FI-02015 TKK, Finland"}]},{"given":"S.","family":"Tretyakov","sequence":"additional","affiliation":[{"name":"Helsinki University of Technology Radio Laboratory\u2215SMARAD, , FI-02015 TKK, Finland"}]}],"member":"317","published-online":{"date-parts":[[2006,2,24]]},"reference":[{"key":"2023063017155680900_c1","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1126\/science.1058847","volume":"292","year":"2001","journal-title":"Science"},{"key":"2023063017155680900_c2","doi-asserted-by":"publisher","first-page":"107401","DOI":"10.1103\/PhysRevLett.90.107401","volume":"90","year":"2003","journal-title":"Phys. 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