Metamaterial eigenmodes beyond homogenization
Metamaterial homogenization theories usually start with crude approximations that are valid in certain limits in zero order, such as small frequencies, wave vectors and material fill fractions. In some cases they remain surprisingly robust exceeding their initial assumptions, such as the well-establ...
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Veröffentlicht in: | Optical materials express 2022-07, Vol.12 (7), p.2747 |
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creator | Günzler, Antonio Schumacher, Cedric Steiner, Ullrich Saba, Matthias |
description | Metamaterial homogenization theories usually start with crude
approximations that are valid in certain limits in zero order, such as
small frequencies, wave vectors and material fill fractions. In some
cases they remain surprisingly robust exceeding their initial
assumptions, such as the well-established Maxwell-Garnett theory for
elliptical inclusions that can produce reliable results for fill
fractions far above its theoretical limitations. We here present a
rigorous solution of Maxwell’s equations in binary periodic
materials employing a combined Greens-Galerkin procedure to obtain a
low-dimensional eigenproblem for the evanescent Floquet eigenmodes of
the material. In its general form, our method provides an accurate
solution of the multi-valued complex Floquet bandstructure, which
currently cannot be obtained with established solvers. It is thus
shown to be valid in regimes where homogenization theories naturally
break down. For small frequencies and wave numbers in lowest order,
our method simplifies to the Maxwell-Garnett result for 2D cylinder
and 3D sphere packings. It therefore provides the missing explanation
why Maxwell-Garnett works well up to extremely high fill fractions of
approximately 50% depending on the constituent materials,
provided the inclusions are arranged on an isotropic lattice. |
doi_str_mv | 10.1364/OME.457134 |
format | Article |
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approximations that are valid in certain limits in zero order, such as
small frequencies, wave vectors and material fill fractions. In some
cases they remain surprisingly robust exceeding their initial
assumptions, such as the well-established Maxwell-Garnett theory for
elliptical inclusions that can produce reliable results for fill
fractions far above its theoretical limitations. We here present a
rigorous solution of Maxwell’s equations in binary periodic
materials employing a combined Greens-Galerkin procedure to obtain a
low-dimensional eigenproblem for the evanescent Floquet eigenmodes of
the material. In its general form, our method provides an accurate
solution of the multi-valued complex Floquet bandstructure, which
currently cannot be obtained with established solvers. It is thus
shown to be valid in regimes where homogenization theories naturally
break down. For small frequencies and wave numbers in lowest order,
our method simplifies to the Maxwell-Garnett result for 2D cylinder
and 3D sphere packings. It therefore provides the missing explanation
why Maxwell-Garnett works well up to extremely high fill fractions of
approximately 50% depending on the constituent materials,
provided the inclusions are arranged on an isotropic lattice.</description><identifier>ISSN: 2159-3930</identifier><identifier>EISSN: 2159-3930</identifier><identifier>DOI: 10.1364/OME.457134</identifier><language>eng</language><publisher>Washington: Optical Society of America</publisher><subject>Homogenization ; Inclusions ; Maxwell's equations ; Metamaterials</subject><ispartof>Optical materials express, 2022-07, Vol.12 (7), p.2747</ispartof><rights>Copyright Optical Society of America Jul 1, 2022</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c295t-143e699891dbaaa25175e1571cb222a20d4428ec72d119e716b5911d21f5b41d3</citedby><cites>FETCH-LOGICAL-c295t-143e699891dbaaa25175e1571cb222a20d4428ec72d119e716b5911d21f5b41d3</cites><orcidid>0000-0001-5281-4506</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,860,27903,27904</link.rule.ids></links><search><creatorcontrib>Günzler, Antonio</creatorcontrib><creatorcontrib>Schumacher, Cedric</creatorcontrib><creatorcontrib>Steiner, Ullrich</creatorcontrib><creatorcontrib>Saba, Matthias</creatorcontrib><title>Metamaterial eigenmodes beyond homogenization</title><title>Optical materials express</title><description>Metamaterial homogenization theories usually start with crude
approximations that are valid in certain limits in zero order, such as
small frequencies, wave vectors and material fill fractions. In some
cases they remain surprisingly robust exceeding their initial
assumptions, such as the well-established Maxwell-Garnett theory for
elliptical inclusions that can produce reliable results for fill
fractions far above its theoretical limitations. We here present a
rigorous solution of Maxwell’s equations in binary periodic
materials employing a combined Greens-Galerkin procedure to obtain a
low-dimensional eigenproblem for the evanescent Floquet eigenmodes of
the material. In its general form, our method provides an accurate
solution of the multi-valued complex Floquet bandstructure, which
currently cannot be obtained with established solvers. It is thus
shown to be valid in regimes where homogenization theories naturally
break down. For small frequencies and wave numbers in lowest order,
our method simplifies to the Maxwell-Garnett result for 2D cylinder
and 3D sphere packings. It therefore provides the missing explanation
why Maxwell-Garnett works well up to extremely high fill fractions of
approximately 50% depending on the constituent materials,
provided the inclusions are arranged on an isotropic lattice.</description><subject>Homogenization</subject><subject>Inclusions</subject><subject>Maxwell's equations</subject><subject>Metamaterials</subject><issn>2159-3930</issn><issn>2159-3930</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNpNkM1Lw0AQxRdRsNRe_AsC3oTUndmPZI9S6ge09KLnZZOdaEqTrbvpof71RuLBd5nH4zEz_Bi7Bb4EoeXDbrteSlWAkBdshqBMLozgl__8NVuktOejlMYSccbyLQ2ucwPF1h0yaj-o74KnlFV0Dr3PPkMXxqz9dkMb-ht21bhDosXfnLP3p_Xb6iXf7J5fV4-bvEajhhykIG1MacBXzjlUUCiC8bO6QkSH3EuJJdUFegBDBehKGQCP0KhKghdzdjftPcbwdaI02H04xX48aVGXUsuSazW27qdWHUNKkRp7jG3n4tkCt79E7EjETkTED3ECUQ8</recordid><startdate>20220701</startdate><enddate>20220701</enddate><creator>Günzler, Antonio</creator><creator>Schumacher, Cedric</creator><creator>Steiner, Ullrich</creator><creator>Saba, Matthias</creator><general>Optical Society of America</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0001-5281-4506</orcidid></search><sort><creationdate>20220701</creationdate><title>Metamaterial eigenmodes beyond homogenization</title><author>Günzler, Antonio ; Schumacher, Cedric ; Steiner, Ullrich ; Saba, Matthias</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c295t-143e699891dbaaa25175e1571cb222a20d4428ec72d119e716b5911d21f5b41d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Homogenization</topic><topic>Inclusions</topic><topic>Maxwell's equations</topic><topic>Metamaterials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Günzler, Antonio</creatorcontrib><creatorcontrib>Schumacher, Cedric</creatorcontrib><creatorcontrib>Steiner, Ullrich</creatorcontrib><creatorcontrib>Saba, Matthias</creatorcontrib><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Optical materials express</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Günzler, Antonio</au><au>Schumacher, Cedric</au><au>Steiner, Ullrich</au><au>Saba, Matthias</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Metamaterial eigenmodes beyond homogenization</atitle><jtitle>Optical materials express</jtitle><date>2022-07-01</date><risdate>2022</risdate><volume>12</volume><issue>7</issue><spage>2747</spage><pages>2747-</pages><issn>2159-3930</issn><eissn>2159-3930</eissn><abstract>Metamaterial homogenization theories usually start with crude
approximations that are valid in certain limits in zero order, such as
small frequencies, wave vectors and material fill fractions. In some
cases they remain surprisingly robust exceeding their initial
assumptions, such as the well-established Maxwell-Garnett theory for
elliptical inclusions that can produce reliable results for fill
fractions far above its theoretical limitations. We here present a
rigorous solution of Maxwell’s equations in binary periodic
materials employing a combined Greens-Galerkin procedure to obtain a
low-dimensional eigenproblem for the evanescent Floquet eigenmodes of
the material. In its general form, our method provides an accurate
solution of the multi-valued complex Floquet bandstructure, which
currently cannot be obtained with established solvers. It is thus
shown to be valid in regimes where homogenization theories naturally
break down. For small frequencies and wave numbers in lowest order,
our method simplifies to the Maxwell-Garnett result for 2D cylinder
and 3D sphere packings. It therefore provides the missing explanation
why Maxwell-Garnett works well up to extremely high fill fractions of
approximately 50% depending on the constituent materials,
provided the inclusions are arranged on an isotropic lattice.</abstract><cop>Washington</cop><pub>Optical Society of America</pub><doi>10.1364/OME.457134</doi><orcidid>https://orcid.org/0000-0001-5281-4506</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Homogenization Inclusions Maxwell's equations Metamaterials |
title | Metamaterial eigenmodes beyond homogenization |
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