@article{antonakakis_high-frequency_2013,
	title = {High-frequency homogenization of zero-frequency stop band photonic and phononic crystals},
	volume = {15},
	issn = {1367-2630},
	url = {http://stacks.iop.org/1367-2630/15/i=10/a=103014?key=crossref.18ce11708bc45131ce26b67afde4a2fe},
	doi = {10.1088/1367-2630/15/10/103014},
	abstract = {We present an accurate methodology for representing the physics of waves, in periodic structures,{\textbackslash}nthrough effective properties for a replacement bulk medium: this is valid even for media with{\textbackslash}nzero-frequency stop bands and where high-frequency phenomena dominate. Since the work of Lord{\textbackslash}nRayleigh in 1892, low-frequency (or quasi-static) behaviour has been neatly encapsulated in{\textbackslash}neffective anisotropic media; the various parameters come from asymptotic analysis relying upon the{\textbackslash}nratio of the array pitch to the wavelength being sufficiently small. However, such classical{\textbackslash}nhomogenization theories break down in the high-frequency or stop band regime whereby the wavelength{\textbackslash}nto pitch ratio is of order one. Furthermore, arrays of inclusions with Dirichlet data lead to a{\textbackslash}nzero-frequency stop band, with the salient consequence that classical homogenization is invalid.{\textbackslash}nHigher-frequency phenomena are of significant importance in photonics (transverse magnetic waves{\textbackslash}npropagating in infinite conducting parallel fibres), phononics (anti-plane shear waves propagating},
	number = {10},
	journal = {New Journal of Physics},
	author = {Antonakakis, T. and Craster, R. V. and Guenneau, S.},
	year = {2013},
	note = {arXiv: 1304.5782},
	pages = {103014},
}

{"_id":"SMGWj9MeXg6BeDQMj","bibbaseid":"antonakakis-craster-guenneau-highfrequencyhomogenizationofzerofrequencystopbandphotonicandphononiccrystals-2013","author_short":["Antonakakis, T.","Craster, R. V.","Guenneau, S."],"bibdata":{"bibtype":"article","type":"article","title":"High-frequency homogenization of zero-frequency stop band photonic and phononic crystals","volume":"15","issn":"1367-2630","url":"http://stacks.iop.org/1367-2630/15/i=10/a=103014?key=crossref.18ce11708bc45131ce26b67afde4a2fe","doi":"10.1088/1367-2630/15/10/103014","abstract":"We present an accurate methodology for representing the physics of waves, in periodic structures,\\nthrough effective properties for a replacement bulk medium: this is valid even for media with\\nzero-frequency stop bands and where high-frequency phenomena dominate. Since the work of Lord\\nRayleigh in 1892, low-frequency (or quasi-static) behaviour has been neatly encapsulated in\\neffective anisotropic media; the various parameters come from asymptotic analysis relying upon the\\nratio of the array pitch to the wavelength being sufficiently small. However, such classical\\nhomogenization theories break down in the high-frequency or stop band regime whereby the wavelength\\nto pitch ratio is of order one. Furthermore, arrays of inclusions with Dirichlet data lead to a\\nzero-frequency stop band, with the salient consequence that classical homogenization is invalid.\\nHigher-frequency phenomena are of significant importance in photonics (transverse magnetic waves\\npropagating in infinite conducting parallel fibres), phononics (anti-plane shear waves propagating","number":"10","journal":"New Journal of Physics","author":[{"propositions":[],"lastnames":["Antonakakis"],"firstnames":["T."],"suffixes":[]},{"propositions":[],"lastnames":["Craster"],"firstnames":["R.","V."],"suffixes":[]},{"propositions":[],"lastnames":["Guenneau"],"firstnames":["S."],"suffixes":[]}],"year":"2013","note":"arXiv: 1304.5782","pages":"103014","bibtex":"@article{antonakakis_high-frequency_2013,\n\ttitle = {High-frequency homogenization of zero-frequency stop band photonic and phononic crystals},\n\tvolume = {15},\n\tissn = {1367-2630},\n\turl = {http://stacks.iop.org/1367-2630/15/i=10/a=103014?key=crossref.18ce11708bc45131ce26b67afde4a2fe},\n\tdoi = {10.1088/1367-2630/15/10/103014},\n\tabstract = {We present an accurate methodology for representing the physics of waves, in periodic structures,{\\textbackslash}nthrough effective properties for a replacement bulk medium: this is valid even for media with{\\textbackslash}nzero-frequency stop bands and where high-frequency phenomena dominate. Since the work of Lord{\\textbackslash}nRayleigh in 1892, low-frequency (or quasi-static) behaviour has been neatly encapsulated in{\\textbackslash}neffective anisotropic media; the various parameters come from asymptotic analysis relying upon the{\\textbackslash}nratio of the array pitch to the wavelength being sufficiently small. However, such classical{\\textbackslash}nhomogenization theories break down in the high-frequency or stop band regime whereby the wavelength{\\textbackslash}nto pitch ratio is of order one. Furthermore, arrays of inclusions with Dirichlet data lead to a{\\textbackslash}nzero-frequency stop band, with the salient consequence that classical homogenization is invalid.{\\textbackslash}nHigher-frequency phenomena are of significant importance in photonics (transverse magnetic waves{\\textbackslash}npropagating in infinite conducting parallel fibres), phononics (anti-plane shear waves propagating},\n\tnumber = {10},\n\tjournal = {New Journal of Physics},\n\tauthor = {Antonakakis, T. and Craster, R. V. and Guenneau, S.},\n\tyear = {2013},\n\tnote = {arXiv: 1304.5782},\n\tpages = {103014},\n}\n\n","author_short":["Antonakakis, T.","Craster, R. V.","Guenneau, S."],"key":"antonakakis_high-frequency_2013","id":"antonakakis_high-frequency_2013","bibbaseid":"antonakakis-craster-guenneau-highfrequencyhomogenizationofzerofrequencystopbandphotonicandphononiccrystals-2013","role":"author","urls":{"Paper":"http://stacks.iop.org/1367-2630/15/i=10/a=103014?key=crossref.18ce11708bc45131ce26b67afde4a2fe"},"metadata":{"authorlinks":{}},"html":""},"bibtype":"article","biburl":"https://bibbase.org/zotero/davidrpoa","dataSources":["fvS7tt2THEKMbWDXR"],"keywords":[],"search_terms":["high","frequency","homogenization","zero","frequency","stop","band","photonic","phononic","crystals","antonakakis","craster","guenneau"],"title":"High-frequency homogenization of zero-frequency stop band photonic and phononic crystals","year":2013}