Plane-wave scattering by a photonic crystal slab: Multipole modal formulation and accuracy

Chen, PY; Byrne, MA; Asatryan, AA; Botten, LC; Dossou, KB; Tuniz, A; McPhedran, RC; De Sterke, CM; Poulton, CG; Steel, MJ

Plane-wave scattering by a photonic crystal slab: Multipole modal formulation and accuracy

Chen, PY Byrne, MA Asatryan, AA

Botten, LC

Dossou, KB

Tuniz, A McPhedran, RC De Sterke, CM Poulton, CG

Steel, MJ

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Publication Type:: Journal Article
Citation:: Waves in Random and Complex Media, 2012, 22 (4), pp. 531 - 570
Issue Date:: 2012-11-01

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Field	Value	Language
dc.contributor.author	Chen, PY	en_US
dc.contributor.author	Byrne, MA	en_US
dc.contributor.author	Asatryan, AA https://orcid.org/0000-0003-1372-0413	en_US
dc.contributor.author	Botten, LC https://orcid.org/0000-0001-6471-6954	en_US
dc.contributor.author	Dossou, KB https://orcid.org/0000-0002-2342-8945	en_US
dc.contributor.author	Tuniz, A	en_US
dc.contributor.author	McPhedran, RC	en_US
dc.contributor.author	De Sterke, CM	en_US
dc.contributor.author	Poulton, CG https://orcid.org/0000-0002-2707-3424	en_US
dc.contributor.author	Steel, MJ	en_US
dc.date.issued	2012-11-01	en_US
dc.identifier.citation	Waves in Random and Complex Media, 2012, 22 (4), pp. 531 - 570	en_US
dc.identifier.issn	1745-5030	en_US
dc.identifier.uri	http://hdl.handle.net/10453/22784
dc.description.abstract	The optical properties of photonic crystal slabs are often simulated with general three-dimensional methods such as finite-difference time-domain. Here we develop a multipole modal method, which is specialized to exploit two symmetries of the photonic crystal slab: the slab's vertically invariant nature allows the field to be expressed in Bloch modes, while the cylindrical inclusions allow the Bloch modes themselves to be expressed in the multipole basis. We find the multipole method to be fast and efficient in finding the Bloch modes, with convergence approaching the numerical accuracy possible. By matching the Bloch modes to plane waves at the top and bottom interfaces of the photonic crystal, the field scattered by the slab is calculated. Values of transmittance and reflectance accurate to 2-3 digits are easily and quickly achieved, whereas 5-6 digits are possible with greater numbers of modes and plane waves in field expansions. Higher accuracy is limited by Gibbs-related phenomena arising from the matching at the interface of necessarily discontinuous Bloch modes to necessarily continuous plane waves. We believe this limit may be present in all modal methods that use Bloch modes to expand the field within the photonic crystal. © 2012 Taylor and Francis Group, LLC.	en_US
dc.relation	http://purl.org/au-research/grants/arc/CE110001018
dc.relation.ispartof	Waves in Random and Complex Media	en_US
dc.relation.isbasedon	10.1080/17455030.2012.731090	en_US
dc.subject.classification	Optics	en_US
dc.title	Plane-wave scattering by a photonic crystal slab: Multipole modal formulation and accuracy	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	22	en_US
utslib.for	0203 Classical Physics	en_US
utslib.for	0205 Optical Physics	en_US
utslib.for	0299 Other Physical Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	22	en_US

Abstract:

The optical properties of photonic crystal slabs are often simulated with general three-dimensional methods such as finite-difference time-domain. Here we develop a multipole modal method, which is specialized to exploit two symmetries of the photonic crystal slab: the slab's vertically invariant nature allows the field to be expressed in Bloch modes, while the cylindrical inclusions allow the Bloch modes themselves to be expressed in the multipole basis. We find the multipole method to be fast and efficient in finding the Bloch modes, with convergence approaching the numerical accuracy possible. By matching the Bloch modes to plane waves at the top and bottom interfaces of the photonic crystal, the field scattered by the slab is calculated. Values of transmittance and reflectance accurate to 2-3 digits are easily and quickly achieved, whereas 5-6 digits are possible with greater numbers of modes and plane waves in field expansions. Higher accuracy is limited by Gibbs-related phenomena arising from the matching at the interface of necessarily discontinuous Bloch modes to necessarily continuous plane waves. We believe this limit may be present in all modal methods that use Bloch modes to expand the field within the photonic crystal. © 2012 Taylor and Francis Group, LLC.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/22784