Dispersion relation and band gaps of 3D photonic crystals made of spheres
In this paper, we introduce a dispersion equation for 3D photonic crystals made of parallel layers of non-overlapping spheres, valid when both wavelength and separation between layers are much larger than the distance between neighbouring spheres. This equation is based on the Korringa-Kohn-Rostoker...
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todo:paper_19378726_v19_n_p1_Guller2023-10-03T16:36:42Z Dispersion relation and band gaps of 3D photonic crystals made of spheres Güller, F. Inchaussandague, M.E. Depine, R.A. 3D photonic crystals Band gaps Constitutive parameters Dispersion equations Dispersion relations Homogeneous media Host mediums Korringa-kohn-rostoker Numerical code Spectral position Wave calculations Dispersion (waves) Energy gap Permittivity Photonic crystals Three dimensional Spheres In this paper, we introduce a dispersion equation for 3D photonic crystals made of parallel layers of non-overlapping spheres, valid when both wavelength and separation between layers are much larger than the distance between neighbouring spheres. This equation is based on the Korringa-Kohn-Rostoker (KKR) wave calculation method developed by Stefanou et al. and can be used to predict the spectral positions of bandgaps in structures made of dispersive spheres. Perfect agreement between the spectral positions of bandgaps predicted with our simplified equation and those obtained with the numerical code MULTEM2 was observed. We find that this simplified relation allows us to identify two types of bandgaps: those related to the constitutive parameters of the spheres and those related to the three dimensional periodicity (distance between layers). Bandgaps of the first type are independent of the frequency and the distance between layers, while those of the second type depend only on these two quantities. We then analyze the influence of the constitutive parameters of the spheres on the spectral position of bandgaps for spheres immersed in dielectric or magnetic homogeneous media. The number and positions of the bandgaps are affected by the permitivity (permeability) of the host medium if the spheres have dispersive permitivity (permeability). Fil:Inchaussandague, M.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Depine, R.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_19378726_v19_n_p1_Guller |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
3D photonic crystals Band gaps Constitutive parameters Dispersion equations Dispersion relations Homogeneous media Host mediums Korringa-kohn-rostoker Numerical code Spectral position Wave calculations Dispersion (waves) Energy gap Permittivity Photonic crystals Three dimensional Spheres |
spellingShingle |
3D photonic crystals Band gaps Constitutive parameters Dispersion equations Dispersion relations Homogeneous media Host mediums Korringa-kohn-rostoker Numerical code Spectral position Wave calculations Dispersion (waves) Energy gap Permittivity Photonic crystals Three dimensional Spheres Güller, F. Inchaussandague, M.E. Depine, R.A. Dispersion relation and band gaps of 3D photonic crystals made of spheres |
topic_facet |
3D photonic crystals Band gaps Constitutive parameters Dispersion equations Dispersion relations Homogeneous media Host mediums Korringa-kohn-rostoker Numerical code Spectral position Wave calculations Dispersion (waves) Energy gap Permittivity Photonic crystals Three dimensional Spheres |
description |
In this paper, we introduce a dispersion equation for 3D photonic crystals made of parallel layers of non-overlapping spheres, valid when both wavelength and separation between layers are much larger than the distance between neighbouring spheres. This equation is based on the Korringa-Kohn-Rostoker (KKR) wave calculation method developed by Stefanou et al. and can be used to predict the spectral positions of bandgaps in structures made of dispersive spheres. Perfect agreement between the spectral positions of bandgaps predicted with our simplified equation and those obtained with the numerical code MULTEM2 was observed. We find that this simplified relation allows us to identify two types of bandgaps: those related to the constitutive parameters of the spheres and those related to the three dimensional periodicity (distance between layers). Bandgaps of the first type are independent of the frequency and the distance between layers, while those of the second type depend only on these two quantities. We then analyze the influence of the constitutive parameters of the spheres on the spectral position of bandgaps for spheres immersed in dielectric or magnetic homogeneous media. The number and positions of the bandgaps are affected by the permitivity (permeability) of the host medium if the spheres have dispersive permitivity (permeability). |
format |
JOUR |
author |
Güller, F. Inchaussandague, M.E. Depine, R.A. |
author_facet |
Güller, F. Inchaussandague, M.E. Depine, R.A. |
author_sort |
Güller, F. |
title |
Dispersion relation and band gaps of 3D photonic crystals made of spheres |
title_short |
Dispersion relation and band gaps of 3D photonic crystals made of spheres |
title_full |
Dispersion relation and band gaps of 3D photonic crystals made of spheres |
title_fullStr |
Dispersion relation and band gaps of 3D photonic crystals made of spheres |
title_full_unstemmed |
Dispersion relation and band gaps of 3D photonic crystals made of spheres |
title_sort |
dispersion relation and band gaps of 3d photonic crystals made of spheres |
url |
http://hdl.handle.net/20.500.12110/paper_19378726_v19_n_p1_Guller |
work_keys_str_mv |
AT gullerf dispersionrelationandbandgapsof3dphotoniccrystalsmadeofspheres AT inchaussandagueme dispersionrelationandbandgapsof3dphotoniccrystalsmadeofspheres AT depinera dispersionrelationandbandgapsof3dphotoniccrystalsmadeofspheres |
_version_ |
1782028492433522688 |