Two-dimensional Green&#x2019;s tensor for gyrotropic clusters composed of circular cylinders

Ara A. Asatryan; Lindsay C. Botten; Kejie Fang; Shanhui Fan; Ross C. McPhedran

doi:10.1364/JOSAA.31.002294

Journal of the Optical Society of America A
Vol. 31,
Issue 10,
pp. 2294-2303
(2014)
•https://doi.org/10.1364/JOSAA.31.002294

Two-dimensional Green’s tensor for gyrotropic clusters composed of circular cylinders

Ara A. Asatryan, Lindsay C. Botten, Kejie Fang, Shanhui Fan, and Ross C. McPhedran

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Ara A. Asatryan, Lindsay C. Botten, Kejie Fang, Shanhui Fan, and Ross C. McPhedran, "Two-dimensional Green’s tensor for gyrotropic clusters composed of circular cylinders," J. Opt. Soc. Am. A 31, 2294-2303 (2014)

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Abstract

The construction of Green’s tensor for two-dimensional gyrotropic photonic clusters composed of cylinders with circular cross sections using the semi-analytic multipole method is presented. The high efficiency and accuracy of the method is demonstrated. The developed method is applied to gyrotropic clusters that support topological chiral Hall edge states. The remarkable tolerance of chiral Hall edge modes toward substantial cluster separation is revealed. The transformation of chiral Hall edge states as the cluster separation increases is also presented. The excitation of chiral Hall edge modes for different source orientations is considered. Both gyroelectric and gyromagnetic (ferrite) clusters are treated.

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$N_{p} = 2 M + 1$	$E_{z}$	$H_{x}$	$H_{y}$
3	$- 0.0033568320 + i 0.0013388036$	$- 0.0006632724 - i 0.0060792630$	$- 0.0009175906 + i 0.0061410684$
5	$- 0.0032723380 + i 0.0013442870$	$- 0.0007338791 - i 0.0060234433$	$0.0060679854 - i 0.0009883445$
7	$- 0.0032779380 + i 0.0013440207$	$- 0.0007261071 - i 0.0060265626$	$- 0.0009804147 + i 0.0060428333$
9	$- 0.0032779073 + i 0.0013440324$	$- 0.0007269206 - i 0.0060264830$	$- 0.0009812651 + i 0.0060428056$
11	$- 0.0032779094 + i 0.0013440326$	$- 0.0007268787 - i 0.0060264984$	$- 0.0009812215 + i 0.0060428194$
13	$- 0.0032779095 + i 0.0013440326$	$- 0.0007268787 - i 0.0060264985$	$- 0.0009812216 + i 0.0060428197$

$N_{p} = 2 M + 1$	$H_{z}$	$E_{x}$	$E_{y}$
3	$- 0.1296345389 - i 0.0426618457$	$0.0235906111 + i 0.0053348044$	$- 0.0223966957 - i 0.0105906933$
5	$- 0.1342563355 - i 0.0435310832$	$0.0241285949 + i 0.0056508534$	$- 0.0023157907 - i 0.0108383670$
7	$- 0.1339561230 - i 0.0433692220$	$0.0240700719 + i 0.0056030484$	$- 0.0231278238 - i 0.0108021538$
9	$- 0.1339531835 - i 0.0433672910$	$0.0240716603 + i 0.0056048730$	$- 0.0231257418 - i 0.0108009142$
11	$- 0.1339533817 - i 0.0433674547$	$0.0240716710 + i 0.0056048832$	$- 0.0231257666 - i 0.0108009245$
13	$- 0.1339533834 - i 0.0433674497$	$0.0240716694 + i 0.0056048836$	$- 0.0231257688 - i 0.0108009248$

$N_{p} = 2 M + 1$	$E_{z}$	$H_{x}$	$H_{y}$
3	$- 0.0033568320 + i 0.0013388036$	$- 0.0006632724 - i 0.0060792630$	$- 0.0009175906 + i 0.0061410684$
5	$- 0.0032723380 + i 0.0013442870$	$- 0.0007338791 - i 0.0060234433$	$0.0060679854 - i 0.0009883445$
7	$- 0.0032779380 + i 0.0013440207$	$- 0.0007261071 - i 0.0060265626$	$- 0.0009804147 + i 0.0060428333$
9	$- 0.0032779073 + i 0.0013440324$	$- 0.0007269206 - i 0.0060264830$	$- 0.0009812651 + i 0.0060428056$
11	$- 0.0032779094 + i 0.0013440326$	$- 0.0007268787 - i 0.0060264984$	$- 0.0009812215 + i 0.0060428194$
13	$- 0.0032779095 + i 0.0013440326$	$- 0.0007268787 - i 0.0060264985$	$- 0.0009812216 + i 0.0060428197$

$N_{p} = 2 M + 1$	$H_{z}$	$E_{x}$	$E_{y}$
3	$- 0.1296345389 - i 0.0426618457$	$0.0235906111 + i 0.0053348044$	$- 0.0223966957 - i 0.0105906933$
5	$- 0.1342563355 - i 0.0435310832$	$0.0241285949 + i 0.0056508534$	$- 0.0023157907 - i 0.0108383670$
7	$- 0.1339561230 - i 0.0433692220$	$0.0240700719 + i 0.0056030484$	$- 0.0231278238 - i 0.0108021538$
9	$- 0.1339531835 - i 0.0433672910$	$0.0240716603 + i 0.0056048730$	$- 0.0231257418 - i 0.0108009142$
11	$- 0.1339533817 - i 0.0433674547$	$0.0240716710 + i 0.0056048832$	$- 0.0231257666 - i 0.0108009245$
13	$- 0.1339533834 - i 0.0433674497$	$0.0240716694 + i 0.0056048836$	$- 0.0231257688 - i 0.0108009248$

Abstract

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Tables (2)

Equations (40)

Journal of the Optical Society of America A