Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part II. Properties and implementation

Lindsay C. Botten; Nicolae-Alexandru P. Nicorovici; Ara A. Asatryan; Ross C. McPhedran; C. Martijn de Sterke; Peter A. Robinson

doi:10.1364/JOSAA.17.002177

Journal of the Optical Society of America A
Vol. 17,
Issue 12,
pp. 2177-2190
(2000)
•https://doi.org/10.1364/JOSAA.17.002177

Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part II. Properties and implementation

Lindsay C. Botten, Nicolae-Alexandru P. Nicorovici, Ara A. Asatryan, Ross C. McPhedran, C. Martijn de Sterke, and Peter A. Robinson

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Lindsay C. Botten, Nicolae-Alexandru P. Nicorovici, Ara A. Asatryan, Ross C. McPhedran, C. Martijn de Sterke, and Peter A. Robinson, "Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part II. Properties and implementation," J. Opt. Soc. Am. A 17, 2177-2190 (2000)

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Abstract

A numerical implementation and generalized conservation properties of a formulation for calculating wave propagation through stacked gratings comprising metallic and dielectric cylinders are presented. The basic formulation of the method was given in a companion paper [J. Opt. Soc. Am. A. 17, 2165 (2000)]. Here, details of the numerical implementation of the method are discussed and are illustrated for the ensemble average of a strongly scattering structure with refractive index and radius disorder. Also presented are a comprehensive treatment of energy conservation and generalized phase relations, as well as reciprocity.

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Equations (119)

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$N_{p}$	$N_{m}$
$N_{p}$	7	13	19	21
7	$4.0825297568 \times 10^{- 7}$	$4.0406616552 \times 10^{- 7}$	$4.0406784960 \times 10^{- 7}$	$4.0406784903 \times 10^{- 7}$
11	$4.0406909274 \times 10^{- 7}$	$4.2955391832 \times 10^{- 7}$	$4.2955542719 \times 10^{- 7}$	$4.2955542656 \times 10^{- 7}$
15	$4.0672205507 \times 10^{- 7}$	$4.0336094214 \times 10^{- 7}$	$4.0336112143 \times 10^{- 7}$	$4.0336111934 \times 10^{- 7}$
21	$4.0364204502 \times 10^{- 7}$	$4.0028392669 \times 10^{- 7}$	$4.0028471134 \times 10^{- 7}$	$4.0028471036 \times 10^{- 7}$
23	$4.0364174476 \times 10^{- 7}$	$4.0028373607 \times 10^{- 7}$	$4.0028452078 \times 10^{- 7}$	$4.0028451981 \times 10^{- 7}$
25	$4.0346930688 \times 10^{- 7}$	$4.0013197275 \times 10^{- 7}$	$4.0013241997 \times 10^{- 7}$	$4.0013241777 \times 10^{- 7}$
27	$4.0347045999 \times 10^{- 7}$	$4.0013161534 \times 10^{- 7}$	$4.0013204424 \times 10^{- 7}$	$4.0013204255 \times 10^{- 7}$
29	$4.0347044331 \times 10^{- 7}$	$4.0013159758 \times 10^{- 7}$	$4.0013202657 \times 10^{- 7}$	$4.0013202488 \times 10^{- 7}$

$N_{p}$	$N_{m}$
$N_{p}$	7	13	19	21
21	$1.9404365818 \times 10^{- 4}$	$1.9394676994 \times 10^{- 4}$	$1.9394680745 \times 10^{- 4}$	$1.9394680742 \times 10^{- 4}$
41	$4.2412272590 \times 10^{- 5}$	$4.2382310304 \times 10^{- 5}$	$4.2382362810 \times 10^{- 5}$	$4.2382362770 \times 10^{- 5}$
61	$4.0551351355 \times 10^{- 5}$	$4.0549638230 \times 10^{- 5}$	$4.0549564239 \times 10^{- 5}$	$4.0549564075 \times 10^{- 5}$
81	$4.0167894388 \times 10^{- 5}$	$4.0162275568 \times 10^{- 5}$	$4.0162155481 \times 10^{- 5}$	$4.0162155402 \times 10^{- 5}$
101	$4.0156627158 \times 10^{- 5}$	$4.0151631747 \times 10^{- 5}$	$4.0151486641 \times 10^{- 5}$	$4.0151486483 \times 10^{- 5}$
121	$4.0155334708 \times 10^{- 5}$	$4.0150206047 \times 10^{- 5}$	$4.0150052772 \times 10^{- 5}$	$4.0150052649 \times 10^{- 5}$
141	$4.0155273898 \times 10^{- 5}$	$4.0150151556 \times 10^{- 5}$	$4.0149997502 \times 10^{- 5}$	$4.0149997373 \times 10^{- 5}$
161	$4.0155266336 \times 10^{- 5}$	$4.0150142253 \times 10^{- 5}$	$4.0149987893 \times 10^{- 5}$	$4.0149987765 \times 10^{- 5}$

$N_{p}$	$N_{m}$
$N_{p}$	7	13	19	21
7	$4.0825297568 \times 10^{- 7}$	$4.0406616552 \times 10^{- 7}$	$4.0406784960 \times 10^{- 7}$	$4.0406784903 \times 10^{- 7}$
11	$4.0406909274 \times 10^{- 7}$	$4.2955391832 \times 10^{- 7}$	$4.2955542719 \times 10^{- 7}$	$4.2955542656 \times 10^{- 7}$
15	$4.0672205507 \times 10^{- 7}$	$4.0336094214 \times 10^{- 7}$	$4.0336112143 \times 10^{- 7}$	$4.0336111934 \times 10^{- 7}$
21	$4.0364204502 \times 10^{- 7}$	$4.0028392669 \times 10^{- 7}$	$4.0028471134 \times 10^{- 7}$	$4.0028471036 \times 10^{- 7}$
23	$4.0364174476 \times 10^{- 7}$	$4.0028373607 \times 10^{- 7}$	$4.0028452078 \times 10^{- 7}$	$4.0028451981 \times 10^{- 7}$
25	$4.0346930688 \times 10^{- 7}$	$4.0013197275 \times 10^{- 7}$	$4.0013241997 \times 10^{- 7}$	$4.0013241777 \times 10^{- 7}$
27	$4.0347045999 \times 10^{- 7}$	$4.0013161534 \times 10^{- 7}$	$4.0013204424 \times 10^{- 7}$	$4.0013204255 \times 10^{- 7}$
29	$4.0347044331 \times 10^{- 7}$	$4.0013159758 \times 10^{- 7}$	$4.0013202657 \times 10^{- 7}$	$4.0013202488 \times 10^{- 7}$

$N_{p}$	$N_{m}$
$N_{p}$	7	13	19	21
21	$1.9404365818 \times 10^{- 4}$	$1.9394676994 \times 10^{- 4}$	$1.9394680745 \times 10^{- 4}$	$1.9394680742 \times 10^{- 4}$
41	$4.2412272590 \times 10^{- 5}$	$4.2382310304 \times 10^{- 5}$	$4.2382362810 \times 10^{- 5}$	$4.2382362770 \times 10^{- 5}$
61	$4.0551351355 \times 10^{- 5}$	$4.0549638230 \times 10^{- 5}$	$4.0549564239 \times 10^{- 5}$	$4.0549564075 \times 10^{- 5}$
81	$4.0167894388 \times 10^{- 5}$	$4.0162275568 \times 10^{- 5}$	$4.0162155481 \times 10^{- 5}$	$4.0162155402 \times 10^{- 5}$
101	$4.0156627158 \times 10^{- 5}$	$4.0151631747 \times 10^{- 5}$	$4.0151486641 \times 10^{- 5}$	$4.0151486483 \times 10^{- 5}$
121	$4.0155334708 \times 10^{- 5}$	$4.0150206047 \times 10^{- 5}$	$4.0150052772 \times 10^{- 5}$	$4.0150052649 \times 10^{- 5}$
141	$4.0155273898 \times 10^{- 5}$	$4.0150151556 \times 10^{- 5}$	$4.0149997502 \times 10^{- 5}$	$4.0149997373 \times 10^{- 5}$
161	$4.0155266336 \times 10^{- 5}$	$4.0150142253 \times 10^{- 5}$	$4.0149987893 \times 10^{- 5}$	$4.0149987765 \times 10^{- 5}$

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Equations (119)

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