Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs

Thore Magath; Andriy E. Serebryannikov

doi:10.1364/JOSAA.22.002405

Journal of the Optical Society of America A
Vol. 22,
Issue 11,
pp. 2405-2418
(2005)
•https://doi.org/10.1364/JOSAA.22.002405

Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs

Thore Magath and Andriy E. Serebryannikov

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Thore Magath and Andriy E. Serebryannikov, "Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs," J. Opt. Soc. Am. A 22, 2405-2418 (2005)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

A fast coupled-integral-equation (CIE) technique is developed to compute the plane-TE-wave scattering by a wide class of periodic 2D inhomogeneous structures with curvilinear boundaries, which includes finite-thickness relief and rod gratings made of homogeneous material as special cases. The CIEs in the spectral domain are derived from the standard volume electric field integral equation. The kernel of the CIEs is of Picard type and offers therefore the possibility of deriving recursions, which allow the computation of the convolution integrals occurring in the CIEs with linear amounts of arithmetic complexity and memory. To utilize this advantage, the CIEs are solved iteratively. We apply the biconjugate gradient stabilized method. To make the iterative solution process faster, an efficient preconditioning operator (PO) is proposed that is based on a formal analytical inversion of the CIEs. The application of the PO also takes only linear complexity and memory. Numerical studies are carried out to demonstrate the potential and flexibility of the CIE technique proposed. Though the best efficiency and accuracy are observed at either low permittivity contrast or high conductivity, the technique can be used in a wide range of variation of material parameters of the structures including when they contain components made of both dielectrics with high permittivity and typical metals.

Full Article | PDF Article

More Like This

Rigorous integral equation analysis of nonsymmetric coupled grating slab waveguides

Nikolaos L. Tsitsas, Dimitra I. Kaklamani, and Nikolaos K. Uzunoglu
J. Opt. Soc. Am. A 23(11) 2888-2905 (2006)

Multilevel Green's function interpolation method for analysis of 3-D frequency selective structures using volume/surface integral equation

Yan Shi and Chi Hou Chan
J. Opt. Soc. Am. A 27(2) 308-318 (2010)

Fast convergence with spectral volume integral equation for crossed block-shaped gratings with improved material interface conditions

Martijn C. van Beurden
J. Opt. Soc. Am. A 28(11) 2269-2278 (2011)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (18)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (7)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (38)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Order	Diffraction Efficiency for $h_{1} ∕ d = 0.1$				Diffraction Efficiency for $h_{1} ∕ d = 1.0$
Order	MMM^a	RFM^a	CIE^a-I^b	CIE^a-IV^b	MMM	IM^a	CIE-II^b	CIE-III^b	CIE-IV
$R_{- 2}$	0.011 60	0.011 55	0.011 56	0.011 56	0.413 48	0.422	0.4189	0.4234	0.4231
$R_{- 1}$	0.206 7	0.206 35	0.206 42	0.206 38	0.335 31	0.329	0.3301	0.3283	0.3297
$R_{0}$	0.760 20	0.760 79	0.760 66	0.760 75	0.201 77	0.199	0.2016	0.1993	0.1985

$k h$	Q	N	PB	J	$t [s]$	Diffraction Efficiency
$k h$	Q	N	PB	J	$t [s]$	$T_{- 1}$	$T_{0}$	$T_{1}$
$4 π$	400	50	$7.78 \times 10^{- 6}$	300	668	0.2539	0.0041	0.3200
$4 π$	200	20	$3.11 \times 10^{- 5}$	195	68	0.2535	0.0042	0.3192
$4 π$	100	10	$1.25 \times 10^{- 4}$	240	18	0.2532	0.0042	0.3157
2.0	200	5	$1.11 \times 10^{- 10}$	12	6.9	0.0239	0.8766	—
2.0	100	5	$3.25 \times 10^{- 10}$	12	3.4	0.0240	0.8767	—
2.0	25	5	$7.19 \times 10^{- 8}$	12	1.9	0.0244	0.8775	—

$k h$	Q	N	PB	J	$t [s]$	Diffraction Efficiency
3.8	500	30	$9.68 \times 10^{- 7}$	118	132	$0.1632 (R_{- 2})$	$0.5312 (R_{- 1})$	$0.0650 (R_{0})$	$0.1538 (R_{1})$
3.8	200	20	$6.05 \times 10^{- 6}$	138	47	$0.1635 (R_{- 2})$	$0.5316 (R_{- 1})$	$0.0654 (R_{0})$	$0.1538 (R_{1})$
3.8	100	10	$2.37 \times 10^{- 5}$	105	10	$0.1623 (R_{- 2})$	$0.5332 (R_{- 1})$	$0.0661 (R_{0})$	$0.1541 (R_{1})$
2.0	500	20	$8.92 \times 10^{- 9}$	48	108	$0.0401 (R_{- 1})$	$0.4777 (R_{0})$	$0.2794 (T_{- 1})$	$0.2029 (T_{0})$
2.0	300	15	$5.10 \times 10^{- 6}$	48	36	$0.0401 (R_{- 1})$	$0.4777 (R_{0})$	$0.2795 (T_{- 1})$	$0.2027 (T_{0})$
2.0	50	10	$3.74 \times 10^{- 8}$	48	3.8	$0.0411 (R_{- 1})$	$0.4723 (R_{0})$	$0.2827 (T_{- 1})$	$0.2038 (T_{0})$

$k h$	Q	N	J	$t [s]$	Diffraction Efficiency
$k h$	Q	N	J	$t [s]$	$R_{- 2}$	$R_{- 1}$	$R_{0}$	$R_{1}$
3.8	500	50	38	268	0.2658	0.3042	0.0248	0.3249
3.8	400	40	43	147	0.2658	0.3042	0.0247	0.3249
3.8	200	20	37	24	0.2657	0.3037	0.0248	0.3243
2.0	500	50	26	236	—	0.3461	0.5715	—
2.0	300	40	25	78	—	0.3460	0.5715	—
2.0	100	10	23	5.7	—	0.3458	0.5703	—

$k h$	Q	N	PB	J	$t [s]$	Diffraction Efficiency
$ϵ_{2 r} = 2.1$
$2 π^{2}$	500	20	$1.97 \times 10^{- 5}$	65	117	$0.2790 (T_{- 1})$	$0.1790 (T_{0})$	$0.0872 (T_{1})$	$0.342 (T_{2})$
$2 π^{2}$	200	20	$1.23 \times 10^{- 4}$	63	29	$0.2785 (T_{- 1})$	$0.1787 (T_{0})$	$0.0876 (T_{1})$	$0.342 (T_{2})$
$2 π^{2}$	100	10	$4.93 \times 10^{- 4}$	73	8.3	$0.2760 (T_{- 1})$	$0.1783 (T_{0})$	$0.0905 (T_{1})$	$0.340 (T_{2})$
$ϵ_{2 r} = 11.4$
$2 π^{2}$	400	60	$1.16 \times 10^{- 5}$	195	638	$0.1379 (T_{- 1})$	$0.3276 (T_{0})$	$0.2032 (R_{- 1})$	$0.1289 (R_{0})$
$2 π^{2}$	300	50	$2.21 \times 10^{- 5}$	192	327	$0.1484 (T_{- 1})$	$0.3669 (T_{0})$	$0.1680 (R_{- 1})$	$0.1280 (R_{0})$
$2 π$	700	20	$3.02 \times 10^{- 9}$	37	188	$0.1773 (T_{- 1})$	$0.0414 (T_{0})$	$0.6592 (R_{- 1})$	$0.1221 (R_{0})$
$2 π$	300	50	$1.05 \times 10^{- 9}$	37	113	$0.1777 (T_{- 1})$	$0.0405 (T_{0})$	$0.6585 (R_{- 1})$	$0.1233 (R_{0})$
$2 π$	100	40	$5.90 \times 10^{- 8}$	38	21	$0.1328 (T_{- 1})$	$0.0633 (T_{0})$	$0.6869 (R_{- 1})$	$0.1169 (R_{0})$
$ϵ_{2 r} = {(1.3 - i 7.6)}^{2}$
$2 π$	600	50	—	24	316	$0.8033 (R_{- 1})$	$0.0656 (R_{0})$	—	—
$2 π$	500	40	—	24	180	$0.8037 (R_{- 1})$	$0.0652 (R_{0})$	—	—
$2 π$	200	40	—	21	40	$0.8025 (R_{- 1})$	$0.0655 (R_{0})$	—	—

$k h$	Q	N	PB	J	$t [s]$	Diffraction Efficiency
$k h$	Q	N	PB	J	$t [s]$	$T_{- 2}$	$T_{- 1}$	$T_{1}$
$3 π$	500	50	$3.71 \times 10^{- 6}$	110	425	$0.1043 (T_{- 2})$	$0.2832 (T_{- 1})$	$0.3452 (T_{1})$
$3 π$	400	40	$5.81 \times 10^{- 6}$	97	212	$0.1043 (T_{- 2})$	$0.2832 (T_{- 1})$	$0.3451 (T_{1})$
$3 π$	200	20	$1.75 \times 10^{- 5}$	92	37	$0.1040 (T_{- 2})$	$0.2830 (T_{- 1})$	$0.3437 (T_{1})$

$k h$	Q	N	PB	J	$t [s]$	Diffraction Efficiency
Inhomogeneous Slab With Curvilinear Boundaries, $d ∕ h = π$
$4 π$	700	50	$4.55 \times 10^{- 6}$	152	860	$0.1585 (R_{- 3})$	$0.1410 (R_{- 2})$	—
$4 π$	500	40	$8.91 \times 10^{- 6}$	180	432	$0.1570 (R_{- 3})$	$0.1416 (R_{- 2})$	—
$4 π$	600	20	$7.19 \times 10^{- 6}$	115	203	$0.0870 (R_{- 1})$	$0.2899 (R_{0})$	—
$4 π$	300	40	$2.45 \times 10^{- 5}$	165	203	$0.1555 (R_{- 3})$	$0.1398 (R_{- 2})$	—
Inhomogeneous Slab With Curvilinear Boundaries, $d ∕ h = 1$
$4 π^{2}$	700	50	$1.12 \times 10^{- 4}$	190	1012	$0.0945 (T_{- 6})$	$0.1134 (R_{1})$	$0.1029 (R_{5})$
$4 π^{2}$	800	40	$8.56 \times 10^{- 5}$	170	832	$0.0947 (T_{- 6})$	$0.1143 (R_{1})$	$0.1024 (R_{5})$
$4 π^{2}$	700	30	$1.14 \times 10^{- 4}$	200	530	$0.0938 (T_{- 6})$	$0.1114 (R_{1})$	$0.1027 (R_{5})$
Inhomogeneous Slab With Curvilinear Boundaries And Metallic Insert, $d ∕ h = π$
$4 π$	600	50	—	117	779	$0.1646 (R_{- 3})$	$0.1083 (R_{0})$	$0.1081 (R_{3})$
$4 π$	500	50	—	105	512	$0.1647 (R_{- 3})$	$0.1075 (R_{0})$	$0.1079 (R_{3})$
$4 π$	500	30	—	110	326	$0.1619 (R_{- 3})$	$0.1059 (R_{0})$	$0.1093 (R_{3})$

Abstract

Cited By

Figures (18)

Tables (7)

Equations (38)

Journal of the Optical Society of America A