Abstract

A numerical improvement of the Fourier modal method with adaptive spatial resolution is obtained. It is shown that the solutions of all the eigenvalue problems corresponding to homogeneous regions can be deduced straightforwardly from the solution of one of these problems. Numerical examples demonstrate that computation time saving can be substantial.

© 2009 Optical Society of America

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References

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  14. B. Guizal, H. Yala, and D. Felbacq, “Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution,” Opt. Lett. 34, 2790-2792 (2009).
    [CrossRef] [PubMed]

2009

A. Khavasi and K. Mehrany, “Adaptive spatial resolution in fast, efficient, and stable analysis of metallic lamellar gratings at microwave frequencies,” IEEE Trans. Antennas Propag. 57, 1115-1121 (2009).
[CrossRef]

B. Guizal, H. Yala, and D. Felbacq, “Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution,” Opt. Lett. 34, 2790-2792 (2009).
[CrossRef] [PubMed]

2005

2002

Y. Pagani, B. Guizal, D. VanLabeke, A. Vial, and F. Baida, “Diffraction hysteresis loop modeling in magneto-optical gratings,” Opt. Commun. 209, 237-244 (2002).
[CrossRef]

T. Vallius and M. Honkanen, “Reformulation of the Fourier modal method with adaptive spatial resolution: application to multilevel profiles,” Opt. Express 10, 24-34 (2002).
[PubMed]

1999

1998

L. Li, “Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials,” J. Mod. Opt. 45, 1313-1334 (1998).
[CrossRef]

1997

1996

1994

1978

K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. A 68, 1206-1210 (1978).
[CrossRef]

Baida, F.

Y. Pagani, B. Guizal, D. VanLabeke, A. Vial, and F. Baida, “Diffraction hysteresis loop modeling in magneto-optical gratings,” Opt. Commun. 209, 237-244 (2002).
[CrossRef]

Felbacq, D.

Granet, G.

Guizal, B.

Honkanen, M.

Hugonin, J. P.

Khavasi, A.

A. Khavasi and K. Mehrany, “Adaptive spatial resolution in fast, efficient, and stable analysis of metallic lamellar gratings at microwave frequencies,” IEEE Trans. Antennas Propag. 57, 1115-1121 (2009).
[CrossRef]

Knop, K.

K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. A 68, 1206-1210 (1978).
[CrossRef]

Lalanne, P.

Li, L.

Mehrany, K.

A. Khavasi and K. Mehrany, “Adaptive spatial resolution in fast, efficient, and stable analysis of metallic lamellar gratings at microwave frequencies,” IEEE Trans. Antennas Propag. 57, 1115-1121 (2009).
[CrossRef]

Morris, G. M.

Noponen, E.

Pagani, Y.

Y. Pagani, B. Guizal, D. VanLabeke, A. Vial, and F. Baida, “Diffraction hysteresis loop modeling in magneto-optical gratings,” Opt. Commun. 209, 237-244 (2002).
[CrossRef]

Turunen, J.

Vallius, T.

VanLabeke, D.

Y. Pagani, B. Guizal, D. VanLabeke, A. Vial, and F. Baida, “Diffraction hysteresis loop modeling in magneto-optical gratings,” Opt. Commun. 209, 237-244 (2002).
[CrossRef]

Vial, A.

Y. Pagani, B. Guizal, D. VanLabeke, A. Vial, and F. Baida, “Diffraction hysteresis loop modeling in magneto-optical gratings,” Opt. Commun. 209, 237-244 (2002).
[CrossRef]

Yala, H.

IEEE Trans. Antennas Propag.

A. Khavasi and K. Mehrany, “Adaptive spatial resolution in fast, efficient, and stable analysis of metallic lamellar gratings at microwave frequencies,” IEEE Trans. Antennas Propag. 57, 1115-1121 (2009).
[CrossRef]

J. Mod. Opt.

L. Li, “Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials,” J. Mod. Opt. 45, 1313-1334 (1998).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

Y. Pagani, B. Guizal, D. VanLabeke, A. Vial, and F. Baida, “Diffraction hysteresis loop modeling in magneto-optical gratings,” Opt. Commun. 209, 237-244 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (2)

Fig. 1
Fig. 1

Geometry of the diffraction problem. Each layer can be either a homogeneous one or a grating with the same period d.

Fig. 2
Fig. 2

Computation time for the solution of the eigenvalue problems versus the number of retained Fourier harmonics.

Tables (2)

Tables Icon

Table 1 Comparison of the Eigenvalues Computed (a) Directly by an Eigenvalue Solver and (b) by Use of Eq. (9) a

Tables Icon

Table 2 Comparison of the Eigenvalues Computed (a) Directly by an Eigenvalue Solver and (b) by use of Eq. (9) a

Equations (13)

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2 E z x 2 + 2 E z y 2 + k 0 2 ϵ ( x ) E z = 0 ( TE ) ,
x 1 ϵ ( x ) H z x + 1 ϵ ( x ) 2 H z y 2 + k 0 2 H z = 0 ( TM ) .
d 2 E z d y 2 = { α 2 k 0 2 ϵ } E z = A TE E z ( TE ) ,
d 2 H z d y 2 = 1 ϵ 1 { α ϵ 1 α k 0 2 I d } H z = A TM H z ( TM ) ,
ψ ( y ) = P { e D y a + e D y b } , d ψ d y = P D { e D y a e D y b } .
1 f u ( 1 f E z u ) + 2 E z y 2 + k 0 2 ϵ ( u ) E z = 0 ( TE ) ,
1 f u ( 1 ϵ ( u ) 1 f H z u ) + 1 ϵ ( u ) 2 H z y 2 + k 0 2 H z = 0 ( TM ) ,
d 2 E z d y 2 = { f 1 α f 1 α k 0 2 ϵ } E z = A TE E z ( TE ) ,
d 2 H z d y 2 = 1 ϵ 1 { f 1 α ϵ 1 f 1 α k 0 2 I d } H z = A TM H z ( TM ) ,
d 2 ψ in d y 2 = { f 1 α f 1 α k 0 2 ϵ in I d } ψ in = A in ψ in , ψ in = E z , in or H z , in .
{ A in = f 1 α f 1 α k 0 2 ϵ in I d A q = f 1 α f 1 α k 0 2 ϵ q I d } A q = A in + k 0 2 ( ϵ in ϵ q ) I d .
P in A q P in 1 = D in 2 + k 0 2 ( ϵ in ϵ q ) I d because A in = P in D in 2 P in 1 .
D q 2 = D in 2 + k 0 2 ( ϵ in ϵ q ) I d .

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