Abstract

Based on the waveguide mode (WGM) method, coupling interaction of electromagnetic wave in a groove doublet configuration is studied. The formulation obtained by WGM method for a single groove [Prog. Electromagn. Res. 18, 1–17 (1998)] is extended to two grooves. By exploring the total scattered field of the configuration, coupling interaction ratios are defined to describe the interaction between grooves quantitatively. Since each groove in this groove doublet configuration is regarded as the basic unit, the effects of coupling interaction on the scattered fields of each groove can be investigated respectively. Numerical results show that an oscillatory behavior of coupling interaction is damped with increasing groove spacing. The incident and scattering angle dependence of coupling interaction is symmetrical when the two grooves are the same. For the case of two subwavelength grooves, the coupling interaction is not sensitive to the incident angle and scattering angle. Although the case of two grooves is discussed for simplicity, the formulation developed in this article can be generalized to arbitrary number of grooves. Moreover, our study offers a simple alternative to investigate and design metallic gratings, compact directional antennas, couplers, and other devices especially in low frequency regime such as THz and microwave domain.

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References

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  1. K. Barkeshli and J. L. Volakis, “TE scattering by a two-dimensional groove in a ground plane using higher order boundary conditions,” IEEE Trans. Antenn. Propag. 38(9), 1421–1428 (1990).
    [CrossRef]
  2. K. W. Whites, E. Michielssen, and R. Mittra, “Approximating the scattering by a material-filled 2-D trough in an infinite plane using the impedance boundary condition,” IEEE Trans. Antenn. Propag. 41(2), 146–153 (1993).
    [CrossRef]
  3. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
    [CrossRef]
  4. M. A. Morgan and F. K. Schwering, “Mode expansion solution for scattering by a material filled rectangular groove,” Prog. Electromagn. Res. PIER 18, 1–17 (1998).
    [CrossRef]
  5. M. A. Basha, S. Chaudhuri, and S. Safavi-Naeini, “A study of coupling interactions in finite arbitrarily-shaped grooves in electromagnetic scattering problem,” Opt. Express 18(3), 2743–2752 (2010).
    [CrossRef] [PubMed]
  6. R. E. Collin, Field Theory of Guided Waves (IEEE Press, New York, 1991).
  7. L. Chen, J. T. Robinson, and M. Lipson, “Role of radiation and surface plasmon polaritons in the optical interactions between a nano-slit and a nano-groove on a metal surface,” Opt. Express 14(26), 12629–12636 (2006).
    [CrossRef] [PubMed]

2010 (1)

2006 (1)

1998 (1)

M. A. Morgan and F. K. Schwering, “Mode expansion solution for scattering by a material filled rectangular groove,” Prog. Electromagn. Res. PIER 18, 1–17 (1998).
[CrossRef]

1995 (1)

1993 (1)

K. W. Whites, E. Michielssen, and R. Mittra, “Approximating the scattering by a material-filled 2-D trough in an infinite plane using the impedance boundary condition,” IEEE Trans. Antenn. Propag. 41(2), 146–153 (1993).
[CrossRef]

1990 (1)

K. Barkeshli and J. L. Volakis, “TE scattering by a two-dimensional groove in a ground plane using higher order boundary conditions,” IEEE Trans. Antenn. Propag. 38(9), 1421–1428 (1990).
[CrossRef]

Barkeshli, K.

K. Barkeshli and J. L. Volakis, “TE scattering by a two-dimensional groove in a ground plane using higher order boundary conditions,” IEEE Trans. Antenn. Propag. 38(9), 1421–1428 (1990).
[CrossRef]

Basha, M. A.

Chaudhuri, S.

Chen, L.

Gaylord, T. K.

Grann, E. B.

Lipson, M.

Michielssen, E.

K. W. Whites, E. Michielssen, and R. Mittra, “Approximating the scattering by a material-filled 2-D trough in an infinite plane using the impedance boundary condition,” IEEE Trans. Antenn. Propag. 41(2), 146–153 (1993).
[CrossRef]

Mittra, R.

K. W. Whites, E. Michielssen, and R. Mittra, “Approximating the scattering by a material-filled 2-D trough in an infinite plane using the impedance boundary condition,” IEEE Trans. Antenn. Propag. 41(2), 146–153 (1993).
[CrossRef]

Moharam, M. G.

Morgan, M. A.

M. A. Morgan and F. K. Schwering, “Mode expansion solution for scattering by a material filled rectangular groove,” Prog. Electromagn. Res. PIER 18, 1–17 (1998).
[CrossRef]

Pommet, D. A.

Robinson, J. T.

Safavi-Naeini, S.

Schwering, F. K.

M. A. Morgan and F. K. Schwering, “Mode expansion solution for scattering by a material filled rectangular groove,” Prog. Electromagn. Res. PIER 18, 1–17 (1998).
[CrossRef]

Volakis, J. L.

K. Barkeshli and J. L. Volakis, “TE scattering by a two-dimensional groove in a ground plane using higher order boundary conditions,” IEEE Trans. Antenn. Propag. 38(9), 1421–1428 (1990).
[CrossRef]

Whites, K. W.

K. W. Whites, E. Michielssen, and R. Mittra, “Approximating the scattering by a material-filled 2-D trough in an infinite plane using the impedance boundary condition,” IEEE Trans. Antenn. Propag. 41(2), 146–153 (1993).
[CrossRef]

IEEE Trans. Antenn. Propag. (2)

K. Barkeshli and J. L. Volakis, “TE scattering by a two-dimensional groove in a ground plane using higher order boundary conditions,” IEEE Trans. Antenn. Propag. 38(9), 1421–1428 (1990).
[CrossRef]

K. W. Whites, E. Michielssen, and R. Mittra, “Approximating the scattering by a material-filled 2-D trough in an infinite plane using the impedance boundary condition,” IEEE Trans. Antenn. Propag. 41(2), 146–153 (1993).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Prog. Electromagn. Res. (1)

M. A. Morgan and F. K. Schwering, “Mode expansion solution for scattering by a material filled rectangular groove,” Prog. Electromagn. Res. PIER 18, 1–17 (1998).
[CrossRef]

Other (1)

R. E. Collin, Field Theory of Guided Waves (IEEE Press, New York, 1991).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the groove doublet configuration, including the geometrical parameters W 1, W 2, d 1, d 2, and Λ. A THz plane TM wave is incident upon the configuration, with the angle of incidence θi . The material in both regions are the same, where εr I = εr II = εr , and μr I = μr II = μr .

Fig. 2
Fig. 2

The CIR versus the groove spacing for (a) D-S, (b) D-NS, and (c) S-NS, with θi = θ 1 = 0, εr = 1, and μr = 1.

Fig. 3
Fig. 3

The CIR versus the incident angle and scattering angle for (a) D-S with Λ = 2.1λ 0, (b) D-NS with Λ = 5λ 0, and (c) S-NS with Λ = 3.7λ 0, when εr = 1, and μr = 1.

Equations (22)

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H j S ( ρ j , θ j ) H 0 W j i k 0 2 π ρ j e i k 0 ρ j n j = 0 N j c j n j L j n j ( θ j ) y ^ ,
L j n j ( θ j ) = i u n j k 0 W j ε r 0 W j cos ( n j π W j x ) e i k 0 x sin θ j d x = u n j k 0 ε r [ 1 ( 1 ) n j e i k 0 W j sin θ j ] k 0 W j sin θ j ( n j π ) 2 ( k 0 W j sin θ j ) 2 ,
a j n j = [ 1 ( 1 ) n j e i k 0 W j sin θ i ] i ε n j k 0 W j sin θ i ( n j π ) 2 ( k 0 W j sin θ i ) 2
n j 0 ,
H 1 S ( x ) H 0 W 1 [ n 1 = 0 N 1 c 1 n 1 L 1 n 1 ( π 2 ) ] i k 0 2 π x e i k 0 x y ^ = H 2 e i k 0 x x y ^ ,
H 2 = H 0 W 1 [ n 1 = 0 N 1 c 1 n 1 L 1 n 1 ( π 2 ) ] i k 0 2 π .
J 2 S = 2 H 2 e i k 0 x x x ^ H 2 n 2 = 0 N 2 a 2 n 2 cos [ n 2 π W 2 ( x Λ ) ] x ^ ,
a 2 n 2 = 2 W 2 Λ Λ + W 2 e i k 0 x x cos [ n 2 π W 2 ( x Λ ) ] d x .
H 2 y ( x , z ) H 2 n 2 = 0 N 2 b 2 n 2 cos [ n 2 π W 2 ( x Λ ) ] cosh [ γ 2 n 2 ( z + d 2 ) ] ,
E 2 x ( x , z ) i E 2 k 0 ε r 0 n 2 = 0 N 2 b 2 n 2 γ 2 n 2 cos [ n 2 π W 2 ( x Λ ) ] sinh [ γ 2 n 2 ( z + d 2 ) ] ,
H 2 y ( x , z ) H 2 n 2 = 0 N 2 c 2 n 2 cos [ n 2 π W 2 ( x Λ ) ] exp ( u 2 n 2 z ) ,
E 2 x ( x , z ) i E 2 k 0 ε r 0 n 2 = 0 N 2 c 2 n 2 u 2 n 2 cos [ n 2 π W 2 ( x Λ ) ] exp ( u 2 n 2 z ) ,
c 2 n 2 = sinh ( γ 2 n 2 d 2 ) b 2 n 2 = [ exp ( 2 u 2 n 2 d 2 ) 1 ] a 2 n 2 .
H 2 S ( ρ 2 , θ 2 ) H 2 W 2 i k 0 2 π ρ 2 e i k 0 ρ 2 n 2 = 0 N 2 c 2 n 2 L 2 n 2 ( θ 2 ) y ^ ,
H 2 S c o m ( ρ 2 , θ 2 ) = H 2 S + H 2 S = H 0 W 2 i k 0 2 π ρ 2 e i k 0 ρ 2 n 2 = 0 N 2 ( c 2 n 2 + F n 2 1 2 ) L 2 n 2 ( θ 2 ) y ^ ,
F n 2 1 2 = W 1 [ n 1 = 0 N 1 c 1 n 1 L 1 n 1 ( π 2 ) ] i k 0 2 π c 2 n 2 .
H 1 S c o m ( ρ 1 , θ 1 ) = H 1 S + H 1 S = H 0 W 1 i k 0 2 π ρ 1 e i k 0 ρ 1 n 1 = 0 N 1 ( c 1 n 1 + F n 1 2 1 ) L 1 n 1 ( θ 1 ) y ^ ,
F n 1 2 1 = W 2 [ n 2 = 0 N 2 c 2 n 2 L 2 n 2 ( π 2 ) ] i k 0 2 π c 1 n 1 .
a 1 n 1 = 2 W 1 0 W 1 e i k 0 ( Λ x ) Λ x cos ( n 1 π W 1 x ) d x .
H S t o t a l ( ρ 1 , θ 1 ) = H 1 S c o m ( ρ 1 , θ 1 ) + H 2 S c o m ( ρ 2 ( ρ 1 , θ 1 ) , θ 2 ( ρ 1 , θ 1 ) ) .
{ ρ 2 ( ρ 1 , θ 1 ) = ρ 1 2 + Λ 2 2 Λ ρ 1 sin θ 1 ) θ 2 ( ρ 1 , θ 1 ) = arctan ( tan θ 1 Λ ρ 1 cos θ 1 ) .
C I R = σ t o t a l σ σ = lim ρ 1 2 π ρ 1 ( | H S t o t a l | 2 | H S | 2 ) / | H S | 2 ,

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