Abstract

The coupling interactions in electromagnetic scattering from a finite array of two-dimensional identical cavities engraved in a perfectly electric conducting screen covered with stratified dielectric coating are presented using an algorithm based on the hybrid finite element-boundary integral method. The solution to the scattering from a finite array of cavities is approximated using the array factor method, which does not take into account the coupling between the cavities, and is compared to the recently developed finite element-boundary element method to demonstrate the importance of the inclusion of the coupling effect. Dependence of the coupling interactions between the cavities on various parameters such as separation periods, incident angle of the plane-wave excitation, and permittivity and thickness of the dielectric coating is demonstrated quantitatively through several numerical examples.

© 2012 Optical Society of America

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References

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  1. M. A. Basha, S. K. Chaudhuri, S. Safavi-Naeini, and H. J. Eom, “Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane,” J. Opt. Soc. Am. A 24, 1647–1655 (2007).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. B. Alavikia and O. M. Ramahi, “Hybrid finite element-boundary integral algorithm to solve the problem of scattering from a finite array of cavities with multi-layer stratified dielectric coating,” J. Opt. Soc. Am. A 28, 2192–2199 (2011).
    [CrossRef]
  6. M. I. Aksun, “A robust approach for the derivation of closed-form Green’s functions,” IEEE Trans. Microwave Theory Tech. 44, 651–658 (1996).
    [CrossRef]
  7. M. I. Aksun, F. Çalışkan, and L. Gürel, “An efficient method for electromagnetic characterization of 2-D geometries in stratified media,” IEEE Trans. Microwave Theory Tech. 50, 1264–1274 (2002).
    [CrossRef]

2011 (1)

2010 (1)

2009 (1)

2007 (1)

2002 (1)

M. I. Aksun, F. Çalışkan, and L. Gürel, “An efficient method for electromagnetic characterization of 2-D geometries in stratified media,” IEEE Trans. Microwave Theory Tech. 50, 1264–1274 (2002).
[CrossRef]

1996 (1)

M. I. Aksun, “A robust approach for the derivation of closed-form Green’s functions,” IEEE Trans. Microwave Theory Tech. 44, 651–658 (1996).
[CrossRef]

1991 (1)

O. M. Ramahi and R. Mittra, “Finite element solution for a class of unbounded geometries,” IEEE Trans. Antennas Propag. 39, 244–250 (1991).
[CrossRef]

Aksun, M. I.

M. I. Aksun, F. Çalışkan, and L. Gürel, “An efficient method for electromagnetic characterization of 2-D geometries in stratified media,” IEEE Trans. Microwave Theory Tech. 50, 1264–1274 (2002).
[CrossRef]

M. I. Aksun, “A robust approach for the derivation of closed-form Green’s functions,” IEEE Trans. Microwave Theory Tech. 44, 651–658 (1996).
[CrossRef]

Alavikia, B.

Basha, M. A.

Çaliskan, F.

M. I. Aksun, F. Çalışkan, and L. Gürel, “An efficient method for electromagnetic characterization of 2-D geometries in stratified media,” IEEE Trans. Microwave Theory Tech. 50, 1264–1274 (2002).
[CrossRef]

Chaudhuri, S.

Chaudhuri, S. K.

Eom, H. J.

Gürel, L.

M. I. Aksun, F. Çalışkan, and L. Gürel, “An efficient method for electromagnetic characterization of 2-D geometries in stratified media,” IEEE Trans. Microwave Theory Tech. 50, 1264–1274 (2002).
[CrossRef]

Mittra, R.

O. M. Ramahi and R. Mittra, “Finite element solution for a class of unbounded geometries,” IEEE Trans. Antennas Propag. 39, 244–250 (1991).
[CrossRef]

Ramahi, O. M.

Safavi-Naeini, S.

IEEE Trans. Antennas Propag. (1)

O. M. Ramahi and R. Mittra, “Finite element solution for a class of unbounded geometries,” IEEE Trans. Antennas Propag. 39, 244–250 (1991).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

M. I. Aksun, “A robust approach for the derivation of closed-form Green’s functions,” IEEE Trans. Microwave Theory Tech. 44, 651–658 (1996).
[CrossRef]

M. I. Aksun, F. Çalışkan, and L. Gürel, “An efficient method for electromagnetic characterization of 2-D geometries in stratified media,” IEEE Trans. Microwave Theory Tech. 50, 1264–1274 (2002).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Express (1)

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Figures (16)

Fig. 1.
Fig. 1.

Schematic of a grating surface consisting of a finite array of cavities covered with a conducting coating and engraved in an infinite-sized PEC screen.

Fig. 2.
Fig. 2.

Schematic of the scattering problem from conducting screen containing a finite periodic array of identical cavities coated with a dielectric layer. The distance between the ΓO contour and aperture opening is exaggerated for clarity.

Fig. 3.
Fig. 3.

Schematic of the equivalent magnetic current and its image for different polarization located inside the HSD.

Fig. 4.
Fig. 4.

Amplitude of the total electric far field for an array of three identical rectangular cavities shown in Fig. 1 covered with a single-layer dielectric coating, TMz case, ϕinc=150°, w=0.5λ, d=0.16λ, P=1λ, εr1=1.000010.000001j, εr2=4, and ts=0.4λ. Case 1, method presented in this work for the cavities with coating; Case 2, method presented in [3] for the cavities without coating.

Fig. 5.
Fig. 5.

Amplitude of the total magnetic far field for an array of three identical rectangular cavities shown in Fig. 1 covered with a single-layer dielectric coating, TEz case, ϕinc=120°, w=0.5λ, d=0.16λ, P=1λ, εr1=1.000010.000001j, εr2=4, and ts=0.4λ. Case 1, method presented in this work for the cavities with coating; Case 2, method presented in [3] for the cavities without coating.

Fig. 6.
Fig. 6.

Schematic of an array of two cavities engraved in an infinite-sized PEC screen and covered with a single-layer dielectric coating.

Fig. 7.
Fig. 7.

Amplitude of the total electric far field for an array of two identical rectangular cavities shown in Fig. 6 covered with a single-layer dielectric coating, TMz case, normal incident calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, P=1λ, εr1=1.60.00001j, εr2=2.1, and ts=0.9λ.

Fig. 8.
Fig. 8.

Amplitude of the total electric far field for an array of two identical rectangular cavities shown in Fig. 6 covered with a single-layer dielectric coating, TMz case, ϕinc=120°, calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, εr1=1.60.00001j, εr2=2.1, and ts=0.9λ. (a) P=1λ, (b) P=4λ, and (c) P=8λ.

Fig. 9.
Fig. 9.

Amplitude of the total electric far field for an array of two identical rectangular cavities shown in Fig. 6 covered with a single-layer dielectric coating, TMz case, ϕinc=175°, calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, εr1=1.60.00001j, εr2=2.1, and ts=0.9λ. (a) P=1λ, (b) P=4λ, and (c) P=8λ.

Fig. 10.
Fig. 10.

Amplitude of the total electric far field for an array of two identical rectangular cavities shown in Fig. 6 covered with a single-layer lossy dielectric coating, TMz case, ϕinc=120°, calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, P=1λ, εr1=1.60.01j, εr2=2.1, and ts=0.9λ.

Fig. 11.
Fig. 11.

Amplitude of the total electric far field for an array of two identical rectangular cavities shown in Fig. 6 covered with a single-layer dielectric coating, TMz case, ϕinc=120°, calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, εr1=1.60.00001j, εr2=2.1, and ts=0.05λ. (a) P=1λ and (b) P=4λ.

Fig. 12.
Fig. 12.

Amplitude of the total electric far field for an array of eight identical rectangular cavities covered with a single-layer dielectric coating, TMz case, ϕinc=120°, calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, εr1=1.60.00001j, εr2=2.1, and ts=0.9λ. (a) P=1λ and (b) P=8λ.

Fig. 13.
Fig. 13.

Amplitude of the total magnetic far field for an array of two identical rectangular cavities shown in Fig. 6 covered with a single-layer dielectric coating, TEz case, normal incident calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, P=1λ, εr1=1.60.00001j, εr2=2.1, and ts=0.9λ.

Fig. 14.
Fig. 14.

Amplitude of the total magnetic far field for an array of two identical rectangular cavities shown in Fig. 6 covered with a single-layer dielectric coating, TEz case, ϕinc=120°, calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, εr1=1.60.00001j, εr2=2.1, and ts=0.9λ. (a) P=1λ and (b) P=4λ.

Fig. 15.
Fig. 15.

Amplitude of the total magnetic far field for an array of two identical rectangular cavities shown in Fig. 6 covered with a single-layer dielectric coating, TEz case, ϕinc=175°, calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, εr1=1.60.00001j, εr2=2.1, and ts=0.9λ. (a) P=1λ and (b) P=4λ.

Fig. 16.
Fig. 16.

Amplitude of the total magnetic far field for an array of eight identical rectangular cavities covered with a single-layer dielectric coating, TEz case, ϕinc=120°, calculated using the FE-SIE and the AF method. w=0.5λ, d=0.25λ, εr1=1.60.00001j, εr2=2.1, and ts=0.9λ. (a) P=1λ and (b) P=8λ.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

·(1p(ρ)uzt)+q(ρ)k02uzt=0,
[MiiMib0MbiMbbMbo0MobMoo](j)[uiubuo](j)=[000](j),
[[M](1)000[M](2)000[M](J)][[u](1)[u](2)[u](J)]=[000].
uz(ρ)=uza(ρ)j=1JΓBjuz(ρ)Ge(ρ,ρ)ndΓ
uz(ρ)=uza(ρ)+j=1JΓBjGh(ρ,ρ)uz(ρ)ndΓ
[uo]=[S][ub]+[T].
[[u0](1)[u0](2)[u0](J)]=[[S](11)[S](12)[S](1J)[S](21)[S](22)[S](2J)[S](J1)[S](J2)[S](JJ)][[ub](1)[ub](2)[ub](J)]+[[T](1)[T](2)[T](J)],
[[M](1)[C](12)[C](1J)[C](21)[M](2)[C](2J)[C](J1)[C](J2)[M](J)][[u](1)[u](2)[u](J)]=[[F](1)[F](2)[F](J)],
[C](ij)=[000[Mbo](i)[S](ij)].
[M](j)=[[Mii](j)[Mib](j)[Mbi](j)[Mbb](j)+[Mbo](j)[S](jj)],
[F](j)=[0[Mbo](j)[T](j)],
[u](j)=[[ui](j)[ub](j)],
E(ρ)=2z^j=1JΓBj(Ez(ρ)|y=0)yGHSD(ρ,ρ)dx,
H(ρ)=+2z^j=1JΓBj(yH(ρ)|y=0)GHSD(ρ,ρ)dx,
GHSD(y,y,kx)=ejky0yejky1yj(ky1+ky0)ej(ky1ky0)ts,ts<y.
GHSD(y,y,kx)=q=1QαqeSqky0ejky0yjky0,ts<y.
GHSD(ρ,ρ)=j4q=1QαqH02(k0Rq),
E(ρ)=z^k0sinϕ|j=1JΓBj(Ez(ρ)|y=0)(q=1Qαqejk0Rq)dx|,
H(ρ)=z^1k0|j=1JΓBj(yH(ρ)|y=0)(q=1Qαqejk0Rq)dx|,

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