Abstract

This work presents a hybrid finite element boundary integral algorithm to solve the problem of scattering from finite and infinite arrays of two-dimensional overfilled cavities engraved in a perfectly electric conducting flat screen. The solution region is divided into interior regions containing the cavities and their protruding portions, and the region exterior to the overfilled cavities. The finite element formulation is applied only inside the interior regions to derive a linear system of equations associated with field unknowns. Using two-boundary formulation, the surface integral equation employing the half-space Green’s function is applied on the boundary located at the interface of protruding portions of the cavities and the half-space as a boundary constraint to truncate the solution region. Placing the truncation boundary on the protruding portions of the cavities results in highly efficient solution in terms of computational resources, which makes the algorithm well suited for the optimization problems involving scattering from grating surfaces. The near fields are generated for finite and infinite arrays of overfilled cavities with different dimensions.

© 2012 Optical Society of America

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  1. S. Kawata, “Near-field microscope probes utilizing surface plasmon polaritons,” Appl. Phys. 81, 15–27 (2001).
    [CrossRef]
  2. F. Wei and Z. Liu, “Plasmonic structured illumination microscopy,” Nano Lett. 10, 2531–2536 (2010).
    [CrossRef]
  3. H. Hu, C. Ma, and Z. Liu, “Plasmonic dark field microscopy,” Appl. Phys. 96, 113107 (2010).
    [CrossRef]
  4. Y. Ngu, M. Peckerar, M. Dagenais, J. Barry, and B. Dutt, “Lithography, plasmonics, and subwavelength aperture exposure technology,” J. Vac. Sci. Technol. B 25–6, 2471–2475 (2007).
    [CrossRef]
  5. Y. Xiong, Zh. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. 93, 111116 (2008).
  6. R. F. Harrington and J. R. Mautz, “A generalized network formulation for aperture problems,” IEEE Trans. Antenna Propag. 24, 870–873 (1976).
    [CrossRef]
  7. D. T. Auckland and R. F. Harrington, “Electromagnetic transmission through a filled slit in a conducting plane of finite thickness, TE case,” IEEE Trans. Microwave Theory Tech. 26, 499–505 (1978).
    [CrossRef]
  8. K. Barkeshli and J. L. Volakis, “TE scattering by a two-dimensional groove in a ground plane using higher order boundary conditions,” IEEE Trans. Antenna Propag. 38, 1421–1428 (1990).
    [CrossRef]
  9. K. Barkeshli and J. L. Volakis, “Scattering from narrow rectangular filled grooves,” IEEE Trans. Antenna Propag. 39, 804–810 (1991).
    [CrossRef]
  10. Y.-L. Kok, “Boundary-value solution to electromagnetic scattering by a rectangular groove in a ground plane,” J. Opt. Soc. Am. A 9, 302–311 (1992).
    [CrossRef]
  11. T. J. Park, H. J. Eom, and K. Yoshitomi, “An analytic solution for transverse-magnetic scattering from a rectangular channel in a conducting plane,” J. Appl. Phys. 73, 3571–3573 (1993).
    [CrossRef]
  12. T. J. Park, H. J. Eom, and K. Yoshitomi, “An analysis of transverse electric scattering from a rectangular channel in a conducting plane,” Radio Sci. 28, 663–673 (1993).
    [CrossRef]
  13. T. J. Park, H. J. Eom, and K. Yoshitomi, “Analysis of TM scattering from finite rectangular grooves in a conducting plane,” J. Opt. Soc. Am. A 10, 905–911 (1993).
    [CrossRef]
  14. R. A. Depine and D. C. Skigin, “Scattering from metallic surfaces having a finite number of rectangular grooves,” J. Opt. Soc. Am. A 11, 2844–2850 (1994).
    [CrossRef]
  15. S. H. Kang, H. J. Eom, and T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
    [CrossRef]
  16. T. J. Park, S. H. Kang, and H. J. Eom, “TE scattering from a slit in a thick conducting screen: Revisited,” IEEE Trans. Antenna Propag. 42, 112–114 (1994).
    [CrossRef]
  17. H. J. Eom, “Slit array antenna,” in Electromagnetic Wave Theory for Boundary-Value Problems (Springer, 2004), pp. 251–257.
  18. 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).
    [CrossRef]
  19. M. A. Basha, S. K. Chaudhuri, and S. Safavi-Naeini, “Electromagnetic scattering from multiple arbitrary shape grooves: a generalized formulation,” in Proceedings of IEEE MTT-S International Microwave Symposium Digest (2007), pp. 1935–1938.
  20. O. M. Ramahi and R. Mittra, “Finite element solution for a class of unbounded geometries,” IEEE Trans. Antennas Propag. 39, 244–250 (1991).
    [CrossRef]
  21. J. M. Jin and J. L. Volakis, “TM scattering by an inhomogeneously filled aperture in a thick conducting plane,” IEE Proc. Microwaves Antennas Propag. 137, 153–159(1990).
    [CrossRef]
  22. J. M. Jin and J. L. Volakis, “TE scattering by an inhomogeneously filled thick conducting plane,” IEEE Trans. Antennas Propag. 38, 1280–1286 (1990).
    [CrossRef]
  23. B. Alavikia and O. M. Ramahi, “Finite-element solution of the problem of scattering from cavities in metallic screens using the surface integral equation as a boundary constraint,” J. Opt. Soc. Am. A 26, 1915–1925 (2009).
    [CrossRef]
  24. B. Alavikia and O. M. Ramahi, “An efficient method using finite-elements and the surface integral equation to solve the problem of scattering from infinite periodic conducting grating,” Radio Sci. 46, RS1001 (2011).
    [CrossRef]
  25. T. Van and A. Wood, “Analysis of transient electromagnetic scattering from overfilled cavities,” SIAM J. Appl. Math. 64, 688–708 (2003).
  26. J. Q. Huang and A. H. Wood, “Numerical simulation of electromagnetic scattering induced by an overfilled cavity in the ground plane,” IEEE Antennas Wireless Propag. Lett. 4, 224–228 (2005).
    [CrossRef]
  27. A. Wood, “Analysis of electromagnetic scattering from an overfilled cavity in the ground plane,” J. Comput. Phys. 215, 630–641 (2006).
    [CrossRef]
  28. K. Du, “Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities,” J. Comput. Phys. 230, 5822–5835 (2011).
    [CrossRef]
  29. B. Alavikia and O. M. Ramahi, “Fundamental limitations on the use of open-region boundary conditions and matched layers to solve the problem of gratings in metallic screens,” ACES J. 25, 652–658 (2010).
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2011 (2)

B. Alavikia and O. M. Ramahi, “An efficient method using finite-elements and the surface integral equation to solve the problem of scattering from infinite periodic conducting grating,” Radio Sci. 46, RS1001 (2011).
[CrossRef]

K. Du, “Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities,” J. Comput. Phys. 230, 5822–5835 (2011).
[CrossRef]

2010 (3)

B. Alavikia and O. M. Ramahi, “Fundamental limitations on the use of open-region boundary conditions and matched layers to solve the problem of gratings in metallic screens,” ACES J. 25, 652–658 (2010).

F. Wei and Z. Liu, “Plasmonic structured illumination microscopy,” Nano Lett. 10, 2531–2536 (2010).
[CrossRef]

H. Hu, C. Ma, and Z. Liu, “Plasmonic dark field microscopy,” Appl. Phys. 96, 113107 (2010).
[CrossRef]

2009 (1)

2008 (1)

Y. Xiong, Zh. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. 93, 111116 (2008).

2007 (2)

Y. Ngu, M. Peckerar, M. Dagenais, J. Barry, and B. Dutt, “Lithography, plasmonics, and subwavelength aperture exposure technology,” J. Vac. Sci. Technol. B 25–6, 2471–2475 (2007).
[CrossRef]

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).
[CrossRef]

2006 (1)

A. Wood, “Analysis of electromagnetic scattering from an overfilled cavity in the ground plane,” J. Comput. Phys. 215, 630–641 (2006).
[CrossRef]

2005 (1)

J. Q. Huang and A. H. Wood, “Numerical simulation of electromagnetic scattering induced by an overfilled cavity in the ground plane,” IEEE Antennas Wireless Propag. Lett. 4, 224–228 (2005).
[CrossRef]

2003 (1)

T. Van and A. Wood, “Analysis of transient electromagnetic scattering from overfilled cavities,” SIAM J. Appl. Math. 64, 688–708 (2003).

2001 (1)

S. Kawata, “Near-field microscope probes utilizing surface plasmon polaritons,” Appl. Phys. 81, 15–27 (2001).
[CrossRef]

1994 (2)

R. A. Depine and D. C. Skigin, “Scattering from metallic surfaces having a finite number of rectangular grooves,” J. Opt. Soc. Am. A 11, 2844–2850 (1994).
[CrossRef]

T. J. Park, S. H. Kang, and H. J. Eom, “TE scattering from a slit in a thick conducting screen: Revisited,” IEEE Trans. Antenna Propag. 42, 112–114 (1994).
[CrossRef]

1993 (4)

S. H. Kang, H. J. Eom, and T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analytic solution for transverse-magnetic scattering from a rectangular channel in a conducting plane,” J. Appl. Phys. 73, 3571–3573 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analysis of transverse electric scattering from a rectangular channel in a conducting plane,” Radio Sci. 28, 663–673 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “Analysis of TM scattering from finite rectangular grooves in a conducting plane,” J. Opt. Soc. Am. A 10, 905–911 (1993).
[CrossRef]

1992 (1)

1991 (2)

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

K. Barkeshli and J. L. Volakis, “Scattering from narrow rectangular filled grooves,” IEEE Trans. Antenna Propag. 39, 804–810 (1991).
[CrossRef]

1990 (3)

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

J. M. Jin and J. L. Volakis, “TM scattering by an inhomogeneously filled aperture in a thick conducting plane,” IEE Proc. Microwaves Antennas Propag. 137, 153–159(1990).
[CrossRef]

J. M. Jin and J. L. Volakis, “TE scattering by an inhomogeneously filled thick conducting plane,” IEEE Trans. Antennas Propag. 38, 1280–1286 (1990).
[CrossRef]

1978 (1)

D. T. Auckland and R. F. Harrington, “Electromagnetic transmission through a filled slit in a conducting plane of finite thickness, TE case,” IEEE Trans. Microwave Theory Tech. 26, 499–505 (1978).
[CrossRef]

1976 (1)

R. F. Harrington and J. R. Mautz, “A generalized network formulation for aperture problems,” IEEE Trans. Antenna Propag. 24, 870–873 (1976).
[CrossRef]

Alavikia, B.

B. Alavikia and O. M. Ramahi, “An efficient method using finite-elements and the surface integral equation to solve the problem of scattering from infinite periodic conducting grating,” Radio Sci. 46, RS1001 (2011).
[CrossRef]

B. Alavikia and O. M. Ramahi, “Fundamental limitations on the use of open-region boundary conditions and matched layers to solve the problem of gratings in metallic screens,” ACES J. 25, 652–658 (2010).

B. Alavikia and O. M. Ramahi, “Finite-element solution of the problem of scattering from cavities in metallic screens using the surface integral equation as a boundary constraint,” J. Opt. Soc. Am. A 26, 1915–1925 (2009).
[CrossRef]

Auckland, D. T.

D. T. Auckland and R. F. Harrington, “Electromagnetic transmission through a filled slit in a conducting plane of finite thickness, TE case,” IEEE Trans. Microwave Theory Tech. 26, 499–505 (1978).
[CrossRef]

Barkeshli, K.

K. Barkeshli and J. L. Volakis, “Scattering from narrow rectangular filled grooves,” IEEE Trans. Antenna Propag. 39, 804–810 (1991).
[CrossRef]

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

Barry, J.

Y. Ngu, M. Peckerar, M. Dagenais, J. Barry, and B. Dutt, “Lithography, plasmonics, and subwavelength aperture exposure technology,” J. Vac. Sci. Technol. B 25–6, 2471–2475 (2007).
[CrossRef]

Basha, M. A.

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).
[CrossRef]

M. A. Basha, S. K. Chaudhuri, and S. Safavi-Naeini, “Electromagnetic scattering from multiple arbitrary shape grooves: a generalized formulation,” in Proceedings of IEEE MTT-S International Microwave Symposium Digest (2007), pp. 1935–1938.

Chaudhuri, S. K.

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).
[CrossRef]

M. A. Basha, S. K. Chaudhuri, and S. Safavi-Naeini, “Electromagnetic scattering from multiple arbitrary shape grooves: a generalized formulation,” in Proceedings of IEEE MTT-S International Microwave Symposium Digest (2007), pp. 1935–1938.

Dagenais, M.

Y. Ngu, M. Peckerar, M. Dagenais, J. Barry, and B. Dutt, “Lithography, plasmonics, and subwavelength aperture exposure technology,” J. Vac. Sci. Technol. B 25–6, 2471–2475 (2007).
[CrossRef]

Depine, R. A.

Du, K.

K. Du, “Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities,” J. Comput. Phys. 230, 5822–5835 (2011).
[CrossRef]

Dutt, B.

Y. Ngu, M. Peckerar, M. Dagenais, J. Barry, and B. Dutt, “Lithography, plasmonics, and subwavelength aperture exposure technology,” J. Vac. Sci. Technol. B 25–6, 2471–2475 (2007).
[CrossRef]

Eom, H. J.

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).
[CrossRef]

T. J. Park, S. H. Kang, and H. J. Eom, “TE scattering from a slit in a thick conducting screen: Revisited,” IEEE Trans. Antenna Propag. 42, 112–114 (1994).
[CrossRef]

S. H. Kang, H. J. Eom, and T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “Analysis of TM scattering from finite rectangular grooves in a conducting plane,” J. Opt. Soc. Am. A 10, 905–911 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analysis of transverse electric scattering from a rectangular channel in a conducting plane,” Radio Sci. 28, 663–673 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analytic solution for transverse-magnetic scattering from a rectangular channel in a conducting plane,” J. Appl. Phys. 73, 3571–3573 (1993).
[CrossRef]

H. J. Eom, “Slit array antenna,” in Electromagnetic Wave Theory for Boundary-Value Problems (Springer, 2004), pp. 251–257.

Harrington, R. F.

D. T. Auckland and R. F. Harrington, “Electromagnetic transmission through a filled slit in a conducting plane of finite thickness, TE case,” IEEE Trans. Microwave Theory Tech. 26, 499–505 (1978).
[CrossRef]

R. F. Harrington and J. R. Mautz, “A generalized network formulation for aperture problems,” IEEE Trans. Antenna Propag. 24, 870–873 (1976).
[CrossRef]

Hu, H.

H. Hu, C. Ma, and Z. Liu, “Plasmonic dark field microscopy,” Appl. Phys. 96, 113107 (2010).
[CrossRef]

Huang, J. Q.

J. Q. Huang and A. H. Wood, “Numerical simulation of electromagnetic scattering induced by an overfilled cavity in the ground plane,” IEEE Antennas Wireless Propag. Lett. 4, 224–228 (2005).
[CrossRef]

Jin, J. M.

J. M. Jin and J. L. Volakis, “TE scattering by an inhomogeneously filled thick conducting plane,” IEEE Trans. Antennas Propag. 38, 1280–1286 (1990).
[CrossRef]

J. M. Jin and J. L. Volakis, “TM scattering by an inhomogeneously filled aperture in a thick conducting plane,” IEE Proc. Microwaves Antennas Propag. 137, 153–159(1990).
[CrossRef]

Kang, S. H.

T. J. Park, S. H. Kang, and H. J. Eom, “TE scattering from a slit in a thick conducting screen: Revisited,” IEEE Trans. Antenna Propag. 42, 112–114 (1994).
[CrossRef]

S. H. Kang, H. J. Eom, and T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

Kawata, S.

S. Kawata, “Near-field microscope probes utilizing surface plasmon polaritons,” Appl. Phys. 81, 15–27 (2001).
[CrossRef]

Kok, Y.-L.

Liu, Z.

F. Wei and Z. Liu, “Plasmonic structured illumination microscopy,” Nano Lett. 10, 2531–2536 (2010).
[CrossRef]

H. Hu, C. Ma, and Z. Liu, “Plasmonic dark field microscopy,” Appl. Phys. 96, 113107 (2010).
[CrossRef]

Liu, Zh.

Y. Xiong, Zh. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. 93, 111116 (2008).

Ma, C.

H. Hu, C. Ma, and Z. Liu, “Plasmonic dark field microscopy,” Appl. Phys. 96, 113107 (2010).
[CrossRef]

Mautz, J. R.

R. F. Harrington and J. R. Mautz, “A generalized network formulation for aperture problems,” IEEE Trans. Antenna Propag. 24, 870–873 (1976).
[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]

Ngu, Y.

Y. Ngu, M. Peckerar, M. Dagenais, J. Barry, and B. Dutt, “Lithography, plasmonics, and subwavelength aperture exposure technology,” J. Vac. Sci. Technol. B 25–6, 2471–2475 (2007).
[CrossRef]

Park, T. J.

T. J. Park, S. H. Kang, and H. J. Eom, “TE scattering from a slit in a thick conducting screen: Revisited,” IEEE Trans. Antenna Propag. 42, 112–114 (1994).
[CrossRef]

S. H. Kang, H. J. Eom, and T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analytic solution for transverse-magnetic scattering from a rectangular channel in a conducting plane,” J. Appl. Phys. 73, 3571–3573 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analysis of transverse electric scattering from a rectangular channel in a conducting plane,” Radio Sci. 28, 663–673 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “Analysis of TM scattering from finite rectangular grooves in a conducting plane,” J. Opt. Soc. Am. A 10, 905–911 (1993).
[CrossRef]

Peckerar, M.

Y. Ngu, M. Peckerar, M. Dagenais, J. Barry, and B. Dutt, “Lithography, plasmonics, and subwavelength aperture exposure technology,” J. Vac. Sci. Technol. B 25–6, 2471–2475 (2007).
[CrossRef]

Ramahi, O. M.

B. Alavikia and O. M. Ramahi, “An efficient method using finite-elements and the surface integral equation to solve the problem of scattering from infinite periodic conducting grating,” Radio Sci. 46, RS1001 (2011).
[CrossRef]

B. Alavikia and O. M. Ramahi, “Fundamental limitations on the use of open-region boundary conditions and matched layers to solve the problem of gratings in metallic screens,” ACES J. 25, 652–658 (2010).

B. Alavikia and O. M. Ramahi, “Finite-element solution of the problem of scattering from cavities in metallic screens using the surface integral equation as a boundary constraint,” J. Opt. Soc. Am. A 26, 1915–1925 (2009).
[CrossRef]

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

Safavi-Naeini, S.

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).
[CrossRef]

M. A. Basha, S. K. Chaudhuri, and S. Safavi-Naeini, “Electromagnetic scattering from multiple arbitrary shape grooves: a generalized formulation,” in Proceedings of IEEE MTT-S International Microwave Symposium Digest (2007), pp. 1935–1938.

Skigin, D. C.

Van, T.

T. Van and A. Wood, “Analysis of transient electromagnetic scattering from overfilled cavities,” SIAM J. Appl. Math. 64, 688–708 (2003).

Volakis, J. L.

K. Barkeshli and J. L. Volakis, “Scattering from narrow rectangular filled grooves,” IEEE Trans. Antenna Propag. 39, 804–810 (1991).
[CrossRef]

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

J. M. Jin and J. L. Volakis, “TE scattering by an inhomogeneously filled thick conducting plane,” IEEE Trans. Antennas Propag. 38, 1280–1286 (1990).
[CrossRef]

J. M. Jin and J. L. Volakis, “TM scattering by an inhomogeneously filled aperture in a thick conducting plane,” IEE Proc. Microwaves Antennas Propag. 137, 153–159(1990).
[CrossRef]

Wei, F.

F. Wei and Z. Liu, “Plasmonic structured illumination microscopy,” Nano Lett. 10, 2531–2536 (2010).
[CrossRef]

Wood, A.

A. Wood, “Analysis of electromagnetic scattering from an overfilled cavity in the ground plane,” J. Comput. Phys. 215, 630–641 (2006).
[CrossRef]

T. Van and A. Wood, “Analysis of transient electromagnetic scattering from overfilled cavities,” SIAM J. Appl. Math. 64, 688–708 (2003).

Wood, A. H.

J. Q. Huang and A. H. Wood, “Numerical simulation of electromagnetic scattering induced by an overfilled cavity in the ground plane,” IEEE Antennas Wireless Propag. Lett. 4, 224–228 (2005).
[CrossRef]

Xiong, Y.

Y. Xiong, Zh. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. 93, 111116 (2008).

Yoshitomi, K.

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analytic solution for transverse-magnetic scattering from a rectangular channel in a conducting plane,” J. Appl. Phys. 73, 3571–3573 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “Analysis of TM scattering from finite rectangular grooves in a conducting plane,” J. Opt. Soc. Am. A 10, 905–911 (1993).
[CrossRef]

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analysis of transverse electric scattering from a rectangular channel in a conducting plane,” Radio Sci. 28, 663–673 (1993).
[CrossRef]

Zhang, X.

Y. Xiong, Zh. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. 93, 111116 (2008).

ACES J. (1)

B. Alavikia and O. M. Ramahi, “Fundamental limitations on the use of open-region boundary conditions and matched layers to solve the problem of gratings in metallic screens,” ACES J. 25, 652–658 (2010).

Appl. Phys. (3)

S. Kawata, “Near-field microscope probes utilizing surface plasmon polaritons,” Appl. Phys. 81, 15–27 (2001).
[CrossRef]

H. Hu, C. Ma, and Z. Liu, “Plasmonic dark field microscopy,” Appl. Phys. 96, 113107 (2010).
[CrossRef]

Y. Xiong, Zh. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. 93, 111116 (2008).

IEE Proc. Microwaves Antennas Propag. (1)

J. M. Jin and J. L. Volakis, “TM scattering by an inhomogeneously filled aperture in a thick conducting plane,” IEE Proc. Microwaves Antennas Propag. 137, 153–159(1990).
[CrossRef]

IEEE Antennas Wireless Propag. Lett. (1)

J. Q. Huang and A. H. Wood, “Numerical simulation of electromagnetic scattering induced by an overfilled cavity in the ground plane,” IEEE Antennas Wireless Propag. Lett. 4, 224–228 (2005).
[CrossRef]

IEEE Trans. Antenna Propag. (4)

R. F. Harrington and J. R. Mautz, “A generalized network formulation for aperture problems,” IEEE Trans. Antenna Propag. 24, 870–873 (1976).
[CrossRef]

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

K. Barkeshli and J. L. Volakis, “Scattering from narrow rectangular filled grooves,” IEEE Trans. Antenna Propag. 39, 804–810 (1991).
[CrossRef]

T. J. Park, S. H. Kang, and H. J. Eom, “TE scattering from a slit in a thick conducting screen: Revisited,” IEEE Trans. Antenna Propag. 42, 112–114 (1994).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

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

J. M. Jin and J. L. Volakis, “TE scattering by an inhomogeneously filled thick conducting plane,” IEEE Trans. Antennas Propag. 38, 1280–1286 (1990).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

S. H. Kang, H. J. Eom, and T. J. Park, “TM-scattering from a slit in a thick conducting screen: revisited,” IEEE Trans. Microwave Theory Tech. 41, 895–899 (1993).
[CrossRef]

D. T. Auckland and R. F. Harrington, “Electromagnetic transmission through a filled slit in a conducting plane of finite thickness, TE case,” IEEE Trans. Microwave Theory Tech. 26, 499–505 (1978).
[CrossRef]

J. Appl. Phys. (1)

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analytic solution for transverse-magnetic scattering from a rectangular channel in a conducting plane,” J. Appl. Phys. 73, 3571–3573 (1993).
[CrossRef]

J. Comput. Phys. (2)

A. Wood, “Analysis of electromagnetic scattering from an overfilled cavity in the ground plane,” J. Comput. Phys. 215, 630–641 (2006).
[CrossRef]

K. Du, “Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities,” J. Comput. Phys. 230, 5822–5835 (2011).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Vac. Sci. Technol. B (1)

Y. Ngu, M. Peckerar, M. Dagenais, J. Barry, and B. Dutt, “Lithography, plasmonics, and subwavelength aperture exposure technology,” J. Vac. Sci. Technol. B 25–6, 2471–2475 (2007).
[CrossRef]

Nano Lett. (1)

F. Wei and Z. Liu, “Plasmonic structured illumination microscopy,” Nano Lett. 10, 2531–2536 (2010).
[CrossRef]

Radio Sci. (2)

T. J. Park, H. J. Eom, and K. Yoshitomi, “An analysis of transverse electric scattering from a rectangular channel in a conducting plane,” Radio Sci. 28, 663–673 (1993).
[CrossRef]

B. Alavikia and O. M. Ramahi, “An efficient method using finite-elements and the surface integral equation to solve the problem of scattering from infinite periodic conducting grating,” Radio Sci. 46, RS1001 (2011).
[CrossRef]

SIAM J. Appl. Math. (1)

T. Van and A. Wood, “Analysis of transient electromagnetic scattering from overfilled cavities,” SIAM J. Appl. Math. 64, 688–708 (2003).

Other (3)

COMSOL Version 3.5, “COMSOL MULTIPHYSICS,” http://www.comsol.com/ .

M. A. Basha, S. K. Chaudhuri, and S. Safavi-Naeini, “Electromagnetic scattering from multiple arbitrary shape grooves: a generalized formulation,” in Proceedings of IEEE MTT-S International Microwave Symposium Digest (2007), pp. 1935–1938.

H. J. Eom, “Slit array antenna,” in Electromagnetic Wave Theory for Boundary-Value Problems (Springer, 2004), pp. 251–257.

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Figures (11)

Fig. 1.
Fig. 1.

Schematic of the scattering problem from two overfilled cavities with arbitrary shapes and fillings in an infinite perfect electric conductor screen. The red dashed curve represents the interior region.

Fig. 2.
Fig. 2.

Schematic of the surface integral contour for two overfilled cavities in an infinite perfect electric conductor screen.

Fig. 3.
Fig. 3.

Schematic of the scattering problem from an infinite array of identical overfilled cavities with arbitrary shapes and fillings in an infinite perfect electric conductor screen. The red dashed curve represents the interior region of a cavity in the mth unit cell.

Fig. 4.
Fig. 4.

Schematic of the surface integral contour for an infinite array of identical overfilled cavities in an infinite perfect electric conductor screen.

Fig. 5.
Fig. 5.

Schematic of the scattering problem from five identical overfilled rectangular cavities with semicircle protruding in an infinite perfect electric conductor screen. The width and the depth of the cavities and the radius of the protruding portions are denoted by w, h, and R, respectively. The cavities are separated by the distance of d.

Fig. 6.
Fig. 6.

Amplitude of the total E-field at the aperture of five identical overfilled rectangular cavities with semicircle protruding in an infinite PEC screen shown in Fig. 5, TMz case and normal incidence, calculated using the method presented in this work (FEM-TFSIE), COMSOL (FEM-COMSOL), and the method reported in [28] (FEM-Semi-Ellipse-TBC). w=0.1λ, h=0.2λ, R=0.05λ, and d=0.4λ. The cavities are overfilled with dielectric material having permittivity of εr=41j.

Fig. 7.
Fig. 7.

Amplitude of the total H-field at the aperture of five identical overfilled rectangular cavities with semicircle protruding in an infinite PEC screen shown in Fig. 5, TEz case and normal incidence, calculated using the method presented in this work (FEM-TFSIE), COMSOL (FEM-COMSOL), and the method reported in [28] (FEM-Semi-Ellipse-TBC). w=0.1λ, h=0.2λ, R=0.05λ, and d=0.4λ. The cavities are overfilled with dielectric material having permittivity of εr=41j.

Fig. 8.
Fig. 8.

Schematic of the domain truncation using ABC or PML in the scattering problem from an array of overfilled cavities engraved in an infinite PEC screen.

Fig. 9.
Fig. 9.

Schematic of the scattering problem from an infinite array of identical overfilled rectangular cavities with semicircle protruding in an infinite perfect electric conductor screen. The width and the depth of the cavities and the radius of the protruding portions are denoted by w, h, and R, respectively. The periodicity of the array is denoted by P.

Fig. 10.
Fig. 10.

Amplitude of the total E-field at the aperture of an infinite array of identical overfilled rectangular cavities with semicircle protruding in an infinite PEC screen shown in Fig. 9, TMz case and incident angle of θ=30°, calculated using the method presented in this work (FEM-TFSIE), and COMSOL (FEM-COMSOL). w=0.5λ, h=1.0λ, R=0.25λ, P=0.75λ, εr1=2.1(10.5j), and εr2=4(10.5j).

Fig. 11.
Fig. 11.

Amplitude of the total H-field at the aperture of an infinite array of identical overfilled rectangular cavities with semicircle protruding in an infinite PEC screen shown in Fig. 9, TEz case and normal incident, calculated using the method presented in this work (FEM-TFSIE), and COMSOL (FEM-COMSOL). w=0.5λ, h=1.0λ, R=0.25λ, and P=0.75λ, εr1=2.1(10.5j), and εr2=4(10.5j).

Equations (23)

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·(1p(ρ)uzt(ρ))+q(ρ)k02uzt(ρ)=jωg(ρ),
[MiiMib0MbiMbbMbo0MobMoo][uiubuo]=[FiFbFo],
2uz(ρ)+k02uz(ρ)=jωp(ρ)gz(ρ),ρΩ,
2G(ρ,ρ)+k02G(ρ,ρ)=δ(ρρ)ρ,ρΩ
G(ρ,ρ)=j4H0(2)(k0|ρρs|)±j4H0(2)(k0|ρρi|),
uz(ρ)=jωΩp(ρ)gz(ρ)G(ρ,ρ)dΩΓ(uz(ρ)G(ρ,ρ)nG(ρ,ρ)uz(ρ)n)dΓ,
uz(ρ)=uza(ρ)ΓB1+ΓB2(uz(ρ)G(ρ,ρ)nG(ρ,ρ)uz(ρ)n)dΓ.
uz(ρ)=j=1nuzjψj(ρ).
uz(ρ)n=uz(ρ)uz(ρ)Δn.
[uo]=[T][SI][ub]+[SII]{[uo][ub]},
SijI=ρjΔlρj+Δlψj(ρj)G(ρi,ρj)ndl
SijII=ρjΔlρj+ΔlG(ρi,ρj)ψj(ρj)Δndl.
[uo]={[I][SII]}1[T]{[I][SII]}1{[SII]+[SI]}[ub],
[MiiMibMbiMbbMbo(ISII)1(SII+SI)][uiub]=[FiFbMbo(ISII)1T].
[MiiMib0MbiMbbMbo0MobMoo]m[uiubuo]m=[FiFbFo]m,
[M][u]=[F][M]0[u]0=[F]0[M][u]=[F],
uz(ρ)=jωΩp(ρ)gz(ρ)G(ρ,ρ)dΩΓ(uz(ρ)G(ρ,ρ)nG(ρ,ρ)uz(ρ)n)dΓ,
uz(ρ)=uza(ρ)m=ΓBm(uz(ρm)G(ρ,ρm)nG(ρ,ρm)uz(ρm)n)dΓ,
uz(ρm)=uz(ρn)ej(mn)(k0sinθ)P,
uz(ρ)=uza(ρ)ΓB0(uz(ρ)GQ(ρ,ρ)nGQ(ρ,ρ)uz(ρ)n)dΓ,
GQ(ρ,ρ)=m=ejm(k0sinθ)PG(ρ,ρ+mPx^).
[uo]=[T][SI][ub]+[SII]{[uo][ub]},
[MiiMibMbiMbbMbo(ISII)1(SII+SI)]m=0[uiub]m=0=[FiFbMbo(ISII)1T]m=0.

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