Abstract

This work presents a hybrid finite-element-boundary integral algorithm to solve the problem of scattering from a finite and infinite array of two-dimensional cavities engraved in a perfectly electric conducting screen covered with a stratified dielectric layer. The solution region is divided into interior regions containing the cavities and the region exterior to the cavities. The finite-element formulation is applied only inside the interior regions to derive a linear system of equations associated with unknown field values. Using a two-boundary formulation, the surface integral equation employing the grounded dielectric slab Green’s function in the spatial domain is applied at the opening of the cavities as a boundary constraint to truncate the solution region. Placing the truncation boundary at the opening of the cavities and inside the dielectric layer results in a 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 an array of cavities with different dimensions and inhomogeneous fillings covered with dielectric layers.

© 2011 Optical Society of America

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References

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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] [PubMed]
  3. H. Hu, C. Ma, and Z. Liu, “Plasmonic dark field microscopy,” Appl. Phys. Lett. 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, 2471–2475 (2007).
    [CrossRef]
  5. Y. Xiong, Z. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal–dielectric multilayers,” Appl. Phys. Lett. 93, 111116 (2008).
    [CrossRef]
  6. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
    [CrossRef]
  7. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–823 (2002).
    [CrossRef] [PubMed]
  8. J. M. Jin and J. L. Volakis, “TM scattering by an inhomogeneously filled aperture in a thick conducting plane,” IEE Proc. Microw. Antennas Propag. 137, 153–159 (1990).
    [CrossRef]
  9. 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]
  10. 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]
  11. 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, doi:10.1029/2010RS004466 (2011).
    [CrossRef]
  12. J. M. Jin and J. L. Volakis, “A finite-element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures,” IEEE Trans. Antennas Propag. 39, 97–104 (1991).
    [CrossRef]
  13. J. M. Jin and J. L. Volakis, “Electromagnetic scattering by and transmission through a three-dimensional slot in a thick conducting plane,” IEEE Trans. Antennas Propag. 39, 543–550(1991).
    [CrossRef]
  14. B. H. McDonald and A. Wexler, “Finite-element solution of unbounded field problems,” IEEE Trans. Microwave Theor. Tech. 20, 841–847 (1972).
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  15. A. Parsa and R. Paknys, “Interior Green’s function solution for a thick and finite dielectric slab,” IEEE Trans. Antennas Propag. 55, 3504–3514 (2007).
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  22. F. Mesa, R. R. Biox, and F. Medina, “Closed-form expressions of multilayered planar Green’s functions that account for the continuous spectrum in the far field,” IEEE Trans. Microwave Theor. Tech. 56, 1601–1614 (2008).
    [CrossRef]
  23. A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microwave Theor. Tech. 58, 602–613(2010).
    [CrossRef]
  24. R. R. Biox, A. L. Fructos, and F. Medina, “Closed-form uniform asymptotic expansions of Green’s functions in layered media,” IEEE Trans. Antennas Propag. 58, 2934–2945 (2010).
    [CrossRef]
  25. L. B. Felson and N. Marcuvitz, “Space- and time-dependent linear fields,” in Radiation and Scattering of the Waves (IEEE, 1994), pp. 87–88.
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2011 (1)

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, doi:10.1029/2010RS004466 (2011).
[CrossRef]

2010 (4)

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

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

A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microwave Theor. Tech. 58, 602–613(2010).
[CrossRef]

R. R. Biox, A. L. Fructos, and F. Medina, “Closed-form uniform asymptotic expansions of Green’s functions in layered media,” IEEE Trans. Antennas Propag. 58, 2934–2945 (2010).
[CrossRef]

2009 (1)

2008 (2)

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

F. Mesa, R. R. Biox, and F. Medina, “Closed-form expressions of multilayered planar Green’s functions that account for the continuous spectrum in the far field,” IEEE Trans. Microwave Theor. Tech. 56, 1601–1614 (2008).
[CrossRef]

2007 (3)

R. R. Biox, F. Mesa, and F. Medina, “Application of total least squares to the derivation of closed-form Green’s functions for planar layered media,” IEEE Trans. Microwave Theor. Tech. 55, 268–280 (2007).
[CrossRef]

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

A. Parsa and R. Paknys, “Interior Green’s function solution for a thick and finite dielectric slab,” IEEE Trans. Antennas Propag. 55, 3504–3514 (2007).
[CrossRef]

2005 (1)

M. I. Aksun and G. Dural, “Clarification of issues on the closed-form Green’s functions in stratified media,” IEEE Trans. Antennas Propag. 53, 3644–3653 (2005).
[CrossRef]

2002 (2)

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

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–823 (2002).
[CrossRef] [PubMed]

2001 (1)

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

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

1996 (1)

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

1995 (1)

G. Dural and M. I. Aksun, “Closed form Green’s function for general sources and stratified media,” IEEE Trans. Microwave Theor. Tech. 43, 1545–1552 (1995).
[CrossRef]

1991 (2)

J. M. Jin and J. L. Volakis, “A finite-element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures,” IEEE Trans. Antennas Propag. 39, 97–104 (1991).
[CrossRef]

J. M. Jin and J. L. Volakis, “Electromagnetic scattering by and transmission through a three-dimensional slot in a thick conducting plane,” IEEE Trans. Antennas Propag. 39, 543–550(1991).
[CrossRef]

1990 (3)

K. A. Michalski and D. Zheng, “Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media, part I: theory,” IEEE Trans. Antennas Propag. 38, 335–344 (1990).
[CrossRef]

J. M. Jin and J. L. Volakis, “TM scattering by an inhomogeneously filled aperture in a thick conducting plane,” IEE Proc. Microw. 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]

1984 (1)

D. M. Pozar and D. H. Schaubert, “Scan blindness in infinite phased arrays of printed dipoles,” IEEE Trans. Antennas Propag. 32, 602–610 (1984).
[CrossRef]

1972 (1)

B. H. McDonald and A. Wexler, “Finite-element solution of unbounded field problems,” IEEE Trans. Microwave Theor. Tech. 20, 841–847 (1972).
[CrossRef]

Aksun, M. I.

A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microwave Theor. Tech. 58, 602–613(2010).
[CrossRef]

M. I. Aksun and G. Dural, “Clarification of issues on the closed-form Green’s functions in stratified media,” IEEE Trans. Antennas Propag. 53, 3644–3653 (2005).
[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 Theor. Tech. 50, 1264–1274(2002).
[CrossRef]

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

G. Dural and M. I. Aksun, “Closed form Green’s function for general sources and stratified media,” IEEE Trans. Microwave Theor. Tech. 43, 1545–1552 (1995).
[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, doi:10.1029/2010RS004466 (2011).
[CrossRef]

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]

Alparslan, A.

A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microwave Theor. Tech. 58, 602–613(2010).
[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, 2471–2475 (2007).
[CrossRef]

Biox, R. R.

R. R. Biox, A. L. Fructos, and F. Medina, “Closed-form uniform asymptotic expansions of Green’s functions in layered media,” IEEE Trans. Antennas Propag. 58, 2934–2945 (2010).
[CrossRef]

F. Mesa, R. R. Biox, and F. Medina, “Closed-form expressions of multilayered planar Green’s functions that account for the continuous spectrum in the far field,” IEEE Trans. Microwave Theor. Tech. 56, 1601–1614 (2008).
[CrossRef]

R. R. Biox, F. Mesa, and F. Medina, “Application of total least squares to the derivation of closed-form Green’s functions for planar layered media,” IEEE Trans. Microwave Theor. Tech. 55, 268–280 (2007).
[CrossRef]

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 Theor. Tech. 50, 1264–1274(2002).
[CrossRef]

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, 2471–2475 (2007).
[CrossRef]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–823 (2002).
[CrossRef] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–823 (2002).
[CrossRef] [PubMed]

Dural, G.

M. I. Aksun and G. Dural, “Clarification of issues on the closed-form Green’s functions in stratified media,” IEEE Trans. Antennas Propag. 53, 3644–3653 (2005).
[CrossRef]

G. Dural and M. I. Aksun, “Closed form Green’s function for general sources and stratified media,” IEEE Trans. Microwave Theor. Tech. 43, 1545–1552 (1995).
[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, 2471–2475 (2007).
[CrossRef]

Ebbesen, T. W.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–823 (2002).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Felson, L. B.

L. B. Felson and N. Marcuvitz, “Space- and time-dependent linear fields,” in Radiation and Scattering of the Waves (IEEE, 1994), pp. 87–88.

Fructos, A. L.

R. R. Biox, A. L. Fructos, and F. Medina, “Closed-form uniform asymptotic expansions of Green’s functions in layered media,” IEEE Trans. Antennas Propag. 58, 2934–2945 (2010).
[CrossRef]

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–823 (2002).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

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 Theor. Tech. 50, 1264–1274(2002).
[CrossRef]

Hu, H.

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

Jin, J. M.

J. M. Jin and J. L. Volakis, “A finite-element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures,” IEEE Trans. Antennas Propag. 39, 97–104 (1991).
[CrossRef]

J. M. Jin and J. L. Volakis, “Electromagnetic scattering by and transmission through a three-dimensional slot in a thick conducting plane,” IEEE Trans. Antennas Propag. 39, 543–550(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]

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

Kawata, S.

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

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–823 (2002).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–823 (2002).
[CrossRef] [PubMed]

Liu, Z.

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

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

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

Ma, C.

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

Marcuvitz, N.

L. B. Felson and N. Marcuvitz, “Space- and time-dependent linear fields,” in Radiation and Scattering of the Waves (IEEE, 1994), pp. 87–88.

Martin-Moreno, L.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–823 (2002).
[CrossRef] [PubMed]

McDonald, B. H.

B. H. McDonald and A. Wexler, “Finite-element solution of unbounded field problems,” IEEE Trans. Microwave Theor. Tech. 20, 841–847 (1972).
[CrossRef]

Medina, F.

R. R. Biox, A. L. Fructos, and F. Medina, “Closed-form uniform asymptotic expansions of Green’s functions in layered media,” IEEE Trans. Antennas Propag. 58, 2934–2945 (2010).
[CrossRef]

F. Mesa, R. R. Biox, and F. Medina, “Closed-form expressions of multilayered planar Green’s functions that account for the continuous spectrum in the far field,” IEEE Trans. Microwave Theor. Tech. 56, 1601–1614 (2008).
[CrossRef]

R. R. Biox, F. Mesa, and F. Medina, “Application of total least squares to the derivation of closed-form Green’s functions for planar layered media,” IEEE Trans. Microwave Theor. Tech. 55, 268–280 (2007).
[CrossRef]

Mesa, F.

F. Mesa, R. R. Biox, and F. Medina, “Closed-form expressions of multilayered planar Green’s functions that account for the continuous spectrum in the far field,” IEEE Trans. Microwave Theor. Tech. 56, 1601–1614 (2008).
[CrossRef]

R. R. Biox, F. Mesa, and F. Medina, “Application of total least squares to the derivation of closed-form Green’s functions for planar layered media,” IEEE Trans. Microwave Theor. Tech. 55, 268–280 (2007).
[CrossRef]

Michalski, K. A.

A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microwave Theor. Tech. 58, 602–613(2010).
[CrossRef]

K. A. Michalski and D. Zheng, “Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media, part I: theory,” IEEE Trans. Antennas Propag. 38, 335–344 (1990).
[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, 2471–2475 (2007).
[CrossRef]

Paknys, R.

A. Parsa and R. Paknys, “Interior Green’s function solution for a thick and finite dielectric slab,” IEEE Trans. Antennas Propag. 55, 3504–3514 (2007).
[CrossRef]

Parsa, A.

A. Parsa and R. Paknys, “Interior Green’s function solution for a thick and finite dielectric slab,” IEEE Trans. Antennas Propag. 55, 3504–3514 (2007).
[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, 2471–2475 (2007).
[CrossRef]

Pozar, D. M.

D. M. Pozar and D. H. Schaubert, “Scan blindness in infinite phased arrays of printed dipoles,” IEEE Trans. Antennas Propag. 32, 602–610 (1984).
[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, doi:10.1029/2010RS004466 (2011).
[CrossRef]

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]

Schaubert, D. H.

D. M. Pozar and D. H. Schaubert, “Scan blindness in infinite phased arrays of printed dipoles,” IEEE Trans. Antennas Propag. 32, 602–610 (1984).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Volakis, J. L.

J. M. Jin and J. L. Volakis, “A finite-element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures,” IEEE Trans. Antennas Propag. 39, 97–104 (1991).
[CrossRef]

J. M. Jin and J. L. Volakis, “Electromagnetic scattering by and transmission through a three-dimensional slot in a thick conducting plane,” IEEE Trans. Antennas Propag. 39, 543–550(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]

J. M. Jin and J. L. Volakis, “TM scattering by an inhomogeneously filled aperture in a thick conducting plane,” IEE Proc. Microw. 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] [PubMed]

Wexler, A.

B. H. McDonald and A. Wexler, “Finite-element solution of unbounded field problems,” IEEE Trans. Microwave Theor. Tech. 20, 841–847 (1972).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Xiong, Y.

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

Zhang, X.

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

Zheng, D.

K. A. Michalski and D. Zheng, “Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media, part I: theory,” IEEE Trans. Antennas Propag. 38, 335–344 (1990).
[CrossRef]

Appl. Phys. (1)

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

Appl. Phys. Lett. (2)

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

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

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Figures (17)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

Schematic of the surface integral contour in the half-space above the cavities.

Fig. 4
Fig. 4

Schematic of the grounded dielectric slab and equivalent short circuit (S.C.) transmission line model.

Fig. 5
Fig. 5

Schematics of (a) a single unit source and (b) an infinite periodic array of unit sources, located inside the grounded dielectric slab.

Fig. 6
Fig. 6

Normalized magnitude of the partial sum of the series (a) for the TM case [Eq. (24)] and (b) for the TE case [Eq. (25)] versus change in lateral distance of the source point and field point ( | x x | ). t s = 0.25 λ , ε / ε = 0.5 , k x 0 = k 0 / 2 , y = 0.01 λ , and y = 0 .

Fig. 7
Fig. 7

Normalized magnitude of the partial sum of the series (a) for the TM case [Eq. (24)] and (b) for the TE case [Eq. (25)] versus change in thickness of the dielectric coating ( t s ). | x x | = 0.6 λ , ε / ε = 0.5 , k x 0 = k 0 / 2 , y = 0.01 λ , and y = 0 .

Fig. 8
Fig. 8

Normalized magnitude of the partial sum of the series (a) for the TM case [Eq. (24)] and (b) for the TE case [Eq. (25)] versus change in the loss tangent of the dielectric coating ( ε / ε ). | x x | = 0.6 λ , t s = 0.25 λ , k x 0 = k 0 / 2 , y = 0.01 λ , and y = 0 .

Fig. 9
Fig. 9

Magnitude of the partial sum of the series (a) for the TM case [Eq. (24)] and (b) for the TE case [Eq. (25)] versus change in periodicity of the infinite array (P) inside the lossless dielectric coating. | x x | = 0 , t s = 0.25 λ , k x 0 = k 0 / 2 , y = 0.01 λ , and y = 0 .

Fig. 10
Fig. 10

Magnitude of the partial sum of the series (a) for the TM case [Eq. (24)] and (b) for the TE case [Eq. (25)] versus change in periodicity of the infinite array (P) inside the lossy dielectric coating with ε / ε = 0.5 . | x x | = 0 , t s = 0.25 λ , k x 0 = k 0 / 2 , y = 0.01 λ , and y = 0 .

Fig. 11
Fig. 11

Schematic of the scattering problem from a conducting screen containing two nonuniform cavities coated with a dielectric layer.

Fig. 12
Fig. 12

Schematic of the surface integral contour in the half-space above two cavities with different shapes and fillings.

Fig. 13
Fig. 13

Amplitude of the total E field at the aperture of an infinite array of bottle-shaped cavities with dielectric coating and inhomogeneous filling, TM case, θ = 45 . ε r 1 = 1.4 ( 1 0.5 j ) , ε r 2 = 2.1 , ε r 3 = 4 , w 1 = 0.4 λ , w 2 = 1 λ , d 1 = 0.4 λ , d 2 = 0.5 λ , P = 1.2 λ , and t s = 0.25 λ .

Fig. 14
Fig. 14

Amplitude of the total H field at the aperture of an infinite array of rectangular cavities with dielectric coating and inhomogeneous filling, TE case, θ = 30 . w = 0.6 λ , d = 0.4 λ , ε r 1 = 1.4 ( 1 0.5 j ) , ε r 2 = 4 , ε r 3 = 2.1 , P = 1 λ , and t s = 0.25 λ .

Fig. 15
Fig. 15

Amplitude of the total E field at the aperture of two rectangular cavities with different dimensions and fillings, covered with dielectric coating, TM case, θ = 15 . w 1 × d 1 = 0.6 λ × 0.4 λ , w 2 × d 2 = 0.4 λ × 0.8 λ , separated by D = 0.05 λ , ε r 1 = 1.4 ( 1 0.5 j ) , ε r 2 = 4 ( 1 0.5 j ) , ε r 3 = 2.1 ( 1 0.5 j ) , and t s = 0.25 λ .

Fig. 16
Fig. 16

Amplitude of the total H field at the aperture of two rectangular cavities with different dimensions and fillings, covered with dielectric coating, TE case, θ = 15 . w 1 × d 1 = 0.6 λ × 0.4 λ , w 2 × d 2 = 0.4 λ × 0.8 λ , separated by D = 0.05 λ , ε r 1 = 1.4 ( 1 0.5 j ) , ε r 2 = 4 ( 1 0.5 j ) , ε r 3 = 2.1 ( 1 0.5 j ) , and t s = 0.25 λ .

Fig. 17
Fig. 17

Amplitude of the far-field for two rectangular cavities with different dimensions and fillings shown in inset of Fig. 15, covered with dielectric coating, TM case, θ = 15 . w 1 × d 1 = 0.6 λ × 0.4 λ , w 2 × d 2 = 0.4 λ × 0.8 λ , separated by D = 0.05 λ , ε r 1 = 1.4 ( 1 0.5 j ) , ε r 2 = 4 ( 1 0.5 j ) , ε r 3 = 2.1 ( 1 0.5 j ) , and t s = 0.25 λ .

Equations (36)

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· ( 1 p ( ρ ) u t ) + q ( ρ ) k 0 2 u t = 0 ,
[ M i i M i b 0 M b i M b b M b o 0 M o b M o o ] m [ u i u b u o ] m = [ F i F b F o ] m ,
u z ( ρ ) = Ω g z ( ρ ) G e , h ( ρ , ρ ) d Ω Γ + Γ ( u z ( ρ ) G e , h ( ρ , ρ ) n G e , h ( ρ , ρ ) u z ( ρ ) n ) d Γ .
u z ( ρ ) = u z excit ( ρ ) m = Γ B m u z ( ρ ) G e ( ρ , ρ ) n d Γ ,
u z ( ρ ) = u z excit ( ρ ) + m = Γ B m G h ( ρ , ρ ) u z ( ρ ) n d Γ .
u z ( ρ + m P x ^ ) = u z ( ρ ) e j m k x 0 P ,
u z ( ρ ) = u z excit ( ρ ) Γ B u z ( ρ ) G Q e ( ρ , ρ ) n d Γ
u z ( ρ ) = u z excit ( ρ ) + Γ B G Q h ( ρ , ρ ) u z ( ρ ) n d Γ
G Q e , h ( ρ , ρ ) = m = e j m k x 0 P G e , h ( ρ , ρ ) .
u z excit ( ρ ) = E z inc ( x , t s ) e j k y 0 t s ( 2 Z in Z in + Z 0 ) sin ( k y 1 y ) sin ( k y 1 t s ) ,
u z excit ( ρ ) = H z inc ( x , t s ) e j k y 0 t s ( cos ( θ inc ) cos ( θ t s ) 2 Z 0 Z in + Z 0 ) cos ( k y 1 y ) cos ( k y 1 t s )
[ u o ] = [ T ] + [ S ] [ u b ]
[ u o ] = { [ I ] + [ S ] } 1 [ T ] + { [ I ] + [ S ] } 1 [ S ] [ u b ]
[ M i i M i b M b i M b b + M b o S ] [ u i u b ] = [ F i F b M b o T ]
[ M i i M i b M b i M b b + M b o ( I + S ) 1 S ] [ u i u b ] = [ F i F b M b o ( I + S ) 1 T ]
G e , h ( x , y ; x , y ) = 1 2 π e j k x | x x | Q e , h ( y , y , k x ) d k x ,
Q e ( y , y , k x ) = { j k y 0 sin ( k y 1 ( t s y ) ) + k y 1 cos ( k y 1 ( t s y ) ) k y 1 ( j k y 0 sin ( k y 1 t s ) + k y 1 cos ( k y 1 t s ) ) sin ( k y 1 y ) , y y < t s , e j k y 0 ( y t s ) ( j k y 0 sin ( k y 1 t s ) + k y 1 cos ( k y 1 t s ) ) sin ( k y 1 y ) , y < t s y ,
Q h ( y , y , k x ) = { j k y 0 sin ( k y 1 ( t s y ) ) + k y 1 cos ( k y 1 ( t s y ) ) k y 1 ( j k y 0 cos ( k y 1 t s ) k y 1 sin ( k y 1 t s ) ) cos ( k y 1 y ) , y y < t s , e j k y 0 ( y t s ) ( j k y 0 cos ( k y 1 t s ) k y 1 sin ( k y 1 t s ) ) cos ( k y 1 y ) , y < t s y ,
lim | x | ( 1 2 π ( x j k x ) e j k x | x x | Q e , h ( y , y , k x ) d k x ) = 0 .
lim ρ ( ρ j k 0 ) ( 1 2 π e j k x | x x | Q e , h ( y , y , k x ) d k x ) = 0 ,
G Q e , h ( x , y ; x , y ) = m = e j m k x 0 P ( 1 2 π e j k x | x ( x + m P ) | Q e , h ( y , y , k x ) d k x ) .
G Q e , h ( x , y ; x , y ) = 1 P m = e j k x m | x x | Q e , h ( y , y , k x m ) ,
k x m = k x 0 + 2 m π P .
S N e = 1 P m = N N e j k x m | x x | y Q e ( y , y , k x m ) ,
S N h = 1 P m = N N e j k x m | x y | Q h ( y , y , k x m ) .
G S e , h ( x , y ; x , y ) = lim P ( 1 P m = e j k x m | x x | Q e , h ( y , y , k x m ) ) .
[ M 1 ] [ u 1 ] = [ F 1 ] [ M 2 ] [ u 2 ] = [ F 2 ] ,
[ [ M 1 ] 0 0 [ M 2 ] ] [ [ u 1 ] [ u 2 ] ] = [ [ F 1 ] [ F 2 ] ] .
u z ( ρ ) = u z excit ( ρ ) Γ B 1 + Γ B 2 u z ( ρ ) G S e ( ρ , ρ ) n d Γ
u z ( ρ ) = u z excit ( ρ ) + Γ B 1 + Γ B 2 G S h ( ρ , ρ ) u z ( ρ ) n d Γ
[ [ M 1 ] [ C 12 ] [ C 21 ] [ M 2 ] ] [ [ u 1 ] [ u 2 ] ] = [ [ F 1 ] [ F 2 ] ] ,
[ [ M ( 1 ) ] [ C ( 12 ) ] [ C ( 1 N ) ] [ C ( 21 ) ] [ M ( 2 ) ] [ C ( 2 N ) ] [ C ( N 1 ) ] [ C ( N 2 ) ] [ M ( N ) ] ] [ [ u ( 1 ) ] [ u ( 2 ) ] [ u ( N ) ] ] = [ [ F ( 1 ) ] [ F ( 2 ) ] [ F ( N ) ] ] .
E ( ρ ) = 1 j ω ε ( × × ( Γ J ( ρ ) G ( ρ , ρ ) d Γ ) J ( ρ ) ) ,
G ( ρ , ρ ) = lim P ( 1 P m = e j k x m | x x | e j k y 0 y e j k y 1 y j ( k y 1 + k y 0 ) e ( j ( k y 1 k y 0 ) t s ) ) , y < t s < y .
J ( ρ ) = z ^ 1 j ω μ E z ( ρ ) n .
E ( ρ ) = z ^ Γ E z ( ρ ) n G ( ρ , ρ ) d Γ .

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