Abstract

The microwave transmission through hole arrays in thick metal plates for both large holes (cut-off below onset of diffraction) and small holes (cut-off above onset of diffraction) have been compared through both experiment and modelling. Enhanced transmission is in part mediated by the excitation of diffractively coupled surface waves. Large holes, with cut-off below the onset of diffraction (due to the hole periodicity), are able to support multiple modes in transmission when the depth of the holes is sufficient to support quantisation in the propagation direction. Small holes, with cut-off above the onset of diffraction however only support two coupled surface modes (symmetric and anti-symmetric) below diffraction.

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2011

G. Xiao and H. Yang, “The effect of array periodicity on the filtering characteristics of metal/dielectric photonic crystals,” J. Semicond. 32(4), 044004 (2011).
[CrossRef]

2010

J. D. Edmunds, M. C. Taylor, A. P. Hibbins, J. R. Sambles, and I. J. Youngs, “Babinet’s principle and the band structure of surface waves on patterned metal arrays,” J. Appl. Phys. 107(10), 103108 (2010).
[CrossRef]

2009

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. Rodier, J. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How holes can obscure the view: suppressed transmission through an ultrathin metal film by a subwavelength hole array,” Phys. Rev. Lett. 103(20), 203901 (2009).
[CrossRef] [PubMed]

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102(7), 073901 (2009).
[CrossRef] [PubMed]

2008

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

A. A. Kirilenko and A. O. Perov, “On the common nature of the enhanced and resonance transmission through the periodical set of holes,” IEEE Trans. Antenn. Propag. 56(10), 3210–3216 (2008).
[CrossRef]

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008).
[CrossRef]

2007

J. Bravo-Abad, L. Martín-Moreno, F. J. García-Vidal, E. Hendry, and J. Gómez-Rivas, “Transmission of light through periodic arrays of square holes: From a metallic wire mesh to an array of tiny holes,” Phys. Rev. B 76(24), 241102 (2007).
[CrossRef]

J. R. Suckling, J. R. Sambles, and C. R. Lawrence, “Resonant transmission of microwaves through a hexagonal array of holes in a thin metal layer,” N. J. Phys. 9(4), 101 (2007).
[CrossRef]

2006

B. Hou, Z. H. Hang, W. J. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89(13), 131917 (2006).
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006).
[CrossRef] [PubMed]

2005

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[CrossRef] [PubMed]

M. Beruete, M. Sorolla, I. Campillo, and J. S. Dolado, “Increase of the transmission in cut-off metallic hole arrays,” IEEE Microw. Wirel. Compon. Lett. 15(2), 116–118 (2005).
[CrossRef]

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

2004

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[CrossRef] [PubMed]

2001

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

2000

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

1999

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays on Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999).
[CrossRef]

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yabolonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech. 47(11), 2059–2074 (1999).
[CrossRef]

1998

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(6668), 667–669 (1998).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

1973

R. Ulrich and M. Tacke, “Submillimeter waveguiding on periodic metallic structure,” Appl. Phys. Lett. 22(5), 251–253 (1973).
[CrossRef]

1971

C. C. Chen, “Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes,” IEEE Trans. Microw. Theory Tech. 19(5), 475–481 (1971).
[CrossRef]

1944

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944).
[CrossRef]

1909

A. Sommerfeld, “Über die Ausbreitlung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. 28(4), 665–736 (1909).
[CrossRef]

1907

J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. 328(10), 846–866 (1907).
[CrossRef]

1899

A. Sommerfeld, “Ueber die Fortpflanzung elektrodynamischer Wellen längs eines Drahtes,” Ann. Phys. 67, 233–290 (1899).

Alexopolous, N. G.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yabolonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech. 47(11), 2059–2074 (1999).
[CrossRef]

Andrews, S. R.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[CrossRef] [PubMed]

Bartoli, F. J.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

Beruete, M.

M. Beruete, M. Sorolla, I. Campillo, and J. S. Dolado, “Increase of the transmission in cut-off metallic hole arrays,” IEEE Microw. Wirel. Compon. Lett. 15(2), 116–118 (2005).
[CrossRef]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[CrossRef] [PubMed]

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944).
[CrossRef]

Billaudeau, C.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. Rodier, J. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Braun, J.

J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How holes can obscure the view: suppressed transmission through an ultrathin metal film by a subwavelength hole array,” Phys. Rev. Lett. 103(20), 203901 (2009).
[CrossRef] [PubMed]

Bravo-Abad, J.

J. Bravo-Abad, L. Martín-Moreno, F. J. García-Vidal, E. Hendry, and J. Gómez-Rivas, “Transmission of light through periodic arrays of square holes: From a metallic wire mesh to an array of tiny holes,” Phys. Rev. B 76(24), 241102 (2007).
[CrossRef]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[CrossRef] [PubMed]

Broas, R. F. J.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yabolonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech. 47(11), 2059–2074 (1999).
[CrossRef]

Campillo, I.

M. Beruete, M. Sorolla, I. Campillo, and J. S. Dolado, “Increase of the transmission in cut-off metallic hole arrays,” IEEE Microw. Wirel. Compon. Lett. 15(2), 116–118 (2005).
[CrossRef]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[CrossRef] [PubMed]

Chan, C. T.

B. Hou, Z. H. Hang, W. J. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89(13), 131917 (2006).
[CrossRef]

Chen, C. C.

C. C. Chen, “Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes,” IEEE Trans. Microw. Theory Tech. 19(5), 475–481 (1971).
[CrossRef]

Collin, S.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. Rodier, J. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Devaux, E.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[CrossRef] [PubMed]

Ding, Y. J.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[CrossRef] [PubMed]

Dolado, J. S.

M. Beruete, M. Sorolla, I. Campillo, and J. S. Dolado, “Increase of the transmission in cut-off metallic hole arrays,” IEEE Microw. Wirel. Compon. Lett. 15(2), 116–118 (2005).
[CrossRef]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[CrossRef] [PubMed]

Dressel, M.

J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How holes can obscure the view: suppressed transmission through an ultrathin metal film by a subwavelength hole array,” Phys. Rev. Lett. 103(20), 203901 (2009).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays on Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

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(6668), 667–669 (1998).
[CrossRef]

Edmunds, J. D.

J. D. Edmunds, M. C. Taylor, A. P. Hibbins, J. R. Sambles, and I. J. Youngs, “Babinet’s principle and the band structure of surface waves on patterned metal arrays,” J. Appl. Phys. 107(10), 103108 (2010).
[CrossRef]

Enoch, S.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

Evans, B. R.

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Fu, Z.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

Gan, Q.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

García-Vidal, F. J.

J. Bravo-Abad, L. Martín-Moreno, F. J. García-Vidal, E. Hendry, and J. Gómez-Rivas, “Transmission of light through periodic arrays of square holes: From a metallic wire mesh to an array of tiny holes,” Phys. Rev. B 76(24), 241102 (2007).
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006).
[CrossRef] [PubMed]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays on Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

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(6668), 667–669 (1998).
[CrossRef]

Gómez-Rivas, J.

J. Bravo-Abad, L. Martín-Moreno, F. J. García-Vidal, E. Hendry, and J. Gómez-Rivas, “Transmission of light through periodic arrays of square holes: From a metallic wire mesh to an array of tiny holes,” Phys. Rev. B 76(24), 241102 (2007).
[CrossRef]

Gompf, B.

J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How holes can obscure the view: suppressed transmission through an ultrathin metal film by a subwavelength hole array,” Phys. Rev. Lett. 103(20), 203901 (2009).
[CrossRef] [PubMed]

Grupp, D. E.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

Hang, Z. H.

B. Hou, Z. H. Hang, W. J. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89(13), 131917 (2006).
[CrossRef]

Hendry, E.

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008).
[CrossRef]

J. Bravo-Abad, L. Martín-Moreno, F. J. García-Vidal, E. Hendry, and J. Gómez-Rivas, “Transmission of light through periodic arrays of square holes: From a metallic wire mesh to an array of tiny holes,” Phys. Rev. B 76(24), 241102 (2007).
[CrossRef]

Hibbins, A. P.

J. D. Edmunds, M. C. Taylor, A. P. Hibbins, J. R. Sambles, and I. J. Youngs, “Babinet’s principle and the band structure of surface waves on patterned metal arrays,” J. Appl. Phys. 107(10), 103108 (2010).
[CrossRef]

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102(7), 073901 (2009).
[CrossRef] [PubMed]

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008).
[CrossRef]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Hou, B.

B. Hou, Z. H. Hang, W. J. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89(13), 131917 (2006).
[CrossRef]

Kim, T. J.

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

Kirilenko, A. A.

A. A. Kirilenko and A. O. Perov, “On the common nature of the enhanced and resonance transmission through the periodical set of holes,” IEEE Trans. Antenn. Propag. 56(10), 3210–3216 (2008).
[CrossRef]

Kobiela, G.

J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How holes can obscure the view: suppressed transmission through an ultrathin metal film by a subwavelength hole array,” Phys. Rev. Lett. 103(20), 203901 (2009).
[CrossRef] [PubMed]

Krishnan, A.

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

Lalanne, P.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. Rodier, J. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Lawrence, C. R.

J. R. Suckling, J. R. Sambles, and C. R. Lawrence, “Resonant transmission of microwaves through a hexagonal array of holes in a thin metal layer,” N. J. Phys. 9(4), 101 (2007).
[CrossRef]

Lezec, H. J.

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays on Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

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(6668), 667–669 (1998).
[CrossRef]

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102(7), 073901 (2009).
[CrossRef] [PubMed]

Lomakin, V.

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[CrossRef]

Maier, S. A.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006).
[CrossRef] [PubMed]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

Martín-Moreno, L.

J. Bravo-Abad, L. Martín-Moreno, F. J. García-Vidal, E. Hendry, and J. Gómez-Rivas, “Transmission of light through periodic arrays of square holes: From a metallic wire mesh to an array of tiny holes,” Phys. Rev. B 76(24), 241102 (2007).
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Michielssen, E.

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71(23), 235117 (2005).
[CrossRef]

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[CrossRef] [PubMed]

Neviere, M.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

Nevière, M.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

Pardo, F.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. Rodier, J. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Pelouard, J.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. Rodier, J. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Pendry, J.

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

Pendry, J. B.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

Perov, A. O.

A. A. Kirilenko and A. O. Perov, “On the common nature of the enhanced and resonance transmission through the periodical set of holes,” IEEE Trans. Antenn. Propag. 56(10), 3210–3216 (2008).
[CrossRef]

Popov, E.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

Reinisch, R.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000).
[CrossRef]

Rodier, J.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. Rodier, J. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Sambles, J. R.

J. D. Edmunds, M. C. Taylor, A. P. Hibbins, J. R. Sambles, and I. J. Youngs, “Babinet’s principle and the band structure of surface waves on patterned metal arrays,” J. Appl. Phys. 107(10), 103108 (2010).
[CrossRef]

M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. 102(7), 073901 (2009).
[CrossRef] [PubMed]

E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008).
[CrossRef]

J. R. Suckling, J. R. Sambles, and C. R. Lawrence, “Resonant transmission of microwaves through a hexagonal array of holes in a thin metal layer,” N. J. Phys. 9(4), 101 (2007).
[CrossRef]

A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308(5722), 670–672 (2005).
[CrossRef] [PubMed]

Sauvan, C.

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. Rodier, J. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009).
[CrossRef]

Sheng, P.

B. Hou, Z. H. Hang, W. J. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89(13), 131917 (2006).
[CrossRef]

Sievenpiper, D.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yabolonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech. 47(11), 2059–2074 (1999).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, “Über die Ausbreitlung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. 28(4), 665–736 (1909).
[CrossRef]

A. Sommerfeld, “Ueber die Fortpflanzung elektrodynamischer Wellen längs eines Drahtes,” Ann. Phys. 67, 233–290 (1899).

Sorolla, M.

M. Beruete, M. Sorolla, I. Campillo, and J. S. Dolado, “Increase of the transmission in cut-off metallic hole arrays,” IEEE Microw. Wirel. Compon. Lett. 15(2), 116–118 (2005).
[CrossRef]

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimeter-wave transmission through subwavelength hole arrays,” Opt. Lett. 29(21), 2500–2502 (2004).
[CrossRef] [PubMed]

Suckling, J. R.

J. R. Suckling, J. R. Sambles, and C. R. Lawrence, “Resonant transmission of microwaves through a hexagonal array of holes in a thin metal layer,” N. J. Phys. 9(4), 101 (2007).
[CrossRef]

Tacke, M.

R. Ulrich and M. Tacke, “Submillimeter waveguiding on periodic metallic structure,” Appl. Phys. Lett. 22(5), 251–253 (1973).
[CrossRef]

Taylor, M. C.

J. D. Edmunds, M. C. Taylor, A. P. Hibbins, J. R. Sambles, and I. J. Youngs, “Babinet’s principle and the band structure of surface waves on patterned metal arrays,” J. Appl. Phys. 107(10), 103108 (2010).
[CrossRef]

Thio, T.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001).
[CrossRef] [PubMed]

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays on Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999).
[CrossRef]

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998).
[CrossRef]

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(6668), 667–669 (1998).
[CrossRef]

Ulrich, R.

R. Ulrich and M. Tacke, “Submillimeter waveguiding on periodic metallic structure,” Appl. Phys. Lett. 22(5), 251–253 (1973).
[CrossRef]

Wen, W. J.

B. Hou, Z. H. Hang, W. J. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89(13), 131917 (2006).
[CrossRef]

Wolff, P. A.

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001).
[CrossRef]

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays on Cr films,” J. Opt. Soc. Am. B 16(10), 1743–1748 (1999).
[CrossRef]

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(6668), 667–669 (1998).
[CrossRef]

Xiao, G.

G. Xiao and H. Yang, “The effect of array periodicity on the filtering characteristics of metal/dielectric photonic crystals,” J. Semicond. 32(4), 044004 (2011).
[CrossRef]

Yabolonovitch, E.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yabolonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech. 47(11), 2059–2074 (1999).
[CrossRef]

Yang, H.

G. Xiao and H. Yang, “The effect of array periodicity on the filtering characteristics of metal/dielectric photonic crystals,” J. Semicond. 32(4), 044004 (2011).
[CrossRef]

Youngs, I. J.

J. D. Edmunds, M. C. Taylor, A. P. Hibbins, J. R. Sambles, and I. J. Youngs, “Babinet’s principle and the band structure of surface waves on patterned metal arrays,” J. Appl. Phys. 107(10), 103108 (2010).
[CrossRef]

Zenneck, J.

J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. 328(10), 846–866 (1907).
[CrossRef]

Zhang, L.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yabolonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech. 47(11), 2059–2074 (1999).
[CrossRef]

Ann. Phys.

J. Zenneck, “Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie,” Ann. Phys. 328(10), 846–866 (1907).
[CrossRef]

A. Sommerfeld, “Ueber die Fortpflanzung elektrodynamischer Wellen längs eines Drahtes,” Ann. Phys. 67, 233–290 (1899).

A. Sommerfeld, “Über die Ausbreitlung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. 28(4), 665–736 (1909).
[CrossRef]

Appl. Phys. Lett.

R. Ulrich and M. Tacke, “Submillimeter waveguiding on periodic metallic structure,” Appl. Phys. Lett. 22(5), 251–253 (1973).
[CrossRef]

B. Hou, Z. H. Hang, W. J. Wen, C. T. Chan, and P. Sheng, “Microwave transmission through metallic hole arrays: surface electric field measurements,” Appl. Phys. Lett. 89(13), 131917 (2006).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett.

M. Beruete, M. Sorolla, I. Campillo, and J. S. Dolado, “Increase of the transmission in cut-off metallic hole arrays,” IEEE Microw. Wirel. Compon. Lett. 15(2), 116–118 (2005).
[CrossRef]

IEEE Trans. Antenn. Propag.

A. A. Kirilenko and A. O. Perov, “On the common nature of the enhanced and resonance transmission through the periodical set of holes,” IEEE Trans. Antenn. Propag. 56(10), 3210–3216 (2008).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yabolonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech. 47(11), 2059–2074 (1999).
[CrossRef]

C. C. Chen, “Diffraction of electromagnetic waves by a conducting screen perforated periodically with circular holes,” IEEE Trans. Microw. Theory Tech. 19(5), 475–481 (1971).
[CrossRef]

J. Appl. Phys.

J. D. Edmunds, M. C. Taylor, A. P. Hibbins, J. R. Sambles, and I. J. Youngs, “Babinet’s principle and the band structure of surface waves on patterned metal arrays,” J. Appl. Phys. 107(10), 103108 (2010).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

J. Opt. Soc. Am. B

J. Semicond.

G. Xiao and H. Yang, “The effect of array periodicity on the filtering characteristics of metal/dielectric photonic crystals,” J. Semicond. 32(4), 044004 (2011).
[CrossRef]

N. J. Phys.

J. R. Suckling, J. R. Sambles, and C. R. Lawrence, “Resonant transmission of microwaves through a hexagonal array of holes in a thin metal layer,” N. J. Phys. 9(4), 101 (2007).
[CrossRef]

Nature

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(6668), 667–669 (1998).
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Opt. Commun.

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Figures (12)

Fig. 1
Fig. 1

Unit cell of the sample and coordinate system illustrating the plane of incidence, angle of incidence, θ, hole diameter, a, and hole depth, h.

Fig. 2
Fig. 2

Modal matching eigenmode solutions without inclusion of diffracted orders (only specular components of the electric fields used) for 4 mm diameter holes in a square array of 5.5 mm pitch and 10 mm depth. N indicates the longitudinal quantisation of the electric field in the z direction. Solid lines indicate positions of modes supported. Asymptotic frequencies illustrated.

Fig. 3
Fig. 3

Schematic representation of dispersion of surface modes when f c < f diff . Modes folded into the first Brillouin zone to represent the effect of first order diffraction. Solid lines indicate zero order surface modes, dotted line indicate diffracted surface modes. Short dash line indicates zero order light line and long dash line indicates diffracted light line.

Fig. 4
Fig. 4

Normal incidence transmission measurements for 4 mm diameter holes in a square array of 5.5 mm pitch, 9.94 mm thick aluminium. Fit achieved using FEM modelling also illustrated.

Fig. 5
Fig. 5

FEM model predictions of the x-component of the electric field (parallel to the incident electric field). Amplitude plotted through the centre of the 4 mm diameter, 9.94 mm deep holes(θ = 0°).

Fig. 6
Fig. 6

(a) Experimental zero order transmission measurements for the 9.94 mm thick square array of 4.05 mm diameter holes, 5.5 mm pitch, as a function of in-plane momentum, kx. Diffracted light lines illustrated. (b) Detailed plot of resonant transmission maxima.

Fig. 7
Fig. 7

Experimental and modelled normal incidence transmission maxima as a function of hole depth for an array of 4.05 mm diameter holes, 5.5 mm pitch.

Fig. 8
Fig. 8

Calculated eigenmode solutions without inclusion of diffracted orders for 3 mm diameter holes in a square array of 5.5 mm pitch and 2 mm depth. Solid lines indicate position of the modes supported. N indicates the longitudinal quantisation number for the electric field in the z direction.

Fig. 9
Fig. 9

Schematic representation of dispersion of surface modes when f c > f diff . Modes folded into the first Brillouin zone to represent the effect of first order diffraction. Solid lines indicate zero order surface modes, dotted line indicate diffracted surface modes. Short dash line indicates zero order light line and long dash line indicates diffracted light line.

Fig. 10
Fig. 10

Experimentally measured normal incidence transmission for 3.1 mm diameter holes in a square array of 5.5 mm pitch and 1.905 mm depth.

Fig. 11
Fig. 11

FEM model predictions of the x-component of the electric field (parallel to the incident electric field). Amplitude plotted through the centre of the 3.15 mm diameter, 2 mm deep holes. Interfaces illustrated by dotted lines.

Fig. 12
Fig. 12

Experimental and modelled (FEM) normal incidence transmission maxima for 3.15 mm diameter holes in a square array of 5.5 mm pitch for various hole depths. Error bars represent the approximate error in determining resonant frequency.

Equations (7)

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f c(1,1) = 1.841 c 2 π a .
f c(1,1,N) c 2 π ε ( 1.841 a ) 2 + ( N π L ) 2 .
m 1 , m 2 A m 1 , m 2 exp ( i ( k x + 2 m 1 π d ) x ) exp ( i ( 2 m 2 π d ) y ) exp ( i k z m 1 , m 2 z ) ,
m 1 , m 2 B m 1 , m 2 exp ( i ( k x + 2 m 1 π d ) x ) exp ( i ( 2 m 2 π d ) y ) exp ( i k z m 1 , m 2 z ) ,
( C 1 , 1 exp ( i q z 1 , 1 z ) + D 1 , 1 exp ( i q z 1 , 1 z ) ) J 1 ( 1.841 a r ) cos ( φ ) r ,
k z m 1 , m 2 = k 0 2 + ( k x + 2 m 1 π d ) 2 + ( 2 m 2 π d ) 2
q z = k 0 2 + ( 1.841 a ) 2 ,

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