Abstract

We propose an ultrafast all-optical technique to control and beam the light emerging from a sub-wavelength slit in a planar gold film by exciting a transient grating in the area around the slit. A FDTD model is used to show how excitation of surface plasmon polaritons by the grating governs the beaming process. Both the grating and the beaming effect are shown to decay on a picosecond time-scale. An on-off contrast of 5 dB is obtained for the beaming, with a divergence angle of only 2.4 degrees.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
  4. L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef]

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105(1), 017402 (2010).
[CrossRef] [PubMed]

2009

N. Rotenberg, J. N. Caspers, and H. M. van Driel, “Tunable ultrafast control of plasmonic coupling to gold films,” Phys. Rev. B 80(24), 245420 (2009).
[CrossRef]

2008

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[CrossRef] [PubMed]

2007

B. Guo, Q. Gan, G. Song, J. Gao, and L. Chen, “Numerical study of a high-resolution far-field scanning optical microscope via a surface plasmon-modulated light source,” J. Lightwave Technol. 25(3), 830–833 (2007).
[CrossRef]

J. Christensen, A. I. Fernandez-Dominguez, F. De Leon-Perez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Collimation of sound assisted by acoustic surface waves,” Nat. Phys. 3(12), 851–852 (2007).
[CrossRef]

2006

D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh, and C. K. Lee, “Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings,” Opt. Express 14(8), 3503–3511 (2006).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Beaming matter waves from a subwavelength aperture,” Phys. Rev. A 74(2), 021601 (2006).
[CrossRef]

C. T. Wang, C. L. Du, Y. G. Lv, and X. G. Luo, “Surface electromagnetic wave excitation and diffraction by subwavelength slit with periodically patterned metallic grooves,” Opt. Express 14(12), 5671–5681 (2006).
[CrossRef] [PubMed]

Z. Sun, “Beam splitting with a modified metallic nano-optic lens,” Appl. Phys. Lett. 89(26), 261119 (2006).
[CrossRef]

Z. Lin and L. V. Zhigilei, “Thermal excitation of d band electrons in Au: implications for laser-induced phase transformations,” 6261, Proc. SPIE 62610U (2006).
[CrossRef]

2005

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A, Pure Appl. Opt. 7(2), S159–S164 (2005).
[CrossRef]

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), L364–L366 (2005).
[CrossRef]

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

2003

F. J. Garcı́a-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003).
[CrossRef] [PubMed]

2002

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(5582), 820–822 (2002).
[CrossRef] [PubMed]

2000

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251(1-3), 237–258 (2000).
[CrossRef]

1999

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]

1996

1995

1994

C.-K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, “Femtosecond-tunable measurement of electron thermailization in gold,” Phys. Rev. B 50, 15337 (1994).
[CrossRef]

1974

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Eksp. Teor. Fiz. 66, 776–781 (1974) (Sov. Phys. JETP 39, 375 (1974)).

1973

R. Rosei, F. Antonangeli, and U. Grassano, “d Bands position and width in gold from very low temperature thermomodulation measurements,” Surf. Sci. 37, 689–699 (1973).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1971

N. E. Christensen and B. O. Seraphin, “Relativistic band calculation and the optical properties of gold,” Phys. Rev. B 4(10), 3321–3344 (1971).
[CrossRef]

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

1944

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

Acioli, L. H.

C.-K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, “Femtosecond-tunable measurement of electron thermailization in gold,” Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Akarca-Biyikli, S. S.

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A, Pure Appl. Opt. 7(2), S159–S164 (2005).
[CrossRef]

Anisimov, S. I.

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Eksp. Teor. Fiz. 66, 776–781 (1974) (Sov. Phys. JETP 39, 375 (1974)).

Antonangeli, F.

R. Rosei, F. Antonangeli, and U. Grassano, “d Bands position and width in gold from very low temperature thermomodulation measurements,” Surf. Sci. 37, 689–699 (1973).
[CrossRef]

Averitt, R. D.

Baba, T.

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), L364–L366 (2005).
[CrossRef]

Bethe, H. A.

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

Betz, M.

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105(1), 017402 (2010).
[CrossRef] [PubMed]

Bonn, M.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[CrossRef] [PubMed]

Bulu, I.

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A, Pure Appl. Opt. 7(2), S159–S164 (2005).
[CrossRef]

Capasso, F.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Caspers, J. N.

N. Rotenberg, J. N. Caspers, and H. M. van Driel, “Tunable ultrafast control of plasmonic coupling to gold films,” Phys. Rev. B 80(24), 245420 (2009).
[CrossRef]

Chang, C. K.

Chang, Y. C.

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Chen, L.

Chen, Y. C.

D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh, and C. K. Lee, “Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings,” Opt. Express 14(8), 3503–3511 (2006).
[CrossRef] [PubMed]

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Christensen, J.

J. Christensen, A. I. Fernandez-Dominguez, F. De Leon-Perez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Collimation of sound assisted by acoustic surface waves,” Nat. Phys. 3(12), 851–852 (2007).
[CrossRef]

Christensen, N. E.

N. E. Christensen and B. O. Seraphin, “Relativistic band calculation and the optical properties of gold,” Phys. Rev. B 4(10), 3321–3344 (1971).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Conrad, U.

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251(1-3), 237–258 (2000).
[CrossRef]

Davies, A. G.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

De Leon-Perez, F.

J. Christensen, A. I. Fernandez-Dominguez, F. De Leon-Perez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Collimation of sound assisted by acoustic surface waves,” Nat. Phys. 3(12), 851–852 (2007).
[CrossRef]

Degiron, A.

L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[CrossRef] [PubMed]

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(5582), 820–822 (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(5582), 820–822 (2002).
[CrossRef] [PubMed]

Du, C. L.

Ebbesen, T. W.

F. J. Garcı́a-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003).
[CrossRef] [PubMed]

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(5582), 820–822 (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(6668), 667–669 (1998).
[CrossRef]

Fan, J. A.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Fernandez-Dominguez, A. I.

J. Christensen, A. I. Fernandez-Dominguez, F. De Leon-Perez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Collimation of sound assisted by acoustic surface waves,” Nat. Phys. 3(12), 851–852 (2007).
[CrossRef]

Fernández-Domínguez, A. I.

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Beaming matter waves from a subwavelength aperture,” Phys. Rev. A 74(2), 021601 (2006).
[CrossRef]

Fujikata, J.

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), L364–L366 (2005).
[CrossRef]

Fujimoto, J. G.

C.-K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, “Femtosecond-tunable measurement of electron thermailization in gold,” Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Gan, Q.

Gao, J.

Garci´a-Vidal, F. J.

F. J. Garcı́a-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

Garcia-Vidal, F. J.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[CrossRef] [PubMed]

J. Christensen, A. I. Fernandez-Dominguez, F. De Leon-Perez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Collimation of sound assisted by acoustic surface waves,” Nat. Phys. 3(12), 851–852 (2007).
[CrossRef]

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Beaming matter waves from a subwavelength aperture,” Phys. Rev. A 74(2), 021601 (2006).
[CrossRef]

L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[CrossRef] [PubMed]

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(5582), 820–822 (2002).
[CrossRef] [PubMed]

García-Vidal, F. J.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003).
[CrossRef] [PubMed]

Gaylord, T. K.

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(6668), 667–669 (1998).
[CrossRef]

Grann, E. B.

Grassano, U.

R. Rosei, F. Antonangeli, and U. Grassano, “d Bands position and width in gold from very low temperature thermomodulation measurements,” Surf. Sci. 37, 689–699 (1973).
[CrossRef]

Güdde, J.

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251(1-3), 237–258 (2000).
[CrossRef]

Guo, B.

Halas, N. J.

Hendry, E.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[CrossRef] [PubMed]

Hibbins, A. P.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[CrossRef] [PubMed]

Hohlfeld, J.

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251(1-3), 237–258 (2000).
[CrossRef]

Huang, K. T.

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Ippen, E. P.

C.-K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, “Femtosecond-tunable measurement of electron thermailization in gold,” Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Ishi, T.

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), L364–L366 (2005).
[CrossRef]

Jähnke, V.

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251(1-3), 237–258 (2000).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kapeliovich, B. L.

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Eksp. Teor. Fiz. 66, 776–781 (1974) (Sov. Phys. JETP 39, 375 (1974)).

Kats, M. A.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Khanna, S. P.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Kuan, C. H.

Kuipers, L.

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef]

Lalanne, P.

Lee, C. K.

D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh, and C. K. Lee, “Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings,” Opt. Express 14(8), 3503–3511 (2006).
[CrossRef] [PubMed]

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Lezec, H. J.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003).
[CrossRef] [PubMed]

F. J. Garcı́a-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[CrossRef] [PubMed]

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(5582), 820–822 (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(6668), 667–669 (1998).
[CrossRef]

Li, L.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Liaw, J. W.

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Lin, D. Z.

D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh, and C. K. Lee, “Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings,” Opt. Express 14(8), 3503–3511 (2006).
[CrossRef] [PubMed]

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Lin, M. W.

Lin, Z.

Z. Lin and L. V. Zhigilei, “Thermal excitation of d band electrons in Au: implications for laser-induced phase transformations,” 6261, Proc. SPIE 62610U (2006).
[CrossRef]

Linfield, E. H.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

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(5582), 820–822 (2002).
[CrossRef] [PubMed]

Liu, J. M.

D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh, and C. K. Lee, “Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings,” Opt. Express 14(8), 3503–3511 (2006).
[CrossRef] [PubMed]

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Lockyear, M. J.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[CrossRef] [PubMed]

Luo, X. G.

Lv, Y. G.

Makita, K.

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), L364–L366 (2005).
[CrossRef]

Martin-Moreno, L.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[CrossRef] [PubMed]

J. Christensen, A. I. Fernandez-Dominguez, F. De Leon-Perez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Collimation of sound assisted by acoustic surface waves,” Nat. Phys. 3(12), 851–852 (2007).
[CrossRef]

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Beaming matter waves from a subwavelength aperture,” Phys. Rev. A 74(2), 021601 (2006).
[CrossRef]

F. J. Garcı́a-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[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(5582), 820–822 (2002).
[CrossRef] [PubMed]

Martín-Moreno, L.

L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003).
[CrossRef] [PubMed]

Matthias, E.

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251(1-3), 237–258 (2000).
[CrossRef]

Moharam, M. G.

Moreno, E.

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Beaming matter waves from a subwavelength aperture,” Phys. Rev. A 74(2), 021601 (2006).
[CrossRef]

Morris, G. M.

Ohashi, K.

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), L364–L366 (2005).
[CrossRef]

Ozbay, E.

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A, Pure Appl. Opt. 7(2), S159–S164 (2005).
[CrossRef]

Perelman, T. L.

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Eksp. Teor. Fiz. 66, 776–781 (1974) (Sov. Phys. JETP 39, 375 (1974)).

Pommet, D. A.

Rivas, J. G.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[CrossRef] [PubMed]

Rosei, R.

R. Rosei, F. Antonangeli, and U. Grassano, “d Bands position and width in gold from very low temperature thermomodulation measurements,” Surf. Sci. 37, 689–699 (1973).
[CrossRef]

Rotenberg, N.

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105(1), 017402 (2010).
[CrossRef] [PubMed]

N. Rotenberg, J. N. Caspers, and H. M. van Driel, “Tunable ultrafast control of plasmonic coupling to gold films,” Phys. Rev. B 80(24), 245420 (2009).
[CrossRef]

Seraphin, B. O.

N. E. Christensen and B. O. Seraphin, “Relativistic band calculation and the optical properties of gold,” Phys. Rev. B 4(10), 3321–3344 (1971).
[CrossRef]

Song, G.

Spasenovic, M.

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef]

Sun, C.-K.

C.-K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, “Femtosecond-tunable measurement of electron thermailization in gold,” Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Sun, Z.

Z. Sun, “Beam splitting with a modified metallic nano-optic lens,” Appl. Phys. Lett. 89(26), 261119 (2006).
[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(6668), 667–669 (1998).
[CrossRef]

Vallee, F.

C.-K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, “Femtosecond-tunable measurement of electron thermailization in gold,” Phys. Rev. B 50, 15337 (1994).
[CrossRef]

van Driel, H. M.

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105(1), 017402 (2010).
[CrossRef] [PubMed]

N. Rotenberg, J. N. Caspers, and H. M. van Driel, “Tunable ultrafast control of plasmonic coupling to gold films,” Phys. Rev. B 80(24), 245420 (2009).
[CrossRef]

van Oosten, D.

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef]

Wang, C. T.

Wang, Q. J.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Wellershoff, S.-S.

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251(1-3), 237–258 (2000).
[CrossRef]

Westcott, S. L.

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(6668), 667–669 (1998).
[CrossRef]

Yang, D. L.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

Yeh, C. S.

D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh, and C. K. Lee, “Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings,” Opt. Express 14(8), 3503–3511 (2006).
[CrossRef] [PubMed]

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Yeh, J. T.

D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh, and C. K. Lee, “Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings,” Opt. Express 14(8), 3503–3511 (2006).
[CrossRef] [PubMed]

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Yu, L. B.

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

Yu, N.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Zhigilei, L. V.

Z. Lin and L. V. Zhigilei, “Thermal excitation of d band electrons in Au: implications for laser-induced phase transformations,” 6261, Proc. SPIE 62610U (2006).
[CrossRef]

Appl. Phys. Lett.

F. J. Garcı́a-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

Z. Sun, “Beam splitting with a modified metallic nano-optic lens,” Appl. Phys. Lett. 89(26), 261119 (2006).
[CrossRef]

Chem. Phys.

J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, and E. Matthias, “Electron and lattice dynamics following optical excitation of metals,” Chem. Phys. 251(1-3), 237–258 (2000).
[CrossRef]

Eksp. Teor. Fiz.

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Electron emission from metal surfaces exposed to ultrashort laser pulses,” Eksp. Teor. Fiz. 66, 776–781 (1974) (Sov. Phys. JETP 39, 375 (1974)).

IEEE Trans. Antenn. Propag.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

J. Lightwave Technol.

J. Opt. A, Pure Appl. Opt.

S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A, Pure Appl. Opt. 7(2), S159–S164 (2005).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

T. Ishi, J. Fujikata, K. Makita, T. Baba, and K. Ohashi, “Si nano-photodiode with a surface plasmon antenna,” Jpn. J. Appl. Phys. 44(12), L364–L366 (2005).
[CrossRef]

Nano Lett.

D. van Oosten, M. Spasenović, and L. Kuipers, “Nanohole chains for directional and localized surface plasmon excitation,” Nano Lett. 10(1), 286–290 (2010).
[CrossRef]

Nat. Mater.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010).
[CrossRef] [PubMed]

Nat. Phys.

J. Christensen, A. I. Fernandez-Dominguez, F. De Leon-Perez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Collimation of sound assisted by acoustic surface waves,” Nat. Phys. 3(12), 851–852 (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).
[CrossRef]

Opt. Express

Phys. Rev.

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

Phys. Rev. A

A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Beaming matter waves from a subwavelength aperture,” Phys. Rev. A 74(2), 021601 (2006).
[CrossRef]

Phys. Rev. B

L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. M. Liu, C. S. Yeh, and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71(4), 041405 (2005).
[CrossRef]

C.-K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, “Femtosecond-tunable measurement of electron thermailization in gold,” Phys. Rev. B 50, 15337 (1994).
[CrossRef]

N. E. Christensen and B. O. Seraphin, “Relativistic band calculation and the optical properties of gold,” Phys. Rev. B 4(10), 3321–3344 (1971).
[CrossRef]

N. Rotenberg, J. N. Caspers, and H. M. van Driel, “Tunable ultrafast control of plasmonic coupling to gold films,” Phys. Rev. B 80(24), 245420 (2009).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100(12), 123901 (2008).
[CrossRef] [PubMed]

N. Rotenberg, M. Betz, and H. M. van Driel, “Ultrafast all-optical coupling of light to surface plasmon polaritons on plain metal surfaces,” Phys. Rev. Lett. 105(1), 017402 (2010).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003).
[CrossRef] [PubMed]

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003).
[CrossRef] [PubMed]

Proc. SPIE

Z. Lin and L. V. Zhigilei, “Thermal excitation of d band electrons in Au: implications for laser-induced phase transformations,” 6261, Proc. SPIE 62610U (2006).
[CrossRef]

Science

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(5582), 820–822 (2002).
[CrossRef] [PubMed]

Surf. Sci.

R. Rosei, F. Antonangeli, and U. Grassano, “d Bands position and width in gold from very low temperature thermomodulation measurements,” Surf. Sci. 37, 689–699 (1973).
[CrossRef]

Other

A. Taflov, and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method, second edition (Artech House, Norwood, MA, 2000).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a scheme to control light beaming.

Fig. 2
Fig. 2

(a) The first-order and (b) zero-order diffraction spectra for the TTG experiment, at the delay time corresponding to the peak pump-induced grating. In (a) the curves are the experimental results, taken from Ref. ‎18, while in (b) they are guides to the eye. In both parts the results of the FDTD calculations are shown as circles, while those of the RCWA calculations are shown as squares. In (b), the spectral region where plasmonic coupling occurs is circled.

Fig. 3
Fig. 3

(Media 1) The spatial distribution of the electric field intensity of the light that is transmitted through a sub-wavelength slit (located at the bottom, at 0 on the horizontal scale) in a 50 nm thick gold film, for different delay times. The polarization of the light is shown in the upper right corner of each figure: (a) to (h) are for p-polarized light, while (i) is for s-polarized light and is shown for the same delay time as in (d). All figures are normalized such that a value of 1 corresponds to the highest intensity in (d).

Fig. 4
Fig. 4

The electric field intensity in the area immediately surrounding the slit for both (a) p-polarized and (b) s-polarized excitations. The gold film and the slit are shown in blue lines. The plots are normalized in the same manner as Fig. 3.

Fig. 5
Fig. 5

The spatial distribution of the p-polarized electric field intensity at a distance of 20 μm from the slit, for different delay times. The s-polarized intensity for t = 0.6 ps is shown as a dashed curve. The inset shows the maximum intensity present at each delay time (corresponding to Fig. 3); the curve is a guide to the eye.

Tables (1)

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Table 1 Parameters Used in the TTM

Equations (6)

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N t = N τ 1 N τ 2 + P ( z , t ) ,
P ( z , t ) = ( 1 R ) α e f f I ( t ) e α e f f z 1 e α e f f d ,
C e T e t = z ( K e T e z ) g ( T e T ) + N τ 1 ,
C T t = g ( T e T ) + N τ 2 .
I ( x , t ) = I 1 ( t ) + I 2 ( t ) + 2 I 1 ( t ) I 2 ( t ) cos ( 2 π Λ x ) ,
Λ = λ | sin θ 1 sin θ 2 | ,

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