Abstract

We present 2D measurements of the full THz electric field behind a sample consisting of multiple slits in a metal foil. Our measurements, which have a sub-wavelength spatial, and a sub-period temporal resolution, reveal electric field lines, electric field vortices and saddle points. From our measurements we are able to reconstruct the magnetic field and, finally, the position and time-dependent Poynting vector which shows the flow of energy behind the sample. Our results show that it is possible to study the flow of light near sub-wavelength plasmonic structures such as slit-arrays and, by implication, other metamaterial samples.

© 2007 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  7. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
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  8. G. Lévêque and O. J. F. Martin, “Optical interactions in a plasmonic particle coupled to a metallic film,” Opt. Express 14, 9971–9981 (2006).
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    [Crossref]
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    [Crossref]
  22. H. Caglayan, I. Bulu, and E. Ozbay, “Extraordinary grating-coupled microwave transmission through a subwavelength annular aperture,” Opt. Express 13, 1666–1671 (2005).
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    [Crossref]
  24. Q. Chen, Z. Jiang, G. X. Xu, and X. -C. Zhang, “Near-field terahertz imaging with a dynamic aperture,” Opt. Lett. 25, 1122–1124 (2000).
    [Crossref]
  25. O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, “Terahertz pulse propagation through small apertures,” Appl. Phys. Lett. 79, 907–909 (2001).
    [Crossref]
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    [Crossref]
  27. W. Zhu and A. Nahata, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express 15, 5616–5624 (2007).
    [Crossref] [PubMed]
  28. M. A. Seo, A. J. L. Adam, D. H. Kang, P. C. M. Planken, and D. S. Kim, in preparation (2007).
  29. S. Keiding, D. R. Grischowsky, M. van Exter, and Ch. Fattinger, “Far-Infrared Time-Domain Spectroscopy with Terahertz Deams of Dielectrics and Semiconductors,” J. Opt. Soc. Am. B 7, 2006–2013 (1990).
    [Crossref]
  30. D. H. Auston, “Impulse response of photoconductors in transmission lines,” IEEE J. Quantum Electron. 19, 639–648 (1983).
    [Crossref]
  31. Z. Jiang, M. Li, and X. C. Zhang, “Dielectric constant measurement of thin films by differential time domain spectroscopy,” Appl. Phys. Lett. 76, 3221–3223 (2000).
  32. G. Gallot and D. R. Grischkowsky, “Electro-optic detection of terahertz radiation,” J. Opt. Soc. Am. B 16, 1204–1212 (1999).
    [Crossref]
  33. D. F. Nelson and E. H. Turner, “Electro-optic and piezoelectric coefficients and refractive index of gallium phosphide,” J. Appl. Phys. 39, 3337–3343 (1968).
    [Crossref]
  34. N. C. J. van der Valk, W. A. M. van der Marel, and P. C. M. Planken, “Terahertz polarization imaging,” Opt. Lett. 30, 2802–2804 (2005).
    [Crossref] [PubMed]
  35. J. W. Lee, M. A. Seo, S. C. Jeoung, J. H. Kang, Q-Han Park, and D. S. Kim, “Fabry-Perot Effects in THz Time-domain Spectroscopy of Plasmonic Band-gap Structures,” Appl. Phys. Lett. 88, 071114/1–3 (2006).
  36. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science 308, 670–672 (2005).
    [Crossref] [PubMed]
  37. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
    [Crossref] [PubMed]
  38. K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, “Vector field microscopic imaging of light,” Nat. Photon. 1, 53–56 (2007).
    [Crossref]
  39. J. D. Jackson, Classical ElectrodynamicsThird ed., (John Wiley & Sons, Inc., 1998).
  40. A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74, 1516–1518 (1999).
    [Crossref]
  41. M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294, 1080–1082 (2001).
    [Crossref] [PubMed]

2007 (5)

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[Crossref] [PubMed]

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517–521 (2007).
[Crossref] [PubMed]

Seung Jae Oh, Chul Kang, Inhee Maeng, Joo-Hiuk Son, Nam Ki Cho, Jin Dong Song, Won Jun Choi, Woon-Jo Cho, and Jung Il Lee, “Measurement of carrier concentration captured by InAs/GaAs quantum dots using terahertz time-domain spectroscopy,” Appl. Phys. Lett. 90, 131906/1–3 (2007).
[Crossref]

W. Zhu and A. Nahata, “Electric field vector characterization of terahertz surface plasmons,” Opt. Express 15, 5616–5624 (2007).
[Crossref] [PubMed]

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, “Vector field microscopic imaging of light,” Nat. Photon. 1, 53–56 (2007).
[Crossref]

2006 (7)

J. W. Lee, M. A. Seo, S. C. Jeoung, J. H. Kang, Q-Han Park, and D. S. Kim, “Fabry-Perot Effects in THz Time-domain Spectroscopy of Plasmonic Band-gap Structures,” Appl. Phys. Lett. 88, 071114/1–3 (2006).

F. Miyamaru, M. Tanaka, and M. Hangyo, “Effect of hole diameter on terahertz surface-wave excitation in metal-hole arrays,” Phys. Rev. B 74, 153416/1–4 (2006).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14, 8694–8705 (2006).
[Crossref] [PubMed]

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402/1–4 (2006).
[Crossref]

G. Lévêque and O. J. F. Martin, “Optical interactions in a plasmonic particle coupled to a metallic film,” Opt. Express 14, 9971–9981 (2006).
[Crossref] [PubMed]

K. Yang, L. P. B. Katehi, and J. F. Whitaker, “Electro-optic field mapping system utilizing external gallium arsenide probes,” Appl. Phys. Lett. 77, 486–488 (2006).
[Crossref]

2005 (4)

2004 (3)

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

K. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432, 376–379 (2004).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–791 (2004).
[Crossref] [PubMed]

2002 (2)

G. Zhao, R. N. Schouten, N. van der Valk, W. T. Wenckebach, and P. C. M. Planken, “Design and performance of a THz emission and detection setup based on a semi-insulating GaAs emitter,” Rev. Sci. Instrum. 73, 1715–1719 (2002).
[Crossref]

N. C. J. van der Valk and P. C. M. Planken, “Electro-optic detection of subwavelength terahertz spot sizes in the near field of a metal tip,” Appl. Phys. Lett. 81, 1558–1560 (2002).
[Crossref]

2001 (3)

M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, “Terahertz pulse propagation through small apertures,” Appl. Phys. Lett. 79, 907–909 (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, 1114–1117 (2001).
[Crossref] [PubMed]

2000 (3)

Tae-In Jeon, D. Grischkowsky, A. K. Mukherjee, and Reghu Menon, “Electrical characterization of conducting polypyrrole by THz time-domain spectroscopy,” Appl. Phys. Lett. 77, 2452–2454 (2000).
[Crossref]

Q. Chen, Z. Jiang, G. X. Xu, and X. -C. Zhang, “Near-field terahertz imaging with a dynamic aperture,” Opt. Lett. 25, 1122–1124 (2000).
[Crossref]

Z. Jiang, M. Li, and X. C. Zhang, “Dielectric constant measurement of thin films by differential time domain spectroscopy,” Appl. Phys. Lett. 76, 3221–3223 (2000).

1999 (2)

G. Gallot and D. R. Grischkowsky, “Electro-optic detection of terahertz radiation,” J. Opt. Soc. Am. B 16, 1204–1212 (1999).
[Crossref]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74, 1516–1518 (1999).
[Crossref]

1996 (1)

T. Pfeifer, H. -M. Heiliger, T. Loffler, C. Ohlhoff, C. Meyer, G. Lupke, H. G. Roskos, and H. Kurz, “Optoelectronic On-Chip Characterization of Ultrafast Electric Devices: Measurement Techniques and Applications,” IEEE J. Quantum Electron. 2, 586–604 (1996).
[Crossref]

1995 (1)

Q. Wu and X. C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523–3525 (1995).
[Crossref]

1990 (2)

M. van Exter and D. R. Grischkowsky, “Characterization of an optoelectronic terahertz beam system,” IRE Trans. Microwave Theory and Tech. 38, 1684–1691 (1990).
[Crossref]

S. Keiding, D. R. Grischowsky, M. van Exter, and Ch. Fattinger, “Far-Infrared Time-Domain Spectroscopy with Terahertz Deams of Dielectrics and Semiconductors,” J. Opt. Soc. Am. B 7, 2006–2013 (1990).
[Crossref]

1984 (1)

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy : image recording with resolution lambda/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[Crossref]

1983 (1)

D. H. Auston, “Impulse response of photoconductors in transmission lines,” IEEE J. Quantum Electron. 19, 639–648 (1983).
[Crossref]

1968 (1)

D. F. Nelson and E. H. Turner, “Electro-optic and piezoelectric coefficients and refractive index of gallium phosphide,” J. Appl. Phys. 39, 3337–3343 (1968).
[Crossref]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in Isotropic Media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

1884 (1)

J. H. Poynting, “On the transfer of energy in the electromagnetic field,” Philos. Trans. R. Soc. London 175, 343–361 (1884).
[Crossref]

Adam, A. J. L.

M. A. Seo, A. J. L. Adam, D. H. Kang, P. C. M. Planken, and D. S. Kim, in preparation (2007).

Agrawal, A.

T. Matsui, A. Agrawal, A. Nahata, and Z. V. Vardeny, “Transmission resonances through aperiodic arrays of subwavelength apertures,” Nature 446, 517–521 (2007).
[Crossref] [PubMed]

X. Shou, A. Agrawal, and A. Nahata, “Role of metal film thickness on the enhanced transmission properties of a periodic array apertures,” Opt. Express 13, 9834–9840 (2005).
[Crossref] [PubMed]

Auston, D. H.

D. H. Auston, “Impulse response of photoconductors in transmission lines,” IEEE J. Quantum Electron. 19, 639–648 (1983).
[Crossref]

Balistreri, M. L. M.

M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

Bulu, I.

Caglayan, H.

Chen, Q.

Cho, Nam Ki

Seung Jae Oh, Chul Kang, Inhee Maeng, Joo-Hiuk Son, Nam Ki Cho, Jin Dong Song, Won Jun Choi, Woon-Jo Cho, and Jung Il Lee, “Measurement of carrier concentration captured by InAs/GaAs quantum dots using terahertz time-domain spectroscopy,” Appl. Phys. Lett. 90, 131906/1–3 (2007).
[Crossref]

Cho, Woon-Jo

Seung Jae Oh, Chul Kang, Inhee Maeng, Joo-Hiuk Son, Nam Ki Cho, Jin Dong Song, Won Jun Choi, Woon-Jo Cho, and Jung Il Lee, “Measurement of carrier concentration captured by InAs/GaAs quantum dots using terahertz time-domain spectroscopy,” Appl. Phys. Lett. 90, 131906/1–3 (2007).
[Crossref]

Choi, S. B.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, “Vector field microscopic imaging of light,” Nat. Photon. 1, 53–56 (2007).
[Crossref]

Choi, W. J.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, “Vector field microscopic imaging of light,” Nat. Photon. 1, 53–56 (2007).
[Crossref]

Choi, Won Jun

Seung Jae Oh, Chul Kang, Inhee Maeng, Joo-Hiuk Son, Nam Ki Cho, Jin Dong Song, Won Jun Choi, Woon-Jo Cho, and Jung Il Lee, “Measurement of carrier concentration captured by InAs/GaAs quantum dots using terahertz time-domain spectroscopy,” Appl. Phys. Lett. 90, 131906/1–3 (2007).
[Crossref]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Degiron, A.

Denk, W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy : image recording with resolution lambda/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[Crossref]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[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, 1114–1117 (2001).
[Crossref] [PubMed]

Evans, B. R.

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

Fattinger, Ch.

Federici, J. F.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, “Terahertz pulse propagation through small apertures,” Appl. Phys. Lett. 79, 907–909 (2001).
[Crossref]

Gallot, G.

Garcia-Vidal, F. J.

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

García-Vidal, F. J.

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, 1114–1117 (2001).
[Crossref] [PubMed]

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007).
[Crossref] [PubMed]

Gersen, H.

M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

Grischkowsky, D.

Tae-In Jeon, D. Grischkowsky, A. K. Mukherjee, and Reghu Menon, “Electrical characterization of conducting polypyrrole by THz time-domain spectroscopy,” Appl. Phys. Lett. 77, 2452–2454 (2000).
[Crossref]

Grischkowsky, D. R.

G. Gallot and D. R. Grischkowsky, “Electro-optic detection of terahertz radiation,” J. Opt. Soc. Am. B 16, 1204–1212 (1999).
[Crossref]

M. van Exter and D. R. Grischkowsky, “Characterization of an optoelectronic terahertz beam system,” IRE Trans. Microwave Theory and Tech. 38, 1684–1691 (1990).
[Crossref]

Grischowsky, D. R.

Guo, L.

Hangyo, M.

F. Miyamaru, M. Tanaka, and M. Hangyo, “Effect of hole diameter on terahertz surface-wave excitation in metal-hole arrays,” Phys. Rev. B 74, 153416/1–4 (2006).
[Crossref]

Heiliger, H. -M.

T. Pfeifer, H. -M. Heiliger, T. Loffler, C. Ohlhoff, C. Meyer, G. Lupke, H. G. Roskos, and H. Kurz, “Optoelectronic On-Chip Characterization of Ultrafast Electric Devices: Measurement Techniques and Applications,” IEEE J. Quantum Electron. 2, 586–604 (1996).
[Crossref]

Hibbins, A. P.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402/1–4 (2006).
[Crossref]

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

Hooper, I. R.

A. P. Hibbins, M. J. Lockyear, I. R. Hooper, and J. R. Sambles, “Microwave transmission of a compound metal grating,” Phys. Rev. Lett. 96, 257402/1–4 (2006).
[Crossref]

Hsu, J. W. P.

O. Mitrofanov, M. Lee, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, J. D. Wynn, and J. F. Federici, “Terahertz pulse propagation through small apertures,” Appl. Phys. Lett. 79, 907–909 (2001).
[Crossref]

Hunsche, S.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74, 1516–1518 (1999).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical ElectrodynamicsThird ed., (John Wiley & Sons, Inc., 1998).

Jeon, Tae-In

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Supplementary Material (5)

» Media 1: MOV (3025 KB)     
» Media 2: MOV (3526 KB)     
» Media 3: MOV (1550 KB)     
» Media 4: MOV (2458 KB)     
» Media 5: MOV (3146 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a). Schematic of the terahertz near-field microscopy setup. Electro-optic sampling is used to detect the real-time electric field at each position. We raster-scan the sample first to obtain data along the x-axis and then move the sample upward. We use two GaP crystals with their crystal orientation along the (110) and (001), respectively to detect the x- and z-components of the electric field. (b). The near-field Ez time-traces measured at two equaldistance points (red: left side; blue: right side) 400 µm away from the slit, along with their FFT spectra and phase. (c). Ex amplitudes at a fixed time, 1.4 ps, 2.1 ps, and 3.2 ps, respectively, when the bulk of the terahertz pulse has passed through the slit. An Ex movie for terahertz pulse emanating from a single slit in real time (2.458 MB) is shown [Media 1]. (d). Ez amplitude at a fixed time, 1.4 ps, 2.1 ps, and 3.2 ps. An Ez movie for terahertz pulse emanating from a single slit in real time (3.146 MB) is shown [Media 2]. (e). Fourier-transformed images at temporal phase ωt′=0, obtained from the movie captured in (c)., at the frequencies of 0.3 THz, 0.5 THz, and 1.2 THz. The black lines are Ez fields at z=0.

Fig. 2.
Fig. 2.

(a). Fourier-transform Ex images at 0.5 THz z at ωt=0, π/2, and π. (b) Same as (a) except that we now measure Ez . (c) Same as (A) except that the frequency is 1 THz. (d) Same as (b) except the frequency is 1 THz.

Fig. 3.
Fig. 3.

Electric field vector mapping at 1 THz. An expanded view of the parts enclosed by the red-box regions can be seen in the lower part, showing saddle-point-like and vortex-like features. A Fourier-transformed electric field vector movie at 1 THz running the temporal phase, for light emanating from the multiple slit sample (3.026 MB) is shown. [Media 3]

Fig. 4.
Fig. 4.

(a). Magnetic field profile at 1 THz plotted together with the electric field vectors. A movie at 1 THz running the temporal phase, for light emanating from the multiple slit sample is shown (3.527 MB). The black line denotes the electric field and the background color represents the magnetic field [Media 4]. (b). Poynting vectors at 1 THz calculated from the results shown in (a). A Poynting vector movie at 1 THz running the temporal phase, for light emanating from the multiple slit sample (1.551 MB) is shown [Media 5].

Fig. 5.
Fig. 5.

(a). Time-averaged 2D Poynting vector behind the multiple slit sample at 1 THz, obtained from the 2D electric field vectors measured in the x-z-plane behind the slit sample and from the corresponding magnetic field vectors calculated from the electric field data. (b) FDTD simulation for time-averaged Poynting vector from the multiple slit sample, also at 1 THz.

Equations (2)

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E ( x , 0 , z , ω ) = 1 2 π E ( x , 0 , z , t ) e i ω t ' dt
H ( x , 0 , z , t ) t = c · × E ( x , 0 , z , t )

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