Abstract

We demonstrated quantitative analysis and measurements of near-fields interactions in a terahertz pulse near-field microscope. We developed a self-consistent line dipole image method for the quantitative analysis of the near-field interaction in THz scattering-type scanning optical microscopes. The measurements of approach curves and relative contrasts on gold and silicon substrates were in excellent agreement with calculations.

© 2011 OSA

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    [CrossRef]
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2008 (3)

2007 (3)

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express 15(14), 8550–8565 (2007).
[CrossRef] [PubMed]

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

R. Esteban, R. Vogelgesang, and K. Kern, “Tip-substrate interaction in optical near-field microscopy,” Phys. Rev. B 75(19), 195410 (2007).
[CrossRef]

2005 (1)

T. Yuan, H. Park, J. Xu, H. Han, and X.-C. Zhang, “Field induced THz wave emission with nanometer resolution,” Proc. SPIE 5649, 1–8 (2005).
[CrossRef]

2004 (2)

S. V. Sukhov, “Role of multipole moment of the probe in apertureless near-field optical microscopy,” Ultramicroscopy 101(2-4), 111–122 (2004).
[CrossRef] [PubMed]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattered infrered near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
[CrossRef]

2003 (2)

J. A. Porto, P. Johansson, S. P. Apell, and T. López-Ríos, “Resonance shift effects in apertureless scanning near-field optical microscopy,” Phys. Rev. B 67(8), 085409 (2003).
[CrossRef]

H. T. Chen, R. Kersting, and G. C. Cho, “Terahertz imaging with nanometer resolution,” Appl. Phys. Lett. 83(15), 3009–3011 (2003).
[CrossRef]

2002 (1)

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(9), 1558–1560 (2002).
[CrossRef]

2001 (1)

Q. Chen and X.-C. Zhang, “Semiconductor dynamic aperture for near-field terahertz wave imaging,” IEEE J. Sel. Top. Quantum Electron. 7(4), 608–614 (2001).
[CrossRef]

2000 (3)

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000).
[CrossRef]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[CrossRef] [PubMed]

M. Labardi, S. Patanè, and M. Allegrini, “Artifact-free near-field optical imaging by apertureless microscopy,” Appl. Phys. Lett. 77(5), 621–623 (2000).
[CrossRef]

1998 (2)

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150(1-6), 22–26 (1998).
[CrossRef]

T. C. Choy, A. Alexopoulos, and M. F. Thorpe, “Dielectric function for a material containing hyperspherical inclusions to O(c2) II. Method of images,” Proc. R. Soc. Lond. A 454(1975), 1993–2013 (1998).
[CrossRef]

1997 (1)

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[CrossRef]

1993 (1)

I. V. Lindell, J. C.-E. Sten, and K. I. Nikoskinen, “Electrostatic image method for the interaction of two dielectric spheres,” Radio Sci. 28(3), 319–329 (1993).
[CrossRef]

1992 (1)

I. V. Lindell, M. E. Ermutlu, and A. H. Sihvola, “Electrostatic image theory for layered dielectric sphere,” IEE Proc., H Microw. Antennas Propag. 139(2), 186–192 (1992).
[CrossRef]

1990 (1)

1985 (1)

1983 (1)

P. K. Aravind and H. Metiu, “The effects of the interaction between resonances in the electromagnetic response of a sphere-plane structure: applications to surface enhanced spectroscopy,” Surf. Sci. 124(2-3), 506–528 (1983).
[CrossRef]

Ahn, J.

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

Aizpurua, J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[CrossRef] [PubMed]

Alexander,, R. W.

Alexopoulos, A.

T. C. Choy, A. Alexopoulos, and M. F. Thorpe, “Dielectric function for a material containing hyperspherical inclusions to O(c2) II. Method of images,” Proc. R. Soc. Lond. A 454(1975), 1993–2013 (1998).
[CrossRef]

Allegrini, M.

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

M. Labardi, S. Patanè, and M. Allegrini, “Artifact-free near-field optical imaging by apertureless microscopy,” Appl. Phys. Lett. 77(5), 621–623 (2000).
[CrossRef]

Apell, S. P.

J. A. Porto, P. Johansson, S. P. Apell, and T. López-Ríos, “Resonance shift effects in apertureless scanning near-field optical microscopy,” Phys. Rev. B 67(8), 085409 (2003).
[CrossRef]

Aravind, P. K.

P. K. Aravind and H. Metiu, “The effects of the interaction between resonances in the electromagnetic response of a sphere-plane structure: applications to surface enhanced spectroscopy,” Surf. Sci. 124(2-3), 506–528 (1983).
[CrossRef]

Bachelier, G.

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

Baek, S. H.

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

Bell, R. J.

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[CrossRef]

Brehm, M.

Brener, I.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150(1-6), 22–26 (1998).
[CrossRef]

Cajko, F.

Chang, S.

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

Chen, H. T.

H. T. Chen, R. Kersting, and G. C. Cho, “Terahertz imaging with nanometer resolution,” Appl. Phys. Lett. 83(15), 3009–3011 (2003).
[CrossRef]

Chen, Q.

Q. Chen and X.-C. Zhang, “Semiconductor dynamic aperture for near-field terahertz wave imaging,” IEEE J. Sel. Top. Quantum Electron. 7(4), 608–614 (2001).
[CrossRef]

Cho, G. C.

H. T. Chen, R. Kersting, and G. C. Cho, “Terahertz imaging with nanometer resolution,” Appl. Phys. Lett. 83(15), 3009–3011 (2003).
[CrossRef]

Choy, T. C.

T. C. Choy, A. Alexopoulos, and M. F. Thorpe, “Dielectric function for a material containing hyperspherical inclusions to O(c2) II. Method of images,” Proc. R. Soc. Lond. A 454(1975), 1993–2013 (1998).
[CrossRef]

Cvitkovic, A.

Drachenko, O.

Ermutlu, M. E.

I. V. Lindell, M. E. Ermutlu, and A. H. Sihvola, “Electrostatic image theory for layered dielectric sphere,” IEE Proc., H Microw. Antennas Propag. 139(2), 186–192 (1992).
[CrossRef]

Esteban, R.

R. Esteban, R. Vogelgesang, and K. Kern, “Tip-substrate interaction in optical near-field microscopy,” Phys. Rev. B 75(19), 195410 (2007).
[CrossRef]

Fattinger, Ch.

Grischkowsky, D.

Gucciardi, P. G.

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

Han, H.

T. Yuan, H. Park, J. Xu, H. Han, and X.-C. Zhang, “Field induced THz wave emission with nanometer resolution,” Proc. SPIE 5649, 1–8 (2005).
[CrossRef]

Helm, M.

Hillenbrand, R.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[CrossRef] [PubMed]

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express 15(14), 8550–8565 (2007).
[CrossRef] [PubMed]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattered infrered near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
[CrossRef]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[CrossRef] [PubMed]

Hong, M.

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

Hong, S.-C.

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

Huber, A. J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[CrossRef] [PubMed]

Hunsche, S.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150(1-6), 22–26 (1998).
[CrossRef]

Jhe, W.

P. G. Gucciardi, G. Bachelier, M. Allegrini, J. Ahn, M. Hong, S. Chang, W. Jhe, S.-C. Hong, and S. H. Baek, “Artifacts identification in apertureless near-field optical microscopy,” J. Appl. Phys. 101(6), 064303 (2007).
[CrossRef]

Johansson, P.

J. A. Porto, P. Johansson, S. P. Apell, and T. López-Ríos, “Resonance shift effects in apertureless scanning near-field optical microscopy,” Phys. Rev. B 67(8), 085409 (2003).
[CrossRef]

Keiding, S.

Keilmann, F.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[CrossRef] [PubMed]

H.-G. von Ribbeck, M. Brehm, D. W. van der Weide, S. Winnerl, O. Drachenko, M. Helm, and F. Keilmann, “Spectroscopic THz near-field microscope,” Opt. Express 16(5), 3430–3438 (2008).
[CrossRef] [PubMed]

M. Brehm, A. Schliesser, F. Čajko, I. Tsukerman, and F. Keilmann, “Antenna-mediated back-scattering efficiency in infrared near-field microscopy,” Opt. Express 16(15), 11203–11215 (2008).
[CrossRef] [PubMed]

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattered infrered near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
[CrossRef]

R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85(14), 3029–3032 (2000).
[CrossRef] [PubMed]

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000).
[CrossRef]

Kern, K.

R. Esteban, R. Vogelgesang, and K. Kern, “Tip-substrate interaction in optical near-field microscopy,” Phys. Rev. B 75(19), 195410 (2007).
[CrossRef]

Kersting, R.

H. T. Chen, R. Kersting, and G. C. Cho, “Terahertz imaging with nanometer resolution,” Appl. Phys. Lett. 83(15), 3009–3011 (2003).
[CrossRef]

Knoll, B.

B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182(4-6), 321–328 (2000).
[CrossRef]

Koch, M.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150(1-6), 22–26 (1998).
[CrossRef]

Labardi, M.

M. Labardi, S. Patanè, and M. Allegrini, “Artifact-free near-field optical imaging by apertureless microscopy,” Appl. Phys. Lett. 77(5), 621–623 (2000).
[CrossRef]

Lindell, I. V.

I. V. Lindell, J. C.-E. Sten, and K. I. Nikoskinen, “Electrostatic image method for the interaction of two dielectric spheres,” Radio Sci. 28(3), 319–329 (1993).
[CrossRef]

I. V. Lindell, M. E. Ermutlu, and A. H. Sihvola, “Electrostatic image theory for layered dielectric sphere,” IEE Proc., H Microw. Antennas Propag. 139(2), 186–192 (1992).
[CrossRef]

Long, L. L.

López-Ríos, T.

J. A. Porto, P. Johansson, S. P. Apell, and T. López-Ríos, “Resonance shift effects in apertureless scanning near-field optical microscopy,” Phys. Rev. B 67(8), 085409 (2003).
[CrossRef]

Metiu, H.

P. K. Aravind and H. Metiu, “The effects of the interaction between resonances in the electromagnetic response of a sphere-plane structure: applications to surface enhanced spectroscopy,” Surf. Sci. 124(2-3), 506–528 (1983).
[CrossRef]

Nikoskinen, K. I.

I. V. Lindell, J. C.-E. Sten, and K. I. Nikoskinen, “Electrostatic image method for the interaction of two dielectric spheres,” Radio Sci. 28(3), 319–329 (1993).
[CrossRef]

Novotny, L.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[CrossRef]

Nuss, M. C.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun. 150(1-6), 22–26 (1998).
[CrossRef]

Ocelic, N.

Ordal, M. A.

Park, H.

T. Yuan, H. Park, J. Xu, H. Han, and X.-C. Zhang, “Field induced THz wave emission with nanometer resolution,” Proc. SPIE 5649, 1–8 (2005).
[CrossRef]

Patanè, S.

M. Labardi, S. Patanè, and M. Allegrini, “Artifact-free near-field optical imaging by apertureless microscopy,” Appl. Phys. Lett. 77(5), 621–623 (2000).
[CrossRef]

Planken, P. C. M.

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(9), 1558–1560 (2002).
[CrossRef]

Porto, J. A.

J. A. Porto, P. Johansson, S. P. Apell, and T. López-Ríos, “Resonance shift effects in apertureless scanning near-field optical microscopy,” Phys. Rev. B 67(8), 085409 (2003).
[CrossRef]

Querry, M. R.

Schliesser, A.

Sihvola, A. H.

I. V. Lindell, M. E. Ermutlu, and A. H. Sihvola, “Electrostatic image theory for layered dielectric sphere,” IEE Proc., H Microw. Antennas Propag. 139(2), 186–192 (1992).
[CrossRef]

Sten, J. C.-E.

I. V. Lindell, J. C.-E. Sten, and K. I. Nikoskinen, “Electrostatic image method for the interaction of two dielectric spheres,” Radio Sci. 28(3), 319–329 (1993).
[CrossRef]

Sukhov, S. V.

S. V. Sukhov, “Role of multipole moment of the probe in apertureless near-field optical microscopy,” Ultramicroscopy 101(2-4), 111–122 (2004).
[CrossRef] [PubMed]

Taubner, T.

T. Taubner, R. Hillenbrand, and F. Keilmann, “Nanoscale polymer recognition by spectral signature in scattered infrered near-field microscopy,” Appl. Phys. Lett. 85(21), 5064–5066 (2004).
[CrossRef]

Thorpe, M. F.

T. C. Choy, A. Alexopoulos, and M. F. Thorpe, “Dielectric function for a material containing hyperspherical inclusions to O(c2) II. Method of images,” Proc. R. Soc. Lond. A 454(1975), 1993–2013 (1998).
[CrossRef]

Tsukerman, I.

van der Valk, N. C. J.

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(9), 1558–1560 (2002).
[CrossRef]

van der Weide, D. W.

van Exter, M.

Vogelgesang, R.

R. Esteban, R. Vogelgesang, and K. Kern, “Tip-substrate interaction in optical near-field microscopy,” Phys. Rev. B 75(19), 195410 (2007).
[CrossRef]

von Ribbeck, H.-G.

Winnerl, S.

Wittborn, J.

A. J. Huber, F. Keilmann, J. Wittborn, J. Aizpurua, and R. Hillenbrand, “Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices,” Nano Lett. 8(11), 3766–3770 (2008).
[CrossRef] [PubMed]

Xie, X. S.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).
[CrossRef]

Xu, J.

T. Yuan, H. Park, J. Xu, H. Han, and X.-C. Zhang, “Field induced THz wave emission with nanometer resolution,” Proc. SPIE 5649, 1–8 (2005).
[CrossRef]

Yuan, T.

T. Yuan, H. Park, J. Xu, H. Han, and X.-C. Zhang, “Field induced THz wave emission with nanometer resolution,” Proc. SPIE 5649, 1–8 (2005).
[CrossRef]

Zhang, X.-C.

T. Yuan, H. Park, J. Xu, H. Han, and X.-C. Zhang, “Field induced THz wave emission with nanometer resolution,” Proc. SPIE 5649, 1–8 (2005).
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Figures (4)

Fig. 1
Fig. 1

Schematics of a THz s-SNOM system. (a) the probe-substrate system, (b) the point dipole image method (PDIM), and (c) the self-consistent line dipole image method (LDIM).

Fig. 2
Fig. 2

Near-field distributions (80 nm × 80 nm) of the sphere-substrate system. LDIM calculations on (a) Au substrate and (b) FZ-Si substrate, and FEM simulations on (c) Au substrate and (d) FZ-Si substrate. The diameter of the tungsten sphere is 40 nm and the gap distance is 5 nm.

Fig. 3
Fig. 3

LDIM and PDIM calculations for Au and FZ-Si substrates. (a) x- and z-components of total induced dipole moments, and (b) tip-modulation responses of x- and z-components of the total induced dipole moments. The tungsten tip has a radius of a = 1100 nm, and the dithering amplitude is g 1 = 110 nm. The solid and dashed curves stand for LDIM and PDIM calculations, respectively. The red and blue curves represent calculations for gold and Si substrates, respectively.

Fig. 4
Fig. 4

Approach curves and relative contrasts of a THz pulse s-SNOM. (a) Approach curves on gold (red) and FZ-Si (blue) substrates and (b) calculated relative contrasts. The inset shows the THz scattering pulses on gold and Si substrates. The closed circles represent experimental results, the sold (dashed) lines stand for the LDIM (PDIM) calculations, respectively.

Equations (5)

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d P D = [ α ( 1 β ) 1 α β / ( 32 π h 3 ) u x u x + α ( 1 + β ) 1 α β / ( 16 π h 3 ) u z u z ] E i n
γ ( z , h , L ) = ε p 1 ε p + 1 ( a L ) 3 δ ( z h + z K ) ( I 2 u x u x ) + ε p 1 ( ε p + 1 ) 2 a L 2 ( h z z K ) 1 ε p + 1 [ u ( z h + z K ) u ( z h ) ] [ I + ( ε p 1 ) u z u z ]
p p ( n ) L D ( z , h ) = h a h d z γ ( z , h , h z ) p s ( n 1 ) L D ( z , h ) p s ( n ) L D ( z , h ) = β T p p ( n 1 ) L D ( z , h )
d L D ( h ) = n = 1 [ h a h d z p p ( n ) L D ( z , h ) + h a h d z p s ( n ) L D ( z , h ) ]
E s c ( t ) = E 0 + m = 1 E m cos ( m Ω t )

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