Role of in-plane polarizability of the tip in scattering near-field microscopy of a plasmonic nanoparticle

Deok-Soo Kim; Zee Hwan Kim

doi:10.1364/OE.20.008689

Role of in-plane polarizability of the tip in scattering near-field microscopy of a plasmonic nanoparticle

Deok-Soo Kim and Zee Hwan Kim

Optics Express
Vol. 20,
Issue 8,
pp. 8689-8699
(2012)
•https://doi.org/10.1364/OE.20.008689

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Deok-Soo Kim and Zee Hwan Kim, "Role of in-plane polarizability of the tip in scattering near-field microscopy of a plasmonic nanoparticle," Opt. Express 20, 8689-8699 (2012)

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Related Topics
Table of Contents Category
- Microscopy
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Near-field microscopy (180.4243)
- Surface plasmons (240.6680)

About this Article
History
- Original Manuscript: February 8, 2012
- Revised Manuscript: March 22, 2012
- Manuscript Accepted: March 24, 2012
- Published: March 29, 2012
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 7, Iss. 6

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Open Access

Abstract

We report that a pyramid-shaped scanning probe microscopy tip has non-zero polarizability along the in-plane direction (perpendicular to the tip axis, z) at visible frequency. The in-plane polarizability enables the scattering-type scanning near-field optical microscopy (s-SNOM) to measure the in-plane field component around a plasmon-resonant nanoparticle. Because of the non-zero in-plane polarizability, the cross-polarized s-SNOM images may contain contributions from the in-plane field component of an out-of-plane plasmon mode as well as the out-of-plane field component of an in-plane mode. By comparing a scattering model and experimental s-SNOM images, we estimate the polarization anisotropies of pyramid-shaped Si-tips and metal-coated Si-tips.

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References

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M. Schnell, A. García-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, “Controlling the near-field oscillations of loaded plasmonic nanoantennas,” Nat. Photonics 3(5), 287–291 (2009).
[Crossref]
M. Schnell, A. Garcia-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, “Phase-resolved mapping of the near-field vector and polarization state in nanoscale antenna gaps,” Nano Lett. 10(9), 3524–3528 (2010).
[Crossref] [PubMed]
M. Schnell, P. Alonso-Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]
M. Schnell, A. Garcia-Etxarri, A. J. Huber, K. B. Crozier, A. Borisov, J. Aizpurua, and R. Hillenbrand, “Amplitude- and phase-resolved near-field mapping of infrared antenna modes by transmission-mode scattering-type near-Field microscopy,” J. Phys. Chem. C 114(16), 7341–7345 (2010).
[Crossref]
J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9(6), 2372–2377 (2009).
[Crossref] [PubMed]
R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, “Determination of electric-field, magnetic-field, and electric-current distributions of infrared optical antennas: a near-field optical vector network analyzer,” Phys. Rev. Lett. 105(16), 167403 (2010).
[Crossref] [PubMed]
D.-S. Kim, J. Heo, S.-H. Ahn, S. W. Han, W. S. Yun, and Z. H. Kim, “Real-space mapping of the strongly coupled plasmons of nanoparticle dimers,” Nano Lett. 9(10), 3619–3625 (2009).
[Crossref] [PubMed]
H. Wei, Z. Li, X. Tian, Z. Wang, F. Cong, N. Liu, S. Zhang, P. Nordlander, N. J. Halas, and H. Xu, “Quantum dot-based local field imaging reveals plasmon-based interferometric logic in silver nanowire networks,” Nano Lett. 11(2), 471–475 (2011).
[Crossref] [PubMed]
R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8(10), 3155–3159 (2008).
[Crossref] [PubMed]
B. Deutsch, R. Hillenbrand, and L. Novotny, “Visualizing the optical interaction tensor of a gold nanoparticle pair,” Nano Lett. 10(2), 652–656 (2010).
[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. Photonics 1(1), 53–56 (2007).
[Crossref]
T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]
Y. Abate, A. Schwartzberg, D. Strasser, and S. R. Leone, “Nanometer-scale size dependent imaging of cetyl trimethyl ammonium bromide (CTAB) capped and uncapped gold nanoparticles by apertureless near-field optical microscopy,” Chem. Phys. Lett. 474(1–3), 146–152 (2009).
[Crossref]
P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, “Resolving the electromagnetic mechanism of surface-enhanced light scattering at single hot spots,” Nat. Commun 3, 684 (2012).
[Crossref] [PubMed]
J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single matallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]
E. J. R. Vesseur, R. de Waele, M. Kuttge, and A. Polman, “Direct observation of plasmonic modes in au nanowires using high-resolution cathodoluminescence spectroscopy,” Nano Lett. 7(9), 2843–2846 (2007).
[Crossref] [PubMed]
A. McLeod, A. Weber-Bargioni, Z. Zhang, S. Dhuey, B. Harteneck, J. B. Neaton, S. Cabrini, and P. J. Schuck, “Nonperturbative visualization of nanoscale plasmonic field distributions via photon localization microscopy,” Phys. Rev. Lett. 106(3), 037402 (2011).
[Crossref] [PubMed]
B. S. Guiton, V. Iberi, S. Li, D. N. Leonard, C. M. Parish, P. G. Kotula, M. Varela, G. C. Schatz, S. J. Pennycook, and J. P. Camden, “Correlated optical measurements and plasmon mapping of silver nanorods,” Nano Lett. 11(8), 3482–3488 (2011).
[Crossref] [PubMed]
Z. H. Kim and S. R. Leone, “Polarization-selective mapping of near-field intensity and phase around gold nanoparticles using apertureless near-field microscopy,” Opt. Express 16(3), 1733–1741 (2008).
[Crossref] [PubMed]
R. Vogelgesang and A. Dmitriev, “Real-space imaging of nanoplasmonic resonances,” Analyst (Lond.) 135(6), 1175–1181 (2010).
[Crossref] [PubMed]
J. Sun, P. S. Carney, and J. C. Schotland, “Strong tip effects in near-field scanning optical tomography,” J. Appl. Phys. 102(10), 103103 (2007).
[Crossref]
R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[Crossref]
P. S. Carney, Personal communication, 2012.
R. Hillenbrand and F. Keilmann, “Optical oscillation modes of plasmon particles observed in direct space by phase-contrast near-field microscopy,” Appl. Phys. B 73(3), 239–243 (2001).
[Crossref]
Z. H. Kim, S. H. Ahn, B. Liu, and S. R. Leone, “Nanometer-scale dielectric imaging of semiconductor nanoparticles: size-dependent dipolar coupling and contrast reversal,” Nano Lett. 7(8), 2258–2262 (2007).
[Crossref] [PubMed]
A. Garcia-Etxarri, I. Romero, F. J. G. deAbajo, R. Hillenbrand, and J. Aizpurua, “Influence of the tip in near-field imaging of nanoparticle plasmonic modes: weak and strong coupling regimes,” Phys. Rev. B 79(12), 125439 (2009).
[Crossref]

2012 (1)

P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, “Resolving the electromagnetic mechanism of surface-enhanced light scattering at single hot spots,” Nat. Commun 3, 684 (2012).
[Crossref] [PubMed]

2011 (4)

A. McLeod, A. Weber-Bargioni, Z. Zhang, S. Dhuey, B. Harteneck, J. B. Neaton, S. Cabrini, and P. J. Schuck, “Nonperturbative visualization of nanoscale plasmonic field distributions via photon localization microscopy,” Phys. Rev. Lett. 106(3), 037402 (2011).
[Crossref] [PubMed]

B. S. Guiton, V. Iberi, S. Li, D. N. Leonard, C. M. Parish, P. G. Kotula, M. Varela, G. C. Schatz, S. J. Pennycook, and J. P. Camden, “Correlated optical measurements and plasmon mapping of silver nanorods,” Nano Lett. 11(8), 3482–3488 (2011).
[Crossref] [PubMed]

M. Schnell, P. Alonso-Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]

H. Wei, Z. Li, X. Tian, Z. Wang, F. Cong, N. Liu, S. Zhang, P. Nordlander, N. J. Halas, and H. Xu, “Quantum dot-based local field imaging reveals plasmon-based interferometric logic in silver nanowire networks,” Nano Lett. 11(2), 471–475 (2011).
[Crossref] [PubMed]

2010 (5)

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, “Determination of electric-field, magnetic-field, and electric-current distributions of infrared optical antennas: a near-field optical vector network analyzer,” Phys. Rev. Lett. 105(16), 167403 (2010).
[Crossref] [PubMed]

M. Schnell, A. Garcia-Etxarri, A. J. Huber, K. B. Crozier, A. Borisov, J. Aizpurua, and R. Hillenbrand, “Amplitude- and phase-resolved near-field mapping of infrared antenna modes by transmission-mode scattering-type near-Field microscopy,” J. Phys. Chem. C 114(16), 7341–7345 (2010).
[Crossref]

M. Schnell, A. Garcia-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, “Phase-resolved mapping of the near-field vector and polarization state in nanoscale antenna gaps,” Nano Lett. 10(9), 3524–3528 (2010).
[Crossref] [PubMed]

R. Vogelgesang and A. Dmitriev, “Real-space imaging of nanoplasmonic resonances,” Analyst (Lond.) 135(6), 1175–1181 (2010).
[Crossref] [PubMed]

B. Deutsch, R. Hillenbrand, and L. Novotny, “Visualizing the optical interaction tensor of a gold nanoparticle pair,” Nano Lett. 10(2), 652–656 (2010).
[Crossref] [PubMed]

2009 (5)

M. Schnell, A. García-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, “Controlling the near-field oscillations of loaded plasmonic nanoantennas,” Nat. Photonics 3(5), 287–291 (2009).
[Crossref]

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9(6), 2372–2377 (2009).
[Crossref] [PubMed]

D.-S. Kim, J. Heo, S.-H. Ahn, S. W. Han, W. S. Yun, and Z. H. Kim, “Real-space mapping of the strongly coupled plasmons of nanoparticle dimers,” Nano Lett. 9(10), 3619–3625 (2009).
[Crossref] [PubMed]

Y. Abate, A. Schwartzberg, D. Strasser, and S. R. Leone, “Nanometer-scale size dependent imaging of cetyl trimethyl ammonium bromide (CTAB) capped and uncapped gold nanoparticles by apertureless near-field optical microscopy,” Chem. Phys. Lett. 474(1–3), 146–152 (2009).
[Crossref]

A. Garcia-Etxarri, I. Romero, F. J. G. deAbajo, R. Hillenbrand, and J. Aizpurua, “Influence of the tip in near-field imaging of nanoparticle plasmonic modes: weak and strong coupling regimes,” Phys. Rev. B 79(12), 125439 (2009).
[Crossref]

2008 (2)

Z. H. Kim and S. R. Leone, “Polarization-selective mapping of near-field intensity and phase around gold nanoparticles using apertureless near-field microscopy,” Opt. Express 16(3), 1733–1741 (2008).
[Crossref] [PubMed]

R. Esteban, R. Vogelgesang, J. Dorfmüller, A. Dmitriev, C. Rockstuhl, C. Etrich, and K. Kern, “Direct near-field optical imaging of higher order plasmonic resonances,” Nano Lett. 8(10), 3155–3159 (2008).
[Crossref] [PubMed]

2007 (5)

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. Photonics 1(1), 53–56 (2007).
[Crossref]

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single matallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

E. J. R. Vesseur, R. de Waele, M. Kuttge, and A. Polman, “Direct observation of plasmonic modes in au nanowires using high-resolution cathodoluminescence spectroscopy,” Nano Lett. 7(9), 2843–2846 (2007).
[Crossref] [PubMed]

J. Sun, P. S. Carney, and J. C. Schotland, “Strong tip effects in near-field scanning optical tomography,” J. Appl. Phys. 102(10), 103103 (2007).
[Crossref]

Z. H. Kim, S. H. Ahn, B. Liu, and S. R. Leone, “Nanometer-scale dielectric imaging of semiconductor nanoparticles: size-dependent dipolar coupling and contrast reversal,” Nano Lett. 7(8), 2258–2262 (2007).
[Crossref] [PubMed]

2006 (1)

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

2004 (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[Crossref]

2001 (1)

R. Hillenbrand and F. Keilmann, “Optical oscillation modes of plasmon particles observed in direct space by phase-contrast near-field microscopy,” Appl. Phys. B 73(3), 239–243 (2001).
[Crossref]

Abate, Y.

Ahn, S. H.

Ahn, S.-H.

Aizpurua, J.

Albella, P.

Alkorta, J.

Alonso-Gonzalez, P.

Alonso-González, P.

Arzubiaga, L.

Boreman, G. D.

Borisov, A.

Cabrini, S.

Camden, J. P.

Carney, P. S.

J. Sun, P. S. Carney, and J. C. Schotland, “Strong tip effects in near-field scanning optical tomography,” J. Appl. Phys. 102(10), 103103 (2007).
[Crossref]

Casanova, F.

Chen, J.

Choi, S. B.

Choi, W. J.

Chuvilin, A.

Colliex, C.

Cong, F.

Crozier, K.

Crozier, K. B.

de Abajo, F. J. G.

de Waele, R.

deAbajo, F. J. G.

Deutsch, B.

B. Deutsch, R. Hillenbrand, and L. Novotny, “Visualizing the optical interaction tensor of a gold nanoparticle pair,” Nano Lett. 10(2), 652–656 (2010).
[Crossref] [PubMed]

Dhuey, S.

Dmitriev, A.

R. Vogelgesang and A. Dmitriev, “Real-space imaging of nanoplasmonic resonances,” Analyst (Lond.) 135(6), 1175–1181 (2010).
[Crossref] [PubMed]

Dorfmüller, J.

Esteban, R.

Etrich, C.

Garcia-Etxarri, A.

García-Etxarri, A.

Golmar, F.

Guiton, B. S.

Halas, N. J.

Han, S. W.

Harteneck, B.

Henrard, L.

Heo, J.

Hillenbrand, R.

B. Deutsch, R. Hillenbrand, and L. Novotny, “Visualizing the optical interaction tensor of a gold nanoparticle pair,” Nano Lett. 10(2), 652–656 (2010).
[Crossref] [PubMed]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Huber, A. J.

Hueso, L. E.

Huth, F.

Iberi, V.

Keilmann, F.

Kern, K.

Kihm, H. W.

Kihm, J. E.

Kim, D. S.

Kim, D.-S.

Kim, H.

Kim, J.

Kim, Z. H.

Kociak, M.

Korobkin, D.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Kotula, P. G.

Krenz, P. M.

Kuttge, M.

Lail, B. A.

Lederer, F.

Lee, B.

Lee, K. G.

Leonard, D. N.

Leone, S. R.

Li, S.

Li, Z.

Lienau, C.

Liu, B.

Liu, N.

Liz-Marzan, L. M.

McLeod, A.

Neaton, J. B.

Nelayah, J.

Nordlander, P.

Novotny, L.

B. Deutsch, R. Hillenbrand, and L. Novotny, “Visualizing the optical interaction tensor of a gold nanoparticle pair,” Nano Lett. 10(2), 652–656 (2010).
[Crossref] [PubMed]

Olmon, R. L.

Parish, C. M.

Park, D. J.

Park, Q. H.

Pastoriza-Santos, I.

Pennycook, S. J.

Pertsch, T.

Polman, A.

Potton, R. J.

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[Crossref]

Rang, M.

Raschke, M. B.

Rockstuhl, C.

Romero, I.

Ropers, C.

Saraf, L. V.

Schatz, G. C.

Schnell, M.

Schotland, J. C.

J. Sun, P. S. Carney, and J. C. Schotland, “Strong tip effects in near-field scanning optical tomography,” J. Appl. Phys. 102(10), 103103 (2007).
[Crossref]

Schuck, P. J.

Schwartzberg, A.

Shvets, G.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Stephan, O.

Strasser, D.

Sun, J.

J. Sun, P. S. Carney, and J. C. Schotland, “Strong tip effects in near-field scanning optical tomography,” J. Appl. Phys. 102(10), 103103 (2007).
[Crossref]

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Taverna, D.

Tence, M.

Tian, X.

Urzhumov, Y.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Varela, M.

Vesseur, E. J. R.

Vogelgesang, R.

R. Vogelgesang and A. Dmitriev, “Real-space imaging of nanoplasmonic resonances,” Analyst (Lond.) 135(6), 1175–1181 (2010).
[Crossref] [PubMed]

Wang, Z.

Weber-Bargioni, A.

Wei, H.

Weitz, R. T.

Woo, D. H.

Xu, H.

Yoon, Y. C.

Yun, W. S.

Zhang, S.

Zhang, Z.

Analyst (Lond.) (1)

R. Vogelgesang and A. Dmitriev, “Real-space imaging of nanoplasmonic resonances,” Analyst (Lond.) 135(6), 1175–1181 (2010).
[Crossref] [PubMed]

Appl. Phys. B (1)

Chem. Phys. Lett. (1)

J. Appl. Phys. (1)

J. Sun, P. S. Carney, and J. C. Schotland, “Strong tip effects in near-field scanning optical tomography,” J. Appl. Phys. 102(10), 103103 (2007).
[Crossref]

J. Phys. Chem. C (1)

Nano Lett. (9)

B. Deutsch, R. Hillenbrand, and L. Novotny, “Visualizing the optical interaction tensor of a gold nanoparticle pair,” Nano Lett. 10(2), 652–656 (2010).
[Crossref] [PubMed]

Nat. Commun (1)

Nat. Photonics (3)

Nat. Phys. (1)

Opt. Express (1)

Phys. Rev. B (1)

Phys. Rev. Lett. (2)

Rep. Prog. Phys. (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67(5), 717–754 (2004).
[Crossref]

Science (1)

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a SiC superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

Other (1)

P. S. Carney, Personal communication, 2012.

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Fig. 1

The schematic of s-SNOM setup. M = mirror, QWP = quarter-wave plate, HWP = half-wave plate, BS = 50 / 50 beam splitter, Pol = polarizer, PD = photodiode, L = objective lens. The directions of incident and scattered light are drawn as solid and dashed arrows, respectively. Also shown are the sample coordinates and polarization directions (s and p): the x-axis is parallel to the s-polarization direction, z-axis is perpendicular to the sample plane, y-axis is parallel to the sample-plane projection of the propagation vector of the incident light. The z’-axis is parallel to the electric field vector of a p-polarized excitation light, and is tilted by θ = 30° from the z-axis.

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Fig. 2

Tip-sample interaction model. (a) E₀ = incident field, E_scat = scattered field, α = polarizability tensor of the tip. Also shown is the sample coordinate system. (b) The ST and TS scattering processes in the cross-polarized s-SNOM of a nanoparticle: the polarization states of the incident (black) and scattered (blue) light are shown as double-sided arrows (red). The two double-sided arrows that connect the panels indicate the reciprocal relationships of the possible scattering events.

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Fig. 3

s-SNOM images, simulated field distributions, spectra, and structure of a gold nanoprism. (a) AFM topography. The vertices v₁, v₂, and v₃ point to the positions of top vertices of the nanoprism. (b) Simulated far-field scattering spectra of a nanoprism and the electron-microscopy images of a representative nanoprism (inset). The spectra show both the in-plane (thin black trace) and out-of-plane (thick black line) dipolar resonances. The red arrow points to the excitation wavelength (633 nm) employed in s-SNOM measurements. (c) Excitation and detection geometry and the coordinates used (see also the bottom right of (k) for another coordinate reference). (d)–(k) experimental s-SNOM intensity (|s₃|²) and phase (ϕ₃) maps. The phase images are corrected for the illumination phase gradients (see the main text). To the left of the images, the excitation/detection polarizations (s or p) for each image are shown. (l)–(q) the simulated local field intensity (|E|²) and phase (ϕ) maps sampled 10 nm above the top surface of the nanoprism. To the right of the images, the names of field components are shown. In both the experimental and simulated images, the dashed triangles show the approximate shape of the nanoprism and the positions of vertices. (r) The line-profiles of (f) and (j) (marked as dashed lines). (s) The line profiles of (n) and (q). The abrupt phase-jump (red region) in (f) that appears on the left vertex of the nanoprism arise from the jitter of the AFM feedback loop that occurred during the scan.

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Fig. 4

Possible influence of polarization anisotropy on s-SNOM images. (a) Experimental intensity (|s₃|²) image of a nanoprism obtained with the s/p-polarization. (b), (c), and (d) Intensity distributions of FDTD-simulated field components, $E_{z}^{(x)}$ , $E_{x}^{(z')}$ , and $E_{y}^{(x)}$ , respectively. (e)-(i) Simulated cross-polarized s-SNOM images (|A_s,p|²) calculated with Eq. (8) and the field components shown in (b)-(d), evaluated for tip anisotropies (r = | α_zz / α_xx |) of 50, 10, 5, 1, and 0.1.

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Fig. 5

s-SNOM images obtained with a PtIr-coated Si-tip with similar pyramidal shape. (a) AFM topography. (b)–(g) experimental s-SNOM intensity (|s₃|²) and phase (ϕ₃) maps. To the left of the images, the excitation/detection polarizations (s or p) for each image are shown. (h)-(o) the simulated local field components (intensity, |E|² ; phase, ϕ) sampled 10 nm above the top surface of the nanoprism. To the right of the images, the names of field components are shown. (p)-(s) Simulated cross-polarized s-SNOM images (|A_s,p|²) calculated with Eq. (8) and the field components shown in (h), (l), (j), and (n), evaluated for tip anisotropies (r = |α_zz / α_xx|) of 100, 3.3, 2, and 0.5. The v₁ in (a), and arrows in (b), (c), (q), and (r) points to the vertex position of the nanoprism mentioned in the text. Dashed triangles in the images show the shape of the top-surface of the nanoprism.

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Equations (16)

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E_{scat} ≅ (T S + S T) E_{0} .

A_{i, j} = {\hat{e}}_{j} (TS + ST) (E_{0} {\hat{e}}_{i}) = A_{i, j}^{T S} + A_{i, j}^{S T},

A_{i, j}^{S T} = A_{j, i}^{T S} = b α_{i i} E_{i}^{(j)},

A_{x, x} = 2 b α_{x x} E_{x}^{(x)} a n d A_{z, z} = 2 b α_{z z} E_{z}^{(z)},

A_{x, z} = A_{z, x} = b (α_{z z} E_{z}^{(x)} + α_{x x} E_{x}^{(z)}) .

A_{s, s} = 2 b α_{x x} E_{x}^{(x)},

A_{p, p} = 2 b (α_{z z} E_{z}^{(z')} \cos θ + α_{x x} E_{y}^{(z')} \sin θ),

A_{s, p} = A_{p, s} = b (α_{z z} E_{z}^{(x)} \cos θ + α_{x x} E_{x}^{(z')} + α_{x x} E_{y}^{(x)} \sin θ),

A_{p, p} ≅ 2 b α_{z z} E_{z}^{(z')} \cos θ,

A_{s, p} = A_{p, s} ≅ b (α_{z z} E_{z}^{(x)} + α_{x x} E_{x}^{(z)}) \cos θ .

E_{s c a t} = \sum_{n = 1}^{\infty} {(S_{0} + T)}^{n} E_{0},

S_{0} E (r) = k_{0}^{2} \int d^{3} τ' G (r, r') η (r') E (r'),

T E (r) = k_{0}^{2} \int d^{3} τ' G (r, r') χ (r') E (r') .

E_{scat} (r) ≅ (S + T + S T + T S + S T S) E_{0},

S = \sum_{i = 1}^{\infty} S_{0}^{n} .

E_{scat} = (T S + S T + S T S) E_{0} .