Abstract

We have measured local electric field vectors of local polarizaton on the nanoscale using gold nanoparticle functionalized tips as local field scatterers. In our experiments, the local field induces a dipole-moment in the gold nanoparticle functionalized tip, which then radiates into the far-field, transferring the full information about the local electric field from the near into the far field. The polarization characteristics of the scattered fields are analyzed using a conventional ellipsometry method. The tip dependent scattering function- the polarizability tensor- is fully determined by far field scattering measurements. Once the polarizability tensor for each tip is correctly accounted for in the data analysis, our results show that the finally determined local field polarization vectors are essentially independent of the tip shape.

© 2007 Optical Society of America

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  1. A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope,” Ultramicroscopy 13, 227–231 (1984). http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_ArticleListID=593399642& _sort=d&view=c&_acct=C000013398&_version=1&_urlVersion=0&_userid=198559&md5=7d957a939b 269ad26d465d7bd6adc0b3
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  9. D. Ganic, X. Gan, and M. Gu, “Parametric study of three-dimensional near-field Mie scattering by dielectric particles,” Opt. Commun. 216, 1–10 (2003).
    [Crossref]
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    [Crossref]
  11. P. S. Hauge and F. H. Dill, “Design and operation of ETA, and Automated Ellipsometer,” IBM J. Res. Develop. 17, 472489 (1973). http://domino.watson.ibm.com/tchjr/journalindex.nsf/0b9bc46ed06cbac1852565e6006fe1a0/47d82e1ff4ac d49585256bfa006841c4?OpenDocument
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    [Crossref]
  15. R. Hillenbrand, F. Keilmann, P. Hanarp, D. S. Sutherland, and J. Aizpurua, “Coherent imaging of nanoscale plasmon patterns with a carbon nanotube optical probe,” Appl. Phys. Lett. 83, 368–370 (2003). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000083000002000368000 001&idtype=cvips&gifs=yes
    [Crossref]
  16. R. Dändliker, P. Tortora, L. Vaccaro, and A. Nesci, “Measuring three-dimensional polarization with scanning optical probes,” J. Opt. A 6S18–S23 (2004). http://www.iop.org/EJ/abstract/1464-4258/6/3/003
    [Crossref]
  17. R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Optica Acta 29, 685–689 (1982). http://www.informaworld.com/smpp/content~content=a713820903~db=all
    [Crossref]
  18. R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985). http://ol.osa.org/abstract.cfm?id=8453
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  20. Z. H. Kim and S. R. Leone, “High-resolution apertureless near-field optical imaging using gold nanosphere probes,” J. Phys. Chem.B 110, 19804–19804 (2006). http://pubs.acs.org/cgi-bin/article.cgi/jpcbfk/2006/110/i40/html/jp061398+.html
    [Crossref] [PubMed]
  21. T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2315 (2004). http://pubs.acs.org/cgi-bin/abstract.cgi/nalefd/2004/4/i12/abs/nl048694n.html
    [Crossref]
  22. P. C. Gasson, Geometry of Spatial Forms-Ch. 8 (John Wiley & Sons, New York, USA, 1983).
  23. J. Ellis and A. Dogariu, “Optical polarimetry of random fields,” Phys. Rev. Lett. 95, 203905 (2005). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000095000020203905000 001&idtype=cvips&gifs=Yes
    [Crossref] [PubMed]

2007 (1)

K. G. Lee, H. W. Kihm, and J. E. Kihm, et al, “Vector field microscopic imaging of light,” Nature Photon. 1, 53–56 (2007). http://www.nature.com/nphoton/journal/v1/n1/abs/nphoton.2006.37.html
[Crossref]

2006 (1)

Z. H. Kim and S. R. Leone, “High-resolution apertureless near-field optical imaging using gold nanosphere probes,” J. Phys. Chem.B 110, 19804–19804 (2006). http://pubs.acs.org/cgi-bin/article.cgi/jpcbfk/2006/110/i40/html/jp061398+.html
[Crossref] [PubMed]

2005 (1)

J. Ellis and A. Dogariu, “Optical polarimetry of random fields,” Phys. Rev. Lett. 95, 203905 (2005). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000095000020203905000 001&idtype=cvips&gifs=Yes
[Crossref] [PubMed]

2004 (2)

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2315 (2004). http://pubs.acs.org/cgi-bin/abstract.cgi/nalefd/2004/4/i12/abs/nl048694n.html
[Crossref]

R. Dändliker, P. Tortora, L. Vaccaro, and A. Nesci, “Measuring three-dimensional polarization with scanning optical probes,” J. Opt. A 6S18–S23 (2004). http://www.iop.org/EJ/abstract/1464-4258/6/3/003
[Crossref]

2003 (2)

R. Hillenbrand, F. Keilmann, P. Hanarp, D. S. Sutherland, and J. Aizpurua, “Coherent imaging of nanoscale plasmon patterns with a carbon nanotube optical probe,” Appl. Phys. Lett. 83, 368–370 (2003). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000083000002000368000 001&idtype=cvips&gifs=yes
[Crossref]

D. Ganic, X. Gan, and M. Gu, “Parametric study of three-dimensional near-field Mie scattering by dielectric particles,” Opt. Commun. 216, 1–10 (2003).
[Crossref]

2001 (1)

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202, 72–76 (2001). http://www.blackwell-synergy.com/doi/full/10.1046/j.1365-2818.2001.00817.x
[Crossref] [PubMed]

1994 (2)

F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994). http://scitation.aip.or g/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000065000013001623000 001&idtype=cvips&gifs=yes
[Crossref]

Y. Inouye and S. Kawata, “Near-field scanning optical microscope with a metallic probe tip,” Opt. Lett. 19159–161 (1994). http://ol.osa.org/abstract.cfm?id= 12150
[Crossref] [PubMed]

1992 (1)

E. Betzig, J. K. Trautman, J. S. Weiner, T. D. Harris, and R. Wolfe, “Polarization contrast in near-field scanning optical microscopy,” Appl. Opt. 22, 4563 (1992). http://ao.osa.org/abstract.cfm?id=40089
[Crossref]

1991 (1)

G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A. 8, 483 (1991). http://josaa.osa.org/abstract.cfm?id=4011
[Crossref]

1985 (1)

1984 (2)

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope,” Ultramicroscopy 13, 227–231 (1984). http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_ArticleListID=593399642& _sort=d&view=c&_acct=C000013398&_version=1&_urlVersion=0&_userid=198559&md5=7d957a939b 269ad26d465d7bd6adc0b3
[Crossref]

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984). http://scitation.aip.or g/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000044000007000651000 001&idtype=cvips&gifs=yes
[Crossref]

1982 (1)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Optica Acta 29, 685–689 (1982). http://www.informaworld.com/smpp/content~content=a713820903~db=all
[Crossref]

1979 (1)

1973 (3)

H. F. Hazebroek and A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E: Sci. Instru. 6, 822–826 (1973). http://www.iop.org/EJ/abstract/0022-3735/6/9/013
[Crossref]

D. E. Aspnes, “Foulier transformation detection system for rotating-analyzer ellipsometers,” Opt. Commun. 8, 222–225 (1973).
[Crossref]

P. S. Hauge and F. H. Dill, “Design and operation of ETA, and Automated Ellipsometer,” IBM J. Res. Develop. 17, 472489 (1973). http://domino.watson.ibm.com/tchjr/journalindex.nsf/0b9bc46ed06cbac1852565e6006fe1a0/47d82e1ff4ac d49585256bfa006841c4?OpenDocument
[Crossref]

1970 (1)

R. Greef, “An automatic ellipsometer for use in electrochemical investigations,” Rev. Sci. Instrum. 41, 532538 (1970). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK0000410000040005320000 01&idtype=cvips&gifs=yes
[Crossref]

Aizpurua, J.

R. Hillenbrand, F. Keilmann, P. Hanarp, D. S. Sutherland, and J. Aizpurua, “Coherent imaging of nanoscale plasmon patterns with a carbon nanotube optical probe,” Appl. Phys. Lett. 83, 368–370 (2003). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000083000002000368000 001&idtype=cvips&gifs=yes
[Crossref]

Aspnes, D. E.

D. E. Aspnes, “Foulier transformation detection system for rotating-analyzer ellipsometers,” Opt. Commun. 8, 222–225 (1973).
[Crossref]

Azzam, R. M. A.

R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985). http://ol.osa.org/abstract.cfm?id=8453
[Crossref] [PubMed]

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Optica Acta 29, 685–689 (1982). http://www.informaworld.com/smpp/content~content=a713820903~db=all
[Crossref]

Betzig, E.

E. Betzig, J. K. Trautman, J. S. Weiner, T. D. Harris, and R. Wolfe, “Polarization contrast in near-field scanning optical microscopy,” Appl. Opt. 22, 4563 (1992). http://ao.osa.org/abstract.cfm?id=40089
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics - 7th ed. p.25 Eq. 12 (Cambridge University Press, Cambridge, England, 1999).
[PubMed]

Chew, H.

Dändliker, R.

R. Dändliker, P. Tortora, L. Vaccaro, and A. Nesci, “Measuring three-dimensional polarization with scanning optical probes,” J. Opt. A 6S18–S23 (2004). http://www.iop.org/EJ/abstract/1464-4258/6/3/003
[Crossref]

Denk, W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984). http://scitation.aip.or g/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000044000007000651000 001&idtype=cvips&gifs=yes
[Crossref]

Dill, F. H.

P. S. Hauge and F. H. Dill, “Design and operation of ETA, and Automated Ellipsometer,” IBM J. Res. Develop. 17, 472489 (1973). http://domino.watson.ibm.com/tchjr/journalindex.nsf/0b9bc46ed06cbac1852565e6006fe1a0/47d82e1ff4ac d49585256bfa006841c4?OpenDocument
[Crossref]

Dogariu, A.

J. Ellis and A. Dogariu, “Optical polarimetry of random fields,” Phys. Rev. Lett. 95, 203905 (2005). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000095000020203905000 001&idtype=cvips&gifs=Yes
[Crossref] [PubMed]

Ellis, J.

J. Ellis and A. Dogariu, “Optical polarimetry of random fields,” Phys. Rev. Lett. 95, 203905 (2005). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000095000020203905000 001&idtype=cvips&gifs=Yes
[Crossref] [PubMed]

Gan, X.

D. Ganic, X. Gan, and M. Gu, “Parametric study of three-dimensional near-field Mie scattering by dielectric particles,” Opt. Commun. 216, 1–10 (2003).
[Crossref]

Ganic, D.

D. Ganic, X. Gan, and M. Gu, “Parametric study of three-dimensional near-field Mie scattering by dielectric particles,” Opt. Commun. 216, 1–10 (2003).
[Crossref]

Gasson, P. C.

P. C. Gasson, Geometry of Spatial Forms-Ch. 8 (John Wiley & Sons, New York, USA, 1983).

Greef, R.

R. Greef, “An automatic ellipsometer for use in electrochemical investigations,” Rev. Sci. Instrum. 41, 532538 (1970). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RSINAK0000410000040005320000 01&idtype=cvips&gifs=yes
[Crossref]

Gu, M.

D. Ganic, X. Gan, and M. Gu, “Parametric study of three-dimensional near-field Mie scattering by dielectric particles,” Opt. Commun. 216, 1–10 (2003).
[Crossref]

Håkanson, U.

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2315 (2004). http://pubs.acs.org/cgi-bin/abstract.cgi/nalefd/2004/4/i12/abs/nl048694n.html
[Crossref]

Hanarp, P.

R. Hillenbrand, F. Keilmann, P. Hanarp, D. S. Sutherland, and J. Aizpurua, “Coherent imaging of nanoscale plasmon patterns with a carbon nanotube optical probe,” Appl. Phys. Lett. 83, 368–370 (2003). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000083000002000368000 001&idtype=cvips&gifs=yes
[Crossref]

Harootunian, A.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope,” Ultramicroscopy 13, 227–231 (1984). http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_ArticleListID=593399642& _sort=d&view=c&_acct=C000013398&_version=1&_urlVersion=0&_userid=198559&md5=7d957a939b 269ad26d465d7bd6adc0b3
[Crossref]

Harris, T. D.

E. Betzig, J. K. Trautman, J. S. Weiner, T. D. Harris, and R. Wolfe, “Polarization contrast in near-field scanning optical microscopy,” Appl. Opt. 22, 4563 (1992). http://ao.osa.org/abstract.cfm?id=40089
[Crossref]

Hauge, P. S.

P. S. Hauge and F. H. Dill, “Design and operation of ETA, and Automated Ellipsometer,” IBM J. Res. Develop. 17, 472489 (1973). http://domino.watson.ibm.com/tchjr/journalindex.nsf/0b9bc46ed06cbac1852565e6006fe1a0/47d82e1ff4ac d49585256bfa006841c4?OpenDocument
[Crossref]

Hazebroek, H. F.

H. F. Hazebroek and A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E: Sci. Instru. 6, 822–826 (1973). http://www.iop.org/EJ/abstract/0022-3735/6/9/013
[Crossref]

Hillenbrand, R.

R. Hillenbrand, F. Keilmann, P. Hanarp, D. S. Sutherland, and J. Aizpurua, “Coherent imaging of nanoscale plasmon patterns with a carbon nanotube optical probe,” Appl. Phys. Lett. 83, 368–370 (2003). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000083000002000368000 001&idtype=cvips&gifs=yes
[Crossref]

Holscher, A. A.

H. F. Hazebroek and A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E: Sci. Instru. 6, 822–826 (1973). http://www.iop.org/EJ/abstract/0022-3735/6/9/013
[Crossref]

Inouye, Y.

Isaacson, M.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope,” Ultramicroscopy 13, 227–231 (1984). http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_ArticleListID=593399642& _sort=d&view=c&_acct=C000013398&_version=1&_urlVersion=0&_userid=198559&md5=7d957a939b 269ad26d465d7bd6adc0b3
[Crossref]

Kalkbrenner, T.

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2315 (2004). http://pubs.acs.org/cgi-bin/abstract.cgi/nalefd/2004/4/i12/abs/nl048694n.html
[Crossref]

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202, 72–76 (2001). http://www.blackwell-synergy.com/doi/full/10.1046/j.1365-2818.2001.00817.x
[Crossref] [PubMed]

Kawata, S.

Keilmann, F.

R. Hillenbrand, F. Keilmann, P. Hanarp, D. S. Sutherland, and J. Aizpurua, “Coherent imaging of nanoscale plasmon patterns with a carbon nanotube optical probe,” Appl. Phys. Lett. 83, 368–370 (2003). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000083000002000368000 001&idtype=cvips&gifs=yes
[Crossref]

Kerker, M.

Kihm, H. W.

K. G. Lee, H. W. Kihm, and J. E. Kihm, et al, “Vector field microscopic imaging of light,” Nature Photon. 1, 53–56 (2007). http://www.nature.com/nphoton/journal/v1/n1/abs/nphoton.2006.37.html
[Crossref]

Kihm, J. E.

K. G. Lee, H. W. Kihm, and J. E. Kihm, et al, “Vector field microscopic imaging of light,” Nature Photon. 1, 53–56 (2007). http://www.nature.com/nphoton/journal/v1/n1/abs/nphoton.2006.37.html
[Crossref]

Kim, Z. H.

Z. H. Kim and S. R. Leone, “High-resolution apertureless near-field optical imaging using gold nanosphere probes,” J. Phys. Chem.B 110, 19804–19804 (2006). http://pubs.acs.org/cgi-bin/article.cgi/jpcbfk/2006/110/i40/html/jp061398+.html
[Crossref] [PubMed]

Lanz, M.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984). http://scitation.aip.or g/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000044000007000651000 001&idtype=cvips&gifs=yes
[Crossref]

Lee, K. G.

K. G. Lee, H. W. Kihm, and J. E. Kihm, et al, “Vector field microscopic imaging of light,” Nature Photon. 1, 53–56 (2007). http://www.nature.com/nphoton/journal/v1/n1/abs/nphoton.2006.37.html
[Crossref]

Leone, S. R.

Z. H. Kim and S. R. Leone, “High-resolution apertureless near-field optical imaging using gold nanosphere probes,” J. Phys. Chem.B 110, 19804–19804 (2006). http://pubs.acs.org/cgi-bin/article.cgi/jpcbfk/2006/110/i40/html/jp061398+.html
[Crossref] [PubMed]

Lewis, A.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope,” Ultramicroscopy 13, 227–231 (1984). http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_ArticleListID=593399642& _sort=d&view=c&_acct=C000013398&_version=1&_urlVersion=0&_userid=198559&md5=7d957a939b 269ad26d465d7bd6adc0b3
[Crossref]

Mlynek, J.

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202, 72–76 (2001). http://www.blackwell-synergy.com/doi/full/10.1046/j.1365-2818.2001.00817.x
[Crossref] [PubMed]

Muray, A.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500 Å spatial resolution light microscope,” Ultramicroscopy 13, 227–231 (1984). http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_ArticleListID=593399642& _sort=d&view=c&_acct=C000013398&_version=1&_urlVersion=0&_userid=198559&md5=7d957a939b 269ad26d465d7bd6adc0b3
[Crossref]

Nesci, A.

R. Dändliker, P. Tortora, L. Vaccaro, and A. Nesci, “Measuring three-dimensional polarization with scanning optical probes,” J. Opt. A 6S18–S23 (2004). http://www.iop.org/EJ/abstract/1464-4258/6/3/003
[Crossref]

O’Boyle, M. P.

F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994). http://scitation.aip.or g/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000065000013001623000 001&idtype=cvips&gifs=yes
[Crossref]

Pohl, D. W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984). http://scitation.aip.or g/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000044000007000651000 001&idtype=cvips&gifs=yes
[Crossref]

Ramstein, M.

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F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, “Apertureless near-field optical microscope,” Appl. Phys. Lett. 65, 1623–1625 (1994). http://scitation.aip.or g/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000065000013001623000 001&idtype=cvips&gifs=yes
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E. Betzig, J. K. Trautman, J. S. Weiner, T. D. Harris, and R. Wolfe, “Polarization contrast in near-field scanning optical microscopy,” Appl. Opt. 22, 4563 (1992). http://ao.osa.org/abstract.cfm?id=40089
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Figures (6)

Fig. 1.
Fig. 1.

Schematics of the experimental procedure. (a) The outer-plot (black line) results from a polar plot of the squared-rooted intensities for every detecting polarizer angle. The angle (θmax ) of the measured intensity maximum corresponds to the major axis angle and the square-rooted maximum (minimum) intensity is proportional to the major (minor) axis length. (b) One such experimental polar plot of the scattered light at one selected position is shown as filled circles. The black line is a guide to the eye. The elliptical polarization state is reconstructed (inner red line). (c) The red arrow represents the long axis of the ellipse shown in (b). By back-transformation using the experimentally determined polarizability tensor of the scatterer, the local field vector of local polarization is determined (black arrow).

Fig. 2.
Fig. 2.

(a). Schematic diagram of the tip polarizability tensor measurements. The tip end is illuminated by focusing a 780 nm plane wave and the incident beam polarization is rotated by 360° using a λ/2 plate. The tip axis is oriented along the z-axis and the laser beam is incident along the y-axis. The scattered light is detected in the direction of the incident beam by rotating a linear polarizer in front of the detector. (b) Polar plot of the square-rooted intensity of light scattered off the tip end for every incident light polarization. (c) The outer rim of (b) is fitted as an ellipse and the corresponding polarizability tensor is shown in upper part.

Fig. 3.
Fig. 3.

(a). Experimental setup: A 780 nm cw-mode Ti:Sapphire laser enters at normal incidence into one side facet of an equilaterally shaped prism and is retro-reflected at the other side facet to generate an evanescent standing wave on the top surface. The gold nanoparticle functionalized tip scatters the local fields into far-field region. The detection angle was set about 20° from the prism surface (-y axis). (b) Theoretically calculated local field components as a function of the scatterer position: vertical |Ez |2 (dashed line) and horizontal |Ex |2 (solid line) component, respectively. The corresponding local field vectors of polarization are presented at every position.

Fig. 4.
Fig. 4.

(a). A SEM image of a gold nanoparticle functionalized tip. (b) Polar plots of the square-rooted intensity of light scattered off the tip end for horizontal (open circles) and vertical (filled squares) polarizations of the incident light, respectively. The solid line represents the polar plot of square-rooted total scattered field intensity by rotating the incident beam polarization by 360° in 10 degrees steps. (c) Dependence of the scattered field intensity on the detecting polarizer angle at position x1, i.e., for a maximum of |ES,x |2 (open circles), and at a position x2, i.e., at a maximum of |ES,z |2 (filled squares) of the standing wave generated on the prism surface. The solid lines are fitted by using Eq. (2). The upper part shows polar plots generated from the data. (d) Intensity profiles of the field components ELocal,x (open circles) and ELocal,z (filled squares).

Fig. 5.
Fig. 5.

(a). Far-field tip characterization: experimental (solid line) and fitted (dashed line) data, respectively. (b) Dependence of the scattered field intensity on the detecting polarizer angle at intensity maxima of |ES,x |2 (open circles) and |ES,z |2 (filled squares) of the standing wave generated on the prism surface. (c) Spatial variation of the intensity profiles for the detecting polarizer angles of 0° (open circles) and 90° (filled squares) as a function of the tip position. (d) Intensity profiles of ELocal,x (open circles) and ELocal,z (filled squares) field components obtained by applying the back-transformation to (c), using the experimentally measured polarizability tensor.

Fig. 6.
Fig. 6.

Local field polarization vectors of the evanescent standing wave generated on the prism surface within a 600 nm scan range obtained by using three different gold-particle functionalized tips. The corresponding polarizability tensors are displayed above the scans.

Equations (3)

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E Local ( r ) = ( E x , E z ) = ( a 1 e iωt + i δ 1 , a 2 e iωt + i δ 2 ) , ( a 1 , a 2 > 0 ) ,
I P E S 2 = ( cos φ sin φ ) α ( E Local , x E Local , z ) 2
α = ( cos ζ sin ζ sin ζ cos ζ ) ( a 0 0 1 ) ( cos ζ sin ζ sin ζ cos ζ )

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