Abstract

We use symmetry considerations to understand and unravel near-field measurements, ultimately showing that we can spatially map three distinct fields using only two detectors. As an example, we create 2D field maps of the out-of-plane magnetic field and two in-plane fields for a silicon ridge waveguide. Furthermore, we are able to identify and remove polarization mixing of less than 1/30 of our experimental signals. Since symmetries are prevalent in nanophotonic structures and their near-fields, our method can have an impact on many future near-field measurements.

© 2014 Optical Society of America

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References

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  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).
  2. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2005).
  3. R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
    [CrossRef]
  4. M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
    [CrossRef]
  5. T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, Nat. Photonics 8, 23 (2014).
    [CrossRef]
  6. H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
    [CrossRef]
  7. M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
    [CrossRef]
  8. P. Uebel, M. A. Schmidt, H. W. Lee, and P. S. J. Russell, Opt. Express 20, 28409 (2012).
    [CrossRef]
  9. M. Schnell, A. Garca-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, Nano Lett. 10, 3524 (2010).
    [CrossRef]
  10. M. Schnell, A. Garca-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, Nat. Photonics 3, 287 (2009).
    [CrossRef]
  11. J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
    [CrossRef]
  12. P. Venugopalan, Q. Zhang, X. Li, and M. Gu, Opt. Express 21, 15247 (2013).
    [CrossRef]
  13. B. le Feber, N. Rotenberg, D. M. Beggs, and L. Kuipers, Nat. Photonics 8, 43 (2014).
    [CrossRef]
  14. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).
  15. F. J. Garcia-Vidal, L. Martin-Moreno, T. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
    [CrossRef]

2014

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, Nat. Photonics 8, 23 (2014).
[CrossRef]

B. le Feber, N. Rotenberg, D. M. Beggs, and L. Kuipers, Nat. Photonics 8, 43 (2014).
[CrossRef]

2013

2012

2011

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
[CrossRef]

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

2010

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
[CrossRef]

M. Schnell, A. Garca-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, Nano Lett. 10, 3524 (2010).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, T. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

2009

M. Schnell, A. Garca-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, Nat. Photonics 3, 287 (2009).
[CrossRef]

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
[CrossRef]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef]

Aizpurua, J.

M. Schnell, A. Garca-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, Nano Lett. 10, 3524 (2010).
[CrossRef]

M. Schnell, A. Garca-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, Nat. Photonics 3, 287 (2009).
[CrossRef]

Alkorta, J.

M. Schnell, A. Garca-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, Nano Lett. 10, 3524 (2010).
[CrossRef]

Baba, T.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef]

Bak, W. S.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Banzer, P.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, Nat. Photonics 8, 23 (2014).
[CrossRef]

Bao, K.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Bauer, T.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, Nat. Photonics 8, 23 (2014).
[CrossRef]

Beggs, D. M.

B. le Feber, N. Rotenberg, D. M. Beggs, and L. Kuipers, Nat. Photonics 8, 43 (2014).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Boreman, G. D.

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
[CrossRef]

Burresi, M.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
[CrossRef]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef]

Crozier, K.

M. Schnell, A. Garca-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, Nat. Photonics 3, 287 (2009).
[CrossRef]

Dorfmüller, J.

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
[CrossRef]

Dregely, D.

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
[CrossRef]

Eah, S. H.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Ebbesen, T.

F. J. Garcia-Vidal, L. Martin-Moreno, T. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Engelen, R. J. P.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef]

Esslinger, M.

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
[CrossRef]

Garca-Etxarri, A.

M. Schnell, A. Garca-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, Nano Lett. 10, 3524 (2010).
[CrossRef]

M. Schnell, A. Garca-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, Nat. Photonics 3, 287 (2009).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, T. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Giessen, H.

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
[CrossRef]

Gu, M.

Halas, N. J.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Heideman, R.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
[CrossRef]

Hillenbrand, R.

M. Schnell, A. Garca-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, Nano Lett. 10, 3524 (2010).
[CrossRef]

M. Schnell, A. Garca-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, Nat. Photonics 3, 287 (2009).
[CrossRef]

Huber, A. J.

M. Schnell, A. Garca-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, Nat. Photonics 3, 287 (2009).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

Kampfrath, T.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
[CrossRef]

Kern, K.

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
[CrossRef]

Khunsin, W.

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
[CrossRef]

Kihm, H. W.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Kihm, J. E.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Kim, D. S.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Kim, H.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Kim, Q. H.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Koo, S. M.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Krenz, P. M.

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
[CrossRef]

Kuipers, L.

B. le Feber, N. Rotenberg, D. M. Beggs, and L. Kuipers, Nat. Photonics 8, 43 (2014).
[CrossRef]

F. J. Garcia-Vidal, L. Martin-Moreno, T. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef]

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
[CrossRef]

Lail, B. A.

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
[CrossRef]

le Feber, B.

B. le Feber, N. Rotenberg, D. M. Beggs, and L. Kuipers, Nat. Photonics 8, 43 (2014).
[CrossRef]

Lee, H. W.

Leinse, A.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
[CrossRef]

Leuchs, G.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, Nat. Photonics 8, 23 (2014).
[CrossRef]

Li, X.

Lienau, C.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

Mori, D.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef]

Nordlander, P.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Olmon, R. L.

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
[CrossRef]

Opheij, A.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef]

Orlov, S.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, Nat. Photonics 8, 23 (2014).
[CrossRef]

Park, N. K.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Peschel, U.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, Nat. Photonics 8, 23 (2014).
[CrossRef]

Rang, M.

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
[CrossRef]

Raschke, M. B.

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
[CrossRef]

Rotenberg, N.

B. le Feber, N. Rotenberg, D. M. Beggs, and L. Kuipers, Nat. Photonics 8, 43 (2014).
[CrossRef]

Russell, P. S. J.

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2005).

Saraf, L. V.

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
[CrossRef]

Schmidt, M. A.

Schnell, M.

M. Schnell, A. Garca-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, Nano Lett. 10, 3524 (2010).
[CrossRef]

M. Schnell, A. Garca-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, Nat. Photonics 3, 287 (2009).
[CrossRef]

Schoenmaker, H.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
[CrossRef]

Uebel, P.

van Oosten, D.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
[CrossRef]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef]

Venugopalan, P.

Vogelgesang, R.

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

Zhang, Q.

Nano Lett.

M. Schnell, A. Garca-Etxarri, J. Alkorta, J. Aizpurua, and R. Hillenbrand, Nano Lett. 10, 3524 (2010).
[CrossRef]

J. Dorfmüller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, Nano Lett. 11, 2819 (2011).
[CrossRef]

Nat. Commun.

H. W. Kihm, S. M. Koo, Q. H. Kim, K. Bao, J. E. Kihm, W. S. Bak, S. H. Eah, C. Lienau, H. Kim, P. Nordlander, N. J. Halas, N. K. Park, and D. S. Kim, Nat. Commun. 2, 451 (2011).
[CrossRef]

Nat. Photonics

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, Nat. Photonics 8, 23 (2014).
[CrossRef]

M. Schnell, A. Garca-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, Nat. Photonics 3, 287 (2009).
[CrossRef]

B. le Feber, N. Rotenberg, D. M. Beggs, and L. Kuipers, Nat. Photonics 8, 43 (2014).
[CrossRef]

Opt. Express

Phys. Rev. Lett.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, Phys. Rev. Lett. 102, 033902 (2009).
[CrossRef]

R. L. Olmon, M. Rang, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, Phys. Rev. Lett. 105, 167403 (2010).
[CrossRef]

Rev. Mod. Phys.

F. J. Garcia-Vidal, L. Martin-Moreno, T. Ebbesen, and L. Kuipers, Rev. Mod. Phys. 82, 729 (2010).
[CrossRef]

Science

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, Science 326, 550 (2009).
[CrossRef]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2005).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Sketch of the sample and the tip of the SRP used in this work. The fiber forms the core of the tip. The green and purple arrows near the sample indicate electric fields along x and y . The probe converts these fields to radiation polarized along x and y , indicated by the top purple and green arrows. The polarization-resolved detection of this radiation results in the signals L x and L y . The semi-transparent plane denotes the mirror symmetry of the waveguide ( y z plane). The inset shows scanning electron microscope images of the AP and the SRP. (b) Calculated field profiles 20 nm above the structure. To indicate to which detection channel the far-field radiation from these fields contributes, the borders of the plot windows are color coded to match the colors of field orientations shown in (a). The magnetic fields are multiplied by the free space impedance Z 0 , and the amplitude of all fields is normalized to the maximum of E x . The dashed black lines indicate the edges of the ridge.

Fig. 2.
Fig. 2.

(a) and (b) Top panels: 2D maps of the real part of L x and L y , respectively. Middle and bottom panels: 2D maps of the real part of the signals in L x and L y with even (middle) and odd (bottom) symmetry. In (a) and (b), the dashed black lines indicate the position of the line traces shown in (c) and (d); the multiplication factors refer to scaling of the colormap. (c) and (d) Line traces of the real part of the signal in L x (c) and L y (d) (indicated by the light gray lines), together with the even (dark blue lines) and odd (light blue lines) symmetry components, together with the fitted calculated in plane electric fields (red lines).

Fig. 3.
Fig. 3.

(a) and (b) Top panels: 2D maps of the the real part of L x and L y , respectively. Middle and bottom panels: 2D maps of the real part of the signals in L x and L y with even (middle) and odd (bottom) symmetry. The scaling of the bottom maps in (a) and (b) is indicated in the figures. (c) and (d) Line traces of the even (dark blue lines) and odd symmetry (light blue lines) components of L x and L y , together with the fitted calculated in-plane electric fields (red lines). In (c) the inset shows line traces of the amplitude of L x (green) and L y (purple) along x = 0 . In (d) the dark gray line indicates H z fitted to the signal in L y with even symmetry.

Equations (6)

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L x = α x E x + β x Z 0 H y α x E x ,
L y = α y E y + β y Z 0 H x α y E y ,
L even ( x , y ) = L ( x , y ) + L mir ( x , y ) 2 ,
L odd ( x , y ) = L ( x , y ) L mir ( x , y ) 2 ,
L x α x E x ,
L y α y E y + γ y Z 0 H z ,

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