Abstract

Scanning near-field optical microscopy has been recently applied to the imaging of magnetic samples. It was shown experimentally that an apertureless microscope suffers a substantial loss of resolution when used for magneto-optical imaging compared with that for conventional imaging. No such change is observed for aperture microscopes. We explain this observation by developing a model for the imaging process that incorporates the response of the probe. We calculate real observable properties such as the rotation of polarization at the detector or the circular dichroism signal and thus simulate magneto-optical images of a domain structure in cobalt for both aperture and apertureless microscopes.

© 2002 Optical Society of America

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2000 (4)

N. Richard, A. Dereux, E. Bourillot, T. David, J. P. Goudonnet, F. Scheurer, E. Beaurepaire, “Near-field zone analysis of the Faraday rotation of magneto-optical thin films,” J. Appl. Phys. 88, 2541–2547 (2000).
[CrossRef]

N. Richard, “Optical properties of multilayer structures,” Eur. Phys. J. B 17, 11–14 (2000).
[CrossRef]

J. A. Porto, R. Carminati, J.-J. Greffet, “Theory of electromagnetic field imaging and spectroscopy in scanning near-field optical microscopy,” J. Appl. Phys. 88, 4845–4850 (2000).
[CrossRef]

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

1999 (5)

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near-field optical microscope,” EPJ Appl. Phys. 5, 289–295 (1999).
[CrossRef]

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

S. Grésillon, H. Cory, J. C. Rivoal, A. C. Boccara, “Transmission-mode apertureless near-field microscope: optical and magneto-optical studies,” J. Opt. A 1, 178–184 (1999).
[CrossRef]

O. Bergossi, H. Wioland, S. Hudlet, R. Deturche, P. Royer, “Near field magneto-optical circular dichroism using an apertureless probe,” Jpn. J. Appl. Phys., Part 2 38, L655–L658 (1999).
[CrossRef]

Y. Chen, V. Kottler, C. Chappert, N. Essaidi, “Magneto-optical contrast in near-field optics,” J. Microsc. 194, 495–499 (1999).
[CrossRef]

1998 (6)

P. Fumagalli, A. Rosenberger, G. Eggers, A. Münnemann, N. Held, G. Güntherodt, “Quantitative determination of the local Kerr rotation by scanning near-field magneto-optic microscopy,” Appl. Phys. Lett. 72, 2803–2805 (1998).
[CrossRef]

B. L. Petersen, A. Bauer, G. Meyer, T. Crecelius, G. Kaindl, “Kerr-rotation imaging in scanning near-field optical microscopy using a modified Sagnac interferometer,” Appl. Phys. Lett. 73, 538–540 (1998).
[CrossRef]

F. Matthes, H. Brückl, G. Reiss, “Near-field magneto-optical microscopy in collection and illumination mode,” Ultramicroscopy 71, 243–248 (1998).
[CrossRef]

R. Carminati, M. Nieto-Vesperinas, J.-J. Greffet, “Reciprocity of evanescent electromagnetic waves,” J. Opt. Soc. Am. A 15, 706–712 (1998).
[CrossRef]

H. Cory, A. C. Boccara, J. C. Rivoal, A. Lahrech, “Electric field intensity variation in the vicinity of a perfectly conducting conical probe: application to near-field microscopy,” Microwave Opt. Technol. Lett. 18, 120–124 (1998).
[CrossRef]

G. Wurtz, R. Bachelot, P. Royer, “A reflection mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
[CrossRef]

1997 (5)

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

R. Bachelot, P. Gleyzes, A. C. Boccara, “Reflection mode scanning near-field optical microscopy using an apertureless metallic tip,” Appl. Opt. 36, 2160–2170 (1997).
[CrossRef] [PubMed]

C. Durkan, I. V. Shvets, J. C. Lodder, “Observation of magnetic domains using a reflection-mode scanning near-field optical microscope,” Appl. Phys. Lett. 70, 1323–1325 (1997).
[CrossRef]

S. I. Bozhevolnyi, F. A. Pudonin, “Two-dimensional micro-optics of surface plasmons,” Phys. Rev. Lett. 78, 2823–2826 (1997).
[CrossRef]

V. Kottler, N. Essaidi, N. Ronarch, C. Chappert, Y. Chen, “Dichroic imaging of magnetic domains with a scanning near-field optical microscope,” J. Magn. Magn. Mater. 165, 398–400 (1997).
[CrossRef]

1996 (1)

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

1995 (5)

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, C. Marlière, J. Peretti, “Near-field magneto-optics with polarization sensitive STOM,” Ultramicroscopy 57, 270–276 (1995).
[CrossRef]

D. A. Christensen, “Analysis of near field tip patterns including object interaction using finite-difference time-domain calculations,” Ultramicroscopy 57, 189–195 (1995).
[CrossRef]

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

D. Van Labeke, A. Vial, D. Barchiesi, “Near-field theoretical study of a magneto-optical grating,” Ultramicroscopy 61, 51–55 (1995).
[CrossRef]

F. Forati, A. Dereux, J.-P. Vigneron, C. Girard, F. Scheurer, “Theory of Kerr effect in magnetic multilayered structures,” Ultramicroscopy 61, 57–62 (1995).
[CrossRef]

1994 (4)

L. Novotny, D. W. Pohl, P. Regli, “Light propagation through nanometer-sized structures: the two-dimensional aperture scanning near-field optical microscope,” J. Opt. Soc. Am. A 11, 1768–1779 (1994).
[CrossRef]

Y. Inouye, S. Kawata, “Near-field scanning optical microscopy with a metallic probe tip,” Opt. Lett. 19, 159–161 (1994).
[CrossRef]

T. J. Silva, S. Schultz, D. Weller, “Scanning near-field optical microscope for the imaging of magnetic domains in optically opaque materials,” Appl. Phys. Lett. 65, 658–660 (1994).
[CrossRef]

E. Betzig, R. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1994).
[CrossRef]

1992 (3)

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

J. K. Trautman, E. Betzig, J. S. Weiner, D. J. DiGiovanni, T. D. Harris, F. Hellman, E. M. Gyorgy, “Image contrast in near-field optics,” J. Appl. Phys. 71, 4659–4663 (1992).
[CrossRef]

1954 (1)

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

Aigouy, L.

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

Andreani, F. X.

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

Bachelot, R.

G. Wurtz, R. Bachelot, P. Royer, “A reflection mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
[CrossRef]

R. Bachelot, P. Gleyzes, A. C. Boccara, “Reflection mode scanning near-field optical microscopy using an apertureless metallic tip,” Appl. Opt. 36, 2160–2170 (1997).
[CrossRef] [PubMed]

Barchiesi, D.

D. Van Labeke, A. Vial, D. Barchiesi, “Near-field theoretical study of a magneto-optical grating,” Ultramicroscopy 61, 51–55 (1995).
[CrossRef]

Bauer, A.

B. L. Petersen, A. Bauer, G. Meyer, T. Crecelius, G. Kaindl, “Kerr-rotation imaging in scanning near-field optical microscopy using a modified Sagnac interferometer,” Appl. Phys. Lett. 73, 538–540 (1998).
[CrossRef]

Beaurepaire, E.

N. Richard, A. Dereux, E. Bourillot, T. David, J. P. Goudonnet, F. Scheurer, E. Beaurepaire, “Near-field zone analysis of the Faraday rotation of magneto-optical thin films,” J. Appl. Phys. 88, 2541–2547 (2000).
[CrossRef]

Bergossi, O.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near-field optical microscope,” EPJ Appl. Phys. 5, 289–295 (1999).
[CrossRef]

O. Bergossi, H. Wioland, S. Hudlet, R. Deturche, P. Royer, “Near field magneto-optical circular dichroism using an apertureless probe,” Jpn. J. Appl. Phys., Part 2 38, L655–L658 (1999).
[CrossRef]

Betzig, E.

E. Betzig, R. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1994).
[CrossRef]

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

J. K. Trautman, E. Betzig, J. S. Weiner, D. J. DiGiovanni, T. D. Harris, F. Hellman, E. M. Gyorgy, “Image contrast in near-field optics,” J. Appl. Phys. 71, 4659–4663 (1992).
[CrossRef]

Bielefeldt, H.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Boccara, A. C.

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

S. Grésillon, H. Cory, J. C. Rivoal, A. C. Boccara, “Transmission-mode apertureless near-field microscope: optical and magneto-optical studies,” J. Opt. A 1, 178–184 (1999).
[CrossRef]

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

H. Cory, A. C. Boccara, J. C. Rivoal, A. Lahrech, “Electric field intensity variation in the vicinity of a perfectly conducting conical probe: application to near-field microscopy,” Microwave Opt. Technol. Lett. 18, 120–124 (1998).
[CrossRef]

R. Bachelot, P. Gleyzes, A. C. Boccara, “Reflection mode scanning near-field optical microscopy using an apertureless metallic tip,” Appl. Opt. 36, 2160–2170 (1997).
[CrossRef] [PubMed]

Bourillot, E.

N. Richard, A. Dereux, E. Bourillot, T. David, J. P. Goudonnet, F. Scheurer, E. Beaurepaire, “Near-field zone analysis of the Faraday rotation of magneto-optical thin films,” J. Appl. Phys. 88, 2541–2547 (2000).
[CrossRef]

Bouwkamp, C. J.

C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 35–100 (1954).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, F. A. Pudonin, “Two-dimensional micro-optics of surface plasmons,” Phys. Rev. Lett. 78, 2823–2826 (1997).
[CrossRef]

Brückl, H.

F. Matthes, H. Brückl, G. Reiss, “Near-field magneto-optical microscopy in collection and illumination mode,” Ultramicroscopy 71, 243–248 (1998).
[CrossRef]

Carminati, R.

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

J. A. Porto, R. Carminati, J.-J. Greffet, “Theory of electromagnetic field imaging and spectroscopy in scanning near-field optical microscopy,” J. Appl. Phys. 88, 4845–4850 (2000).
[CrossRef]

R. Carminati, M. Nieto-Vesperinas, J.-J. Greffet, “Reciprocity of evanescent electromagnetic waves,” J. Opt. Soc. Am. A 15, 706–712 (1998).
[CrossRef]

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

Chappert, C.

Y. Chen, V. Kottler, C. Chappert, N. Essaidi, “Magneto-optical contrast in near-field optics,” J. Microsc. 194, 495–499 (1999).
[CrossRef]

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

V. Kottler, N. Essaidi, N. Ronarch, C. Chappert, Y. Chen, “Dichroic imaging of magnetic domains with a scanning near-field optical microscope,” J. Magn. Magn. Mater. 165, 398–400 (1997).
[CrossRef]

Chen, Y.

Y. Chen, V. Kottler, C. Chappert, N. Essaidi, “Magneto-optical contrast in near-field optics,” J. Microsc. 194, 495–499 (1999).
[CrossRef]

V. Kottler, N. Essaidi, N. Ronarch, C. Chappert, Y. Chen, “Dichroic imaging of magnetic domains with a scanning near-field optical microscope,” J. Magn. Magn. Mater. 165, 398–400 (1997).
[CrossRef]

Chichester, R.

E. Betzig, R. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1994).
[CrossRef]

Christensen, D. A.

D. A. Christensen, “Analysis of near field tip patterns including object interaction using finite-difference time-domain calculations,” Ultramicroscopy 57, 189–195 (1995).
[CrossRef]

Cory, H.

S. Grésillon, H. Cory, J. C. Rivoal, A. C. Boccara, “Transmission-mode apertureless near-field microscope: optical and magneto-optical studies,” J. Opt. A 1, 178–184 (1999).
[CrossRef]

H. Cory, A. C. Boccara, J. C. Rivoal, A. Lahrech, “Electric field intensity variation in the vicinity of a perfectly conducting conical probe: application to near-field microscopy,” Microwave Opt. Technol. Lett. 18, 120–124 (1998).
[CrossRef]

Crecelius, T.

B. L. Petersen, A. Bauer, G. Meyer, T. Crecelius, G. Kaindl, “Kerr-rotation imaging in scanning near-field optical microscopy using a modified Sagnac interferometer,” Appl. Phys. Lett. 73, 538–540 (1998).
[CrossRef]

David, T.

N. Richard, A. Dereux, E. Bourillot, T. David, J. P. Goudonnet, F. Scheurer, E. Beaurepaire, “Near-field zone analysis of the Faraday rotation of magneto-optical thin films,” J. Appl. Phys. 88, 2541–2547 (2000).
[CrossRef]

Dereux, A.

N. Richard, A. Dereux, E. Bourillot, T. David, J. P. Goudonnet, F. Scheurer, E. Beaurepaire, “Near-field zone analysis of the Faraday rotation of magneto-optical thin films,” J. Appl. Phys. 88, 2541–2547 (2000).
[CrossRef]

F. Forati, A. Dereux, J.-P. Vigneron, C. Girard, F. Scheurer, “Theory of Kerr effect in magnetic multilayered structures,” Ultramicroscopy 61, 57–62 (1995).
[CrossRef]

Deturche, R.

O. Bergossi, H. Wioland, S. Hudlet, R. Deturche, P. Royer, “Near field magneto-optical circular dichroism using an apertureless probe,” Jpn. J. Appl. Phys., Part 2 38, L655–L658 (1999).
[CrossRef]

DiGiovanni, D. J.

J. K. Trautman, E. Betzig, J. S. Weiner, D. J. DiGiovanni, T. D. Harris, F. Hellman, E. M. Gyorgy, “Image contrast in near-field optics,” J. Appl. Phys. 71, 4659–4663 (1992).
[CrossRef]

Durkan, C.

C. Durkan, I. V. Shvets, J. C. Lodder, “Observation of magnetic domains using a reflection-mode scanning near-field optical microscope,” Appl. Phys. Lett. 70, 1323–1325 (1997).
[CrossRef]

Eggers, G.

P. Fumagalli, A. Rosenberger, G. Eggers, A. Münnemann, N. Held, G. Güntherodt, “Quantitative determination of the local Kerr rotation by scanning near-field magneto-optic microscopy,” Appl. Phys. Lett. 72, 2803–2805 (1998).
[CrossRef]

Essaidi, N.

Y. Chen, V. Kottler, C. Chappert, N. Essaidi, “Magneto-optical contrast in near-field optics,” J. Microsc. 194, 495–499 (1999).
[CrossRef]

V. Kottler, N. Essaidi, N. Ronarch, C. Chappert, Y. Chen, “Dichroic imaging of magnetic domains with a scanning near-field optical microscope,” J. Magn. Magn. Mater. 165, 398–400 (1997).
[CrossRef]

Ferré, J.

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

Finn, P. L.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Forati, F.

F. Forati, A. Dereux, J.-P. Vigneron, C. Girard, F. Scheurer, “Theory of Kerr effect in magnetic multilayered structures,” Ultramicroscopy 61, 57–62 (1995).
[CrossRef]

Froehlich, F.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Fumagalli, P.

P. Fumagalli, A. Rosenberger, G. Eggers, A. Münnemann, N. Held, G. Güntherodt, “Quantitative determination of the local Kerr rotation by scanning near-field magneto-optic microscopy,” Appl. Phys. Lett. 72, 2803–2805 (1998).
[CrossRef]

Girard, C.

F. Forati, A. Dereux, J.-P. Vigneron, C. Girard, F. Scheurer, “Theory of Kerr effect in magnetic multilayered structures,” Ultramicroscopy 61, 57–62 (1995).
[CrossRef]

Gleyzes, P.

Goudonnet, J. P.

N. Richard, A. Dereux, E. Bourillot, T. David, J. P. Goudonnet, F. Scheurer, E. Beaurepaire, “Near-field zone analysis of the Faraday rotation of magneto-optical thin films,” J. Appl. Phys. 88, 2541–2547 (2000).
[CrossRef]

Greffet, J.-J.

J. A. Porto, R. Carminati, J.-J. Greffet, “Theory of electromagnetic field imaging and spectroscopy in scanning near-field optical microscopy,” J. Appl. Phys. 88, 4845–4850 (2000).
[CrossRef]

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

R. Carminati, M. Nieto-Vesperinas, J.-J. Greffet, “Reciprocity of evanescent electromagnetic waves,” J. Opt. Soc. Am. A 15, 706–712 (1998).
[CrossRef]

J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

Grésillon, S.

S. Grésillon, H. Cory, J. C. Rivoal, A. C. Boccara, “Transmission-mode apertureless near-field microscope: optical and magneto-optical studies,” J. Opt. A 1, 178–184 (1999).
[CrossRef]

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

Güntherodt, G.

P. Fumagalli, A. Rosenberger, G. Eggers, A. Münnemann, N. Held, G. Güntherodt, “Quantitative determination of the local Kerr rotation by scanning near-field magneto-optic microscopy,” Appl. Phys. Lett. 72, 2803–2805 (1998).
[CrossRef]

Gyorgy, E. M.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

J. K. Trautman, E. Betzig, J. S. Weiner, D. J. DiGiovanni, T. D. Harris, F. Hellman, E. M. Gyorgy, “Image contrast in near-field optics,” J. Appl. Phys. 71, 4659–4663 (1992).
[CrossRef]

Harris, T. D.

J. K. Trautman, E. Betzig, J. S. Weiner, D. J. DiGiovanni, T. D. Harris, F. Hellman, E. M. Gyorgy, “Image contrast in near-field optics,” J. Appl. Phys. 71, 4659–4663 (1992).
[CrossRef]

Hecht, B.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Held, N.

P. Fumagalli, A. Rosenberger, G. Eggers, A. Münnemann, N. Held, G. Güntherodt, “Quantitative determination of the local Kerr rotation by scanning near-field magneto-optic microscopy,” Appl. Phys. Lett. 72, 2803–2805 (1998).
[CrossRef]

Hellman, F.

J. K. Trautman, E. Betzig, J. S. Weiner, D. J. DiGiovanni, T. D. Harris, F. Hellman, E. M. Gyorgy, “Image contrast in near-field optics,” J. Appl. Phys. 71, 4659–4663 (1992).
[CrossRef]

Hermann, C.

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, C. Marlière, J. Peretti, “Near-field magneto-optics with polarization sensitive STOM,” Ultramicroscopy 57, 270–276 (1995).
[CrossRef]

Hudlet, S.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near-field optical microscope,” EPJ Appl. Phys. 5, 289–295 (1999).
[CrossRef]

O. Bergossi, H. Wioland, S. Hudlet, R. Deturche, P. Royer, “Near field magneto-optical circular dichroism using an apertureless probe,” Jpn. J. Appl. Phys., Part 2 38, L655–L658 (1999).
[CrossRef]

Inouye, Y.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Y. Inouye, S. Kawata, “Near-field scanning optical microscopy with a metallic probe tip,” Opt. Lett. 19, 159–161 (1994).
[CrossRef]

Jamet, J. P.

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

Judkins, J.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Kaindl, G.

B. L. Petersen, A. Bauer, G. Meyer, T. Crecelius, G. Kaindl, “Kerr-rotation imaging in scanning near-field optical microscopy using a modified Sagnac interferometer,” Appl. Phys. Lett. 73, 538–540 (1998).
[CrossRef]

Kann, J. L.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Kawata, S.

Kosobukin, V. A.

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, C. Marlière, J. Peretti, “Near-field magneto-optics with polarization sensitive STOM,” Ultramicroscopy 57, 270–276 (1995).
[CrossRef]

Kottler, V.

Y. Chen, V. Kottler, C. Chappert, N. Essaidi, “Magneto-optical contrast in near-field optics,” J. Microsc. 194, 495–499 (1999).
[CrossRef]

V. Kottler, N. Essaidi, N. Ronarch, C. Chappert, Y. Chen, “Dichroic imaging of magnetic domains with a scanning near-field optical microscope,” J. Magn. Magn. Mater. 165, 398–400 (1997).
[CrossRef]

Lahrech, A.

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

H. Cory, A. C. Boccara, J. C. Rivoal, A. Lahrech, “Electric field intensity variation in the vicinity of a perfectly conducting conical probe: application to near-field microscopy,” Microwave Opt. Technol. Lett. 18, 120–124 (1998).
[CrossRef]

Lampel, G.

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, C. Marlière, J. Peretti, “Near-field magneto-optics with polarization sensitive STOM,” Ultramicroscopy 57, 270–276 (1995).
[CrossRef]

Landau, L.

L. Landau, E. Lifchitz, L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, UK, 1984).

Lifchitz, E.

L. Landau, E. Lifchitz, L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, UK, 1984).

Lodder, J. C.

C. Durkan, I. V. Shvets, J. C. Lodder, “Observation of magnetic domains using a reflection-mode scanning near-field optical microscope,” Appl. Phys. Lett. 70, 1323–1325 (1997).
[CrossRef]

Mackay, K.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near-field optical microscope,” EPJ Appl. Phys. 5, 289–295 (1999).
[CrossRef]

Marlière, C.

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, C. Marlière, J. Peretti, “Near-field magneto-optics with polarization sensitive STOM,” Ultramicroscopy 57, 270–276 (1995).
[CrossRef]

Mathet, V.

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

Matthes, F.

F. Matthes, H. Brückl, G. Reiss, “Near-field magneto-optical microscopy in collection and illumination mode,” Ultramicroscopy 71, 243–248 (1998).
[CrossRef]

Megy, R.

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

Meyer, G.

B. L. Petersen, A. Bauer, G. Meyer, T. Crecelius, G. Kaindl, “Kerr-rotation imaging in scanning near-field optical microscopy using a modified Sagnac interferometer,” Appl. Phys. Lett. 73, 538–540 (1998).
[CrossRef]

Milster, T. D.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Münnemann, A.

P. Fumagalli, A. Rosenberger, G. Eggers, A. Münnemann, N. Held, G. Güntherodt, “Quantitative determination of the local Kerr rotation by scanning near-field magneto-optic microscopy,” Appl. Phys. Lett. 72, 2803–2805 (1998).
[CrossRef]

Nieto-Vesperinas, M.

Novotny, L.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

L. Novotny, D. W. Pohl, P. Regli, “Light propagation through nanometer-sized structures: the two-dimensional aperture scanning near-field optical microscope,” J. Opt. Soc. Am. A 11, 1768–1779 (1994).
[CrossRef]

L. Novotny, D. W. Pohl, “Light propagation in scanning near-field optical microscopy,” in Photons and Local Probes, O. Marti, R. Möller, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), Chap. 2, pp. 21–33.

L. Novotny, “Light propagation and light confinement in near-field optics,” Ph.D. thesis (Swiss Federal Institute of Technology, Zurich, 1996).

Parent, G.

G. Parent, “Phénomènes transitoires en optique de champ proche: durée de vie de fluorescence et propagation d’impulsions dans des mésostructures,” Ph.D. thesis (Université de France-Comté, Besançon, France, 2000).

Peretti, J.

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, C. Marlière, J. Peretti, “Near-field magneto-optics with polarization sensitive STOM,” Ultramicroscopy 57, 270–276 (1995).
[CrossRef]

Petersen, B. L.

B. L. Petersen, A. Bauer, G. Meyer, T. Crecelius, G. Kaindl, “Kerr-rotation imaging in scanning near-field optical microscopy using a modified Sagnac interferometer,” Appl. Phys. Lett. 73, 538–540 (1998).
[CrossRef]

Pitaevskii, L.

L. Landau, E. Lifchitz, L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Oxford, UK, 1984).

Pohl, D. W.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

L. Novotny, D. W. Pohl, P. Regli, “Light propagation through nanometer-sized structures: the two-dimensional aperture scanning near-field optical microscope,” J. Opt. Soc. Am. A 11, 1768–1779 (1994).
[CrossRef]

L. Novotny, D. W. Pohl, “Light propagation in scanning near-field optical microscopy,” in Photons and Local Probes, O. Marti, R. Möller, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), Chap. 2, pp. 21–33.

Porto, J. A.

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

J. A. Porto, R. Carminati, J.-J. Greffet, “Theory of electromagnetic field imaging and spectroscopy in scanning near-field optical microscopy,” J. Appl. Phys. 88, 4845–4850 (2000).
[CrossRef]

Pudonin, F. A.

S. I. Bozhevolnyi, F. A. Pudonin, “Two-dimensional micro-optics of surface plasmons,” Phys. Rev. Lett. 78, 2823–2826 (1997).
[CrossRef]

Regli, P.

Reiss, G.

F. Matthes, H. Brückl, G. Reiss, “Near-field magneto-optical microscopy in collection and illumination mode,” Ultramicroscopy 71, 243–248 (1998).
[CrossRef]

Richard, N.

N. Richard, A. Dereux, E. Bourillot, T. David, J. P. Goudonnet, F. Scheurer, E. Beaurepaire, “Near-field zone analysis of the Faraday rotation of magneto-optical thin films,” J. Appl. Phys. 88, 2541–2547 (2000).
[CrossRef]

N. Richard, “Optical properties of multilayer structures,” Eur. Phys. J. B 17, 11–14 (2000).
[CrossRef]

Rivoal, J. C.

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

L. Aigouy, S. Grésillon, A. Lahrech, A. C. Boccara, J. C. Rivoal, V. Mathet, C. Chappert, J. P. Jamet, J. Ferré, “Apertureless scanning near-field magneto-optical microscopy of magnetic multilayers,” J. Microsc. 194, 295–298 (1999).
[CrossRef]

S. Grésillon, H. Cory, J. C. Rivoal, A. C. Boccara, “Transmission-mode apertureless near-field microscope: optical and magneto-optical studies,” J. Opt. A 1, 178–184 (1999).
[CrossRef]

H. Cory, A. C. Boccara, J. C. Rivoal, A. Lahrech, “Electric field intensity variation in the vicinity of a perfectly conducting conical probe: application to near-field microscopy,” Microwave Opt. Technol. Lett. 18, 120–124 (1998).
[CrossRef]

Ronarch, N.

V. Kottler, N. Essaidi, N. Ronarch, C. Chappert, Y. Chen, “Dichroic imaging of magnetic domains with a scanning near-field optical microscope,” J. Magn. Magn. Mater. 165, 398–400 (1997).
[CrossRef]

Rosenberger, A.

P. Fumagalli, A. Rosenberger, G. Eggers, A. Münnemann, N. Held, G. Güntherodt, “Quantitative determination of the local Kerr rotation by scanning near-field magneto-optic microscopy,” Appl. Phys. Lett. 72, 2803–2805 (1998).
[CrossRef]

Royer, P.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near-field optical microscope,” EPJ Appl. Phys. 5, 289–295 (1999).
[CrossRef]

O. Bergossi, H. Wioland, S. Hudlet, R. Deturche, P. Royer, “Near field magneto-optical circular dichroism using an apertureless probe,” Jpn. J. Appl. Phys., Part 2 38, L655–L658 (1999).
[CrossRef]

G. Wurtz, R. Bachelot, P. Royer, “A reflection mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
[CrossRef]

Safarov, V. I.

V. I. Safarov, V. A. Kosobukin, C. Hermann, G. Lampel, C. Marlière, J. Peretti, “Near-field magneto-optics with polarization sensitive STOM,” Ultramicroscopy 57, 270–276 (1995).
[CrossRef]

Scheurer, F.

N. Richard, A. Dereux, E. Bourillot, T. David, J. P. Goudonnet, F. Scheurer, E. Beaurepaire, “Near-field zone analysis of the Faraday rotation of magneto-optical thin films,” J. Appl. Phys. 88, 2541–2547 (2000).
[CrossRef]

F. Forati, A. Dereux, J.-P. Vigneron, C. Girard, F. Scheurer, “Theory of Kerr effect in magnetic multilayered structures,” Ultramicroscopy 61, 57–62 (1995).
[CrossRef]

Schultz, S.

T. J. Silva, S. Schultz, D. Weller, “Scanning near-field optical microscope for the imaging of magnetic domains in optically opaque materials,” Appl. Phys. Lett. 65, 658–660 (1994).
[CrossRef]

Shvets, I. V.

C. Durkan, I. V. Shvets, J. C. Lodder, “Observation of magnetic domains using a reflection-mode scanning near-field optical microscope,” Appl. Phys. Lett. 70, 1323–1325 (1997).
[CrossRef]

Silva, T. J.

T. J. Silva, S. Schultz, D. Weller, “Scanning near-field optical microscope for the imaging of magnetic domains in optically opaque materials,” Appl. Phys. Lett. 65, 658–660 (1994).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Trautman, J. K.

J. K. Trautman, E. Betzig, J. S. Weiner, D. J. DiGiovanni, T. D. Harris, F. Hellman, E. M. Gyorgy, “Image contrast in near-field optics,” J. Appl. Phys. 71, 4659–4663 (1992).
[CrossRef]

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–195 (1992).
[CrossRef] [PubMed]

Van Labeke, D.

D. Van Labeke, A. Vial, D. Barchiesi, “Near-field theoretical study of a magneto-optical grating,” Ultramicroscopy 61, 51–55 (1995).
[CrossRef]

Vial, A.

D. Van Labeke, A. Vial, D. Barchiesi, “Near-field theoretical study of a magneto-optical grating,” Ultramicroscopy 61, 51–55 (1995).
[CrossRef]

Vigneron, J.-P.

F. Forati, A. Dereux, J.-P. Vigneron, C. Girard, F. Scheurer, “Theory of Kerr effect in magnetic multilayered structures,” Ultramicroscopy 61, 57–62 (1995).
[CrossRef]

Weiner, J. S.

J. K. Trautman, E. Betzig, J. S. Weiner, D. J. DiGiovanni, T. D. Harris, F. Hellman, E. M. Gyorgy, “Image contrast in near-field optics,” J. Appl. Phys. 71, 4659–4663 (1992).
[CrossRef]

Weller, D.

T. J. Silva, S. Schultz, D. Weller, “Scanning near-field optical microscope for the imaging of magnetic domains in optically opaque materials,” Appl. Phys. Lett. 65, 658–660 (1994).
[CrossRef]

Wioland, H.

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near-field optical microscope,” EPJ Appl. Phys. 5, 289–295 (1999).
[CrossRef]

O. Bergossi, H. Wioland, S. Hudlet, R. Deturche, P. Royer, “Near field magneto-optical circular dichroism using an apertureless probe,” Jpn. J. Appl. Phys., Part 2 38, L655–L658 (1999).
[CrossRef]

Wolfe, R.

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

Wurtz, G.

G. Wurtz, R. Bachelot, P. Royer, “A reflection mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
[CrossRef]

Ziolkowski, R. W.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

E. Betzig, J. K. Trautman, R. Wolfe, E. M. Gyorgy, P. L. Finn, “Near-field magneto-optics and high density data storage,” Appl. Phys. Lett. 61, 142–144 (1992).
[CrossRef]

T. J. Silva, S. Schultz, D. Weller, “Scanning near-field optical microscope for the imaging of magnetic domains in optically opaque materials,” Appl. Phys. Lett. 65, 658–660 (1994).
[CrossRef]

C. Durkan, I. V. Shvets, J. C. Lodder, “Observation of magnetic domains using a reflection-mode scanning near-field optical microscope,” Appl. Phys. Lett. 70, 1323–1325 (1997).
[CrossRef]

P. Fumagalli, A. Rosenberger, G. Eggers, A. Münnemann, N. Held, G. Güntherodt, “Quantitative determination of the local Kerr rotation by scanning near-field magneto-optic microscopy,” Appl. Phys. Lett. 72, 2803–2805 (1998).
[CrossRef]

B. L. Petersen, A. Bauer, G. Meyer, T. Crecelius, G. Kaindl, “Kerr-rotation imaging in scanning near-field optical microscopy using a modified Sagnac interferometer,” Appl. Phys. Lett. 73, 538–540 (1998).
[CrossRef]

L. Aigouy, F. X. Andreani, A. C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J.-J. Greffet, R. Megy, “Near-field optical spectroscopy using an incoherent light source,” Appl. Phys. Lett. 76, 397–399 (2000).
[CrossRef]

EPJ Appl. Phys. (1)

H. Wioland, O. Bergossi, S. Hudlet, K. Mackay, P. Royer, “Magneto-optical Faraday imaging with an apertureless scanning near-field optical microscope,” EPJ Appl. Phys. 5, 289–295 (1999).
[CrossRef]

Eur. Phys. J. B (1)

N. Richard, “Optical properties of multilayer structures,” Eur. Phys. J. B 17, 11–14 (2000).
[CrossRef]

J. Appl. Phys. (3)

N. Richard, A. Dereux, E. Bourillot, T. David, J. P. Goudonnet, F. Scheurer, E. Beaurepaire, “Near-field zone analysis of the Faraday rotation of magneto-optical thin films,” J. Appl. Phys. 88, 2541–2547 (2000).
[CrossRef]

J. A. Porto, R. Carminati, J.-J. Greffet, “Theory of electromagnetic field imaging and spectroscopy in scanning near-field optical microscopy,” J. Appl. Phys. 88, 4845–4850 (2000).
[CrossRef]

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[CrossRef]

J. Magn. Magn. Mater. (1)

V. Kottler, N. Essaidi, N. Ronarch, C. Chappert, Y. Chen, “Dichroic imaging of magnetic domains with a scanning near-field optical microscope,” J. Magn. Magn. Mater. 165, 398–400 (1997).
[CrossRef]

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[CrossRef]

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[CrossRef]

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S. Grésillon, H. Cory, J. C. Rivoal, A. C. Boccara, “Transmission-mode apertureless near-field microscope: optical and magneto-optical studies,” J. Opt. A 1, 178–184 (1999).
[CrossRef]

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O. Bergossi, H. Wioland, S. Hudlet, R. Deturche, P. Royer, “Near field magneto-optical circular dichroism using an apertureless probe,” Jpn. J. Appl. Phys., Part 2 38, L655–L658 (1999).
[CrossRef]

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H. Cory, A. C. Boccara, J. C. Rivoal, A. Lahrech, “Electric field intensity variation in the vicinity of a perfectly conducting conical probe: application to near-field microscopy,” Microwave Opt. Technol. Lett. 18, 120–124 (1998).
[CrossRef]

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[CrossRef] [PubMed]

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J.-J. Greffet, R. Carminati, “Image formation in near-field optics,” Prog. Surf. Sci. 56, 133–237 (1997).
[CrossRef]

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[CrossRef]

Rev. Sci. Instrum. (1)

G. Wurtz, R. Bachelot, P. Royer, “A reflection mode apertureless scanning near-field optical microscope developed from a commercial scanning probe microscope,” Rev. Sci. Instrum. 69, 1735–1743 (1998).
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[CrossRef]

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Ultramicroscopy (6)

F. Matthes, H. Brückl, G. Reiss, “Near-field magneto-optical microscopy in collection and illumination mode,” Ultramicroscopy 71, 243–248 (1998).
[CrossRef]

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[CrossRef]

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Other (9)

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For a recent review, see Ultramicroscopy202, Part 1 (April2001) and Part 2 (May2001)

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Figures (11)

Fig. 1
Fig. 1

(a) Scheme of a general SNOM setup and (b) fictitious reciprocal situation.

Fig. 2
Fig. 2

Cone and illumination geometry: definitions of variables for calculation of Debye potentials for a cone.

Fig. 3
Fig. 3

Azimuthal field behavior for different values of m: intensity of the field components shown in a horizontal plane 1 nm below the probe. The m index determines the azimuthal symmetry of the field, and for increasing m the field is less well confined.

Fig. 4
Fig. 4

Dielectric response function: field response to variation in the permittivity of a nonmagnetic material, evaluated for a plane 1 nm below the probe. (a) Component due to the singularity alone and (b) nonsingular component.

Fig. 5
Fig. 5

Illumination and detection geometries for which magneto-optical impulse response functions have been calculated.

Fig. 6
Fig. 6

Response function Hmag for detection and illumination on opposite sides of the probe, with crossed polarizations.

Fig. 7
Fig. 7

Magnetic domain structure imaged in Figs. 8 and 9.

Fig. 8
Fig. 8

Calculated image of the magnetic domain structure shown in Fig. 7, as measured through the rotation angle of the field at the detector relative to its direction in the absence of magnetization.

Fig. 9
Fig. 9

Calculated image of the magnetic domain structure shown in Fig. 7, as measured by using circular dichroism as the imaging mechanism. The difference between intensities at the detector when using right and left circularly polarized illumination is given. These intensities have been calculated in the absence of a background at the detector.

Fig. 10
Fig. 10

(a) Experimental geometry of an illumination-mode MO-SNOM and (b) geometry of the reciprocal illumination-mode experiment.

Fig. 11
Fig. 11

Calculated image of the magnetic domain structure shown in Fig. 7, recorded with an aperture SNOM of aperture diameter 100 nm.

Equations (48)

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A=Eexp(rdet)·pˆ=1iωVErec·Jexp dr.
J(r, ω)=-iωε0[ε(r, ω)-1]·Eexp(r, ω),
J=Jε+JM=-iωε0[(ε1-1)Eexp+ifMeˆ×Eexp],
ε=ε1000ε1000ε1+0-ifM0ifM00000.
Amag=-ifε0VM(eˆ×Eexp)·Erec dr,
Amag=-ifε0VMeˆ·(Eexp×Erec)dr.
Amag(rtip)=VHmag(R-Rtip, z, ztip)M(r)dr,
Hmageˆ·(Eexp×Erec),
A(M=0)(rtip)=VHε(R-Rtip, z, ztip)ε1(r)dr,
Hε(Eexp·Erec),
Edet=Edet,uuˆ+Edet,vvˆ.
tan 2θ=2|Edet,u||Edet,v||Edet,u|2-|Edet,v|2cos δ.
Idichroic=|Edet(R)|2-|Edet(L)|2=2 Re[iEdet(s)·Edet(p)*].
Hmageˆ·[Eprobe(sou)×Eprobe(det)].
Hε[Eprobe(sou)·Eprobe(det)].
A=1iωVEprobe(det)·Jexp dr.
Jexp=(-iω)ε0 (ε1-1)Eprobe(sou)Jε+ifMeˆ×Eprobe(sou)JM.
Er=2r2+k2(ru),
Eθ=1r2rθ(ru)+iksin θμ0ε01/2vϕ,
Eϕ=1r sin θ2rϕ(ru)-ikμ0ε01/2vθ.
u(r, θ, ϕ)=m,pf(r, θ, θ1, m, p)×(m sin mϕ cos β)Ppm(cos θ0)sin θ0+(cos mϕ sin β)θ0Ppm(cos θ0),
v(r, θ, ϕ)=m,pg(r, θ, θ1, m, p)×(cos mϕ cos β)θ0Ppm(cos θ0)-(m sin mϕ sin β)Ppm(cos θ0)sin θ0.
Hmageˆ·[Econe(sou)×Econe(det)],
Er=2r2+k2rf(r, θ, θ1, 0, p1)×(sin β)θ0Pp0(cos θ0),
Eθ=1r2rθrf(r, θ, θ1, 0, p1)×(sin β)θ0Pp0(cos θ0),
Hmagzˆ·[Eprobe(sou)×Erec]=Eprobe(sou)·xˆ.
HεEprobe(sou)·Erec=Eprobe(sou)·yˆ.
Ex=2a2-x2-2y2(a2-x2-y2)1/2,Ey=xy(a2-x2-y2)1/2.
Edet,u=1iωErec(u)·Jexp dV,
Edet,v=1iωErec(v)·Jexp dV,
Edet=uˆEdet,u+vˆEdet,v,
Edet=1iω[uˆErec(u)+vˆErec(v)]·Jexp dV.
Edet=1iωErec(uv)·Jexp dV.
Erec(uv)=(uˆErec(u)+vˆErec(v)).
Edet=auˆ+b exp(iδ)vˆ,
tan 2θ=2abb2-a2cos δ.
η=min|E|/max|E|,
η=a2+b2-(a2-b2)[1+(4a2b2 cos2 δ)/(a2-b2)2]1/2a2+b2+(a2-b2)[1+(4a2b2 cos2 δ)/(a2-b2)2]1/2
Edet(s)=1iωErec(uv)·Jexp(s) dV,
Edet(p)=1iωErec(uv)·Jexp(p) dV.
Rˆ=12(sˆ-ipˆ),Lˆ=12(sˆ+ipˆ).
Jexp(R)=12[Jexp(s)-iJexp(p)],Jexp(L)=12[Jexp(s)+iJexp(p)].
Idichroic=|Edet(R)|2-|Edet(L)|2=2 Re[iEdet(s)Edet(p)*].
f(r, θ, θ1, m, p)=2ik sin θ1εm2p+1p(p+1)×exp-12ipπθ1Ppm(cos θ1)pPpm(cos θ1)
×jp(kr)Ppm(cos θ),
g(r, θ, θ1, m, p)=-2ik sin θ1ε0μ01/2εm2q+1q(q+1)×exp-12iqπPqm(cos θ1)2qθ1Pqm(cos θ1)×jq(kr)Pqm(cos θ).
Er(sing)=i exp-12ip1πsin θ1π(kr)p1-12p1-1Γp1+12×Pp1(cos θ)Pp11(cos θ0)sin βPp11(cos θ1)p1Pp1(cos θ1),
Eθ(sing)=i exp-12ip1πsin θ1π(kr)p1-12p1-1Γp1+12×(1/p1)θPp1(cos θ)Pp11(cos θ0)sin βPp11(cos θ1)p1Pp1(cos θ1).

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