Abstract

Eliminating background-scattering effects from the detected signal is crucial in improving the performance of super-high-resolution apertureless scanning near-field optical microscopy (A-SNOM). Using a simple mathematical model of the A-SNOM detected signal, this study explores the respective effects of the phase modulation depth, the wavelength and angle of the incident light, and the amplitude of the tip vibration on the signal contrast and signal intensity. In general, the results show that the background-noise decays as the order of the Bessel function increases and that higher-order harmonic frequencies yield an improved signal contrast. Additionally, it is found that incident light with a longer wavelength improves the signal contrast for a constant order of modulation frequency. The signal contrast can also be improved by reducing the incident angle of the incident light. Finally, it is demonstrated that sample stage scanning yields an improved imaging result. However, tip scanning provides a reasonable low-cost and faster solution in the smaller scan area. The analytical results presented in this study enable a better understanding of the complex detected signal in A-SNOM and provide insights into methods of improving the signal contrast of the A-SNOM measurement signal.

© 2007 Optical Society of America

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  1. E. H. Synge, “A suggested method for extending the microscopic resolution into the ultramicroscopic region,” Phil. Mag. 6, 356–362 (1928).
  2. G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Helv. Phys. Acta. 55, 726–735 (1982).
  3. G. Binnig, C. F. Quate, and C. Gerber, “Atomic force miscopy,” Phys. Rev. Lett.,  56, 930–933 (1986).
    [Crossref] [PubMed]
  4. D. W. Pohl, S. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ 20,” J. Appl. Phys. 44, 651–653 (1984).
  5. J. D. Jackson, Classical electrodynamics (Wiley, 1999).
  6. J. Wessel, “Surface-enhanced optical microscopy,” J. Opt. Soc. Am. 2, 1538–1540 (1985).
    [Crossref]
  7. H. K. Wickramasinghe and C. C. Williams, “Apertureless near field optical microscope,” US Patent4 947 034 (1990).
  8. Y. Inouye and S. Kawata, “Near-field scanning optical microscope with a metallic probe tip,” Opt. Lett. 19, 159–161 (1994).
    [Crossref] [PubMed]
  9. B. Knoll and F. Keilmann, “Enhanced dielectric contrast in scattering-type scanning near-field optical microscopy,” Opt. Commun. 182, 321–328 (2000).
    [Crossref]
  10. R. Hillenbrand and F. Keilmann, “Complex optical constants on a subwavelength scale,” Phys. Rev. Lett. 85, 3029–3032 (2000).
    [Crossref] [PubMed]
  11. R. Hillenbrand, B. Knoll, and F. Keilmann, “Pure optical contrast in scattering-type scanning near-field microscopy,” J. Microsc. 202, 77–83 (2000).
    [Crossref]
  12. I. Stefanon, S. Blaize, A. Bruyant, S Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Express 13, 5553–5564 (2005).
    [Crossref] [PubMed]
  13. F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Phil. Trans. R. Soc. Lond. A. 362, 787–805 (2004).
    [Crossref]
  14. J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
    [Crossref]
  15. S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
    [Crossref]
  16. P. G. Gucciardi, G. Bachelier, and M. Allegrini, “Far-field background suppression in tip-modulated apertureless near-field optical microscopy,” J. Appl. Phys. 99, Art. No.124309 (2006).
    [Crossref]
  17. Y.L Lo and C.H. Chuang, “New synthetic-heterodyne demodulation for an optical fiber interferometry,” IEEE J. Quantum Electro. 37, 658–663 (2001).
    [Crossref]
  18. M. Micic, N. Klymyshyn, Y. D. Sun, and H. P. Lu, “Finite element method simulation of the field distribution for AFM tip-enhanced surface Raman Scanning Microscopy,” J. Phys. Chem. B.107,1574–1584 (2003).
  19. A. Bek, Apertureless SNOM: a new tool for nano-optics, (Ph.D. Thesis, Max Planck Institute for Solid State Research, Germany, 2004).

2006 (1)

P. G. Gucciardi, G. Bachelier, and M. Allegrini, “Far-field background suppression in tip-modulated apertureless near-field optical microscopy,” J. Appl. Phys. 99, Art. No.124309 (2006).
[Crossref]

2005 (1)

2004 (2)

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Phil. Trans. R. Soc. Lond. A. 362, 787–805 (2004).
[Crossref]

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

2001 (2)

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Y.L Lo and C.H. Chuang, “New synthetic-heterodyne demodulation for an optical fiber interferometry,” IEEE J. Quantum Electro. 37, 658–663 (2001).
[Crossref]

2000 (3)

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

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

R. Hillenbrand, B. Knoll, and F. Keilmann, “Pure optical contrast in scattering-type scanning near-field microscopy,” J. Microsc. 202, 77–83 (2000).
[Crossref]

1994 (1)

1990 (1)

H. K. Wickramasinghe and C. C. Williams, “Apertureless near field optical microscope,” US Patent4 947 034 (1990).

1986 (1)

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force miscopy,” Phys. Rev. Lett.,  56, 930–933 (1986).
[Crossref] [PubMed]

1985 (1)

J. Wessel, “Surface-enhanced optical microscopy,” J. Opt. Soc. Am. 2, 1538–1540 (1985).
[Crossref]

1984 (1)

D. W. Pohl, S. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ 20,” J. Appl. Phys. 44, 651–653 (1984).

1982 (1)

G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Helv. Phys. Acta. 55, 726–735 (1982).

1928 (1)

E. H. Synge, “A suggested method for extending the microscopic resolution into the ultramicroscopic region,” Phil. Mag. 6, 356–362 (1928).

Adam, P. M.

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Allegrini, M.

P. G. Gucciardi, G. Bachelier, and M. Allegrini, “Far-field background suppression in tip-modulated apertureless near-field optical microscopy,” J. Appl. Phys. 99, Art. No.124309 (2006).
[Crossref]

Aubert, S

Aubert, S.

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

Bachelier, G.

P. G. Gucciardi, G. Bachelier, and M. Allegrini, “Far-field background suppression in tip-modulated apertureless near-field optical microscopy,” J. Appl. Phys. 99, Art. No.124309 (2006).
[Crossref]

Bachelot, R.

I. Stefanon, S. Blaize, A. Bruyant, S Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Express 13, 5553–5564 (2005).
[Crossref] [PubMed]

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

Bek, A.

A. Bek, Apertureless SNOM: a new tool for nano-optics, (Ph.D. Thesis, Max Planck Institute for Solid State Research, Germany, 2004).

Bijeon, J. L.

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Binnig, G.

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force miscopy,” Phys. Rev. Lett.,  56, 930–933 (1986).
[Crossref] [PubMed]

G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Helv. Phys. Acta. 55, 726–735 (1982).

Blaize, S.

Bruyant, A.

I. Stefanon, S. Blaize, A. Bruyant, S Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Express 13, 5553–5564 (2005).
[Crossref] [PubMed]

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

Carminati, R.

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Chuang, C.H.

Y.L Lo and C.H. Chuang, “New synthetic-heterodyne demodulation for an optical fiber interferometry,” IEEE J. Quantum Electro. 37, 658–663 (2001).
[Crossref]

Denk, S.

D. W. Pohl, S. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ 20,” J. Appl. Phys. 44, 651–653 (1984).

Gerber, C.

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force miscopy,” Phys. Rev. Lett.,  56, 930–933 (1986).
[Crossref] [PubMed]

Greffet, J. J.

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Gucciardi, P. G.

P. G. Gucciardi, G. Bachelier, and M. Allegrini, “Far-field background suppression in tip-modulated apertureless near-field optical microscopy,” J. Appl. Phys. 99, Art. No.124309 (2006).
[Crossref]

Hillenbrand, R.

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Phil. Trans. R. Soc. Lond. A. 362, 787–805 (2004).
[Crossref]

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

R. Hillenbrand, B. Knoll, and F. Keilmann, “Pure optical contrast in scattering-type scanning near-field microscopy,” J. Microsc. 202, 77–83 (2000).
[Crossref]

Hudlet, S.

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Inouye, Y.

Jackson, J. D.

J. D. Jackson, Classical electrodynamics (Wiley, 1999).

Kawata, S.

Keilmann, F.

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Phil. Trans. R. Soc. Lond. A. 362, 787–805 (2004).
[Crossref]

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

R. Hillenbrand, B. Knoll, and F. Keilmann, “Pure optical contrast in scattering-type scanning near-field microscopy,” J. Microsc. 202, 77–83 (2000).
[Crossref]

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

Klymyshyn, N.

M. Micic, N. Klymyshyn, Y. D. Sun, and H. P. Lu, “Finite element method simulation of the field distribution for AFM tip-enhanced surface Raman Scanning Microscopy,” J. Phys. Chem. B.107,1574–1584 (2003).

Knoll, B.

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

R. Hillenbrand, B. Knoll, and F. Keilmann, “Pure optical contrast in scattering-type scanning near-field microscopy,” J. Microsc. 202, 77–83 (2000).
[Crossref]

Lanz, M.

D. W. Pohl, S. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ 20,” J. Appl. Phys. 44, 651–653 (1984).

Lerondel, G.

I. Stefanon, S. Blaize, A. Bruyant, S Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Express 13, 5553–5564 (2005).
[Crossref] [PubMed]

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

Lo, Y.L

Y.L Lo and C.H. Chuang, “New synthetic-heterodyne demodulation for an optical fiber interferometry,” IEEE J. Quantum Electro. 37, 658–663 (2001).
[Crossref]

Lu, H. P.

M. Micic, N. Klymyshyn, Y. D. Sun, and H. P. Lu, “Finite element method simulation of the field distribution for AFM tip-enhanced surface Raman Scanning Microscopy,” J. Phys. Chem. B.107,1574–1584 (2003).

Micic, M.

M. Micic, N. Klymyshyn, Y. D. Sun, and H. P. Lu, “Finite element method simulation of the field distribution for AFM tip-enhanced surface Raman Scanning Microscopy,” J. Phys. Chem. B.107,1574–1584 (2003).

Pohl, D. W.

D. W. Pohl, S. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ 20,” J. Appl. Phys. 44, 651–653 (1984).

Porto, J. A.

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Quate, C. F.

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force miscopy,” Phys. Rev. Lett.,  56, 930–933 (1986).
[Crossref] [PubMed]

Rohrer, H.

G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Helv. Phys. Acta. 55, 726–735 (1982).

Royer, P.

I. Stefanon, S. Blaize, A. Bruyant, S Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Express 13, 5553–5564 (2005).
[Crossref] [PubMed]

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Stashkevich, A.

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Stashkevich, A. A.

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

Stefanon, I.

Sun, Y. D.

M. Micic, N. Klymyshyn, Y. D. Sun, and H. P. Lu, “Finite element method simulation of the field distribution for AFM tip-enhanced surface Raman Scanning Microscopy,” J. Phys. Chem. B.107,1574–1584 (2003).

Synge, E. H.

E. H. Synge, “A suggested method for extending the microscopic resolution into the ultramicroscopic region,” Phil. Mag. 6, 356–362 (1928).

Walford, J. N.

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

Wessel, J.

J. Wessel, “Surface-enhanced optical microscopy,” J. Opt. Soc. Am. 2, 1538–1540 (1985).
[Crossref]

Wickramasinghe, H. K.

H. K. Wickramasinghe and C. C. Williams, “Apertureless near field optical microscope,” US Patent4 947 034 (1990).

Williams, C. C.

H. K. Wickramasinghe and C. C. Williams, “Apertureless near field optical microscope,” US Patent4 947 034 (1990).

Helv. Phys. Acta. (1)

G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Helv. Phys. Acta. 55, 726–735 (1982).

IEEE J. Quantum Electro. (1)

Y.L Lo and C.H. Chuang, “New synthetic-heterodyne demodulation for an optical fiber interferometry,” IEEE J. Quantum Electro. 37, 658–663 (2001).
[Crossref]

J. Appl. Phys. (3)

J. N. Walford, J. A. Porto, R. Carminati, J. J. Greffet, P. M. Adam, S. Hudlet, J. L. Bijeon, A. Stashkevich, and P. Royer, “Influence of tip modulation on image formation in scanning near-field optical microscopy,” J. Appl. Phys. 89, 5159–5169 (2001).
[Crossref]

D. W. Pohl, S. Denk, and M. Lanz, “Optical stethoscopy: image recording with resolution λ 20,” J. Appl. Phys. 44, 651–653 (1984).

P. G. Gucciardi, G. Bachelier, and M. Allegrini, “Far-field background suppression in tip-modulated apertureless near-field optical microscopy,” J. Appl. Phys. 99, Art. No.124309 (2006).
[Crossref]

J. Microsc. (1)

R. Hillenbrand, B. Knoll, and F. Keilmann, “Pure optical contrast in scattering-type scanning near-field microscopy,” J. Microsc. 202, 77–83 (2000).
[Crossref]

J. Opt. Soc. Am. (1)

J. Wessel, “Surface-enhanced optical microscopy,” J. Opt. Soc. Am. 2, 1538–1540 (1985).
[Crossref]

J. Phys. Chem. B. (1)

M. Micic, N. Klymyshyn, Y. D. Sun, and H. P. Lu, “Finite element method simulation of the field distribution for AFM tip-enhanced surface Raman Scanning Microscopy,” J. Phys. Chem. B.107,1574–1584 (2003).

Opt. Commun. (2)

S. Hudlet, S. Aubert, A. Bruyant, R. Bachelot, P. M. Adam, J. L. Bijeon, G. Lerondel, P. Royer, and A. A. Stashkevich, “Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of background field,” Opt. Commun. 230, 245–251(2004).
[Crossref]

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

Opt. Express (1)

Opt. Lett. (1)

Phil. Mag. (1)

E. H. Synge, “A suggested method for extending the microscopic resolution into the ultramicroscopic region,” Phil. Mag. 6, 356–362 (1928).

Phil. Trans. R. Soc. Lond. A. (1)

F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Phil. Trans. R. Soc. Lond. A. 362, 787–805 (2004).
[Crossref]

Phys. Rev. Lett. (2)

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

G. Binnig, C. F. Quate, and C. Gerber, “Atomic force miscopy,” Phys. Rev. Lett.,  56, 930–933 (1986).
[Crossref] [PubMed]

US Patent (1)

H. K. Wickramasinghe and C. C. Williams, “Apertureless near field optical microscope,” US Patent4 947 034 (1990).

Other (2)

J. D. Jackson, Classical electrodynamics (Wiley, 1999).

A. Bek, Apertureless SNOM: a new tool for nano-optics, (Ph.D. Thesis, Max Planck Institute for Solid State Research, Germany, 2004).

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Figures (10)

Fig. 1.
Fig. 1.

Model of A-SNOM near-field region.

Fig. 2.
Fig. 2.

Variation of signal contrast |S1/S2 in different order of modulated frequency with phase modulation depth ψ 3 in A-SNOM lock-in detection.

Fig. 3.
Fig. 3.

(a). Variation of signal intensity |S1| in different order of modulated frequency with phase modulation depth ψ3 in A-SNOM lock-in detection.

Fig. 3.
Fig. 3.

(b). Partial enlargement of Fig. 3. (a).

Fig. 4.
Fig. 4.

Variation of signal contrast |S1/S2| in different order of modulated frequency with wavelength of incident electric field in A-SNOM lock-in detection.

Fig. 5.
Fig. 5.

Variation of signal intensity |S1| in different order of modulated frequency with wavelength of incident electric field in A-SNOM lock-in detection.

Fig. 6.
Fig. 6.

Variation of signal contrast |S1/S2| in different order of modulated frequency with incident angle of E i in A-SNOM lock-in detection.

Fig. 7.
Fig. 7.

Variation of signal intensity |S1| in different order of modulated frequency with incident angle of E i in A-SNOM lock-in detection.

Fig. 8.
Fig. 8.

Variation of signal intensity |S1| in different order of modulated frequency with phase difference with ψ 1=ψ 2 in A-SNOM lock-in detection.

Fig. 9.
Fig. 9.

Variation of signal contrast |S1/S2| in different order of modulated frequency with phase difference with ψ 1=ψ 2 in A-SNOM lock-in detection.

Equations (34)

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E T S = α eff E i e i ( ω t + ϕ TS ) E T S e i ( ω t + ϕ TS )
Z ( t ) = Z 0 + A cos ( ω 0 t )
E Tip = E T e i ( ω t + ϕ T ) e i ( 2 K sin ( θ ) Z ( t ) )
E S a m p l e = E S e i ( ω t + ϕ S )
E total = { E T S + E Tip + E Sample }
I ( t ) = 2 E T S E S cos ( ϕ TS ϕ S )
+ 2 E T E S cos [ ϕ T ϕ S + 2 K sin ( θ ) Z 0 + 2 K sin ( θ ) A cos ( ω 0 t ) ]
+ 2 E T S E T cos [ ϕ T ϕ TS + 2 K sin ( θ ) Z 0 + 2 K sin ( θ ) A cos ( ω 0 t ) ]
+ E T S 2 + E T 2 + E S 2
I ( t ) = 2 E T S E S cos ( ϕ TS ϕ S )
+ 2 E T E S { [ J 0 ( ψ 3 ) + 2 j = 1 ( 1 ) j J 2 j ( ψ 3 ) cos ( 2 j ω 0 t ) ] cos ( ψ 1 )
2 j = 0 ( 1 ) j J 2 j + 1 ( ψ 3 ) cos [ ( 2 j + 1 ) ω 0 t ] sin ( ψ 1 ) }
+ 2 E T S E T { [ J 0 ( ψ 3 ) + 2 j = 1 ( 1 ) j J 2 j ( ψ 3 ) cos ( 2 j ω 0 t ) ] cos ( ψ 2 )
2 j = 0 ( 1 ) j J 2 j + 1 ( ψ 3 ) cos [ ( 2 j + 1 ) ω 0 t ] sin ( ψ 2 ) }
+ E T S 2 + E T 2 + E S 2
E T S = E T S 0 ω 0 + E T S 1 ω 0 cos ( ω 0 t ) + E T S 2 ω 0 cos ( 2 ω 0 ) + E T S 3 ω 0 cos ( 3 ω 0 t ) +
I ( t ) = 2 n = 0 E T S n ω 0 cos ( n ω 0 t ) E S cos ( ϕ TS ϕ S )
+ 2 E T E S { [ J 0 ( ψ 3 ) + 2 j = 1 ( 1 ) j J 2 j ( ψ 3 ) cos ( 2 j ω 0 t ) ] cos ( ψ 1 )
2 j = 0 ( 1 ) j J 2 j + 1 ( ψ 3 ) cos [ ( 2 j + 1 ) ω 0 t ] sin ( ψ 1 ) }
+ 2 n = 0 E T S n ω 0 cos ( n ω 0 t ) E T { [ J 0 ( ψ 3 ) + 2 j = 1 ( 1 ) j J 2 j ( ψ 3 ) cos ( 2 j ω 0 t ) ] cos ( ψ 2 )
2 j = 0 ( 1 ) j J 2 j + 1 ( ψ 3 ) cos [ ( 2 j + 1 ) ω 0 t ] sin ( ψ 2 ) }
+ n = 0 E T S n ω 0 cos ( n ω 0 t ) m = 0 E T S m ω 0 * cos ( m ω 0 t ) + E T 2 + E S 2
cos ( n ω 0 t ) cos ( m ω 0 t ) = 1 2 { cos [ ( n m ) ω 0 t ] + cos [ ( n + m ) ω 0 t ] }
I ( t ) = 2 E T S 0 ω 0 E S cos ( ϕ TS ϕ S ) + 2 E T E S J 0 ( ψ 3 ) cos ( ψ 1 ) + 2 E T S 0 ω 0 E T J 0 ( ψ 3 ) cos ( ψ 2 )
+ E T S 0 ω 0 E T S 0 ω 0 * + 1 2 n = 1 E T S n ω 0 E T S n ω 0 * + E T 2 + E S 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DC
+ { 2 E T S 1 ω 0 E S cos ( ϕ TS ϕ S ) 4 E T E S J 1 ( ψ 3 ) sin ( ψ 1 ) + 2 E T S 1 ω 0 E T J 0 ( ψ 3 ) cos ( ψ 2 )
4 E T S 0 ω 0 E T J 1 ( ψ 3 ) sin ( ψ 2 ) + 2 E T S 0 ω 0 E T S 1 ω 0 * + n = 1 E T S n ω 0 E T S ( n + 1 ) ω 0 * } cos ( ω 0 t ) . . . . . . . . . . . . . . . . . . . . 1 st ω 0
+ { 2 E T S 2 ω 0 E S cos ( ϕ TS ϕ S ) 4 E T E S J 2 ( ψ 3 ) cos ( ψ 1 ) + 2 E T S 2 ω 0 E T J 0 ( ψ 3 ) cos ( ψ 2 )
4 E T S 0 ω 0 E T J 2 ( ψ 3 ) cos ( ψ 2 ) + 2 E T S 0 ω 0 E T S 2 ω 0 * + n = 1 E T S n ω 0 E T S ( n + 2 ) ω 0 * } cos ( 2 ω 0 t ) . . . . . . . . . . . . . . . . . . 2 nd ω 0
{ 2 E T S 3 ω 0 E S cos ( ϕ TS ϕ S ) + 4 E T E S J 3 ( ψ 3 ) sin ( ψ 1 ) + 2 E T S 3 ω 0 E T J 0 ( ψ 3 ) cos ( ψ 2 )
4 E T S 0 ω 0 E T J 3 ( ψ 3 ) sin ( ψ 2 ) + 2 E T S 0 ω 0 E T S 3 ω 0 * + n = 1 E T S n ω 0 E T S ( n + 3 ) ω 0 * } cos ( 3 ω 0 t ) . . . . . . . . . . . . . . . . . . 3 rd ω 0
{ 2 E T S 4 ω 0 E S cos ( ϕ TS ϕ S ) + 4 E T E S J 4 ( ψ 4 ) cos ( ψ 1 ) + 2 E T S 4 ω 0 E T J 0 ( ψ 3 ) cos ( ψ 2 )
4 E T S 0 ω 0 E T J 4 ( ψ 3 ) cos ( ψ 2 ) + 2 E T S 0 ω 0 E T S 4 ω 0 * + n = 1 E T S n ω 0 E T S ( n + 4 ) ω 0 * } cos ( 4 ω 0 t ) . . . . . . . . . . . . . . . . . . 4 th ω 0
S 1 S 2 n = I n ω 0 ( S 1 ) I n ω 0 ( S 2 )

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