Abstract

We consider a simple analytical model for the electric near field of a semi-infinite conical probe and apply it to study the incident angle dependence of the field for the case of side illumination by both the plane wave and the Gaussian beam. The electric near field is shown to peak when approaching the grazing incidence. In some cases, a peak can also occur at an incident angle somewhat below 90°. The results obtained are in qualitative agreement with those for a thin semi-infinite wire and previously published results for the finite-size conical probes.

© 2007 Optical Society of America

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  1. A. Bouhelier, "Field-enhanced scanning near-field optical microscopy," Microsc. Res. Tech. 69, 563-579 (2006).
    [CrossRef] [PubMed]
  2. L. Novotny, R. X. Bean, and X. S. Xie, "Theory of Nanometric Optical Tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
    [CrossRef]
  3. O. J. F. Martin and C. Girard, "Controlling and tuning strong optical field gradients at a local probe microscope tip apex," Appl. Phys. Lett. 70, 705-707 (1997).
    [CrossRef]
  4. S. Takahashi and A. V. Zayats, "Near-Field Second-Harmonic Generation at a Metal Tip Apex," Appl. Phys. Lett. 80, 3479-3481 (2002).
    [CrossRef]
  5. R. Bachelot, F. H’Dhili, D. Barchiesi, G. Lerondel, R. Fikri, P. Royer, N. Landraud, J. Peretti, F. Chaput, G. Lampel, J. P. Boilot, and K. Lahlil, "Apertureless near-field optical microscopy: a study of the local tip field enhancement using photosensitive Azobenzene-containing films," J. Appl. Phys. 94, 2060-2072 (2003).
    [CrossRef]
  6. R. Ossikovski, Q. Nguen, and G. Picardi, "Simple model for the polarization effects in tip-enhanced Raman Spectroscopy," Phys. Rev. B 75, 045412 (2007).
    [CrossRef]
  7. M. J. Hagmann, "Intensification of Optical Electric Fields caused by the Interaction with a Metal Tip in Photofield Emission and Laser-Assisted Scanning Tunneling Microscopy," J. Vac. Sci. Technol. B 15, 597-601 (1997).
    [CrossRef]
  8. W. X. Sun and Z. X. Shen, "Optimizing the Near Field around Silver Tips," J. Opt. Soc. Am. A 20, 2254-2259 (2003).
    [CrossRef]
  9. R. Esteban, R. Vogelgesang, and K. Kern, "Simulation of Optical Near and Far Fields of Dielectric Apertureless Scanning Probe," Nanotechnology 17, 475-482 (2006).
    [CrossRef]
  10. See, e.g., M. A. Salem, A. H. Kamel, and A. V. Osipov, "Electromagnetic fields in the presence of an infinite dielectric wedge," Proc. R. Soc. A 462, 2503-2522 (2006).
    [CrossRef]
  11. See L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Wiley, 1994) and references therein.
    [CrossRef]
  12. J. J. Bowman, The Cone, in Electromagnetic and Acoustic Scattering by Simple Shapes, J. J. Bowman, T. B. A. Senior, P. L. E. Uslenghi, eds., (Hemisphere, New York, 1987).
  13. J. Van Bladel, "Field singularities at the tip of a Dielectric Cone," IEEE Trans. Antennas Propag. 33, 893-895 (1985).
    [CrossRef]
  14. M. Idemen, "Confluent Tip Singularity of the Electromagnetic Field at the Apex of a Material Cone," Wave Motion 38, 251-277 (2003).
    [CrossRef]
  15. R. M. Roth, N. C. Panoiu, M. M. Adams, R. M. Osgood, Jr., C. C. Neacsu, and M. B. Raschke, "Resonant-Plasmon Field enhancement from asymmetrically illuminated Conical Metallic-Probe Tips," Opt. Express 14, 2921-2931 (2006).
    [CrossRef] [PubMed]
  16. See, e.g., H. Bateman and A. Erdelyi, Higher Transcendental Functions, (McGraw-Hill, 1985) Vol. 1.
  17. See, e.g., R. N. Hall, "The application of non-integral Legendre functions to potential problems," J. Appl. Phys. 20, 925-931 (1949).
    [CrossRef]
  18. Our numerical simulations show that this statement is also valid for ν>0.
  19. A. V. Goncharenko, J. K. Wang, and Y. C. Chang, "Electric Near-Field Enhancement of a Sharp Semi-Infinite Conical Probe: Material and Cone Angle Dependence," Phys. Rev. B 74, 235442 (2006).
    [CrossRef]
  20. W. P. Dyke, J. K. Trolan, W. W. Dolan, and G. Barnes, "The Field Emitter: Fabrication, Electron Microscopy, and Electric Field Calculations," J. Appl. Phys. 24, 570-576 (1953).
    [CrossRef]
  21. J. C. Wiesner and T. E. Everhart, "Point-Cathode Electron Sources - Electron Optics of the Initial Diode Region," J. Appl. Phys. 44, 2140-2148 (1973).
    [CrossRef]
  22. The "bowling" pin shape can be also of interest in its own right because such a geometry can be formed by sputter coating a standard dielectric probe with a metal, see, e.g., D. Hu, M. Micic, N. Klymyshyn, Y. D. Suh, and H. P. Lu, "Correlated Topographic and Spectroscopic Imaging beyond Diffraction limit by Atomic Force Microscopy Metallic Tip-Enhanced Near-Field Fluorescence Lifetime Microscopy," Rev. Sci. Instrum. 74, 3347-3355 (2003).
    [CrossRef]
  23. C. G. Chen, P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, "Analysis of Vector Gaussian Beam Propagation and the Validity of Paraxial and Spherical Approximations," J. Opt. Soc. Am. A 19, 404-412 (2002).
    [CrossRef]
  24. P. C. Chaumet, "Fully vectorial highly nonparaxial beam close to the waist," J. Opt. Soc. Am. A 23, 3197-3202 (2006).
    [CrossRef]
  25. Em. E. Kriezis, P. K. Pandelakis, and A. G. Papagiannakis, "Diffraction of a Gaussian Beam from a Periodic Planar Screen," J. Opt. Soc. Am. A 11, 630-636 (1994).
    [CrossRef]
  26. See, e.g., R. Cicchetti and A. Faraone, "On the optical behavior of the Electromagnetic Field excited by a Semi-Infinite Traveling-Wave Current," IEEE Trans. Antennas Propag. 53, 4015-4025 (2005).
    [CrossRef]
  27. C.A. Balanis, Antenna Theory. Analysis and Design (Wiley, New York, 1997).
  28. D.C. Chang, S.W. Lee, and L. Rispin, "Simple formula for current on a cylindrical receiving antenna," IEEE Trans. Antennas Propag. 26, 683-690 (1978).
    [CrossRef]
  29. O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for Electromagnetic Scattering and Light Confinement," Phys. Rev. Lett. 74, 526-529 (1995).
    [CrossRef] [PubMed]
  30. N. I. Petrov, "Focusing of beams into subwavelength area in an inhomogeneous medium," Opt. Express 9, 658-673 (2001).
    [CrossRef] [PubMed]
  31. N. I. Petrov, "Evanescent and propagating fields of a strongly focused beam," J. Opt. Soc. Am. 20, 2385-2389 (2003).
    [CrossRef]
  32. C. Durkan and I. V. Shvets, "Polarization effects in Reflection-Mode Scanning Near-Field Optical Microscopy," J. Appl. Phys. 83, 1837-1843 (1998).
    [CrossRef]
  33. O. J. F. Martin and C. Girard, "Controlling and Tuning Strong Optical Field Gradients at a Local Probe Microscope Tip Apex," Appl. Phys. Lett. 70, 705 (1997).
    [CrossRef]
  34. M. S. Anderson, "Locally enhanced Raman Spectroscopy with an Atomic Force Microscope," Appl. Phys. Lett. 76, 3130-3132 (2000).
    [CrossRef]
  35. M. S. Anderson and W. T. Pike, "A Raman-Atomic Force Microscope for Apertureless-Near-Field Spectroscopy and Optical Trapping," Rev. Sci. Instrum. 73, 1198-1203 (2002).
    [CrossRef]
  36. D. Richards, "Near-Field Microscopy: throwing light on the Nanoworld," Phil. Trans. R. Soc. Lond. A 361, 2843-2857 (2003).
    [CrossRef]
  37. K. O. Greulich, "Single molecule studies of DNA and RNA," ChemPhysChem 6, 2458-2471 (2005).
    [CrossRef] [PubMed]
  38. K. C. Neuman and S. M. Block, "Optical Trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
    [CrossRef]
  39. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
    [CrossRef] [PubMed]
  40. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized beam," Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  41. D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, and J. F. Maguire, "Nano-Raman Spectroscopy with side-illumination optics," J. Raman Spectrosc. 36, 1068-1075 (2005).
    [CrossRef]
  42. C. C. Neacsu, J. Dreyer, N. Behr, and M. B. Raschke, "Scanning-probe Raman Spectroscopy with single-molecule sensitivity," Phys. Rev. B 73, 193406 (2006).
    [CrossRef]
  43. Q. Nguyen, R. Ossikovski, and J. Schreiber, "Contrast enhancement on Crystalline Silicon in polarized reflection mode tip-enhanced Raman Spectroscopy," Opt. Commun. 274, 231-235 (2007).
    [CrossRef]

2007 (2)

R. Ossikovski, Q. Nguen, and G. Picardi, "Simple model for the polarization effects in tip-enhanced Raman Spectroscopy," Phys. Rev. B 75, 045412 (2007).
[CrossRef]

Q. Nguyen, R. Ossikovski, and J. Schreiber, "Contrast enhancement on Crystalline Silicon in polarized reflection mode tip-enhanced Raman Spectroscopy," Opt. Commun. 274, 231-235 (2007).
[CrossRef]

2006 (7)

C. C. Neacsu, J. Dreyer, N. Behr, and M. B. Raschke, "Scanning-probe Raman Spectroscopy with single-molecule sensitivity," Phys. Rev. B 73, 193406 (2006).
[CrossRef]

R. Esteban, R. Vogelgesang, and K. Kern, "Simulation of Optical Near and Far Fields of Dielectric Apertureless Scanning Probe," Nanotechnology 17, 475-482 (2006).
[CrossRef]

See, e.g., M. A. Salem, A. H. Kamel, and A. V. Osipov, "Electromagnetic fields in the presence of an infinite dielectric wedge," Proc. R. Soc. A 462, 2503-2522 (2006).
[CrossRef]

A. Bouhelier, "Field-enhanced scanning near-field optical microscopy," Microsc. Res. Tech. 69, 563-579 (2006).
[CrossRef] [PubMed]

A. V. Goncharenko, J. K. Wang, and Y. C. Chang, "Electric Near-Field Enhancement of a Sharp Semi-Infinite Conical Probe: Material and Cone Angle Dependence," Phys. Rev. B 74, 235442 (2006).
[CrossRef]

R. M. Roth, N. C. Panoiu, M. M. Adams, R. M. Osgood, Jr., C. C. Neacsu, and M. B. Raschke, "Resonant-Plasmon Field enhancement from asymmetrically illuminated Conical Metallic-Probe Tips," Opt. Express 14, 2921-2931 (2006).
[CrossRef] [PubMed]

P. C. Chaumet, "Fully vectorial highly nonparaxial beam close to the waist," J. Opt. Soc. Am. A 23, 3197-3202 (2006).
[CrossRef]

2005 (3)

See, e.g., R. Cicchetti and A. Faraone, "On the optical behavior of the Electromagnetic Field excited by a Semi-Infinite Traveling-Wave Current," IEEE Trans. Antennas Propag. 53, 4015-4025 (2005).
[CrossRef]

K. O. Greulich, "Single molecule studies of DNA and RNA," ChemPhysChem 6, 2458-2471 (2005).
[CrossRef] [PubMed]

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, and J. F. Maguire, "Nano-Raman Spectroscopy with side-illumination optics," J. Raman Spectrosc. 36, 1068-1075 (2005).
[CrossRef]

2004 (1)

K. C. Neuman and S. M. Block, "Optical Trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

2003 (7)

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

D. Richards, "Near-Field Microscopy: throwing light on the Nanoworld," Phil. Trans. R. Soc. Lond. A 361, 2843-2857 (2003).
[CrossRef]

W. X. Sun and Z. X. Shen, "Optimizing the Near Field around Silver Tips," J. Opt. Soc. Am. A 20, 2254-2259 (2003).
[CrossRef]

M. Idemen, "Confluent Tip Singularity of the Electromagnetic Field at the Apex of a Material Cone," Wave Motion 38, 251-277 (2003).
[CrossRef]

The "bowling" pin shape can be also of interest in its own right because such a geometry can be formed by sputter coating a standard dielectric probe with a metal, see, e.g., D. Hu, M. Micic, N. Klymyshyn, Y. D. Suh, and H. P. Lu, "Correlated Topographic and Spectroscopic Imaging beyond Diffraction limit by Atomic Force Microscopy Metallic Tip-Enhanced Near-Field Fluorescence Lifetime Microscopy," Rev. Sci. Instrum. 74, 3347-3355 (2003).
[CrossRef]

N. I. Petrov, "Evanescent and propagating fields of a strongly focused beam," J. Opt. Soc. Am. 20, 2385-2389 (2003).
[CrossRef]

R. Bachelot, F. H’Dhili, D. Barchiesi, G. Lerondel, R. Fikri, P. Royer, N. Landraud, J. Peretti, F. Chaput, G. Lampel, J. P. Boilot, and K. Lahlil, "Apertureless near-field optical microscopy: a study of the local tip field enhancement using photosensitive Azobenzene-containing films," J. Appl. Phys. 94, 2060-2072 (2003).
[CrossRef]

2002 (3)

S. Takahashi and A. V. Zayats, "Near-Field Second-Harmonic Generation at a Metal Tip Apex," Appl. Phys. Lett. 80, 3479-3481 (2002).
[CrossRef]

C. G. Chen, P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, "Analysis of Vector Gaussian Beam Propagation and the Validity of Paraxial and Spherical Approximations," J. Opt. Soc. Am. A 19, 404-412 (2002).
[CrossRef]

M. S. Anderson and W. T. Pike, "A Raman-Atomic Force Microscope for Apertureless-Near-Field Spectroscopy and Optical Trapping," Rev. Sci. Instrum. 73, 1198-1203 (2002).
[CrossRef]

2001 (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

N. I. Petrov, "Focusing of beams into subwavelength area in an inhomogeneous medium," Opt. Express 9, 658-673 (2001).
[CrossRef] [PubMed]

2000 (1)

M. S. Anderson, "Locally enhanced Raman Spectroscopy with an Atomic Force Microscope," Appl. Phys. Lett. 76, 3130-3132 (2000).
[CrossRef]

1998 (1)

C. Durkan and I. V. Shvets, "Polarization effects in Reflection-Mode Scanning Near-Field Optical Microscopy," J. Appl. Phys. 83, 1837-1843 (1998).
[CrossRef]

1997 (4)

O. J. F. Martin and C. Girard, "Controlling and Tuning Strong Optical Field Gradients at a Local Probe Microscope Tip Apex," Appl. Phys. Lett. 70, 705 (1997).
[CrossRef]

L. Novotny, R. X. Bean, and X. S. Xie, "Theory of Nanometric Optical Tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

O. J. F. Martin and C. Girard, "Controlling and tuning strong optical field gradients at a local probe microscope tip apex," Appl. Phys. Lett. 70, 705-707 (1997).
[CrossRef]

M. J. Hagmann, "Intensification of Optical Electric Fields caused by the Interaction with a Metal Tip in Photofield Emission and Laser-Assisted Scanning Tunneling Microscopy," J. Vac. Sci. Technol. B 15, 597-601 (1997).
[CrossRef]

1995 (1)

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for Electromagnetic Scattering and Light Confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

1994 (1)

1985 (1)

J. Van Bladel, "Field singularities at the tip of a Dielectric Cone," IEEE Trans. Antennas Propag. 33, 893-895 (1985).
[CrossRef]

1978 (1)

D.C. Chang, S.W. Lee, and L. Rispin, "Simple formula for current on a cylindrical receiving antenna," IEEE Trans. Antennas Propag. 26, 683-690 (1978).
[CrossRef]

1973 (1)

J. C. Wiesner and T. E. Everhart, "Point-Cathode Electron Sources - Electron Optics of the Initial Diode Region," J. Appl. Phys. 44, 2140-2148 (1973).
[CrossRef]

1953 (1)

W. P. Dyke, J. K. Trolan, W. W. Dolan, and G. Barnes, "The Field Emitter: Fabrication, Electron Microscopy, and Electric Field Calculations," J. Appl. Phys. 24, 570-576 (1953).
[CrossRef]

1949 (1)

See, e.g., R. N. Hall, "The application of non-integral Legendre functions to potential problems," J. Appl. Phys. 20, 925-931 (1949).
[CrossRef]

Appl. Phys. Lett. (4)

O. J. F. Martin and C. Girard, "Controlling and tuning strong optical field gradients at a local probe microscope tip apex," Appl. Phys. Lett. 70, 705-707 (1997).
[CrossRef]

S. Takahashi and A. V. Zayats, "Near-Field Second-Harmonic Generation at a Metal Tip Apex," Appl. Phys. Lett. 80, 3479-3481 (2002).
[CrossRef]

O. J. F. Martin and C. Girard, "Controlling and Tuning Strong Optical Field Gradients at a Local Probe Microscope Tip Apex," Appl. Phys. Lett. 70, 705 (1997).
[CrossRef]

M. S. Anderson, "Locally enhanced Raman Spectroscopy with an Atomic Force Microscope," Appl. Phys. Lett. 76, 3130-3132 (2000).
[CrossRef]

ChemPhysChem (1)

K. O. Greulich, "Single molecule studies of DNA and RNA," ChemPhysChem 6, 2458-2471 (2005).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag. (3)

J. Van Bladel, "Field singularities at the tip of a Dielectric Cone," IEEE Trans. Antennas Propag. 33, 893-895 (1985).
[CrossRef]

See, e.g., R. Cicchetti and A. Faraone, "On the optical behavior of the Electromagnetic Field excited by a Semi-Infinite Traveling-Wave Current," IEEE Trans. Antennas Propag. 53, 4015-4025 (2005).
[CrossRef]

D.C. Chang, S.W. Lee, and L. Rispin, "Simple formula for current on a cylindrical receiving antenna," IEEE Trans. Antennas Propag. 26, 683-690 (1978).
[CrossRef]

J. Appl. Phys. (5)

C. Durkan and I. V. Shvets, "Polarization effects in Reflection-Mode Scanning Near-Field Optical Microscopy," J. Appl. Phys. 83, 1837-1843 (1998).
[CrossRef]

R. Bachelot, F. H’Dhili, D. Barchiesi, G. Lerondel, R. Fikri, P. Royer, N. Landraud, J. Peretti, F. Chaput, G. Lampel, J. P. Boilot, and K. Lahlil, "Apertureless near-field optical microscopy: a study of the local tip field enhancement using photosensitive Azobenzene-containing films," J. Appl. Phys. 94, 2060-2072 (2003).
[CrossRef]

See, e.g., R. N. Hall, "The application of non-integral Legendre functions to potential problems," J. Appl. Phys. 20, 925-931 (1949).
[CrossRef]

W. P. Dyke, J. K. Trolan, W. W. Dolan, and G. Barnes, "The Field Emitter: Fabrication, Electron Microscopy, and Electric Field Calculations," J. Appl. Phys. 24, 570-576 (1953).
[CrossRef]

J. C. Wiesner and T. E. Everhart, "Point-Cathode Electron Sources - Electron Optics of the Initial Diode Region," J. Appl. Phys. 44, 2140-2148 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

N. I. Petrov, "Evanescent and propagating fields of a strongly focused beam," J. Opt. Soc. Am. 20, 2385-2389 (2003).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Raman Spectrosc. (1)

D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, and J. F. Maguire, "Nano-Raman Spectroscopy with side-illumination optics," J. Raman Spectrosc. 36, 1068-1075 (2005).
[CrossRef]

J. Vac. Sci. Technol. B (1)

M. J. Hagmann, "Intensification of Optical Electric Fields caused by the Interaction with a Metal Tip in Photofield Emission and Laser-Assisted Scanning Tunneling Microscopy," J. Vac. Sci. Technol. B 15, 597-601 (1997).
[CrossRef]

Microsc. Res. Tech. (1)

A. Bouhelier, "Field-enhanced scanning near-field optical microscopy," Microsc. Res. Tech. 69, 563-579 (2006).
[CrossRef] [PubMed]

Nanotechnology (1)

R. Esteban, R. Vogelgesang, and K. Kern, "Simulation of Optical Near and Far Fields of Dielectric Apertureless Scanning Probe," Nanotechnology 17, 475-482 (2006).
[CrossRef]

Opt. Commun. (1)

Q. Nguyen, R. Ossikovski, and J. Schreiber, "Contrast enhancement on Crystalline Silicon in polarized reflection mode tip-enhanced Raman Spectroscopy," Opt. Commun. 274, 231-235 (2007).
[CrossRef]

Opt. Express (2)

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

D. Richards, "Near-Field Microscopy: throwing light on the Nanoworld," Phil. Trans. R. Soc. Lond. A 361, 2843-2857 (2003).
[CrossRef]

Phys. Rev. B (3)

A. V. Goncharenko, J. K. Wang, and Y. C. Chang, "Electric Near-Field Enhancement of a Sharp Semi-Infinite Conical Probe: Material and Cone Angle Dependence," Phys. Rev. B 74, 235442 (2006).
[CrossRef]

R. Ossikovski, Q. Nguen, and G. Picardi, "Simple model for the polarization effects in tip-enhanced Raman Spectroscopy," Phys. Rev. B 75, 045412 (2007).
[CrossRef]

C. C. Neacsu, J. Dreyer, N. Behr, and M. B. Raschke, "Scanning-probe Raman Spectroscopy with single-molecule sensitivity," Phys. Rev. B 73, 193406 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

L. Novotny, R. X. Bean, and X. S. Xie, "Theory of Nanometric Optical Tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

O. J. F. Martin, C. Girard, and A. Dereux, "Generalized field propagator for Electromagnetic Scattering and Light Confinement," Phys. Rev. Lett. 74, 526-529 (1995).
[CrossRef] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. A (1)

See, e.g., M. A. Salem, A. H. Kamel, and A. V. Osipov, "Electromagnetic fields in the presence of an infinite dielectric wedge," Proc. R. Soc. A 462, 2503-2522 (2006).
[CrossRef]

Rev. Sci. Instrum. (3)

The "bowling" pin shape can be also of interest in its own right because such a geometry can be formed by sputter coating a standard dielectric probe with a metal, see, e.g., D. Hu, M. Micic, N. Klymyshyn, Y. D. Suh, and H. P. Lu, "Correlated Topographic and Spectroscopic Imaging beyond Diffraction limit by Atomic Force Microscopy Metallic Tip-Enhanced Near-Field Fluorescence Lifetime Microscopy," Rev. Sci. Instrum. 74, 3347-3355 (2003).
[CrossRef]

K. C. Neuman and S. M. Block, "Optical Trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

M. S. Anderson and W. T. Pike, "A Raman-Atomic Force Microscope for Apertureless-Near-Field Spectroscopy and Optical Trapping," Rev. Sci. Instrum. 73, 1198-1203 (2002).
[CrossRef]

Wave Motion (1)

M. Idemen, "Confluent Tip Singularity of the Electromagnetic Field at the Apex of a Material Cone," Wave Motion 38, 251-277 (2003).
[CrossRef]

Other (5)

C.A. Balanis, Antenna Theory. Analysis and Design (Wiley, New York, 1997).

Our numerical simulations show that this statement is also valid for ν>0.

See L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Wiley, 1994) and references therein.
[CrossRef]

J. J. Bowman, The Cone, in Electromagnetic and Acoustic Scattering by Simple Shapes, J. J. Bowman, T. B. A. Senior, P. L. E. Uslenghi, eds., (Hemisphere, New York, 1987).

See, e.g., H. Bateman and A. Erdelyi, Higher Transcendental Functions, (McGraw-Hill, 1985) Vol. 1.

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Figures (5)

Fig. 1.
Fig. 1.

Two schemes of illumination of a conical probe: side illumination (a) and total internal reflection illumination (b).

Fig. 2.
Fig. 2.

Equipotential surfaces for the “bowling” pin geometry.

Fig. 3.
Fig. 3.

Absolute value of the associated Legendre function P 1ν(cosθ 0) vs the incident angle θ i.

Fig. 4.
Fig. 4.

Dependence of the incident angle θi at which P 1 ν(cosθ 0) peaks vs the parameter ν.

Fig. 5.
Fig. 5.

Electric near field enhancement for a silver (solid lines) and silicon (dashed lines) conical probe at the point r=5 nm, θ=0° vs the beam waist radius.

Equations (22)

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U = 2 i k m = 0 Λ m ν s exp ( i ν s π 2 ) j ν s ( k r ) P ν s m ( cos θ ) { ν s ( ν s + 1 ) 0 π α [ P ν s m ( cos α ) ] 2 sin α d α } 1
× [ m sin m ( φ φ 0 ) cos β ( sin θ 0 ) 1 P ν s m ( cos θ 0 ) + cos m ( φ φ 0 ) sin β θ 0 P ν s m ( cos θ 0 ) ]
V = 2 i η k m = 0 Λ m μ s exp ( i μ s π 2 ) j μ s ( k r ) P μ s m ( cos θ ) { μ s ( μ s + 1 ) 0 π α [ P μ s m ( cos α ) ] 2 sin α d α } 1
× [ m cos m ( φ φ 0 ) cos β θ 0 P μ s m ( cos θ 0 ) m sin m ( φ φ 0 ) sin β ( sin θ 0 ) 1 P μ s m ( cos θ 0 ) ] ,
E ( r , θ ) = r ̂ E r + θ ̂ E θ E 0 C ( k r ) ν 1 P ν 1 ( cos θ 0 ) cos β [ r ̂ + θ ̂ ν θ ] P ν ( cos θ )
ε 1 P ν + 1 ( cos α ) P ν ( cos α ) + ε 2 P ν + 1 ( cos α ) P ν ( cos α ) + ( ε 1 ε 2 ) cos α = 0 .
P ν 1 ( cos θ ) = 1 2 ν ( ν + 1 ) sin θ · 2 F 1 ( 2 + ν , 1 ν ; 2 ; 1 cos θ 2 )
E ( r , θ ) E 0 C ( k r ) ν 1 [ 1 + ν + 1 ν B ( r , r 0 ) ] P ν 1 ( cos θ 0 ) [ r ̂ + θ ̂ ν θ 1 B ( r , r 0 ) 1 + ν + 1 ν B ( r , r 0 ) ] P ν ( cos θ )
ψ 1 ( r , θ ) = ψ 0 ( k r ) ν [ 1 S ( r 0 r ) 2 ν + 1 ] P ν ( cos θ ) .
E i ( x ' , y ' , z ' ) E 0 exp [ ( x ' + y ' ) 2 w 0 2 ] exp ( i k z ' )
A i ( p , q ) = k 2 d x ' d y ' E i ( x ' , y ' , 0 ) exp [ i k ( p x ' + q y ' ) ] = 2 π f 2 exp ( p 2 + q 2 4 f 2 ) ,
E nf ( x ' , y ' , z ' ) = E 0 2 π f 2 π 2 π 2 exp ( 1 4 w 0 2 k 2 sin 2 θ ' ) exp ( i k z ' cos θ ' ) sin θ ' cos θ ' d θ '
0 2 π E ( α , θ 0 , θ ' , φ ' ) exp [ i k ( x ' sin θ ' cos φ ' + y ' sin θ ' sin φ ' ) ] d φ ' ,
E i ( x ' , z ' ) = E 0 k w 0 2 π π 2 π 2 exp ( 1 4 w 0 2 k 2 sin 2 θ ' ) exp [ i k ( x ' sin θ ' + z ' cos θ ' ) ] cos θ ' d θ ' .
E nf ( x ' , z ' ) = E 0 k w 0 2 π π 2 π 2 E ( α , θ 0 θ ' ) exp ( 1 4 w 0 2 k 2 sin 2 θ ' ) exp [ i k ( x ' sin θ ' + z ' cos θ ' ) ] cos θ ' d θ ' .
x ' = ( x s x ) cos θ i + ( z s z ) sin θ i , z ' = ( x s x ) sin θ i ( z s z ) cos θ i .
θ n = cos 1 ( 1 λ 2 l m n ) ,
E z ( r ) = i 4 π ω ε [ 0 I I ( z ' ) ( z ' 2 + k 2 ) G ( r r ' ) d z ' ] ,
E ρ ( r ) = i 4 π ω ε [ 0 I I ( z ' ) ρ ' z ' G ( r r ' ) d z ' ] ,
E ( r ' ) E 0 exp ( i k z z ' ) = E 0 [ cos ( k z ' cos θ i ) + i sin ( k z ' cos θ i ) ] = E 0 Φ ( z ' )
E z ( r ) = E 0 z ( r ) + K V d r ' [ G xz ( r , r ' ) E 0 x ( r ' ) + G yz ( r , r ' ) E 0 y ( r ' ) + G zz ( r , r ' ) E 0 z ( r ' ) ] = E 0 ( r ) sin θ 0
× [ 1 + K V d r ' Φ ( z ' ) G zz ( r , r ' ) ] + E 0 ( r ) cos θ 0 K V d r ' Φ ( z ' ) [ sin φ 0 G zx ( r , r ' ) + cos φ 0 G zy ( r , r ) ] ,

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