Abstract

To address the large number of parameters involved in nano-optical problems, a more efficient computational method is necessary. An integral equation based numerical solution is developed when the particles are illuminated with collimated and focused incident beams. The solution procedure uses the method of weighted residuals, in which the integral equation is reduced to a matrix equation and then solved for the unknown electric field distribution. In the solution procedure, the effects of the surrounding medium and boundaries are taken into account using a Green’s function formulation. Therefore, there is no additional error due to artificial boundary conditions unlike differential equation based techniques, such as finite difference time domain and finite element method. In this formulation, only the scattering nano-particle is discretized. Such an approach results in a lesser number of unknowns in the resulting matrix equation. The results are compared to the analytical Mie series solution for spherical particles, as well as to the finite element method for rectangular metallic particles. The Richards-Wolf vector field equations are combined with the integral equation based formulation to model the interaction of nanoparticles with linearly and radially polarized incident focused beams.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. T. W. McDaniel, W. A. Challener, and K. Sendur, "Issues in heat-assisted perpendicular recording," IEEE Trans. Magn. 39, 1972-1979 (2003).
    [CrossRef]
  4. K. Sendur, W. Challener, and C. Peng, "Ridge waveguide as a near field aperture for high density data storage," J. Appl. Phys. 96, 2743-2752 (2004).
    [CrossRef]
  5. D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution ?/20," Appl. Phys. Lett. 44, 651-653 (1984).
    [CrossRef]
  6. A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 ? spatial resolution light microscope," Ultramicroscopy 13, 227-231 (1984).
    [CrossRef]
  7. A. Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novonty, "High-resolution near-field Raman microscopy of single-walled carbon nanotubes," Phys. Rev. Lett. 90, 095503 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  18. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Dramatic localized electromagnetic enhancement in plasmon resonant nanowires," Chem. Phys. Lett. 341, 1-6 (2001).
    [CrossRef]
  19. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 27 (2000).
    [CrossRef]
  20. J. Jung and T. Sondergaard, "Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface," Phys. Rev. B 77, 245310 (2008).
    [CrossRef]
  21. J. H. Richmond, "Digital computer solutions of the rigorous equations for scattering problems," Proc. IEEE 53, 796-804 (1965).
    [CrossRef]
  22. R. F. Harrington, "Matrix methods for field problems," Proc. IEEE 55, 136-149 (1967).
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  23. R. F. Harrington, Field Computation by Moment Methods, (IEEE Press, New York, NY, 1993).
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    [CrossRef]
  27. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag. 30, 409-418 (1982).
    [CrossRef]
  28. D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag. 33, 276-281 (1984).
    [CrossRef]
  29. All the FEM calculations in this report are performed with High Frequency Structure Simulator (HFSSTM) from Ansoft Inc.
  30. Q2. E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field," Philos. Trans. R. Soc. London Ser. A 253, 349-357 (1959).
  31. Q3. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Philos. Trans. R. Soc. London Ser. A 253, 358-379 (1959).

2008 (3)

L. Wang and X. Xu, "Numerical study of optical nanolithography using nanoscale bow-tie-shaped nano-apertures," J. Microsc. 229, 483-489 (2008).
[CrossRef] [PubMed]

J. Jung and T. Sondergaard, "Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface," Phys. Rev. B 77, 245310 (2008).
[CrossRef]

T. Yamaguchi, "Finite-difference time-domain analysis of hemi-teardrop-shaped near-field optical probe," Electron. Lett. 44, 4455427 (2008).
[CrossRef]

2007 (1)

2006 (1)

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

2005 (3)

2004 (1)

K. Sendur, W. Challener, and C. Peng, "Ridge waveguide as a near field aperture for high density data storage," J. Appl. Phys. 96, 2743-2752 (2004).
[CrossRef]

2003 (3)

T. W. McDaniel, W. A. Challener, and K. Sendur, "Issues in heat-assisted perpendicular recording," IEEE Trans. Magn. 39, 1972-1979 (2003).
[CrossRef]

A. Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novonty, "High-resolution near-field Raman microscopy of single-walled carbon nanotubes," Phys. Rev. Lett. 90, 095503 (2003).
[CrossRef] [PubMed]

W. A. Challener, I. K. Sendur, and C. Peng, "Scattered field formulation of finite difference time domain for a focused light beam in a dense media with lossy materials," Opt. Express 11, 3160-3170 (2003).
[CrossRef] [PubMed]

2002 (1)

J. T. II Krug, E. J. Sánchez, and X. S. Xie, "Design of near-field probes with optimal field enhancement by finite difference time domain electromagnetic simulation," J. Chem. Phys. 116, 10895 (2002).
[CrossRef]

2001 (2)

J. P. Kottmann and O. J. F. Martin, "Plasmon resonant coupling in metallic nanowires," Opt. Express 8, 655-663 (2001).
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Dramatic localized electromagnetic enhancement in plasmon resonant nanowires," Chem. Phys. Lett. 341, 1-6 (2001).
[CrossRef]

2000 (2)

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 27 (2000).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, "Accurate Solution of the Volume Integral Equation for High-Permittivity Scatterers," IEEE Trans. Antennas Propag. 48, 1719-1726 (2000).
[CrossRef]

1984 (3)

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution ?/20," Appl. Phys. Lett. 44, 651-653 (1984).
[CrossRef]

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 ? spatial resolution light microscope," Ultramicroscopy 13, 227-231 (1984).
[CrossRef]

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag. 33, 276-281 (1984).
[CrossRef]

1983 (1)

B. Liedberg, C. Nylander, I. Lundstroem, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

1982 (2)

A. W. Glisson and D. R. Wilton, "Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces," IEEE Trans. Antennas Propag. 28, 593-603 (1982).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag. 30, 409-418 (1982).
[CrossRef]

1967 (1)

R. F. Harrington, "Matrix methods for field problems," Proc. IEEE 55, 136-149 (1967).
[CrossRef]

1965 (1)

J. H. Richmond, "Digital computer solutions of the rigorous equations for scattering problems," Proc. IEEE 53, 796-804 (1965).
[CrossRef]

1959 (2)

Q2. E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field," Philos. Trans. R. Soc. London Ser. A 253, 349-357 (1959).

Q3. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Philos. Trans. R. Soc. London Ser. A 253, 358-379 (1959).

Al-Bundak, O. M.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag. 33, 276-281 (1984).
[CrossRef]

Barchiesi, D.

Batra, S.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Buechel, D.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Butler, C. M.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag. 33, 276-281 (1984).
[CrossRef]

Challener, W.

K. Sendur, W. Challener, and C. Peng, "Ridge waveguide as a near field aperture for high density data storage," J. Appl. Phys. 96, 2743-2752 (2004).
[CrossRef]

Challener, W. A.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

T. W. McDaniel, W. A. Challener, and K. Sendur, "Issues in heat-assisted perpendicular recording," IEEE Trans. Magn. 39, 1972-1979 (2003).
[CrossRef]

W. A. Challener, I. K. Sendur, and C. Peng, "Scattered field formulation of finite difference time domain for a focused light beam in a dense media with lossy materials," Opt. Express 11, 3160-3170 (2003).
[CrossRef] [PubMed]

Denk, W.

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution ?/20," Appl. Phys. Lett. 44, 651-653 (1984).
[CrossRef]

Glisson, A. W.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag. 33, 276-281 (1984).
[CrossRef]

A. W. Glisson and D. R. Wilton, "Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces," IEEE Trans. Antennas Propag. 28, 593-603 (1982).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag. 30, 409-418 (1982).
[CrossRef]

Grosges, T.

Harootunian, A.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 ? spatial resolution light microscope," Ultramicroscopy 13, 227-231 (1984).
[CrossRef]

Harrington, R. F.

R. F. Harrington, "Matrix methods for field problems," Proc. IEEE 55, 136-149 (1967).
[CrossRef]

Hartschuh, A.

A. Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novonty, "High-resolution near-field Raman microscopy of single-walled carbon nanotubes," Phys. Rev. Lett. 90, 095503 (2003).
[CrossRef] [PubMed]

He, S.

Hinata, T.

Hohlfeld, J.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Isaacson, M.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 ? spatial resolution light microscope," Ultramicroscopy 13, 227-231 (1984).
[CrossRef]

Jung, J.

J. Jung and T. Sondergaard, "Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface," Phys. Rev. B 77, 245310 (2008).
[CrossRef]

Kottmann, J. P.

J. P. Kottmann and O. J. F. Martin, "Plasmon resonant coupling in metallic nanowires," Opt. Express 8, 655-663 (2001).
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Dramatic localized electromagnetic enhancement in plasmon resonant nanowires," Chem. Phys. Lett. 341, 1-6 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 27 (2000).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, "Accurate Solution of the Volume Integral Equation for High-Permittivity Scatterers," IEEE Trans. Antennas Propag. 48, 1719-1726 (2000).
[CrossRef]

Kubota, Y.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Lanz, M.

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution ?/20," Appl. Phys. Lett. 44, 651-653 (1984).
[CrossRef]

Lewis, A.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 ? spatial resolution light microscope," Ultramicroscopy 13, 227-231 (1984).
[CrossRef]

Li, L.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Liedberg, B.

B. Liedberg, C. Nylander, I. Lundstroem, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Liu, L.

Lu, B.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Lundstroem, I.

B. Liedberg, C. Nylander, I. Lundstroem, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Martin, O. J. F.

J. P. Kottmann and O. J. F. Martin, "Plasmon resonant coupling in metallic nanowires," Opt. Express 8, 655-663 (2001).
[CrossRef] [PubMed]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Dramatic localized electromagnetic enhancement in plasmon resonant nanowires," Chem. Phys. Lett. 341, 1-6 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 27 (2000).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, "Accurate Solution of the Volume Integral Equation for High-Permittivity Scatterers," IEEE Trans. Antennas Propag. 48, 1719-1726 (2000).
[CrossRef]

McDaniel, T. W.

T. W. McDaniel, W. A. Challener, and K. Sendur, "Issues in heat-assisted perpendicular recording," IEEE Trans. Magn. 39, 1972-1979 (2003).
[CrossRef]

Mihalcea, C.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Milster, T. D.

T. D. Milster, "Horizons for optical data storage," Opt. Photonics News 16, 28-32 (2005).
[CrossRef]

Mountfield, K.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Muray, A.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 ? spatial resolution light microscope," Ultramicroscopy 13, 227-231 (1984).
[CrossRef]

Novonty, L.

A. Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novonty, "High-resolution near-field Raman microscopy of single-walled carbon nanotubes," Phys. Rev. Lett. 90, 095503 (2003).
[CrossRef] [PubMed]

Nylander, C.

B. Liedberg, C. Nylander, I. Lundstroem, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Pelhos, K.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Peng, C.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

K. Sendur, W. Challener, and C. Peng, "Ridge waveguide as a near field aperture for high density data storage," J. Appl. Phys. 96, 2743-2752 (2004).
[CrossRef]

W. A. Challener, I. K. Sendur, and C. Peng, "Scattered field formulation of finite difference time domain for a focused light beam in a dense media with lossy materials," Opt. Express 11, 3160-3170 (2003).
[CrossRef] [PubMed]

Pohl, D. W.

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution ?/20," Appl. Phys. Lett. 44, 651-653 (1984).
[CrossRef]

Rao, S. M.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag. 33, 276-281 (1984).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag. 30, 409-418 (1982).
[CrossRef]

Rausch, T.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Richards, B.

Q3. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Philos. Trans. R. Soc. London Ser. A 253, 358-379 (1959).

Richmond, J. H.

J. H. Richmond, "Digital computer solutions of the rigorous equations for scattering problems," Proc. IEEE 53, 796-804 (1965).
[CrossRef]

Rottmayer, R. E.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Sanchez, E. J.

A. Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novonty, "High-resolution near-field Raman microscopy of single-walled carbon nanotubes," Phys. Rev. Lett. 90, 095503 (2003).
[CrossRef] [PubMed]

Schaubert, D. H.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag. 33, 276-281 (1984).
[CrossRef]

Schultz, S.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Dramatic localized electromagnetic enhancement in plasmon resonant nanowires," Chem. Phys. Lett. 341, 1-6 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 27 (2000).
[CrossRef]

Seigler, M. A.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Sendur, I. K.

Sendur, K.

K. Sendur, W. Challener, and C. Peng, "Ridge waveguide as a near field aperture for high density data storage," J. Appl. Phys. 96, 2743-2752 (2004).
[CrossRef]

T. W. McDaniel, W. A. Challener, and K. Sendur, "Issues in heat-assisted perpendicular recording," IEEE Trans. Magn. 39, 1972-1979 (2003).
[CrossRef]

Smith, D. R.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Dramatic localized electromagnetic enhancement in plasmon resonant nanowires," Chem. Phys. Lett. 341, 1-6 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 27 (2000).
[CrossRef]

Sondergaard, T.

J. Jung and T. Sondergaard, "Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface," Phys. Rev. B 77, 245310 (2008).
[CrossRef]

Vial, A.

Wang, L.

L. Wang and X. Xu, "Numerical study of optical nanolithography using nanoscale bow-tie-shaped nano-apertures," J. Microsc. 229, 483-489 (2008).
[CrossRef] [PubMed]

Weller, D.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Wilton, D. R.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag. 33, 276-281 (1984).
[CrossRef]

A. W. Glisson and D. R. Wilton, "Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces," IEEE Trans. Antennas Propag. 28, 593-603 (1982).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag. 30, 409-418 (1982).
[CrossRef]

Wolf, E.

Q3. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Philos. Trans. R. Soc. London Ser. A 253, 358-379 (1959).

Q2. E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field," Philos. Trans. R. Soc. London Ser. A 253, 349-357 (1959).

Xie, X. S.

A. Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novonty, "High-resolution near-field Raman microscopy of single-walled carbon nanotubes," Phys. Rev. Lett. 90, 095503 (2003).
[CrossRef] [PubMed]

Xu, X.

L. Wang and X. Xu, "Numerical study of optical nanolithography using nanoscale bow-tie-shaped nano-apertures," J. Microsc. 229, 483-489 (2008).
[CrossRef] [PubMed]

Yamaguchi, T.

T. Yamaguchi, "Finite-difference time-domain analysis of hemi-teardrop-shaped near-field optical probe," Electron. Lett. 44, 4455427 (2008).
[CrossRef]

T. Yamaguchi and T. Hinata, "Optical near-field analysis of spherical metals: Application of the FDTD method combined with the ADE method," Opt. Express 15, 11481-11491 (2007).
[CrossRef] [PubMed]

Yang, X.

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. W. Pohl, W. Denk, and M. Lanz, "Optical stethoscopy: image recording with resolution ?/20," Appl. Phys. Lett. 44, 651-653 (1984).
[CrossRef]

Chem. Phys. Lett. (1)

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Dramatic localized electromagnetic enhancement in plasmon resonant nanowires," Chem. Phys. Lett. 341, 1-6 (2001).
[CrossRef]

Electron. Lett. (1)

T. Yamaguchi, "Finite-difference time-domain analysis of hemi-teardrop-shaped near-field optical probe," Electron. Lett. 44, 4455427 (2008).
[CrossRef]

IEEE Trans. Antennas Propag. (4)

A. W. Glisson and D. R. Wilton, "Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces," IEEE Trans. Antennas Propag. 28, 593-603 (1982).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag. 30, 409-418 (1982).
[CrossRef]

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag. 33, 276-281 (1984).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, "Accurate Solution of the Volume Integral Equation for High-Permittivity Scatterers," IEEE Trans. Antennas Propag. 48, 1719-1726 (2000).
[CrossRef]

IEEE Trans. Magn. (2)

R. E. Rottmayer, S. Batra, D. Buechel, W. A. Challener, J. Hohlfeld, Y. Kubota, L. Li, B. Lu, C. Mihalcea, K. Mountfield, K. Pelhos, C. Peng, T. Rausch, M. A. Seigler, D. Weller, and X. Yang, "Heat-assisted magnetic recording," IEEE Trans. Magn. 42, 2417-2421 (2006).
[CrossRef]

T. W. McDaniel, W. A. Challener, and K. Sendur, "Issues in heat-assisted perpendicular recording," IEEE Trans. Magn. 39, 1972-1979 (2003).
[CrossRef]

J. Appl. Phys. (1)

K. Sendur, W. Challener, and C. Peng, "Ridge waveguide as a near field aperture for high density data storage," J. Appl. Phys. 96, 2743-2752 (2004).
[CrossRef]

J. Chem. Phys. (1)

J. T. II Krug, E. J. Sánchez, and X. S. Xie, "Design of near-field probes with optimal field enhancement by finite difference time domain electromagnetic simulation," J. Chem. Phys. 116, 10895 (2002).
[CrossRef]

J. Microsc. (1)

L. Wang and X. Xu, "Numerical study of optical nanolithography using nanoscale bow-tie-shaped nano-apertures," J. Microsc. 229, 483-489 (2008).
[CrossRef] [PubMed]

New J. Phys. (1)

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 27 (2000).
[CrossRef]

Opt. Express (4)

Opt. Photonics News (1)

T. D. Milster, "Horizons for optical data storage," Opt. Photonics News 16, 28-32 (2005).
[CrossRef]

Philos. Trans. R. Soc. London Ser. A (2)

Q2. E. Wolf, "Electromagnetic diffraction in optical systems I. An integral representation of the image field," Philos. Trans. R. Soc. London Ser. A 253, 349-357 (1959).

Q3. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Philos. Trans. R. Soc. London Ser. A 253, 358-379 (1959).

Phys. Rev. B (1)

J. Jung and T. Sondergaard, "Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface," Phys. Rev. B 77, 245310 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

A. Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novonty, "High-resolution near-field Raman microscopy of single-walled carbon nanotubes," Phys. Rev. Lett. 90, 095503 (2003).
[CrossRef] [PubMed]

Proc. IEEE (2)

J. H. Richmond, "Digital computer solutions of the rigorous equations for scattering problems," Proc. IEEE 53, 796-804 (1965).
[CrossRef]

R. F. Harrington, "Matrix methods for field problems," Proc. IEEE 55, 136-149 (1967).
[CrossRef]

Sens. Actuators (1)

B. Liedberg, C. Nylander, I. Lundstroem, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators 4, 299-304 (1983).
[CrossRef]

Ultramicroscopy (1)

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500 ? spatial resolution light microscope," Ultramicroscopy 13, 227-231 (1984).
[CrossRef]

Other (4)

R. F. Harrington, Field Computation by Moment Methods, (IEEE Press, New York, NY, 1993).
[CrossRef]

E. K. Miller, L. Medgyesi-Mitschang, and E. H. Newman, Eds., Computational Electromagnetics (IEEE Press, New York, NY, 1992).

R. C. Hansen, ed., Moment Methods in Antennas and Scattering, (Artech, Boston, MA, 1990).

All the FEM calculations in this report are performed with High Frequency Structure Simulator (HFSSTM) from Ansoft Inc.

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Figures (9)

Fig. 1.
Fig. 1.

Example surface triangulation of (a) a sphere with a radius of R=350 nm and (b) a cube with a side length of L=200 nm. Triangulations are performed in Fortran and visualization performed via Matlab.

Fig. 2.
Fig. 2.

To discretize the induced current, triangular rooftop basis functions are used.

Fig. 3.
Fig. 3.

A comparison of the MWR results with the Mie series solution for the RCS of a conducting sphere with a radius of 140 nm. The operating wavelength is 700 nm. θ and ϕ components of the radar cross section are plotted on various cuts: (a) RCSθ as a function of ϕ on θ=90° cut, (b) RCSθ as a function of θ on ϕ=0° cut, (c) RCSϕ as a function of ϕ on θ=90° cut, and (d) RCSϕ as a function of θ on ϕ=90° cut.

Fig. 4.
Fig. 4.

Percent relative error of MWR results in Fig. 3 compared to the Mie series solution for : (a) RCSθ on θ=90° cut, (b) RCSθ on ϕ=0° cut, (c) RCSϕ on θ=90° cut, and (d) RCSϕ on ϕ=90° cut.

Fig. 5.
Fig. 5.

A comparison of the MWR results with the Mie series solution for the RCS of a conducting sphere with a radius of 350 nm. The operating wavelength is 700 nm. θ and ϕ components of the radar cross section are plotted on various cuts: (a) RCSθ as a function of ϕ on θ=90° cut, (b) RCSθ as a function of θ on ϕ=0° cut, (c) RCSϕ as a function of ϕ on θ=90° cut, and (d) RCSϕ as a function of θ on ϕ=0° cut.

Fig. 6.
Fig. 6.

Percent relative error of MWR results in Fig. 5 compared to the Mie series solution for : (a) RCSθ on θ=90° cut, (b) RCSθ on ϕ=0° cut, (c) RCSϕ on θ=90° cut, and (d) RCSϕ on ϕ=90° cut.

Fig. 7.
Fig. 7.

A comparison of the FEM and MWR results for the radar cross section of a conducting cube with a side length of 200 nm. The operating wavelength for the incident beam is 700 nm. θ component of the radar cross section is plotted on various ϕ cuts: (a) RCSθ as a function of θ on ϕ=0° cut, (b) RCSθ as a function of θ on ϕ=90° cut.

Fig. 8.
Fig. 8.

Electric field components when a linearly polarized focused beam of light interacts with spheres of various sizes. The linearly polarized focused beam is obtained from an optical lens system with a numerical aperture of 0.85. The operating frequency is 700 nm.

Fig. 9.
Fig. 9.

Electric field components when a radially polarized focused beam of light interacts with spheres of various sizes. The radially polarized focused beam is obtained from an optical lens system with a numerical aperture of 0.85. The operating frequency is 700 nm.

Equations (22)

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E tot ( r ) = E inc ( r ) + E scat ( r )
E scat ( r ) = iωμ 4 π S′ dS′ G ( r , r ) · J ( r )
G ( r , r ) = [ I + k 2 ] e ik r r r r
E inc tng ( r ) = t ̂ · iωμ 4 π S′ dS′ [ I + k 2 ] e ik r r r r · J ( r )
J ( r ) j = 1 N I j b j ( r )
b n ( r ) = { l n 2 A n + ρ n + ; r T n + l n 2 A n ρ n ; r T n 0 ; otherwise
E inc tng ( r ) j = 1 N I j { t ̂ · iωμ 4 π S′ dS′ [ I + k 2 ] e ik r r r r · b j ( r ) }
( r ) = E inc tng ( r ) + j = 1 N I j { t ̂ · iωμ 4 π S′ dS′ [ I + k 2 ] e ik r r r r · b j ( r ) }
( r ) , ω i ( r ) = Ω ( r ) · ω i ( r ) d r = 0
Z · I ¯ = V ¯
Z i , j = iωμ 4 π [ S dS w i ( r ) · S′ dS e ik r r r r b j ( r ) + S dS w i ( r ) · k 2 · S′ dS′ e ik r r r r b j ( r ) ]
V i = S dS w i ( r ) · E inc ( r )
S dS w i ( r ) · S′ dS e ik r r r r b j ( r ) = S dS w i ( r ) · ( S′ dS e ik r r 1 r r b j ( r ) + S′ dS 1 r r b j ( r ) )
S dS w i ( r ) · k 2 S′ dS e ik r r r r b j ( r ) = S dS ( · w i ( r ) ) S′ dS e ik r r r r ( · b j ( r ) )
E inc = x ̂ e ikz
RCS = lim r 4 π r 2 E s 2 E i 2
r r r r ̂ · r
E scat FF iωμ 4 π e ikr r S′ J ( r ) e ik r ̂ · r dS′
E scat FF iωμ 4 π e ikr r n = 1 N α n S′ b n ( r ) e ik r ̂ · r dS′
E inc ( r ) = i λ 0 α sin θ 0 2 π a ( θ , ϕ ) e i k · r
a ( θ , ϕ ) = [ cos θ cos θ cos 2 ϕ + sin 2 ϕ cos ϕ sin ϕ cos ϕ sin ϕ sin θ cos ϕ ] cos θ
a ( θ , ϕ ) = [ cos θ cos ϕ cos θ sin ϕ sin θ ] cos θ

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