Surface waves and atomic force microscope probe-particle near-field coupling: discrete dipole approximation with surface interaction
JOSA A, Vol. 27, Issue 10, pp. 2293-2303 (2010)
http://dx.doi.org/10.1364/JOSAA.27.002293
Acrobat PDF (468 KB)
Abstract
Evanescent waves on a surface form due to the collective motion of charges within the medium. They do not carry any energy away from the surface and decay exponentially as a function of the distance. However, if there is any object within the evanescent field, electromagnetic energy within the medium is tunneled away and either absorbed or scattered. In this case, the absorption is localized, and potentially it can be used for selective diagnosis or nanopatterning applications. On the other hand, scattering of evanescent waves can be employed for characterization of nanoscale structures and particles on the surface. In this paper we present a numerical methodology to study the physics of such absorption and scattering mechanisms. We developed a MATLAB implementation of discrete dipole approximation with surface interaction (DDA-SI) in combination with evanescent wave illumination to investigate the near-field coupling between particles on the surface and a probe. This method can be used to explore the effects of a number of physical, geometrical, and material properties for problems involving nanostructures on or in the proximity of a substrate under arbitrary illumination.
© 2010 Optical Society of America
1. INTRODUCTION
1. E. A. Hawes, J. T. Hastings, C. Crofcheck, and M. P. Mengüç, “Spatially selective melting and evaporation of nanosized gold particles,” Opt. Lett. 33, 1383–1385 (2008). [CrossRef] [PubMed]
2. E. Purcell and C. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973). [CrossRef]
3. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
4. M. A. Taubenblatt and T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993). [CrossRef]
5. R. Schmehl, B. M. Nebeker, and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A 14, 3026–3036 (1997). [CrossRef]
6. G. H. Yuan, P. Wang, Y. H. Lu, Y. Cao, D. G. Zhang, H. Ming, and W. D. Xu, “A large-area photolithography technique based on surface plasmons leakage modes,” Opt. Commun. 281, 2680–2684 (2008). [CrossRef]
7. R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, “Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method,” Opt. Commun. 221, 13–22 (2003). [CrossRef]
2. DDA FORMALISM
3. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
3. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
2. E. Purcell and C. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973). [CrossRef]
9. B. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]
10. H. Kimura, “Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transf. 70, 581–594 (2001). [CrossRef]
3. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
3. DDA-SI FORMALISM
14. E. K. Burke and G. J. Miller, “Modeling antennas near to and penetrating a lossy interface,” IEEE Trans. Antennas Propag. AP-32, 1040–1049 (1984). [CrossRef]
3. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
4. EVANESCENT FIELD
19. S. Tojo and M. Hasuo, “Oscillator-strength enhancement of electric-dipole-forbidden transitions in evanescent light at total reflection,” Phys. Rev. A 71, 012508 (2005). [CrossRef]
5. SCATTERED FAR FIELD
5. R. Schmehl, B. M. Nebeker, and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A 14, 3026–3036 (1997). [CrossRef]
3. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
20. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965). [CrossRef]
22. D. W. Mackowski, “Discrete dipole moment method for calculation of the T-matrix for nonspherical particles,” J. Opt. Soc. Am. A 19, 881–893 (2002). [CrossRef]
23. V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete-dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009). [CrossRef]
24. D. A. Schultz, “Plasmon resonant particles for biological detection,” Curr. Opin. Biotechnol. 14, 13–22 (2003). [CrossRef] [PubMed]
6. BENCHMARKING
4. M. A. Taubenblatt and T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993). [CrossRef]
7. AFM PROBE MODEL RESULTS AND DISCUSSION
26. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
28. L. N. Aksyutov, “Temperature dependence of the optical constants of tungsten and gold,” J. Appl. Spectrosc. 26, 656–660 (1977). [CrossRef]
29. B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006). [CrossRef]
30. H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008). [CrossRef] [PubMed]
23. V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete-dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009). [CrossRef]
8. CONCLUSION
32. H. Zhang and E. D. Hirleman, “Prediction of light scattering from particles on a filmed surface using discrete-dipole approximation,” Proc. SPIE 4692, 38–45 (2002). [CrossRef]
33. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996). [CrossRef]
34. A. G. Hoekstra, M. Frijlink, L. B. F. M. Waters, and P. M. A. Sloot, “Radiation forces in the discrete-dipole approximation,” J. Opt. Soc. Am. A 18, 1944–1953 (2001). [CrossRef]
23. V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete-dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009). [CrossRef]
35. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196–S203 (2007). [CrossRef]
ACKNOWLEDGMENTS
1. | E. A. Hawes, J. T. Hastings, C. Crofcheck, and M. P. Mengüç, “Spatially selective melting and evaporation of nanosized gold particles,” Opt. Lett. 33, 1383–1385 (2008). [CrossRef] [PubMed] |
2. | E. Purcell and C. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973). [CrossRef] |
3. | B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef] |
4. | M. A. Taubenblatt and T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993). [CrossRef] |
5. | R. Schmehl, B. M. Nebeker, and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A 14, 3026–3036 (1997). [CrossRef] |
6. | G. H. Yuan, P. Wang, Y. H. Lu, Y. Cao, D. G. Zhang, H. Ming, and W. D. Xu, “A large-area photolithography technique based on surface plasmons leakage modes,” Opt. Commun. 281, 2680–2684 (2008). [CrossRef] |
7. | R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, “Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method,” Opt. Commun. 221, 13–22 (2003). [CrossRef] |
8. | J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998). |
9. | B. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef] |
10. | H. Kimura, “Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transf. 70, 581–594 (2001). [CrossRef] |
11. | A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–737 (1909). |
12. | W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990). |
13. | A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, 1966). |
14. | E. K. Burke and G. J. Miller, “Modeling antennas near to and penetrating a lossy interface,” IEEE Trans. Antennas Propag. AP-32, 1040–1049 (1984). [CrossRef] |
15. | G. J. Burke and A. J. Poggio, Numerical Electromagnetics Code (NEC-4)—Method of Moments, Part I: Program Description—Theory, Tech. Rep. UCID-18834 (Lawrence Livermore Laboratory, 1981). |
16. | R. J. Lytle and D. L. Lager, Numerical Evaluation of Sommerfeld Integrals, Tech. Rep. UCRL-51688 (Lawrence Livermore Laboratory, 1974). |
17. | D. L. Lager and R. J. Lytle, Fotran Subroutines for the Numerical Evaluation of Sommerfeld Integrals Unter Anderem, Tech. Rep. UCRL-51821 (Lawrence Livermore Laboratory, 1975). |
18. | M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999). |
19. | S. Tojo and M. Hasuo, “Oscillator-strength enhancement of electric-dipole-forbidden transitions in evanescent light at total reflection,” Phys. Rev. A 71, 012508 (2005). [CrossRef] |
20. | P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965). [CrossRef] |
21. | M. I. Mischenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, 2000). |
22. | D. W. Mackowski, “Discrete dipole moment method for calculation of the T-matrix for nonspherical particles,” J. Opt. Soc. Am. A 19, 881–893 (2002). [CrossRef] |
23. | V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete-dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009). [CrossRef] |
24. | D. A. Schultz, “Plasmon resonant particles for biological detection,” Curr. Opin. Biotechnol. 14, 13–22 (2003). [CrossRef] [PubMed] |
25. | V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Modelling of high numerical aperture imaging of complex scatterers using T-matrix method,” in Proceedings of ELS XII Helsinki (2010), pp. 138–141. |
26. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef] |
27. | E. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985). |
28. | L. N. Aksyutov, “Temperature dependence of the optical constants of tungsten and gold,” J. Appl. Spectrosc. 26, 656–660 (1977). [CrossRef] |
29. | B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006). [CrossRef] |
30. | H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008). [CrossRef] [PubMed] |
31. | F. N. Dönmezer, M. P. Mengüç, and T. Okutucu, “Dependent absorption and scattering by interacting nanoparticles,” in Proceedings of the Sixth International Symposium on Radiative Transfer (2010). |
32. | H. Zhang and E. D. Hirleman, “Prediction of light scattering from particles on a filmed surface using discrete-dipole approximation,” Proc. SPIE 4692, 38–45 (2002). [CrossRef] |
33. | Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996). [CrossRef] |
34. | A. G. Hoekstra, M. Frijlink, L. B. F. M. Waters, and P. M. A. Sloot, “Radiation forces in the discrete-dipole approximation,” J. Opt. Soc. Am. A 18, 1944–1953 (2001). [CrossRef] |
35. | T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196–S203 (2007). [CrossRef] |
OCIS Codes
(240.0240) Optics at surfaces : Optics at surfaces
(050.1755) Diffraction and gratings : Computational electromagnetic methods
ToC Category:
Optics at Surfaces
History
Original Manuscript: June 25, 2010
Revised Manuscript: August 9, 2010
Manuscript Accepted: August 9, 2010
Published: September 28, 2010
Virtual Issues
Vol. 5, Iss. 14 Virtual Journal for Biomedical Optics
September 24, 2010 Spotlight on Optics
Citation
Vincent L. Y. Loke and M. Pinar Mengüç, "Surface waves and atomic force microscope probe-particle near-field coupling: discrete dipole approximation with surface interaction," J. Opt. Soc. Am. A 27, 2293-2303 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-10-2293
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References
- E. A. Hawes, J. T. Hastings, C. Crofcheck, and M. P. Mengüç, “Spatially selective melting and evaporation of nanosized gold particles,” Opt. Lett. 33, 1383–1385 (2008). [CrossRef] [PubMed]
- E. Purcell and C. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973). [CrossRef]
- B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
- M. A. Taubenblatt and T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993). [CrossRef]
- R. Schmehl, B. M. Nebeker, and E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A 14, 3026–3036 (1997). [CrossRef]
- G. H. Yuan, P. Wang, Y. H. Lu, Y. Cao, D. G. Zhang, H. Ming, and W. D. Xu, “A large-area photolithography technique based on surface plasmons leakage modes,” Opt. Commun. 281, 2680–2684 (2008). [CrossRef]
- R. Fikri, D. Barchiesi, F. H’Dhili, R. Bachelot, A. Vial, and P. Royer, “Modeling recent experiments of apertureless near-field optical microscopy using 2d finite element method,” Opt. Commun. 221, 13–22 (2003). [CrossRef]
- J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998).
- B. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]
- H. Kimura, “Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transf. 70, 581–594 (2001). [CrossRef]
- A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–737 (1909).
- W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990).
- A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, 1966).
- E. K. Burke and G. J. Miller, “Modeling antennas near to and penetrating a lossy interface,” IEEE Trans. Antennas Propag. AP-32, 1040–1049 (1984). [CrossRef]
- G. J. Burke and A. J. Poggio, Numerical Electromagnetics Code (NEC-4)—Method of Moments, Part I: Program Description—Theory, Tech. Rep. UCID-18834 (Lawrence Livermore Laboratory, 1981).
- R. J. Lytle and D. L. Lager, Numerical Evaluation of Sommerfeld Integrals, Tech. Rep. UCRL-51688 (Lawrence Livermore Laboratory, 1974).
- D. L. Lager and R. J. Lytle, Fotran Subroutines for the Numerical Evaluation of Sommerfeld Integrals Unter Anderem, Tech. Rep. UCRL-51821 (Lawrence Livermore Laboratory, 1975).
- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
- S. Tojo and M. Hasuo, “Oscillator-strength enhancement of electric-dipole-forbidden transitions in evanescent light at total reflection,” Phys. Rev. A 71, 012508 (2005). [CrossRef]
- P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965). [CrossRef]
- M. I. Mischenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, 2000).
- D. W. Mackowski, “Discrete dipole moment method for calculation of the T-matrix for nonspherical particles,” J. Opt. Soc. Am. A 19, 881–893 (2002). [CrossRef]
- V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete-dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009). [CrossRef]
- D. A. Schultz, “Plasmon resonant particles for biological detection,” Curr. Opin. Biotechnol. 14, 13–22 (2003). [CrossRef] [PubMed]
- V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Modelling of high numerical aperture imaging of complex scatterers using T-matrix method,” in Proceedings of ELS XII Helsinki (2010), pp. 138–141.
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]
- E.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).
- L. N. Aksyutov, “Temperature dependence of the optical constants of tungsten and gold,” J. Appl. Spectrosc. 26, 656–660 (1977). [CrossRef]
- B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, 62732J (2006). [CrossRef]
- H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008). [CrossRef] [PubMed]
- F. N. Dönmezer, M. P. Mengüç, and T. Okutucu, “Dependent absorption and scattering by interacting nanoparticles,” in Proceedings of the Sixth International Symposium on Radiative Transfer (2010).
- H. Zhang and E. D. Hirleman, “Prediction of light scattering from particles on a filmed surface using discrete-dipole approximation,” Proc. SPIE 4692, 38–45 (2002). [CrossRef]
- Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996). [CrossRef]
- A. G. Hoekstra, M. Frijlink, L. B. F. M. Waters, and P. M. A. Sloot, “Radiation forces in the discrete-dipole approximation,” J. Opt. Soc. Am. A 18, 1944–1953 (2001). [CrossRef]
- T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196–S203 (2007). [CrossRef]
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