Abstract

A numerical approach for the calculation of the internal dipole radiation associated with particles of arbitrary morphology is investigated by using the discrete-dipole approximation (DDA) method. The DDA and analytical solutions for the total radiated power and radiation pattern are compared in the case of spherical host particles. It is shown that the DDA can be quite accurate under the condition that m2, and mkd <0.5, where m is the refractive index of the host particle, k=2π/λ is the wavenumber in vacuum, and d is the distance between two adjacent dipoles in the DDA cubic dipole array. Furthermore, the DDA solutions for the dipole radiation patterns associated with nonspherical host particles are compared with their corresponding counterparts obtained from the finite-difference time-domain method. Excellent agreement between the two results is noted. The DDA method is also applied to the computation of the internal dipole radiation associated with simulated nonspherical sporelike particles. The results suggest that the internal dipole radiation patterns contain a great deal of information about the morphology and composition of the host particle.

© 2006 Optical Society of America

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References

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  1. H. Chew, P. J. McNulty, and M. Kerker, "Model for Raman and fluorescent scattering by molecules embedded in small particles," Phys. Rev. A 13, 396-404 (1976).
    [CrossRef]
  2. H. Chew, "Transition rates of atoms near spherical surfaces," J. Chem. Phys. 87, 1355-1360 (1987).
    [CrossRef]
  3. H. Chew, D. D. Cooke, and M. Kerker, "Raman and fluorescent scattering by molecules embedded in dielectric cylinders," Appl. Opt. 19, 44-52 (1980).
    [CrossRef] [PubMed]
  4. D. S. Wang, M. Kerker, and H. Chew, "Raman and fluorescent scattering by molecules embedded in dielectric spheroids," Appl. Opt. 19, 2315-2328 (1980).
    [CrossRef] [PubMed]
  5. H. Chew, "Radiation and lifetimes of atoms inside dielectric particles," Phys. Rev. A 38, 3410-3416 (1988).
    [CrossRef] [PubMed]
  6. N. Velesco and G. Schweiger, "Geometrical optics calculation of inelastic scattering on large particles," Appl. Opt. 38, 1046-1052 (1999).
    [CrossRef]
  7. N. Félidj, J. Aubard, and G. Lévi, "Discrete dipole approximation for ultraviolet-visible extinction spectra simulation of silver and gold colloids," J. Chem. Phys. 111, 1195-1208 (1999).
    [CrossRef]
  8. E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. H. A. Lorentz, The Theory of Electrons (Dover, 1952).
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    [CrossRef] [PubMed]
  17. F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A Lagendijk, "Local-field effects on spontaneous emission in a dense supercritical gas," Phys. Rev. Lett. 80, 5077-5080 (1998).
    [CrossRef]
  18. K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell's equations in istotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
  19. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  20. M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
    [CrossRef] [PubMed]
  21. R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
    [CrossRef]
  22. C. Li, G. W. Kattawar, and P. Yang, "Identification of aerosols by their backscattered Mueller images," Opt. Express 14, 3616-3621 (2006).
    [CrossRef] [PubMed]
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2006 (1)

2002 (1)

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

1999 (2)

N. Velesco and G. Schweiger, "Geometrical optics calculation of inelastic scattering on large particles," Appl. Opt. 38, 1046-1052 (1999).
[CrossRef]

N. Félidj, J. Aubard, and G. Lévi, "Discrete dipole approximation for ultraviolet-visible extinction spectra simulation of silver and gold colloids," J. Chem. Phys. 111, 1195-1208 (1999).
[CrossRef]

1998 (1)

F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A Lagendijk, "Local-field effects on spontaneous emission in a dense supercritical gas," Phys. Rev. Lett. 80, 5077-5080 (1998).
[CrossRef]

1995 (2)

R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
[CrossRef]

G. L. J. A. Rikken and Y. A. R. R. Kessener, "Local field effects and electric and magnetic dipole transitions in dielectrics," Phys. Rev. Lett. 74, 880-883 (1995).
[CrossRef] [PubMed]

1994 (1)

1991 (2)

J. Gersten and A. Nitzan, "Radiative properties of solvated molecules in dielectric clusters and small particles," J. Chem. Phys. 95, 686-699 (1991).
[CrossRef]

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, "Linear and nonlinear optical measurement of the Lorentz local field," Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

1988 (2)

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

H. Chew, "Radiation and lifetimes of atoms inside dielectric particles," Phys. Rev. A 38, 3410-3416 (1988).
[CrossRef] [PubMed]

1987 (1)

H. Chew, "Transition rates of atoms near spherical surfaces," J. Chem. Phys. 87, 1355-1360 (1987).
[CrossRef]

1980 (2)

1976 (1)

H. Chew, P. J. McNulty, and M. Kerker, "Model for Raman and fluorescent scattering by molecules embedded in small particles," Phys. Rev. A 13, 396-404 (1976).
[CrossRef]

1973 (1)

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

1968 (1)

1966 (1)

K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell's equations in istotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

Aubard, J.

N. Félidj, J. Aubard, and G. Lévi, "Discrete dipole approximation for ultraviolet-visible extinction spectra simulation of silver and gold colloids," J. Chem. Phys. 111, 1195-1208 (1999).
[CrossRef]

Böttcher, C. J. F.

C. J. F. Böttcher, Theory of Electric Polarization (Elsevier, 1973), Vol. 1.

Boyd, R. W.

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, "Linear and nonlinear optical measurement of the Lorentz local field," Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

Bruno, J. G.

R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
[CrossRef]

Chew, H.

H. Chew, "Radiation and lifetimes of atoms inside dielectric particles," Phys. Rev. A 38, 3410-3416 (1988).
[CrossRef] [PubMed]

H. Chew, "Transition rates of atoms near spherical surfaces," J. Chem. Phys. 87, 1355-1360 (1987).
[CrossRef]

H. Chew, D. D. Cooke, and M. Kerker, "Raman and fluorescent scattering by molecules embedded in dielectric cylinders," Appl. Opt. 19, 44-52 (1980).
[CrossRef] [PubMed]

D. S. Wang, M. Kerker, and H. Chew, "Raman and fluorescent scattering by molecules embedded in dielectric spheroids," Appl. Opt. 19, 2315-2328 (1980).
[CrossRef] [PubMed]

H. Chew, P. J. McNulty, and M. Kerker, "Model for Raman and fluorescent scattering by molecules embedded in small particles," Phys. Rev. A 13, 396-404 (1976).
[CrossRef]

Cooke, D. D.

de Lang, D. T. N.

F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A Lagendijk, "Local-field effects on spontaneous emission in a dense supercritical gas," Phys. Rev. Lett. 80, 5077-5080 (1998).
[CrossRef]

Draine, B. T.

B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

Félidj, N.

N. Félidj, J. Aubard, and G. Lévi, "Discrete dipole approximation for ultraviolet-visible extinction spectra simulation of silver and gold colloids," J. Chem. Phys. 111, 1195-1208 (1999).
[CrossRef]

Fernandez, G. L.

R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
[CrossRef]

Flatau, P. J.

Gersten, J.

J. Gersten and A. Nitzan, "Radiative properties of solvated molecules in dielectric clusters and small particles," J. Chem. Phys. 95, 686-699 (1991).
[CrossRef]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Hill, S. C.

R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

Kattawar, G. W.

C. Li, G. W. Kattawar, and P. Yang, "Identification of aerosols by their backscattered Mueller images," Opt. Express 14, 3616-3621 (2006).
[CrossRef] [PubMed]

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

Kerker, M.

Kessener, Y. A. R. R.

G. L. J. A. Rikken and Y. A. R. R. Kessener, "Local field effects and electric and magnetic dipole transitions in dielectrics," Phys. Rev. Lett. 74, 880-883 (1995).
[CrossRef] [PubMed]

Lagendijk, A

F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A Lagendijk, "Local-field effects on spontaneous emission in a dense supercritical gas," Phys. Rev. Lett. 80, 5077-5080 (1998).
[CrossRef]

Lévi, G.

N. Félidj, J. Aubard, and G. Lévi, "Discrete dipole approximation for ultraviolet-visible extinction spectra simulation of silver and gold colloids," J. Chem. Phys. 111, 1195-1208 (1999).
[CrossRef]

Li, C.

Lorentz, H. A.

H. A. Lorentz, The Theory of Electrons (Dover, 1952).

Lucht, R. P.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

Maki, J. J.

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, "Linear and nonlinear optical measurement of the Lorentz local field," Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

Malcuit, M. S.

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, "Linear and nonlinear optical measurement of the Lorentz local field," Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

Mayo, M. W.

R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
[CrossRef]

McNulty, P. J.

H. Chew, P. J. McNulty, and M. Kerker, "Model for Raman and fluorescent scattering by molecules embedded in small particles," Phys. Rev. A 13, 396-404 (1976).
[CrossRef]

Nachman, P.

R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
[CrossRef]

Nitzan, A.

J. Gersten and A. Nitzan, "Radiative properties of solvated molecules in dielectric clusters and small particles," J. Chem. Phys. 95, 686-699 (1991).
[CrossRef]

Opatrny, T.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

Pendleton, J. D.

R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
[CrossRef]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Pilloff, H.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

Pinnick, R. G.

R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Rebane, A.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

Rikken, G. L. J. A.

G. L. J. A. Rikken and Y. A. R. R. Kessener, "Local field effects and electric and magnetic dipole transitions in dielectrics," Phys. Rev. Lett. 74, 880-883 (1995).
[CrossRef] [PubMed]

Schuurmans, F. J. P.

F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A Lagendijk, "Local-field effects on spontaneous emission in a dense supercritical gas," Phys. Rev. Lett. 80, 5077-5080 (1998).
[CrossRef]

Schweiger, G.

Scully, M. O.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

Sipe, J. E.

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, "Linear and nonlinear optical measurement of the Lorentz local field," Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

Sokolov, A. V.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

Sprik, R.

F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A Lagendijk, "Local-field effects on spontaneous emission in a dense supercritical gas," Phys. Rev. Lett. 80, 5077-5080 (1998).
[CrossRef]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Velesco, N.

Wang, D. S.

Wegdam, G. H.

F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A Lagendijk, "Local-field effects on spontaneous emission in a dense supercritical gas," Phys. Rev. Lett. 80, 5077-5080 (1998).
[CrossRef]

Wyatt, P. J.

Yang, P.

Yee, K. S.

K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell's equations in istotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

Zubairy, M. S.

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

Aerosol Sci. Technol. (1)

R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, "Fluorescence particle counter for detecting airborne bacteria and other biological particles," Aerosol Sci. Technol. 23, 653-664 (1995).
[CrossRef]

Appl. Opt. (4)

Astrophys. J. (2)

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, "Numerical solution of initial boundary problems involving Maxwell's equations in istotropic media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).

J. Chem. Phys. (3)

J. Gersten and A. Nitzan, "Radiative properties of solvated molecules in dielectric clusters and small particles," J. Chem. Phys. 95, 686-699 (1991).
[CrossRef]

N. Félidj, J. Aubard, and G. Lévi, "Discrete dipole approximation for ultraviolet-visible extinction spectra simulation of silver and gold colloids," J. Chem. Phys. 111, 1195-1208 (1999).
[CrossRef]

H. Chew, "Transition rates of atoms near spherical surfaces," J. Chem. Phys. 87, 1355-1360 (1987).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Phys. Rev. A (2)

H. Chew, P. J. McNulty, and M. Kerker, "Model for Raman and fluorescent scattering by molecules embedded in small particles," Phys. Rev. A 13, 396-404 (1976).
[CrossRef]

H. Chew, "Radiation and lifetimes of atoms inside dielectric particles," Phys. Rev. A 38, 3410-3416 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, "Linear and nonlinear optical measurement of the Lorentz local field," Phys. Rev. Lett. 67, 972-975 (1991).
[CrossRef] [PubMed]

G. L. J. A. Rikken and Y. A. R. R. Kessener, "Local field effects and electric and magnetic dipole transitions in dielectrics," Phys. Rev. Lett. 74, 880-883 (1995).
[CrossRef] [PubMed]

F. J. P. Schuurmans, D. T. N. de Lang, G. H. Wegdam, R. Sprik, and A Lagendijk, "Local-field effects on spontaneous emission in a dense supercritical gas," Phys. Rev. Lett. 80, 5077-5080 (1998).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

M. O. Scully, G. W. Kattawar, R. P. Lucht, T. Opatrny, H. Pilloff, A. Rebane, A. V. Sokolov, and M. S. Zubairy, "FAST CARS: engineering a laser spectroscopic technique for rapid identification of bacterial spores," Proc. Natl. Acad. Sci. U.S.A. 99, 10994-11001 (2002).
[CrossRef] [PubMed]

Other (4)

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

H. A. Lorentz, The Theory of Electrons (Dover, 1952).

C. J. F. Böttcher, Theory of Electric Polarization (Elsevier, 1973), Vol. 1.

J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

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Figures (11)

Fig. 1
Fig. 1

Two schemes of the DDA formalism, where the shadowed circle represents the source dipole, and the open circles represent the induced dipoles.

Fig. 2
Fig. 2

Comparisons of the results of the normalized radiated power computed from interstitial and substitutional schemes in Fig. 1, with a unit source dipole located at the center: (a) radiated power versus the refractive index of the host particle with a size parameter of k a = 4 ; (b) radiated power versus the size parameter of the host particle with a refractive index of m = 1.33 .

Fig. 3
Fig. 3

Radiated power when the source dipole is located off the center of a cell, for a spherical particle of size parameter k a = 8 , a refractive index of m = 1.33 , and a source dipole located on and oscillating along the z direction: (a) normalized radiated power when the source dipole is moved from the center of one cell to the center of an adjacent cell, 0 α 1 ; (b) radiated power per solid angle versus the scattering angle θ when the source dipole is at the midpoint of the two centers of cell, α = 0.5 .

Fig. 4
Fig. 4

Normalized radiated power versus the location of the source dipole computed from the DDA and analytic methods. The source dipole is located on the z axis and oscillates along either the z or x direction, corresponding to radially or tangentially oriented dipoles. Size parameters k a = 8 and 20 and refractive index m = 1.33 are chosen for the spherical host particle.

Fig. 5
Fig. 5

Radiated power per solid angle versus the scattering angle θ when the source dipole is specified at various locations, for the spherical host particle of size parameter of k a = 8 and refractive index of m = 1.33 , given by the DDA and the analytic method.

Fig. 6
Fig. 6

Same as Fig. 5, but for size parameter of k a = 20 .

Fig. 7
Fig. 7

Radiated power per solid angle, as well as corresponding relative error, versus the scattering angles θ and ϕ, for a source dipole embedded in a spherical host particle of size parameter of k a = 8 and refractive index of m = 1.33 , located on the z axis at z / a = 1 / 2 and oscillating along x ^ + z ^ .

Fig. 8
Fig. 8

Radiated power per solid angle versus the scattering angle θ of internal dipole radiation in cubic and cylindric particles with k a eff = 8 , refractive index of m = 1.33 , and a source dipole located at the center and oscillating along the z direction.

Fig. 9
Fig. 9

Geometries of spore particles simulated in this study: (a) homogenous spheroid of refractive index of m = 1.34 ; (b) same spheroid but with a core and a shell; (c) homogenous cylinder of refractive index of m = 1.34 ; and (d) radial variation of refractive index for particle (b).

Fig. 10
Fig. 10

Comparison of radiated power per solid angle of internal dipole radiation versus scattering angle θ computed for the three geometries specified in Fig. 9. The source dipoles are located at the centers of the host particles and oscillate either along a fixed orientation (the z direction) or along random orientations.

Fig. 11
Fig. 11

Same as Fig. 10, but with source dipoles located at r p = ( a / 2 ) z ^ .

Equations (9)

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E = 1 4 π ϵ 0 { k 2 ( n ^ × p ) × n ^ e i k r r + [ 3 n ^ ( n ^ p ) p ] × ( 1 r 3 i k r 2 ) e i k r } ,
P j = α j E j = α j ( E inc , j k j A j k P k ) ,
d P d Ω = c 2 Z 0 32 π 2 k 4 | j = 0 N [ P j n ^ ( n ^ P j ) ] exp ( i k n ^ r j ) | 2 ,
= 3 ϵ 2 ϵ + 1 2 ( α / r 3 ) ( ϵ 1 ) ,
virtual = ϵ + 2 3 ,
empty = 3 ϵ 2 ϵ + 1 ,
sub = 3 ϵ 2 ϵ + 1 π 3 ( ϵ 1 ) 2 ϵ + 2 .
P 0 = c 2 Z 0 k 4 12 π | p | 2 .
d P d Ω = c 2 Z 0 32 π 2 k 4 | p | 2 sin 2 θ ,

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