Abstract

We present the methodological background, the range of applicability, and the on-line usage of two software packages, MIESCHKA and CYL, which we have developed for light-scattering analysis on nonspherical particles. MIESCHKA solves Maxwell’s equations in a rigorous way but is restricted to axisymmetric geometries, whereas CYL is an approximation for finite columns with nonspherical cross sections. We have established an easy on-line access to both of these programs through the Virtual Laboratory. Its generic software infrastructure was designed to simplify the web-based usage and to support the intercomparability of scientific software.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
    [CrossRef]
  2. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [CrossRef]
  3. M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).
  4. T. Rother, M. Kahnert, A. Doicu, J. Wauer, “Surface Green’s function of the Helmholtz equation in spherical coordinates,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 2002), Vol. 38, pp. 47–95.
    [CrossRef]
  5. T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with noncircular cross sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 1999), Vol. 23, pp. 79–105.
    [CrossRef]
  6. T. Ernst, T. Rother, F. Schreier, J. Wauer, W. Balzer, “DLR’s VirtualLab: scientific software just a mouse click away,” IEEE Comput. Sci. Eng. 5, 70–79 (2003).
    [CrossRef]
  7. T. Rother, “Generalization of the separation of variables method for non-spherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
    [CrossRef]
  8. L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).
  9. N. G. Khlebtsov, “Orientational averaging of light-scattering observables in the T-matrix approach,” Appl. Opt. 31, 5359–5365 (1992).
    [CrossRef] [PubMed]
  10. K. Schmidt, T. Rother, J. Wauer, “The equivalence of applying the extended boundary condition and the continuity conditions for solving electromagnetic scattering problems,” Opt. Commun. 150, 1–4 (1998).
    [CrossRef]
  11. K. Schmidt, J. Wauer, T. Rother, “Application of the separation of variables method to plane wave scattering on non-axisymmetric particles,” in the 12th International Workshop on Lidar Multiple Scattering Experiments, C. Werner, U. G. Oppel, T. Rother, eds., Proc. SPIE5059, 76–85 (2003).
    [CrossRef]
  12. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  13. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  14. J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
    [CrossRef]
  15. W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical particles: a compendium of calculations,” NASA Ref. Pub. 1157 (National Technical Service, Springfield, Va., 1986).
  16. A. Mugnai, W. J. Wiscombe, “Scattering of radiation by moderately nonspherical particles,” J. Atmos. Sci. 37, 1291–1307 (1980).
    [CrossRef]
  17. J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986).
  18. T. Rother, K. Schmidt, S. Havemann, “Light scattering on hexagonal ice columns,” J. Opt. Soc. Am. A 18, 2512–2517 (2001).
    [CrossRef]
  19. M. Hess, R. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
    [CrossRef]
  20. A. Borovoi, I. Grishin, U. Oppel, “Backscattering peak of hexagonal ice columns and plates,” Opt. Lett. 25, 1388–1390 (2000).
    [CrossRef]

2003 (1)

T. Ernst, T. Rother, F. Schreier, J. Wauer, W. Balzer, “DLR’s VirtualLab: scientific software just a mouse click away,” IEEE Comput. Sci. Eng. 5, 70–79 (2003).
[CrossRef]

2001 (1)

2000 (1)

1998 (3)

M. Hess, R. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[CrossRef]

K. Schmidt, T. Rother, J. Wauer, “The equivalence of applying the extended boundary condition and the continuity conditions for solving electromagnetic scattering problems,” Opt. Commun. 150, 1–4 (1998).
[CrossRef]

T. Rother, “Generalization of the separation of variables method for non-spherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
[CrossRef]

1996 (2)

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

1992 (1)

1980 (1)

A. Mugnai, W. J. Wiscombe, “Scattering of radiation by moderately nonspherical particles,” J. Atmos. Sci. 37, 1291–1307 (1980).
[CrossRef]

1971 (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Balzer, W.

T. Ernst, T. Rother, F. Schreier, J. Wauer, W. Balzer, “DLR’s VirtualLab: scientific software just a mouse click away,” IEEE Comput. Sci. Eng. 5, 70–79 (2003).
[CrossRef]

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Borovoi, A.

Doicu, A.

T. Rother, M. Kahnert, A. Doicu, J. Wauer, “Surface Green’s function of the Helmholtz equation in spherical coordinates,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 2002), Vol. 38, pp. 47–95.
[CrossRef]

Ernst, T.

T. Ernst, T. Rother, F. Schreier, J. Wauer, W. Balzer, “DLR’s VirtualLab: scientific software just a mouse click away,” IEEE Comput. Sci. Eng. 5, 70–79 (2003).
[CrossRef]

Grishin, I.

Havemann, S.

T. Rother, K. Schmidt, S. Havemann, “Light scattering on hexagonal ice columns,” J. Opt. Soc. Am. A 18, 2512–2517 (2001).
[CrossRef]

T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with noncircular cross sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 1999), Vol. 23, pp. 79–105.
[CrossRef]

Hess, M.

M. Hess, R. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[CrossRef]

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Hovenier, J. W.

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

Kahnert, M.

T. Rother, M. Kahnert, A. Doicu, J. Wauer, “Surface Green’s function of the Helmholtz equation in spherical coordinates,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 2002), Vol. 38, pp. 47–95.
[CrossRef]

Khlebtsov, N. G.

Koelemeijer, R.

M. Hess, R. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[CrossRef]

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986).

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).

Lumme, K.

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).

Mugnai, A.

A. Mugnai, W. J. Wiscombe, “Scattering of radiation by moderately nonspherical particles,” J. Atmos. Sci. 37, 1291–1307 (1980).
[CrossRef]

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical particles: a compendium of calculations,” NASA Ref. Pub. 1157 (National Technical Service, Springfield, Va., 1986).

Oppel, U.

Rahola, J.

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

Rother, T.

T. Ernst, T. Rother, F. Schreier, J. Wauer, W. Balzer, “DLR’s VirtualLab: scientific software just a mouse click away,” IEEE Comput. Sci. Eng. 5, 70–79 (2003).
[CrossRef]

T. Rother, K. Schmidt, S. Havemann, “Light scattering on hexagonal ice columns,” J. Opt. Soc. Am. A 18, 2512–2517 (2001).
[CrossRef]

T. Rother, “Generalization of the separation of variables method for non-spherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
[CrossRef]

K. Schmidt, T. Rother, J. Wauer, “The equivalence of applying the extended boundary condition and the continuity conditions for solving electromagnetic scattering problems,” Opt. Commun. 150, 1–4 (1998).
[CrossRef]

K. Schmidt, J. Wauer, T. Rother, “Application of the separation of variables method to plane wave scattering on non-axisymmetric particles,” in the 12th International Workshop on Lidar Multiple Scattering Experiments, C. Werner, U. G. Oppel, T. Rother, eds., Proc. SPIE5059, 76–85 (2003).
[CrossRef]

T. Rother, M. Kahnert, A. Doicu, J. Wauer, “Surface Green’s function of the Helmholtz equation in spherical coordinates,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 2002), Vol. 38, pp. 47–95.
[CrossRef]

T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with noncircular cross sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 1999), Vol. 23, pp. 79–105.
[CrossRef]

Schmidt, K.

T. Rother, K. Schmidt, S. Havemann, “Light scattering on hexagonal ice columns,” J. Opt. Soc. Am. A 18, 2512–2517 (2001).
[CrossRef]

K. Schmidt, T. Rother, J. Wauer, “The equivalence of applying the extended boundary condition and the continuity conditions for solving electromagnetic scattering problems,” Opt. Commun. 150, 1–4 (1998).
[CrossRef]

K. Schmidt, J. Wauer, T. Rother, “Application of the separation of variables method to plane wave scattering on non-axisymmetric particles,” in the 12th International Workshop on Lidar Multiple Scattering Experiments, C. Werner, U. G. Oppel, T. Rother, eds., Proc. SPIE5059, 76–85 (2003).
[CrossRef]

T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with noncircular cross sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 1999), Vol. 23, pp. 79–105.
[CrossRef]

Schreier, F.

T. Ernst, T. Rother, F. Schreier, J. Wauer, W. Balzer, “DLR’s VirtualLab: scientific software just a mouse click away,” IEEE Comput. Sci. Eng. 5, 70–79 (2003).
[CrossRef]

Shin, R. T.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

Stammes, P.

M. Hess, R. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).

Tsang, L.

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Voshchinnikov, N. V.

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

Waterman, P. C.

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Wauer, J.

T. Ernst, T. Rother, F. Schreier, J. Wauer, W. Balzer, “DLR’s VirtualLab: scientific software just a mouse click away,” IEEE Comput. Sci. Eng. 5, 70–79 (2003).
[CrossRef]

K. Schmidt, T. Rother, J. Wauer, “The equivalence of applying the extended boundary condition and the continuity conditions for solving electromagnetic scattering problems,” Opt. Commun. 150, 1–4 (1998).
[CrossRef]

K. Schmidt, J. Wauer, T. Rother, “Application of the separation of variables method to plane wave scattering on non-axisymmetric particles,” in the 12th International Workshop on Lidar Multiple Scattering Experiments, C. Werner, U. G. Oppel, T. Rother, eds., Proc. SPIE5059, 76–85 (2003).
[CrossRef]

T. Rother, M. Kahnert, A. Doicu, J. Wauer, “Surface Green’s function of the Helmholtz equation in spherical coordinates,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 2002), Vol. 38, pp. 47–95.
[CrossRef]

Wiscombe, W. J.

A. Mugnai, W. J. Wiscombe, “Scattering of radiation by moderately nonspherical particles,” J. Atmos. Sci. 37, 1291–1307 (1980).
[CrossRef]

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical particles: a compendium of calculations,” NASA Ref. Pub. 1157 (National Technical Service, Springfield, Va., 1986).

Appl. Opt. (1)

IEEE Comput. Sci. Eng. (1)

T. Ernst, T. Rother, F. Schreier, J. Wauer, W. Balzer, “DLR’s VirtualLab: scientific software just a mouse click away,” IEEE Comput. Sci. Eng. 5, 70–79 (2003).
[CrossRef]

J. Atmos. Sci. (1)

A. Mugnai, W. J. Wiscombe, “Scattering of radiation by moderately nonspherical particles,” J. Atmos. Sci. 37, 1291–1307 (1980).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transfer (4)

M. Hess, R. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[CrossRef]

T. Rother, “Generalization of the separation of variables method for non-spherical scattering on dielectric objects,” J. Quant. Spectrosc. Radiat. Transfer 60, 335–353 (1998).
[CrossRef]

J. W. Hovenier, K. Lumme, M. I. Mishchenko, N. V. Voshchinnikov, D. W. Mackowski, J. Rahola, “Computations of scattering matrices of four types of non-spherical particles using diverse methods,” J. Quant. Spectrosc. Radiat. Transfer 55, 695–705 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Opt. Commun. (1)

K. Schmidt, T. Rother, J. Wauer, “The equivalence of applying the extended boundary condition and the continuity conditions for solving electromagnetic scattering problems,” Opt. Commun. 150, 1–4 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. D (1)

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Other (9)

J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986).

W. J. Wiscombe, A. Mugnai, “Single scattering from nonspherical particles: a compendium of calculations,” NASA Ref. Pub. 1157 (National Technical Service, Springfield, Va., 1986).

L. Tsang, J. A. Kong, R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1985).

K. Schmidt, J. Wauer, T. Rother, “Application of the separation of variables method to plane wave scattering on non-axisymmetric particles,” in the 12th International Workshop on Lidar Multiple Scattering Experiments, C. Werner, U. G. Oppel, T. Rother, eds., Proc. SPIE5059, 76–85 (2003).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).

T. Rother, M. Kahnert, A. Doicu, J. Wauer, “Surface Green’s function of the Helmholtz equation in spherical coordinates,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 2002), Vol. 38, pp. 47–95.
[CrossRef]

T. Rother, S. Havemann, K. Schmidt, “Scattering of plane waves on finite cylinders with noncircular cross sections,” in Progress in Electromagnetics Research, J. A. Kong, ed. (EMW Publishing, Cambridge, Mass., 1999), Vol. 23, pp. 79–105.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Comparison of the S11 element of the Stokes matrix for the prolate spheroid (n = 1.5 + 0.01i, asp is 2, kr_v_eff = 5, Φ p = 50°, and Φ p = 0°) obtained with MIESCHKA (curve) and with the T-matrix code described in Hovenier et al.14 (crosses).

Fig. 2
Fig. 2

Comparison of the S11 element of the Stokes matrix for the oblate spheroid (n = 1.5 + 0.01i, asp is 0.5, kr_v_eff = 5, Θ p = 50°, and Φ p = 0°) obtained with MIESCHKA (curve) and with the T-matrix code described in Hovenier et al.14 (crosses).

Fig. 3
Fig. 3

Comparison of the S11 element of the Stokes matrix for the circular cylinder (n = 1.5 + 0.01i, kr_v_eff = 5, asp_cyl = 2, Θ p = 50°, and Φ p = 0°) obtained with MIESCHKA (curve) and with the T-matrix code described in Hovenier et al.14 (crosses).

Fig. 4
Fig. 4

Differential scattering cross section of a Chebyshev particle of the sixth order (hh polarization, n = 1.5 + 0.02i, kr_v_eff = 10, ∊ = +0.1, Θ p = 0°, and Φ p = 0°) obtained with MIESCHKA.

Fig. 5
Fig. 5

Differential scattering cross section of a Chebyshev particle of the sixth order (vv polarization, n = 1.5 + 0.02i, kr_v_eff = 10, ∊ = +0.1, Θ p = 0°, and Φ p = 0°) obtained with MIESCHKA.

Fig. 6
Fig. 6

Comparison of the phase functions of a randomly oriented circular cylinder with an increasing aspect ratio (n = 1.5 + 0.0i and kr = 2) obtained with MIESCHKA (solid curve) and CYL (dashed curve).

Fig. 7
Fig. 7

Comparison of the normalized phase matrix element -P12/P11 for the same particle as in Fig. 6.

Fig. 8
Fig. 8

Comparison of the phase functions of a randomly oriented hexagonal ice column (n = 1.289 + 3.54 10-4 i, λ = 1.6 μm, asp is 3, kr = 100) computed with CYL (solid curve) and the ray-tracing program of Hess et al.19 (dashed curve).

Fig. 9
Fig. 9

Same as in Fig. 8 but with neglected contributions from the top and bottom faces in the GO approach (dashed curve).

Equations (30)

Equations on this page are rendered with MathJax. Learn more.

Einc=e0 expik0zL,
n×Einc+Es=n×Eint,
n×Hinc+Hs=n×Hint,
Esk0r=τ=12n=1l=-nn fτnlΨτnlk0r,
Eintksr=τ=12n=1l=-nn pτnlRgΨτnlksr,
Einck0r=τ=12n=1l=-nn aτnlRgΨτnlk0r,
××RgΨτnlkr-k2RgΨτnlkr=0
Ψτnlkr=γnlk-1×τkrhn1kr·Pnlcos θexpilϕ,
RgΨτnlkr=γnlk-1×τkrjnkr·Pnlcos θexpilϕ.
γnl=2n+14πnn+1n-l!n+l!1/2.
Φτnl1=×RgΨτnlksr,
Φτnl2=RgΨτnlksr,
f=T · a,
T=-Q-1 Rg Q,
Qτnl;τnl=S dS1μs×Rg Ψτnlksr×Ψτnlk0r+1μ0Rg Ψτnlksr××Ψτnlk0r,
Rg Qτnl;τnl=S dS1μs×Rg Ψτnlksr×Rg Ψτnlk0r+1μ0Rg Ψτnlksr××Rg Ψτnlk0r.
dS=r2 sin θer-1rrθeθdθdϕ.
Einck0rL=τ=12n=1l=-nn aτnlL Rg Ψτnlk0rL.
aτnlL,x=in+12n+1π1/2δl1+-1τ-1δl,-1
aτnlL,y=in2n+1π1/2δl1+-1τδl,-1
a=D-1 · aL.
fL=D · f.
Evs=EϕLs,
Ehs=EθLs.
EvsEhs=expik0rrFvvθLFvhθLFhvθLFhhθL EvincEhinc.
FvαθL=-1k0n=1l=-nn γnl-in+1 expilϕL×f2nlL,αlsin θL Pnlcos θL+f1nlL,αθL Pnlcos θL,
FhαθL=ik0n=1l=-nn γnl-in+1 expilϕL×f1nlL,αlsin θL Pnlcos θL+f2nlL,αθL Pnlcos θL.
τ=12n=1l=-nn  l=-n=|l|τ=12
l=-n=|l|  l=-lcutlcutn=|l|ncut, lcutncut.
Esr=S dSiωμ0Gr, r · n×Hsr+×Gr, r · n×Esr.

Metrics