Abstract

Within the framework of generalized Lorenz–Mie theory, scattering from a homogeneous spheroidal particle illuminated by an on-axis zero-order Bessel beam is formulated analytically, with special attention paid to the investigation of internal and near-surface fields. Numerical results concerning the spatial distributions of internal and near-surface fields are presented for various parameter values, such as the half-cone angle of the incident zero-order Bessel beam, the major axis, the minor axis, and the refractive index of the spheroid. The study of internal and near-surface field distributions will contribute to the understanding of Bessel beam scattering by nonspherical particles with sizes close to the incident wavelength.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2014 (3)

L. Han, G. Gouesbet, Y. Han, G. Gréhan, and J. Wang, “Intrinsic method for the evaluation of beam shape coefficients in spheroidal coordinates for on-axis standard configuration,” Opt. Commun. 310, 125–137 (2014).
[CrossRef]

L. Han, Y. Han, Z. Cui, and J. Wang, “Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory,” J. Quant. Spectrosc. Radiat. Transfer 147, 279–287 (2014).
[CrossRef]

L. Han, Y. Han, G. Gouesbet, J. Wang, and G. Gréhan, “Photonic jet generated by spheroidal particle with Gaussian-beam illumination,” J. Opt. Soc. Am. B 31, 1476–1483 (2014).
[CrossRef]

2013 (5)

2012 (1)

2011 (4)

F. Mitri, “Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere,” Opt. Lett. 36, 766–768 (2011).
[CrossRef]

M. J. Mendes, I. Tobías, A. Martí, and A. Luque, “Light concentration in the near-field of dielectric spheroidal particles with mesoscopic sizes,” Opt. Express 19, 16207–16222 (2011).
[CrossRef]

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

G. Gouesbet, F. Xu, and Y. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

2010 (2)

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom 12, 32–34 (2010).

M. J. Mendes, I. Tobías, A. Martí, and A. Luque, “Near-field scattering by dielectric spheroidal particles with sizes on the order of the illuminating wavelength,” J. Opt. Soc. Am. B 27, 1221–1231 (2010).
[CrossRef]

2008 (5)

P. Ferrand, J. Wenger, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, and H. Rigneault, “Direct imaging of photonic nanojets,” Opt. Express 16, 6930–6940 (2008).
[CrossRef]

S. C. Kong, A. Sahakian, A. Taflove, and V. Backman, “Photonic nanojet-enabled optical data storage,” Opt. Express 16, 13713–13719 (2008).
[CrossRef]

A. Devilez, B. Stout, N. Bonod, and E. Popov, “Spectral analysis of three-dimensional photonic jets,” Opt. Express 16, 14200–14212 (2008).
[CrossRef]

E. Mcleod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3, 413–417 (2008).
[CrossRef]

S. C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

2007 (4)

2006 (1)

Y. Han, H. Zhang, and X. Sun, “Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries,” Appl. Phys. B 84, 485–492 (2006).
[CrossRef]

2005 (4)

2004 (2)

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1214–1220 (2004).
[CrossRef]

Y. P. Han, L. C. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz–Mie theory framework,” Opt. Commun. 231, 71–77 (2004).
[CrossRef]

2003 (1)

2001 (3)

2000 (3)

1999 (2)

C. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

S. V. Tsinopoulos and D. Polyzos, “Scattering of He-Ne laser light by an average-sized red blood cell,” Appl. Opt. 38, 5499–5510 (1999).
[CrossRef]

1997 (1)

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

1995 (2)

1993 (2)

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993).
[CrossRef]

N. Voshchinnikov and V. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

1992 (2)

A. R. Sebak and B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268–274 (1992).
[CrossRef]

L.-P. Hsiang and G. M. Faeth, “Near-limit drop deformation and secondary breakup,” Int. J. Multiphase Flow 18, 635–652 (1992).
[CrossRef]

1991 (1)

S. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

1990 (1)

N. Roth, K. Anders, and A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37 (1990).
[CrossRef]

1979 (1)

1975 (1)

Alessandri, K.

Allen, K. W.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom 12, 32–34 (2010).

Anders, K.

N. Roth, K. Anders, and A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37 (1990).
[CrossRef]

Antoszyk, A. N.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom 12, 32–34 (2010).

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

C. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Arnold, C. B.

E. Mcleod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3, 413–417 (2008).
[CrossRef]

Asano, S.

Astratov, V. N.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom 12, 32–34 (2010).

Backman, V.

Barbastathis, G.

Bartley, D.

Bartley, D. L.

Barton, J.

Bonod, N.

Cai, X.

Challener, W.

Chen, Z.

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1214–1220 (2004).
[CrossRef]

Chen, Z. G.

Cui, Z.

L. Han, Y. Han, Z. Cui, and J. Wang, “Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory,” J. Quant. Spectrosc. Radiat. Transfer 147, 279–287 (2014).
[CrossRef]

Z. Cui, Y. Han, and L. Han, “Scattering of a zero-order Bessel beam by arbitrarily shaped homogeneous dielectric particles,” J. Opt. Soc. Am. A 30, 1913–1920 (2013).
[CrossRef]

Darafsheh, A.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom 12, 32–34 (2010).

Devilez, A.

Dholakia, K.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

C. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Duan, Y.

Esarey, E.

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

Faeth, G. M.

L.-P. Hsiang and G. M. Faeth, “Near-limit drop deformation and secondary breakup,” Int. J. Multiphase Flow 18, 635–652 (1992).
[CrossRef]

Fahrbach, F. O.

Fan, J.

J. Fan, E. Parra, and H. Milchberg, “Resonant self-trapping and absorption of intense Bessel beams,” Phys. Rev. Lett. 84, 3085–3088 (2000).
[CrossRef]

Farafonov, V.

N. Voshchinnikov and V. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

Ferrand, P.

Flammer, C.

C. Flammer, Spheroidal Wave Functions (Stanford University, 1957).

Fried, N. M.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom 12, 32–34 (2010).

Frohn, A.

N. Roth, K. Anders, and A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37 (1990).
[CrossRef]

Fu, Q.

Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Ghenuche, P.

Gouesbet, G.

L. Han, G. Gouesbet, Y. Han, G. Gréhan, and J. Wang, “Intrinsic method for the evaluation of beam shape coefficients in spheroidal coordinates for on-axis standard configuration,” Opt. Commun. 310, 125–137 (2014).
[CrossRef]

L. Han, Y. Han, G. Gouesbet, J. Wang, and G. Gréhan, “Photonic jet generated by spheroidal particle with Gaussian-beam illumination,” J. Opt. Soc. Am. B 31, 1476–1483 (2014).
[CrossRef]

L. Han, Y. Han, J. Wang, and G. Gouesbet, “Internal and near-surface field distributions for a spheroidal particle illuminated by a focused Gaussian beam: on-axis case,” J. Quant. Spectrosc. Radiat. Transfer 126, 38–43 (2013).
[CrossRef]

G. Gouesbet, F. Xu, and Y. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

F. Xu, K. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007).
[CrossRef]

Y. P. Han, L. C. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz–Mie theory framework,” Opt. Commun. 231, 71–77 (2004).
[CrossRef]

Y. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination,” Appl. Opt. 42, 6621–6629 (2003).
[CrossRef]

Greenaway, R. S.

Gréhan, G.

L. Han, G. Gouesbet, Y. Han, G. Gréhan, and J. Wang, “Intrinsic method for the evaluation of beam shape coefficients in spheroidal coordinates for on-axis standard configuration,” Opt. Commun. 310, 125–137 (2014).
[CrossRef]

L. Han, Y. Han, G. Gouesbet, J. Wang, and G. Gréhan, “Photonic jet generated by spheroidal particle with Gaussian-beam illumination,” J. Opt. Soc. Am. B 31, 1476–1483 (2014).
[CrossRef]

F. Xu, K. Ren, G. Gouesbet, G. Gréhan, and X. Cai, “Generalized Lorenz-Mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid,” J. Opt. Soc. Am. A 24, 119–131 (2007).
[CrossRef]

Y. P. Han, L. C. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz–Mie theory framework,” Opt. Commun. 231, 71–77 (2004).
[CrossRef]

Y. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination,” Appl. Opt. 42, 6621–6629 (2003).
[CrossRef]

Guo, W.

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Gurchenkov, V.

Hafizi, B.

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

Han, G.

Han, L.

L. Han, Y. Han, Z. Cui, and J. Wang, “Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory,” J. Quant. Spectrosc. Radiat. Transfer 147, 279–287 (2014).
[CrossRef]

L. Han, G. Gouesbet, Y. Han, G. Gréhan, and J. Wang, “Intrinsic method for the evaluation of beam shape coefficients in spheroidal coordinates for on-axis standard configuration,” Opt. Commun. 310, 125–137 (2014).
[CrossRef]

L. Han, Y. Han, G. Gouesbet, J. Wang, and G. Gréhan, “Photonic jet generated by spheroidal particle with Gaussian-beam illumination,” J. Opt. Soc. Am. B 31, 1476–1483 (2014).
[CrossRef]

L. Han, Y. Han, J. Wang, and G. Gouesbet, “Internal and near-surface field distributions for a spheroidal particle illuminated by a focused Gaussian beam: on-axis case,” J. Quant. Spectrosc. Radiat. Transfer 126, 38–43 (2013).
[CrossRef]

Z. Cui, Y. Han, and L. Han, “Scattering of a zero-order Bessel beam by arbitrarily shaped homogeneous dielectric particles,” J. Opt. Soc. Am. A 30, 1913–1920 (2013).
[CrossRef]

Han, Y.

L. Han, G. Gouesbet, Y. Han, G. Gréhan, and J. Wang, “Intrinsic method for the evaluation of beam shape coefficients in spheroidal coordinates for on-axis standard configuration,” Opt. Commun. 310, 125–137 (2014).
[CrossRef]

L. Han, Y. Han, Z. Cui, and J. Wang, “Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory,” J. Quant. Spectrosc. Radiat. Transfer 147, 279–287 (2014).
[CrossRef]

L. Han, Y. Han, G. Gouesbet, J. Wang, and G. Gréhan, “Photonic jet generated by spheroidal particle with Gaussian-beam illumination,” J. Opt. Soc. Am. B 31, 1476–1483 (2014).
[CrossRef]

L. Han, Y. Han, J. Wang, and G. Gouesbet, “Internal and near-surface field distributions for a spheroidal particle illuminated by a focused Gaussian beam: on-axis case,” J. Quant. Spectrosc. Radiat. Transfer 126, 38–43 (2013).
[CrossRef]

Z. Cui, Y. Han, and L. Han, “Scattering of a zero-order Bessel beam by arbitrarily shaped homogeneous dielectric particles,” J. Opt. Soc. Am. A 30, 1913–1920 (2013).
[CrossRef]

G. Gouesbet, F. Xu, and Y. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

Y. Han, H. Zhang, and G. Han, “The expansion coefficients of arbitrary shaped beam in oblique illumination,” Opt. Express 15, 735–746 (2007).
[CrossRef]

Y. Han, H. Zhang, and X. Sun, “Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries,” Appl. Phys. B 84, 485–492 (2006).
[CrossRef]

H. Zhang and Y. Han, “Scattering by a confocal multilayered spheroidal particle illuminated by an axial Gaussian beam,” IEEE Trans. Antennas Propag. 53, 1514–1518 (2005).
[CrossRef]

Y. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination,” Appl. Opt. 42, 6621–6629 (2003).
[CrossRef]

Y. Han and Z. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509 (2001).
[CrossRef]

Han, Y. P.

Y. P. Han, L. C. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz–Mie theory framework,” Opt. Commun. 231, 71–77 (2004).
[CrossRef]

Hasan, M.

H. Seidfaraji, M. Hasan, and J. J. Simpson, “A feasibility study of microjets applied to breast cancer detection,” in 2012 International Conference on Electromagnetics in Advanced Applications (IEEE, 2012), pp. 949–951.

Heifetz, A.

S. C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

Herminghaus, S.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993).
[CrossRef]

Hirst, E.

Hong, M.

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Hsiang, L.-P.

L.-P. Hsiang and G. M. Faeth, “Near-limit drop deformation and secondary breakup,” Int. J. Multiphase Flow 18, 635–652 (1992).
[CrossRef]

Itagi, A.

Katranji, E. G.

Katsnelson, A.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18, 485302 (2007).
[CrossRef]

Kaye, P. H.

Kerr, M. D.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom 12, 32–34 (2010).

Khan, A.

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Khilo, A. N.

Klepárník, K.

D. Maděránková, I. Provazník, and K. Klepárník, “Numerical modeling of photonic nanojet behind dielectric microcylinder,” in Proceedings of World Congress on Medical Physics and Biomedical Engineering, O. Dossel and W. C. Schlegel, eds. (Springer, 2010), pp. 1135–1138.

Kong, S. C.

S. C. Kong, A. Sahakian, A. Taflove, and V. Backman, “Photonic nanojet-enabled optical data storage,” Opt. Express 16, 13713–13719 (2008).
[CrossRef]

S. C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

Lecler, S.

Li, L.

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Li, X.

Liu, C.-Y.

C.-Y. Liu, “Ultra-elongated photonic nanojets generated by a graded-index microellipsoid,” Prog. Electromagn. Res. Lett. 37, 153–165 (2013).
[CrossRef]

Liu, Z.

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Luk’yanchuk, B.

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Luque, A.

Maderánková, D.

D. Maděránková, I. Provazník, and K. Klepárník, “Numerical modeling of photonic nanojet behind dielectric microcylinder,” in Proceedings of World Congress on Medical Physics and Biomedical Engineering, O. Dossel and W. C. Schlegel, eds. (Springer, 2010), pp. 1135–1138.

Martí, A.

Mcleod, E.

E. Mcleod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3, 413–417 (2008).
[CrossRef]

McQueen, C.

C. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Méès, L. C.

Y. P. Han, L. C. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz–Mie theory framework,” Opt. Commun. 231, 71–77 (2004).
[CrossRef]

Memis, O. G.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18, 485302 (2007).
[CrossRef]

Mendes, M. J.

Meyrueis, P.

Milchberg, H.

J. Fan, E. Parra, and H. Milchberg, “Resonant self-trapping and absorption of intense Bessel beams,” Phys. Rev. Lett. 84, 3085–3088 (2000).
[CrossRef]

Mishra, S.

S. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

Mitri, F.

Mohseni, H.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18, 485302 (2007).
[CrossRef]

Nassoy, P.

Parra, E.

J. Fan, E. Parra, and H. Milchberg, “Resonant self-trapping and absorption of intense Bessel beams,” Phys. Rev. Lett. 84, 3085–3088 (2000).
[CrossRef]

Pianta, M.

Polyzos, D.

Popov, E.

Provazník, I.

D. Maděránková, I. Provazník, and K. Klepárník, “Numerical modeling of photonic nanojet behind dielectric microcylinder,” in Proceedings of World Congress on Medical Physics and Biomedical Engineering, O. Dossel and W. C. Schlegel, eds. (Springer, 2010), pp. 1135–1138.

Ren, K.

Ren, K. F.

Y. P. Han, L. C. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz–Mie theory framework,” Opt. Commun. 231, 71–77 (2004).
[CrossRef]

Rigneault, H.

Rohrbach, A.

Roth, N.

N. Roth, K. Anders, and A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37 (1990).
[CrossRef]

Ryzhevich, A. A.

Sahakian, A.

Sahakian, A. V.

S. C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

Sebak, A. R.

A. R. Sebak and B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268–274 (1992).
[CrossRef]

Secker, D. R.

Seidfaraji, H.

H. Seidfaraji, M. Hasan, and J. J. Simpson, “A feasibility study of microjets applied to breast cancer detection,” in 2012 International Conference on Electromagnetics in Advanced Applications (IEEE, 2012), pp. 949–951.

Sibbett, W.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Simpson, J. J.

H. Seidfaraji, M. Hasan, and J. J. Simpson, “A feasibility study of microjets applied to breast cancer detection,” in 2012 International Conference on Electromagnetics in Advanced Applications (IEEE, 2012), pp. 949–951.

Sinha, B. P.

A. R. Sebak and B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268–274 (1992).
[CrossRef]

Sprangle, P.

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

Stout, B.

Sun, W.

Sun, X.

Y. Han, H. Zhang, and X. Sun, “Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries,” Appl. Phys. B 84, 485–492 (2006).
[CrossRef]

Taflove, A.

Takakura, Y.

Tobías, I.

Tsinopoulos, S. V.

Videen, G.

Voshchinnikov, N.

N. Voshchinnikov and V. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

Wang, J.

L. Han, G. Gouesbet, Y. Han, G. Gréhan, and J. Wang, “Intrinsic method for the evaluation of beam shape coefficients in spheroidal coordinates for on-axis standard configuration,” Opt. Commun. 310, 125–137 (2014).
[CrossRef]

L. Han, Y. Han, Z. Cui, and J. Wang, “Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory,” J. Quant. Spectrosc. Radiat. Transfer 147, 279–287 (2014).
[CrossRef]

L. Han, Y. Han, G. Gouesbet, J. Wang, and G. Gréhan, “Photonic jet generated by spheroidal particle with Gaussian-beam illumination,” J. Opt. Soc. Am. B 31, 1476–1483 (2014).
[CrossRef]

L. Han, Y. Han, J. Wang, and G. Gouesbet, “Internal and near-surface field distributions for a spheroidal particle illuminated by a focused Gaussian beam: on-axis case,” J. Quant. Spectrosc. Radiat. Transfer 126, 38–43 (2013).
[CrossRef]

Wang, Z.

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Wenger, J.

Wu, W.

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18, 485302 (2007).
[CrossRef]

Wu, Z.

Wu, Z. S.

Y. P. Han, L. C. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz–Mie theory framework,” Opt. Commun. 231, 71–77 (2004).
[CrossRef]

Wulle, T.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993).
[CrossRef]

Xu, F.

Yamamoto, G.

Ying, H. S.

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom 12, 32–34 (2010).

Zhang, B.

Zhang, H.

Y. Han, H. Zhang, and G. Han, “The expansion coefficients of arbitrary shaped beam in oblique illumination,” Opt. Express 15, 735–746 (2007).
[CrossRef]

Y. Han, H. Zhang, and X. Sun, “Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries,” Appl. Phys. B 84, 485–492 (2006).
[CrossRef]

H. Zhang and Y. Han, “Scattering by a confocal multilayered spheroidal particle illuminated by an axial Gaussian beam,” IEEE Trans. Antennas Propag. 53, 1514–1518 (2005).
[CrossRef]

Am. J. Phys. (1)

C. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Appl. Opt. (10)

Y. Han, G. Gréhan, and G. Gouesbet, “Generalized Lorenz-Mie theory for a spheroidal particle with off-axis Gaussian-beam illumination,” Appl. Opt. 42, 6621–6629 (2003).
[CrossRef]

S. Asano and G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
[CrossRef]

S. Asano, “Light scattering properties of spheroidal particles,” Appl. Opt. 18, 712–723 (1979).
[CrossRef]

J. Barton, “Internal and near-surface electromagnetic fields for a spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 5542–5551 (1995).
[CrossRef]

J. Barton, “Internal and near-surface electromagnetic fields for an absorbing spheroidal particle with arbitrary illumination,” Appl. Opt. 34, 8472–8473 (1995).
[CrossRef]

S. V. Tsinopoulos and D. Polyzos, “Scattering of He-Ne laser light by an average-sized red blood cell,” Appl. Opt. 38, 5499–5510 (1999).
[CrossRef]

D. R. Secker, P. H. Kaye, R. S. Greenaway, E. Hirst, D. L. Bartley, and G. Videen, “Light scattering from deformed droplets and droplets with inclusions. I. Experimental results,” Appl. Opt. 39, 5023–5030 (2000).
[CrossRef]

G. Videen, W. Sun, Q. Fu, D. R. Secker, R. S. Greenaway, P. H. Kaye, E. Hirst, and D. Bartley, “Light scattering from deformed droplets and droplets with inclusions. II. Theoretical treatment,” Appl. Opt. 39, 5031–5039 (2000).
[CrossRef]

Y. Han and Z. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt. 40, 2501–2509 (2001).
[CrossRef]

P. Ghenuche, H. Rigneault, and J. Wenger, “Photonic nanojet focusing for hollow-core photonic crystal fiber probes,” Appl. Opt. 51, 8637–8640 (2012).
[CrossRef]

Appl. Phys. B (1)

Y. Han, H. Zhang, and X. Sun, “Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries,” Appl. Phys. B 84, 485–492 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

S. C. Kong, A. V. Sahakian, A. Heifetz, A. Taflove, and V. Backman, “Robust detection of deeply subwavelength pits in simulated optical data-storage disks using photonic jets,” Appl. Phys. Lett. 92, 211102 (2008).
[CrossRef]

Astrophys. Space Sci. (1)

N. Voshchinnikov and V. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

A. R. Sebak and B. P. Sinha, “Scattering by a conducting spheroidal object with dielectric coating at axial incidence,” IEEE Trans. Antennas Propag. 40, 268–274 (1992).
[CrossRef]

H. Zhang and Y. Han, “Scattering by a confocal multilayered spheroidal particle illuminated by an axial Gaussian beam,” IEEE Trans. Antennas Propag. 53, 1514–1518 (2005).
[CrossRef]

Int. J. Multiphase Flow (1)

L.-P. Hsiang and G. M. Faeth, “Near-limit drop deformation and secondary breakup,” Int. J. Multiphase Flow 18, 635–652 (1992).
[CrossRef]

J. Laser Appl. (1)

N. Roth, K. Anders, and A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37 (1990).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Opt. Soc. Am. B (2)

J. Quant. Spectrosc. Radiat. Transfer (3)

G. Gouesbet, F. Xu, and Y. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

L. Han, Y. Han, Z. Cui, and J. Wang, “Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory,” J. Quant. Spectrosc. Radiat. Transfer 147, 279–287 (2014).
[CrossRef]

L. Han, Y. Han, J. Wang, and G. Gouesbet, “Internal and near-surface field distributions for a spheroidal particle illuminated by a focused Gaussian beam: on-axis case,” J. Quant. Spectrosc. Radiat. Transfer 126, 38–43 (2013).
[CrossRef]

Nanotechnology (1)

W. Wu, A. Katsnelson, O. G. Memis, and H. Mohseni, “A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars,” Nanotechnology 18, 485302 (2007).
[CrossRef]

Nat. Commun. (1)

Z. Wang, W. Guo, L. Li, B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50  nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Nat. Nanotechnol. (1)

E. Mcleod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3, 413–417 (2008).
[CrossRef]

Opt. Commun. (4)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Y. P. Han, L. C. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz–Mie theory framework,” Opt. Commun. 231, 71–77 (2004).
[CrossRef]

L. Han, G. Gouesbet, Y. Han, G. Gréhan, and J. Wang, “Intrinsic method for the evaluation of beam shape coefficients in spheroidal coordinates for on-axis standard configuration,” Opt. Commun. 310, 125–137 (2014).
[CrossRef]

S. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
[CrossRef]

Opt. Express (8)

Y. Han, H. Zhang, and G. Han, “The expansion coefficients of arbitrary shaped beam in oblique illumination,” Opt. Express 15, 735–746 (2007).
[CrossRef]

P. Ferrand, J. Wenger, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, and H. Rigneault, “Direct imaging of photonic nanojets,” Opt. Express 16, 6930–6940 (2008).
[CrossRef]

S. C. Kong, A. Sahakian, A. Taflove, and V. Backman, “Photonic nanojet-enabled optical data storage,” Opt. Express 16, 13713–13719 (2008).
[CrossRef]

A. Devilez, B. Stout, N. Bonod, and E. Popov, “Spectral analysis of three-dimensional photonic jets,” Opt. Express 16, 14200–14212 (2008).
[CrossRef]

F. O. Fahrbach, V. Gurchenkov, K. Alessandri, P. Nassoy, and A. Rohrbach, “Light-sheet microscopy in thick media using scanned Bessel beams and two-photon fluorescence excitation,” Opt. Express 21, 13824–13839 (2013).
[CrossRef]

M. J. Mendes, I. Tobías, A. Martí, and A. Luque, “Light concentration in the near-field of dielectric spheroidal particles with mesoscopic sizes,” Opt. Express 19, 16207–16222 (2011).
[CrossRef]

Z. Chen, A. Taflove, and V. Backman, “Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique,” Opt. Express 12, 1214–1220 (2004).
[CrossRef]

X. Li, Z. G. Chen, A. Taflove, and V. Backman, “Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets,” Opt. Express 13, 526–533 (2005).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. E (1)

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

J. Fan, E. Parra, and H. Milchberg, “Resonant self-trapping and absorption of intense Bessel beams,” Phys. Rev. Lett. 84, 3085–3088 (2000).
[CrossRef]

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401–1404 (1993).
[CrossRef]

Prog. Electromagn. Res. Lett. (1)

C.-Y. Liu, “Ultra-elongated photonic nanojets generated by a graded-index microellipsoid,” Prog. Electromagn. Res. Lett. 37, 153–165 (2013).
[CrossRef]

SPIE Newsroom (1)

V. N. Astratov, A. Darafsheh, M. D. Kerr, K. W. Allen, N. M. Fried, A. N. Antoszyk, and H. S. Ying, “Photonic nanojets for laser surgery,” SPIE Newsroom 12, 32–34 (2010).

Other (3)

H. Seidfaraji, M. Hasan, and J. J. Simpson, “A feasibility study of microjets applied to breast cancer detection,” in 2012 International Conference on Electromagnetics in Advanced Applications (IEEE, 2012), pp. 949–951.

D. Maděránková, I. Provazník, and K. Klepárník, “Numerical modeling of photonic nanojet behind dielectric microcylinder,” in Proceedings of World Congress on Medical Physics and Biomedical Engineering, O. Dossel and W. C. Schlegel, eds. (Springer, 2010), pp. 1135–1138.

C. Flammer, Spheroidal Wave Functions (Stanford University, 1957).

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Figures (5)

Fig. 1.
Fig. 1.

Spheroidal particle illuminated by an on-axis incident zero-order Bessel beam.

Fig. 2.
Fig. 2.

(a) Intensity distributions along the z axis for a spheroid illuminated by a plane wave and a zero-order Bessel beam with β=0°. The dashed lines mark the particle boundary. (b) Normalized external and internal intensity spatial distributions over the xz plane for the spheroid illuminated by a plane wave. The particle borders are represented by the white lines. The semi-major axis of the spheroid is a=1.0λ, the axis ratio is a/b=1.5, and the relative refractive index is nII/nI=1.45.

Fig. 3.
Fig. 3.

Normalized external and internal intensity spatial distributions over the xz plane with the half-cone angle β as the parameter: (a) β=10°, (b) β=15°, and (c) β=20°. All the parameters of the spheroid for this case are the same as for Fig. 2. The particle borders are represented by the white lines.

Fig. 4.
Fig. 4.

Normalized external and internal intensity spatial distributions over the xz plane for a spheroid (nII/nI=1.414) with different semi-major and semi-minor axes illuminated by a zero-order Bessel beam with β=20°: (a) a=1.0λ, a/b=1.75; (b) a=1.0λ, a/b=1.5; (c) a=1.0λ, a/b=1.25; (d) a=1.0λ, a/b=1.0; (e) b=1.0λ, a/b=1.2; (f) b=1.0λ, a/b=1.4; and (g) b=1.0λ, a/b=1.6. The particle borders are represented by the white lines.

Fig. 5.
Fig. 5.

Normalized external and internal intensity spatial distributions over the xz plane with the refractive index as the parameter: (a) nII=1.33, (b) nII=1.414, (c) nII=1.45, and (d) nII=1.5. The incident zero-order Bessel beam has half-cone angle β=30°. The semi-major axis of the spheroid is a=0.8λ, the axis ratio is a/b=1.1, and the surrounding medium is air (refractive index nI=1.0). The particle borders are represented by the white lines.

Equations (61)

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Ei=E0n=1in+1[2Gn,TE1Mo1nr(1)(cI;ξ,η,ϕ)+2Gn,TM1Ne1nr(1)(cI;ξ,η,ϕ)],
Hi=ikIωμ0H0n=1in+1[2Gn,TM1Me1nr(1)(cI;ξ,η,ϕ)2Gn,TE1No1nr(1)(cI;ξ,η,ϕ)],
Gn,TM1=iGn,TE1,
Es=E0n=1in[αn1Mo1nr(3)(cI;ξ,η,ϕ)iβn1Ne1nr(3)(cI;ξ,η,ϕ)],
Hs=kIωμ0H0n=1in[βn1Me1nr(3)(cI;ξ,η,ϕ)+iαn1No1nr(3)(cI;ξ,η,ϕ)],
Ew=E0n=1in[γn1Mo1nr(1)(cII;ξ,η,ϕ)iδn1Ne1nr(1)(cII;ξ,η,ϕ)],
Hw=kIIωμ0H0n=1in[δn1Me1nr(1)(cII;ξ,η,ϕ)+iγn1No1nr(1)(cII;ξ,η,ϕ)],
Eηi+Eηs=Eηw,Eφi+Eφs=EφwHηi+Hηs=Hηw,Hφi+Hφs=Hφw}atξ=ξ0,
n=1in[Γ][αn1βn1δn1γn1]=n=1in[G][Un1,(1)(cI)Vn1,(1)(cI)Xn1,(1)(cI)Yn1,(1)(cI)],
[Γ]=[Vn1,(3)(cI)Un1,(3)(cI)Un1,(1)(cII)Vn1,(1)(cII)Un1,(3)(cI)Vn1,(3)(cI)kIIkIVn1,(1)(cII)kIIkIUn1,(1)(cII)Yn1,(3)(cI)Xn1,(3)(cI)Xn1,(1)(cII)Yn1,(1)(cII)Xn1,(3)(cI)Yn1,(3)(cI)kIIkIYn1,(1)(cII)kIIkIXn1,(1)(cII)],
[G]=2i[Gn,TE1Gn,TE100Gn,TE1Gn,TE10000Gn,TE1Gn,TE100Gn,TE1Gn,TE1].
Eξi(ξ,η,ϕ)=E0n=1in+1[2Gn,TE1Mo1nξr(1)(cI;ξ,η,ϕ)+2Gn,TM1Ne1nξr(1)(cI;ξ,η,ϕ)].
Eξi(ξ,η,ϕ)=2E0n=1,in+1Gn,TE1[Mo1nξr(1)(cI;ξ,η,ϕ)+iNe1nξr(1)(cI;ξ,η,ϕ)].
eξ(ξ,η)=2n=1,in+1A1,n,ξ(cI;ξ,η)Gn,TE1,
eξ(ξ,η)=Eξi(ξ,η,ϕ)E0cosϕ,
A1,n,ξ(cI;ξ,η)=1cosϕ[Mo1nξr(1)(cI;ξ,η,ϕ)+iNe1nξr(1)(cI;ξ,η,ϕ)],
[eξ(ξ,η1)eξ(ξ,η2)eξ(ξ,η3)eξ(ξ,η4)]=2[i2A11ξ(cI;ξ,η1)i3A12ξ(cI;ξ,η1)inA1(n1)ξ(cI;ξ,η1)in+1A1nξ(cI;ξ,η1)i2A11ξ(cI;ξ,η2)i3A12ξ(cI;ξ,η2)inA1(n1)ξ(cI;ξ,η2)in+1A1nξ(cI;ξ,η2)i2A11ξ(cI;ξ,η3)i3A12ξ(cI;ξ,η3)inA1(n1)ξ(cI;ξ,η3)in+1A1nξ(cI;ξ,η3)i2A11ξ(cI;ξ,η4)i3A12ξ(cI;ξ,η4)inA1(n1)ξ(cI;ξ,η4)in+1A1nξ(cI;ξ,η4)][G1,TE1G2,TE1Gn1,TE1Gn,TE1].
[G1,TE1G2,TE1Gn1,TE1Gn,TE1]=12[i2A11ξ(cI;ξ,η1)i3A12ξ(cI;ξ,η1)inA1(n1)ξ(cI;ξ,η1)in+1A1nξ(cI;ξ,η1)i2A11ξ(cI;ξ,η2)i3A12ξ(cI;ξ,η2)inA1(n1)ξ(cI;ξ,η2)in+1A1nξ(cI;ξ,η2)i2A11ξ(cI;ξ,η3)i3A12ξ(cI;ξ,η3)inA1(n1)ξ(cI;ξ,η3)in+1A1nξ(cI;ξ,η3)i2A11ξ(cI;ξ,η4)i3A12ξ(cI;ξ,η4)inA1(n1)ξ(cI;ξ,η4)in+1A1nξ(cI;ξ,η4)]1[eξ(ξ,η1)eξ(ξ,η2)eξ(ξ,η3)eξ(ξ,η4)],
Eξi=E02{ξ(1η2ξ2η2)12(bkR2k2)J0(kRr)+1k(ξ2η2)12[kRξkf(ξ21)12ikRbη(ξ21)12]J1(kRr)}×cosϕexp(ikzfηξ),
Eξs=E0n=1in[αn1Mo1n,ξr(3)(cI;ξ,η,ϕ)iβn1Ne1n,ξr(3)(cI;ξ,η,ϕ)],
Eηs=E0n=1in[αn1Mo1n,ηr(3)(cI;ξ,η,ϕ)iβn1Ne1n,ηr(3)(cI;ξ,η,ϕ)],
Eϕs=E0n=1in[αn1Mo1n,ϕr(3)(cI;ξ,η,ϕ)iβn1Ne1n,ϕr(3)(cI;ξ,η,ϕ)].
Eξw=E0n=1in[γn1Mo1n,ξr(1)(cII;ξ,η,ϕ)iδn1Ne1n,ξr(1)(cII;ξ,η,ϕ)],
Eηw=E0n=1in[γn1Mo1n,ηr(1)(cII;ξ,η,ϕ)iδn1Ne1n,ηr(1)(cII;ξ,η,ϕ)],
Eϕw=E0n=1in[γn1Mo1n,ϕr(1)(cII;ξ,η,ϕ)iδn1Ne1n,ϕr(1)(cII;ξ,η,ϕ)].
Is=EsEs*=EηsEηs*+EξsEξs*+EϕsEϕs*,
Iw=EwEw*=EηwEηw*+EξwEξw*+EϕwEϕw*,
Mmn=Mmn,ξξ^+Mmn,ηη^+Mmn,ϕϕ^,
Nmn=Nmn,ξξ^+Nmn,ηη^+Nmn,ϕϕ^,
Mmn,ξr(i)=imη[(ξ2η2)(ξ21)]12R|m|n(i)(c,ξ)×S|m|n(c,η)exp(imϕ),
Mmn,ηr(i)=imξ[(ξ2η2)(1η2)]12R|m|n(i)(c,ξ)×S|m|n(c,η)exp(imϕ),
Mmn,ϕr(i)=[(ξ21)(1η2)]12(ξ2η2)[ξR|m|n(i)(c,ξ)S|m|n(c,η)ηR|m|n(i)(c,ξ)S|m|n(c,η)]exp(imϕ),
Nmn,ξr(i)=(ξ21)12c(ξ2η2)32{ξ[λ|m|nc2η2+m2(ξ21)]×S|m|n(c,η)R|m|n(i)(c,ξ)2ξη(1η2)(ξ2η2)S|m|n(c,η)R|m|n(i)(c,ξ)+η(1η2)S|m|n(c,η)R|m|n(i)(c,ξ)+ξ2(13η2)+η2(η2+1)(ξ2η2)S|m|n(c,η)R|m|n(i)(c,ξ)}×exp(imϕ),
Nmn,ηr(i)=(1η2)12c(ξ2η2)32{ξ(ξ21)R|m|n(i)(c,ξ)S|m|n(c,η)+ξ2(ξ2+1)+η2(13ξ2)(ξ2η2)×R|m|n(i)(c,ξ)S|m|n(c,η)η[λ|m|nξ2c2m2(1η2)]×R|m|n(i)(c,ξ)S|m|n(c,η)+2ξη(ξ21)(ξ2η2)R|m|n(i)(c,ξ)S|m|n(c,η)}exp(imϕ),
Nmn,ϕr(i)=im[(ξ21)(1η2)]12c(ξ2η2)×[η(ξ21)R|m|n(i)(c,ξ)S|m|n(c,η)+ξ(1η2)R|m|n(i)(c,ξ)S|m|n(c,η)+(ξ2η2)(ξ21)(1η2)R|m|n(i)(c,ξ)S|m|n(c,η)]×exp(imϕ),
M(eo)mn,ξr(i)=mη[(ξ2η2)(ξ21)]12R|m|n(i)(c,ξ)S|m|n(c,η)×(sin(mϕ)cos(mϕ)),
M(eo)mn,ηr(i)=mξ[(ξ2η2)(1η2)]12R|m|n(i)(c,ξ)S|m|n(c,η)×(sin(mϕ)cos(mϕ)),
M(eo)mn,ϕr(i)=[(ξ21)(1η2)]12(ξ2η2)[ξR|m|n(i)(c,ξ)S|m|n(c,η)ηR|m|n(i)(c,ξ)S|m|n(c,η)](cos(mϕ)sin(mϕ)),
N(eo)mn,ξr(i)=(ξ21)12c(ξ2η2)32{ξ[λ|m|nc2η2+m2(ξ21)]×S|m|n(c,η)R|m|n(i)(c,ξ)2ξη(1η2)(ξ2η2)S|m|n(c,η)R|m|n(i)(c,ξ)+η(1η2)S|m|n(c,η)R|m|n(i)(c,ξ)+ξ2(13η2)+η2(η2+1)(ξ2η2)×S|m|n(c,η)R|m|n(i)(c,ξ)}(cos(mϕ)sin(mϕ)),
N(eo)mn,ηr(i)=(1η2)12c(ξ2η2)32{ξ(ξ21)R|m|n(i)(c,ξ)S|m|n(c,η)+ξ2(ξ2+1)+η2(13ξ2)(ξ2η2)×R|m|n(i)(c,ξ)S|m|n(c,η)η[λ|m|nξ2c2m2(1η2)]×R|m|n(i)(c,ξ)S|m|n(c,η)+2ξη(ξ21)(ξ2η2)R|m|n(i)(c,ξ)S|m|n(c,η)}×(cos(mϕ)sin(mϕ)),
N(eo)mn,ϕr(i)=m[(ξ21)(1η2)]12c(ξ2η2)×[η(ξ21)R|m|n(i)(c,ξ)S|m|n(c,η)+ξ(1η2)R|m|n(i)(c,ξ)S|m|n(c,η)+(ξ2η2)(ξ21)(1η2)R|m|n(i)(c,ξ)S|m|n(c,η)]×(sin(mϕ)cos(mϕ)).
Ex=12E0[(bkR2x2k2r02)J0(kRr0)kR(r022x2)k2r03J1(kRr0)]exp(ikzz),
Ey=12E0[2kRxyk2r03J1(kRr0)kR2xyk2r02J0(kRr0)]exp(ikzz),
Ez=12E0[ikRbxkr0J1(kRr0)]exp(ikzz),
kR=ksinβ,
kz=kcosβ,
r0=(x2+y2)12,
b=1+kzk,
x=f(1η2)12(ξ21)12cosϕ,
y=f(1η2)12(ξ21)12sinϕ,
z=fηξ,
ξ^=ξ(1η2ξ2η2)12cosϕx^+ξ(1η2ξ2η2)12sinϕy^+η(ξ21ξ2η2)12z^,
η^=η(ξ21ξ2η2)12cosϕx^η(ξ21ξ2η2)12sinϕy^+ξ(1η2ξ2η2)12z^,
ϕ^=sinϕx^+cosϕy^,
Eξ=E02{ξ(1η2ξ2η2)12(bkR2k2)J0(kRr)+1k(ξ2η2)12×[kRξkf(ξ21)12ikRbη(ξ21)12]J1(kRr)}×cosϕexp(ikzfηξ),
Eη=E02{η(ξ21ξ2η2)12(kR2k2b)J0(kRr)+[kRηk2f(1η2)12(ξ2η2)12ikRbξ2k(1η2ξ2η2)12J1(kRr)]}×cosϕexp(ikzfηξ),
Eϕ=E02[bJ0(kRr)+kRJ1(kRr)k2f(1η2)12(ξ2η2)12]×sinϕexp(ikzfηξ)
kR=ksinβ,
kz=kcosβ,
r=f(1η2)12(ξ21)12,
b=1+kzk.

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