Abstract

The electromagnetic (EM) radiation force-per-length exerted on a pair of electrically-conducting cylindrical particles of circular and non-circular cross-sections is examined using a formal semi-analytical method based on boundary matching in cylindrical coordinates. Initially, the scattering coefficients of the particle pair are determined by imposing suitable boundary conditions leading linear systems of equations computed via matrix inversion and numerical integration procedures. Standard cylindrical (Bessel and Hankel) wave functions are used and closed-form expressions for the dimensionless longitudinal and transverse radiation force functions are evaluated assuming either magnetic (TE) or electric (TM) plane wave incidences. Particle pairs with smooth and corrugated surfaces are considered and numerical computations are performed with emphasis on the distance separating their centers of mass, the angle of incidence of the incident illuminating field and the surface roughness. Adequate convergence plots confirm the validity of the method to evaluate the radiation force functions, and the model is adaptable to any frequency range (i.e. Rayleigh, Mie or geometrical optics regimes). The results can find potential applications in optical tweezers and other related applications in fluid dynamics. In addition, the acoustical analogue is discussed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles

References

  • View by:
  • |
  • |
  • |

  1. F. G. Mitri, “Pushing, pulling and electromagnetic radiation force cloaking by a pair of conducting cylindrical particles,” J. Quant. Spectrosc. Radiat. Transf. 206, 142–150 (2018).
    [Crossref]
  2. K. Dholakia and P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82(2), 1767–1791 (2010).
    [Crossref]
  3. F. G. Mitri, “Acoustic attraction, repulsion and radiation force cancellation on a pair of rigid particles with arbitrary cross-sections in 2D: Circular cylinders example,” Ann. Phys. 386, 1–14 (2017).
    [Crossref]
  4. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).
  5. F. G. Mitri, “Electromagnetic radiation force on electrically conducting smooth and corrugated elliptical cylinders,” https://arxiv.org/abs/1803.09397 (2018).
  6. J. P. Barton, “Electromagnetic-field calculations for irregularly shaped, layered cylindrical particles with focused illumination,” Appl. Opt. 36(6), 1312–1319 (1997).
    [Crossref] [PubMed]
  7. F. Léon, F. Chati, and J.-M. Conoir, “Modal theory applied to the acoustic scattering by elastic cylinders of arbitrary cross section,” J. Acoust. Soc. Am. 116(2), 686–692 (2004).
    [Crossref]
  8. F. G. Mitri, “Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder,” J. Appl. Phys. 118(18), 184902 (2015).
    [Crossref]
  9. F. G. Mitri, “Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves,” J. Appl. Phys. 118(21), 214903 (2015).
    [Crossref]
  10. F. G. Mitri, “Radiation forces and torque on a rigid elliptical cylinder in acoustical plane progressive and (quasi)standing waves with arbitrary incidence,” Phys. Fluids 28(7), 077104 (2016) (See also the Reply to some misleading and inaccurate comments at: https://arxiv.org/abs/1703.00487 ).
    [Crossref]
  11. F. G. Mitri, “Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves,” Ultrasonics 66, 27–33 (2016).
    [Crossref] [PubMed]
  12. F. G. Mitri, “Radiation force and torque of light-sheets,” J. Opt. 19(6), 065403 (2017).
    [Crossref]
  13. F. G. Mitri, “Pulling and spinning reversal of a subwavelength absorptive sphere in adjustable vector Airy light-sheets,” Appl. Phys. Lett. 110(18), 181112 (2017).
    [Crossref]
  14. F. G. Mitri, “Interaction of Bessel pincers light-sheets with an absorptive subwavelength sphere coated by a plasmonic layer,” J. Opt. Soc. Am. B 34(7), 1471–1477 (2017).
    [Crossref]
  15. F. G. Mitri, “Negative optical radiation force and spin torques on subwavelength prolate and oblate spheroids in fractional Bessel-Gauss pincers light-sheets,” J. Opt. Soc. Am. A 34(7), 1246–1254 (2017).
    [Crossref] [PubMed]
  16. F. G. Mitri, “Adjustable vector Airy light-sheet single optical tweezers: negative radiation forces on a subwavelength spheroid and spin torque reversal,” Eur. Phys. J. D 72(1), 21 (2018).
    [Crossref]
  17. F. G. Mitri, “Optical Bessel beam illumination of a subwavelength prolate gold (Au) spheroid coated by a layer of plasmonic material: radiation force, spin and orbital torques,” J. Phys. Commun. 1(1), 015001 (2017).
    [Crossref]
  18. F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
    [Crossref]
  19. F. G. Mitri, “Reverse orbiting and spinning of a Rayleigh dielectric spheroid in a J0 Bessel optical beam,” J. Opt. Soc. Am. B 34(10), 2169–2178 (2017).
    [Crossref]
  20. R. Yang, R. Li, S. Qin, C. Y. Ding, and F. G. Mitri, “Direction reversal of the optical spin torque on a Rayleigh absorptive sphere in vector Bessel polarized beams,” J. Opt. 19(2), 025602 (2017).
    [Crossref]
  21. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63(12), 1233–1236 (1989).
    [Crossref] [PubMed]
  22. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249(4970), 749–754 (1990).
    [Crossref] [PubMed]
  23. T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, “Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field,” J. Opt. Soc. Am. A 23(9), 2324–2330 (2006).
    [Crossref] [PubMed]
  24. O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18(24), 25389–25402 (2010).
    [Crossref] [PubMed]
  25. J. Chen, J. Ng, P. Wang, and Z. Lin, “Analytical partial wave expansion of vector Bessel beam and its application to optical binding,” Opt. Lett. 35(10), 1674–1676 (2010).
    [Crossref] [PubMed]
  26. T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. At. Mol. Opt. Phys. 43(10), 102001 (2010).
    [Crossref]
  27. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University Press, 2006).
  28. A. Sebak and L. Shafai, “Generalized solutions for electromagnetic scattering by elliptical structures,” Comput. Phys. Commun. 68(1-3), 315–330 (1991).
    [Crossref]
  29. A. K. Hamid and M. I. Hussein, “Electromagnetic scattering by two parallel conducting elliptic cylinders: iterative solution,” in IEEE International Symposium on Electromagnetic Compatibility ’03, Vol. 21 (2003), pp. 21–24.
  30. A. K. Hamid and M. I. Hussein, “Iterative solution to the electromagnetic plane wave scattering by two parallel conducting elliptic cylinders,” J. Electromagn. Waves Appl. 17(6), 813–828 (2003).
    [Crossref]
  31. A. K. Hamid, “Scattering by two infinitely long dielectric-coated confocal conducting elliptic cylinders,” J. Electromagn. Waves Appl. 18(11), 1427–1441 (2004).
    [Crossref]
  32. G. P. Zouros, “Electromagnetic plane wave scattering by arbitrarily oriented elliptical dielectric cylinders,” J. Opt. Soc. Am. A 28(11), 2376–2384 (2011).
    [Crossref] [PubMed]
  33. N. Dodgson and C. Sozou, “The deformation of a liquid drop by an electric field,” Z. Angew. Math. Phys. 38(3), 424–432 (1987).
    [Crossref]
  34. S. D. Deshmukh and R. M. Thaokar, “Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field,” Phys. Fluids 24(3), 032105 (2012).
    [Crossref]
  35. S. Sankaran and D. A. Saville, “Experiments on the stability of a liquid bridge in an axial electric field,” Phys. Fluids A Fluid Dyn. 5(4), 1081–1083 (1993).
    [Crossref]
  36. S. Mhatre, “Dielectrophoretic motion and deformation of a liquid drop in an axisymmetric non-uniform AC electric field,” Sens. Actuators B Chem. 239, 1098–1108 (2017).
    [Crossref]
  37. F. G. Mitri, “Acoustic radiation force on oblate and prolate spheroids in Bessel beams,” Wave Motion 57, 231–238 (2015).
    [Crossref]
  38. F. G. Mitri, “Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62(10), 1809–1818 (2015).
    [Crossref] [PubMed]
  39. F. G. Mitri, “Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid,” Ann. Phys. 363, 262–274 (2015).
    [Crossref]
  40. F. G. Mitri, “Acoustical pulling force on rigid spheroids in single Bessel vortex tractor beams,” Europhys. Lett. 112(3), 34002 (2015).
    [Crossref]
  41. Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
    [Crossref]
  42. Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
    [Crossref]
  43. F. G. Mitri, “Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves,” Ultrasonics 74, 62–71 (2017).
    [Crossref] [PubMed]
  44. Acoustic, Electromagnetic and Elastic Wave Scattering—Focus on the T-Matrix Approach, V. K. Varadan and V. V. Varadan, eds. (Pergamon, 1980).
  45. L. F. Shampine, “Vectorized adaptive quadrature in MATLAB,” J. Comput. Appl. Math. 211(2), 131–140 (2008).
    [Crossref]

2018 (2)

F. G. Mitri, “Pushing, pulling and electromagnetic radiation force cloaking by a pair of conducting cylindrical particles,” J. Quant. Spectrosc. Radiat. Transf. 206, 142–150 (2018).
[Crossref]

F. G. Mitri, “Adjustable vector Airy light-sheet single optical tweezers: negative radiation forces on a subwavelength spheroid and spin torque reversal,” Eur. Phys. J. D 72(1), 21 (2018).
[Crossref]

2017 (12)

F. G. Mitri, “Optical Bessel beam illumination of a subwavelength prolate gold (Au) spheroid coated by a layer of plasmonic material: radiation force, spin and orbital torques,” J. Phys. Commun. 1(1), 015001 (2017).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

F. G. Mitri, “Reverse orbiting and spinning of a Rayleigh dielectric spheroid in a J0 Bessel optical beam,” J. Opt. Soc. Am. B 34(10), 2169–2178 (2017).
[Crossref]

R. Yang, R. Li, S. Qin, C. Y. Ding, and F. G. Mitri, “Direction reversal of the optical spin torque on a Rayleigh absorptive sphere in vector Bessel polarized beams,” J. Opt. 19(2), 025602 (2017).
[Crossref]

F. G. Mitri, “Radiation force and torque of light-sheets,” J. Opt. 19(6), 065403 (2017).
[Crossref]

F. G. Mitri, “Pulling and spinning reversal of a subwavelength absorptive sphere in adjustable vector Airy light-sheets,” Appl. Phys. Lett. 110(18), 181112 (2017).
[Crossref]

F. G. Mitri, “Interaction of Bessel pincers light-sheets with an absorptive subwavelength sphere coated by a plasmonic layer,” J. Opt. Soc. Am. B 34(7), 1471–1477 (2017).
[Crossref]

F. G. Mitri, “Negative optical radiation force and spin torques on subwavelength prolate and oblate spheroids in fractional Bessel-Gauss pincers light-sheets,” J. Opt. Soc. Am. A 34(7), 1246–1254 (2017).
[Crossref] [PubMed]

F. G. Mitri, “Acoustic attraction, repulsion and radiation force cancellation on a pair of rigid particles with arbitrary cross-sections in 2D: Circular cylinders example,” Ann. Phys. 386, 1–14 (2017).
[Crossref]

S. Mhatre, “Dielectrophoretic motion and deformation of a liquid drop in an axisymmetric non-uniform AC electric field,” Sens. Actuators B Chem. 239, 1098–1108 (2017).
[Crossref]

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

F. G. Mitri, “Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves,” Ultrasonics 74, 62–71 (2017).
[Crossref] [PubMed]

2016 (3)

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

F. G. Mitri, “Radiation forces and torque on a rigid elliptical cylinder in acoustical plane progressive and (quasi)standing waves with arbitrary incidence,” Phys. Fluids 28(7), 077104 (2016) (See also the Reply to some misleading and inaccurate comments at: https://arxiv.org/abs/1703.00487 ).
[Crossref]

F. G. Mitri, “Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves,” Ultrasonics 66, 27–33 (2016).
[Crossref] [PubMed]

2015 (6)

F. G. Mitri, “Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder,” J. Appl. Phys. 118(18), 184902 (2015).
[Crossref]

F. G. Mitri, “Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves,” J. Appl. Phys. 118(21), 214903 (2015).
[Crossref]

F. G. Mitri, “Acoustic radiation force on oblate and prolate spheroids in Bessel beams,” Wave Motion 57, 231–238 (2015).
[Crossref]

F. G. Mitri, “Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62(10), 1809–1818 (2015).
[Crossref] [PubMed]

F. G. Mitri, “Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid,” Ann. Phys. 363, 262–274 (2015).
[Crossref]

F. G. Mitri, “Acoustical pulling force on rigid spheroids in single Bessel vortex tractor beams,” Europhys. Lett. 112(3), 34002 (2015).
[Crossref]

2012 (1)

S. D. Deshmukh and R. M. Thaokar, “Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field,” Phys. Fluids 24(3), 032105 (2012).
[Crossref]

2011 (1)

2010 (4)

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18(24), 25389–25402 (2010).
[Crossref] [PubMed]

J. Chen, J. Ng, P. Wang, and Z. Lin, “Analytical partial wave expansion of vector Bessel beam and its application to optical binding,” Opt. Lett. 35(10), 1674–1676 (2010).
[Crossref] [PubMed]

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. At. Mol. Opt. Phys. 43(10), 102001 (2010).
[Crossref]

K. Dholakia and P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82(2), 1767–1791 (2010).
[Crossref]

2008 (1)

L. F. Shampine, “Vectorized adaptive quadrature in MATLAB,” J. Comput. Appl. Math. 211(2), 131–140 (2008).
[Crossref]

2006 (1)

2004 (2)

F. Léon, F. Chati, and J.-M. Conoir, “Modal theory applied to the acoustic scattering by elastic cylinders of arbitrary cross section,” J. Acoust. Soc. Am. 116(2), 686–692 (2004).
[Crossref]

A. K. Hamid, “Scattering by two infinitely long dielectric-coated confocal conducting elliptic cylinders,” J. Electromagn. Waves Appl. 18(11), 1427–1441 (2004).
[Crossref]

2003 (1)

A. K. Hamid and M. I. Hussein, “Iterative solution to the electromagnetic plane wave scattering by two parallel conducting elliptic cylinders,” J. Electromagn. Waves Appl. 17(6), 813–828 (2003).
[Crossref]

1997 (1)

1993 (1)

S. Sankaran and D. A. Saville, “Experiments on the stability of a liquid bridge in an axial electric field,” Phys. Fluids A Fluid Dyn. 5(4), 1081–1083 (1993).
[Crossref]

1991 (1)

A. Sebak and L. Shafai, “Generalized solutions for electromagnetic scattering by elliptical structures,” Comput. Phys. Commun. 68(1-3), 315–330 (1991).
[Crossref]

1990 (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249(4970), 749–754 (1990).
[Crossref] [PubMed]

1989 (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63(12), 1233–1236 (1989).
[Crossref] [PubMed]

1987 (1)

N. Dodgson and C. Sozou, “The deformation of a liquid drop by an electric field,” Z. Angew. Math. Phys. 38(3), 424–432 (1987).
[Crossref]

Andrews, D. L.

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. At. Mol. Opt. Phys. 43(10), 102001 (2010).
[Crossref]

Barton, J. P.

Brzobohatý, O.

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249(4970), 749–754 (1990).
[Crossref] [PubMed]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63(12), 1233–1236 (1989).
[Crossref] [PubMed]

Chai, Y.

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Chati, F.

F. Léon, F. Chati, and J.-M. Conoir, “Modal theory applied to the acoustic scattering by elastic cylinders of arbitrary cross section,” J. Acoust. Soc. Am. 116(2), 686–692 (2004).
[Crossref]

Chen, J.

Cižmár, T.

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18(24), 25389–25402 (2010).
[Crossref] [PubMed]

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. At. Mol. Opt. Phys. 43(10), 102001 (2010).
[Crossref]

Conoir, J.-M.

F. Léon, F. Chati, and J.-M. Conoir, “Modal theory applied to the acoustic scattering by elastic cylinders of arbitrary cross section,” J. Acoust. Soc. Am. 116(2), 686–692 (2004).
[Crossref]

Deshmukh, S. D.

S. D. Deshmukh and R. M. Thaokar, “Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field,” Phys. Fluids 24(3), 032105 (2012).
[Crossref]

Dholakia, K.

K. Dholakia and P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82(2), 1767–1791 (2010).
[Crossref]

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. At. Mol. Opt. Phys. 43(10), 102001 (2010).
[Crossref]

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18(24), 25389–25402 (2010).
[Crossref] [PubMed]

Ding, C. Y.

R. Yang, R. Li, S. Qin, C. Y. Ding, and F. G. Mitri, “Direction reversal of the optical spin torque on a Rayleigh absorptive sphere in vector Bessel polarized beams,” J. Opt. 19(2), 025602 (2017).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

Dodgson, N.

N. Dodgson and C. Sozou, “The deformation of a liquid drop by an electric field,” Z. Angew. Math. Phys. 38(3), 424–432 (1987).
[Crossref]

Fournier, J.-M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249(4970), 749–754 (1990).
[Crossref] [PubMed]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63(12), 1233–1236 (1989).
[Crossref] [PubMed]

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249(4970), 749–754 (1990).
[Crossref] [PubMed]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63(12), 1233–1236 (1989).
[Crossref] [PubMed]

Gong, Z.

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Grzegorczyk, T. M.

Guo, L. X.

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

Hamid, A. K.

A. K. Hamid, “Scattering by two infinitely long dielectric-coated confocal conducting elliptic cylinders,” J. Electromagn. Waves Appl. 18(11), 1427–1441 (2004).
[Crossref]

A. K. Hamid and M. I. Hussein, “Iterative solution to the electromagnetic plane wave scattering by two parallel conducting elliptic cylinders,” J. Electromagn. Waves Appl. 17(6), 813–828 (2003).
[Crossref]

Hussein, M. I.

A. K. Hamid and M. I. Hussein, “Iterative solution to the electromagnetic plane wave scattering by two parallel conducting elliptic cylinders,” J. Electromagn. Waves Appl. 17(6), 813–828 (2003).
[Crossref]

Karásek, V.

Kemp, B. A.

Kong, J. A.

Léon, F.

F. Léon, F. Chati, and J.-M. Conoir, “Modal theory applied to the acoustic scattering by elastic cylinders of arbitrary cross section,” J. Acoust. Soc. Am. 116(2), 686–692 (2004).
[Crossref]

Li, R.

R. Yang, R. Li, S. Qin, C. Y. Ding, and F. G. Mitri, “Direction reversal of the optical spin torque on a Rayleigh absorptive sphere in vector Bessel polarized beams,” J. Opt. 19(2), 025602 (2017).
[Crossref]

Li, R. X.

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

Li, W.

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Lin, Z.

Mhatre, S.

S. Mhatre, “Dielectrophoretic motion and deformation of a liquid drop in an axisymmetric non-uniform AC electric field,” Sens. Actuators B Chem. 239, 1098–1108 (2017).
[Crossref]

Mitri, F. G.

F. G. Mitri, “Adjustable vector Airy light-sheet single optical tweezers: negative radiation forces on a subwavelength spheroid and spin torque reversal,” Eur. Phys. J. D 72(1), 21 (2018).
[Crossref]

F. G. Mitri, “Pushing, pulling and electromagnetic radiation force cloaking by a pair of conducting cylindrical particles,” J. Quant. Spectrosc. Radiat. Transf. 206, 142–150 (2018).
[Crossref]

F. G. Mitri, “Optical Bessel beam illumination of a subwavelength prolate gold (Au) spheroid coated by a layer of plasmonic material: radiation force, spin and orbital torques,” J. Phys. Commun. 1(1), 015001 (2017).
[Crossref]

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

F. G. Mitri, “Acoustic attraction, repulsion and radiation force cancellation on a pair of rigid particles with arbitrary cross-sections in 2D: Circular cylinders example,” Ann. Phys. 386, 1–14 (2017).
[Crossref]

F. G. Mitri, “Radiation force and torque of light-sheets,” J. Opt. 19(6), 065403 (2017).
[Crossref]

F. G. Mitri, “Pulling and spinning reversal of a subwavelength absorptive sphere in adjustable vector Airy light-sheets,” Appl. Phys. Lett. 110(18), 181112 (2017).
[Crossref]

R. Yang, R. Li, S. Qin, C. Y. Ding, and F. G. Mitri, “Direction reversal of the optical spin torque on a Rayleigh absorptive sphere in vector Bessel polarized beams,” J. Opt. 19(2), 025602 (2017).
[Crossref]

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

F. G. Mitri, “Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves,” Ultrasonics 74, 62–71 (2017).
[Crossref] [PubMed]

F. G. Mitri, “Interaction of Bessel pincers light-sheets with an absorptive subwavelength sphere coated by a plasmonic layer,” J. Opt. Soc. Am. B 34(7), 1471–1477 (2017).
[Crossref]

F. G. Mitri, “Negative optical radiation force and spin torques on subwavelength prolate and oblate spheroids in fractional Bessel-Gauss pincers light-sheets,” J. Opt. Soc. Am. A 34(7), 1246–1254 (2017).
[Crossref] [PubMed]

F. G. Mitri, “Reverse orbiting and spinning of a Rayleigh dielectric spheroid in a J0 Bessel optical beam,” J. Opt. Soc. Am. B 34(10), 2169–2178 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

F. G. Mitri, “Radiation forces and torque on a rigid elliptical cylinder in acoustical plane progressive and (quasi)standing waves with arbitrary incidence,” Phys. Fluids 28(7), 077104 (2016) (See also the Reply to some misleading and inaccurate comments at: https://arxiv.org/abs/1703.00487 ).
[Crossref]

F. G. Mitri, “Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves,” Ultrasonics 66, 27–33 (2016).
[Crossref] [PubMed]

F. G. Mitri, “Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder,” J. Appl. Phys. 118(18), 184902 (2015).
[Crossref]

F. G. Mitri, “Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves,” J. Appl. Phys. 118(21), 214903 (2015).
[Crossref]

F. G. Mitri, “Acoustic radiation force on oblate and prolate spheroids in Bessel beams,” Wave Motion 57, 231–238 (2015).
[Crossref]

F. G. Mitri, “Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62(10), 1809–1818 (2015).
[Crossref] [PubMed]

F. G. Mitri, “Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid,” Ann. Phys. 363, 262–274 (2015).
[Crossref]

F. G. Mitri, “Acoustical pulling force on rigid spheroids in single Bessel vortex tractor beams,” Europhys. Lett. 112(3), 34002 (2015).
[Crossref]

Ng, J.

Qin, S.

R. Yang, R. Li, S. Qin, C. Y. Ding, and F. G. Mitri, “Direction reversal of the optical spin torque on a Rayleigh absorptive sphere in vector Bessel polarized beams,” J. Opt. 19(2), 025602 (2017).
[Crossref]

Romero, L. C. D.

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. At. Mol. Opt. Phys. 43(10), 102001 (2010).
[Crossref]

Sankaran, S.

S. Sankaran and D. A. Saville, “Experiments on the stability of a liquid bridge in an axial electric field,” Phys. Fluids A Fluid Dyn. 5(4), 1081–1083 (1993).
[Crossref]

Saville, D. A.

S. Sankaran and D. A. Saville, “Experiments on the stability of a liquid bridge in an axial electric field,” Phys. Fluids A Fluid Dyn. 5(4), 1081–1083 (1993).
[Crossref]

Sebak, A.

A. Sebak and L. Shafai, “Generalized solutions for electromagnetic scattering by elliptical structures,” Comput. Phys. Commun. 68(1-3), 315–330 (1991).
[Crossref]

Shafai, L.

A. Sebak and L. Shafai, “Generalized solutions for electromagnetic scattering by elliptical structures,” Comput. Phys. Commun. 68(1-3), 315–330 (1991).
[Crossref]

Shampine, L. F.

L. F. Shampine, “Vectorized adaptive quadrature in MATLAB,” J. Comput. Appl. Math. 211(2), 131–140 (2008).
[Crossref]

Šiler, M.

Sozou, C.

N. Dodgson and C. Sozou, “The deformation of a liquid drop by an electric field,” Z. Angew. Math. Phys. 38(3), 424–432 (1987).
[Crossref]

Thaokar, R. M.

S. D. Deshmukh and R. M. Thaokar, “Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field,” Phys. Fluids 24(3), 032105 (2012).
[Crossref]

Wang, P.

Yang, R.

R. Yang, R. Li, S. Qin, C. Y. Ding, and F. G. Mitri, “Direction reversal of the optical spin torque on a Rayleigh absorptive sphere in vector Bessel polarized beams,” J. Opt. 19(2), 025602 (2017).
[Crossref]

Zemánek, P.

Zhao, Y.

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Zouros, G. P.

Ann. Phys. (2)

F. G. Mitri, “Acoustic attraction, repulsion and radiation force cancellation on a pair of rigid particles with arbitrary cross-sections in 2D: Circular cylinders example,” Ann. Phys. 386, 1–14 (2017).
[Crossref]

F. G. Mitri, “Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid,” Ann. Phys. 363, 262–274 (2015).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

F. G. Mitri, “Pulling and spinning reversal of a subwavelength absorptive sphere in adjustable vector Airy light-sheets,” Appl. Phys. Lett. 110(18), 181112 (2017).
[Crossref]

Comput. Phys. Commun. (1)

A. Sebak and L. Shafai, “Generalized solutions for electromagnetic scattering by elliptical structures,” Comput. Phys. Commun. 68(1-3), 315–330 (1991).
[Crossref]

Eur. Phys. J. D (1)

F. G. Mitri, “Adjustable vector Airy light-sheet single optical tweezers: negative radiation forces on a subwavelength spheroid and spin torque reversal,” Eur. Phys. J. D 72(1), 21 (2018).
[Crossref]

Europhys. Lett. (1)

F. G. Mitri, “Acoustical pulling force on rigid spheroids in single Bessel vortex tractor beams,” Europhys. Lett. 112(3), 34002 (2015).
[Crossref]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

F. G. Mitri, “Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62(10), 1809–1818 (2015).
[Crossref] [PubMed]

J. Acoust. Soc. Am. (1)

F. Léon, F. Chati, and J.-M. Conoir, “Modal theory applied to the acoustic scattering by elastic cylinders of arbitrary cross section,” J. Acoust. Soc. Am. 116(2), 686–692 (2004).
[Crossref]

J. Appl. Phys. (2)

F. G. Mitri, “Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder,” J. Appl. Phys. 118(18), 184902 (2015).
[Crossref]

F. G. Mitri, “Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves,” J. Appl. Phys. 118(21), 214903 (2015).
[Crossref]

J. Comput. Appl. Math. (1)

L. F. Shampine, “Vectorized adaptive quadrature in MATLAB,” J. Comput. Appl. Math. 211(2), 131–140 (2008).
[Crossref]

J. Electromagn. Waves Appl. (2)

A. K. Hamid and M. I. Hussein, “Iterative solution to the electromagnetic plane wave scattering by two parallel conducting elliptic cylinders,” J. Electromagn. Waves Appl. 17(6), 813–828 (2003).
[Crossref]

A. K. Hamid, “Scattering by two infinitely long dielectric-coated confocal conducting elliptic cylinders,” J. Electromagn. Waves Appl. 18(11), 1427–1441 (2004).
[Crossref]

J. Opt. (2)

R. Yang, R. Li, S. Qin, C. Y. Ding, and F. G. Mitri, “Direction reversal of the optical spin torque on a Rayleigh absorptive sphere in vector Bessel polarized beams,” J. Opt. 19(2), 025602 (2017).
[Crossref]

F. G. Mitri, “Radiation force and torque of light-sheets,” J. Opt. 19(6), 065403 (2017).
[Crossref]

J. Opt. Soc. Am. A (3)

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

J. Phys. At. Mol. Opt. Phys. (1)

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. At. Mol. Opt. Phys. 43(10), 102001 (2010).
[Crossref]

J. Phys. Commun. (1)

F. G. Mitri, “Optical Bessel beam illumination of a subwavelength prolate gold (Au) spheroid coated by a layer of plasmonic material: radiation force, spin and orbital torques,” J. Phys. Commun. 1(1), 015001 (2017).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (2)

F. G. Mitri, R. X. Li, L. X. Guo, and C. Y. Ding, “Optical tractor Bessel polarized beams,” J. Quant. Spectrosc. Radiat. Transf. 187, 97–115 (2017).
[Crossref]

F. G. Mitri, “Pushing, pulling and electromagnetic radiation force cloaking by a pair of conducting cylindrical particles,” J. Quant. Spectrosc. Radiat. Transf. 206, 142–150 (2018).
[Crossref]

J. Sound Vibrat. (1)

Z. Gong, W. Li, F. G. Mitri, Y. Chai, and Y. Zhao, “Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio,” J. Sound Vibrat. 383, 233–247 (2016).
[Crossref]

Ocean Eng. (1)

Z. Gong, W. Li, Y. Chai, Y. Zhao, and F. G. Mitri, “T-matrix method for acoustical Bessel beam scattering from a rigid finite cylinder with spheroidal endcaps,” Ocean Eng. 129, 507–519 (2017).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Fluids (2)

S. D. Deshmukh and R. M. Thaokar, “Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field,” Phys. Fluids 24(3), 032105 (2012).
[Crossref]

F. G. Mitri, “Radiation forces and torque on a rigid elliptical cylinder in acoustical plane progressive and (quasi)standing waves with arbitrary incidence,” Phys. Fluids 28(7), 077104 (2016) (See also the Reply to some misleading and inaccurate comments at: https://arxiv.org/abs/1703.00487 ).
[Crossref]

Phys. Fluids A Fluid Dyn. (1)

S. Sankaran and D. A. Saville, “Experiments on the stability of a liquid bridge in an axial electric field,” Phys. Fluids A Fluid Dyn. 5(4), 1081–1083 (1993).
[Crossref]

Phys. Rev. Lett. (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63(12), 1233–1236 (1989).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

K. Dholakia and P. Zemánek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82(2), 1767–1791 (2010).
[Crossref]

Science (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249(4970), 749–754 (1990).
[Crossref] [PubMed]

Sens. Actuators B Chem. (1)

S. Mhatre, “Dielectrophoretic motion and deformation of a liquid drop in an axisymmetric non-uniform AC electric field,” Sens. Actuators B Chem. 239, 1098–1108 (2017).
[Crossref]

Ultrasonics (2)

F. G. Mitri, “Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves,” Ultrasonics 66, 27–33 (2016).
[Crossref] [PubMed]

F. G. Mitri, “Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves,” Ultrasonics 74, 62–71 (2017).
[Crossref] [PubMed]

Wave Motion (1)

F. G. Mitri, “Acoustic radiation force on oblate and prolate spheroids in Bessel beams,” Wave Motion 57, 231–238 (2015).
[Crossref]

Z. Angew. Math. Phys. (1)

N. Dodgson and C. Sozou, “The deformation of a liquid drop by an electric field,” Z. Angew. Math. Phys. 38(3), 424–432 (1987).
[Crossref]

Other (5)

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University Press, 2006).

A. K. Hamid and M. I. Hussein, “Electromagnetic scattering by two parallel conducting elliptic cylinders: iterative solution,” in IEEE International Symposium on Electromagnetic Compatibility ’03, Vol. 21 (2003), pp. 21–24.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Publications, 1965).

F. G. Mitri, “Electromagnetic radiation force on electrically conducting smooth and corrugated elliptical cylinders,” https://arxiv.org/abs/1803.09397 (2018).

Acoustic, Electromagnetic and Elastic Wave Scattering—Focus on the T-Matrix Approach, V. K. Varadan and V. V. Varadan, eds. (Pergamon, 1980).

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 (25)

Fig. 1
Fig. 1 A graphic describing the interaction of an incident electric field polarized along the axial z-direction perpendicular to the plane of the figure (known also as TM polarization) with a pair of arbitrary-shaped particles in 2D separated by a distance d. The cylindrical coordinate system (r,θ, z) is referenced to the center of the first particle while the primed one (r’,θ’, z’) is located at the center of mass of the second one.
Fig. 2
Fig. 2 Panels (a)–(e) display the geometrical cross-sections of the cylindrical particle pairs considered in this study with circular [i.e., panel (a)] and other non-circular forms with smooth boundaries. The particle in the left-hand side of each panel corresponds to object 1 in Fig. 1, while the one in the right-hand side is denoted as particle 2.
Fig. 3
Fig. 3 Panels (a)–(e) display the geometrical cross-sections of the cylindrical particle pairs considered in this study with circular and non-circular forms with some objects having corrugated surfaces. The particle in the left-hand side of each panel corresponds to object 1 in Fig. 1, while the one in the right-hand side is denoted as particle 2.
Fig. 4
Fig. 4 Convergence plots for the longitudinal and transverse dimensionless radiation force functions assuming TE polarization versus the truncation order |nmax| for a pair or circular cylinders with smooth surfaces as shown in panel (a) of Fig. 2.
Fig. 5
Fig. 5 The same as in Fig. 4, but for a pair of circular and elliptical cylinders with smooth surfaces as shown in panel (b) of Fig. 2.
Fig. 6
Fig. 6 The same as in Fig. 4, but for a pair of circular and elliptical cylinders with smooth surfaces as shown in panel (c) of Fig. 2.
Fig. 7
Fig. 7 The same as in Fig. 4, but for a pair of elliptical cylinders with smooth surfaces as shown in panel (d) of Fig. 2.
Fig. 8
Fig. 8 The same as in Fig. 4, but for a pair of elliptical cylinders with smooth surfaces as shown in panel (e) of Fig. 2.
Fig. 9
Fig. 9 The same as in Fig. 4, but for a smooth circular and corrugated cylinder pair as shown in panel (a) of Fig. 3.
Fig. 10
Fig. 10 The same as in Fig. 4, but for an elliptical with a smooth surface and a corrugated cylinder pair as shown in panel (b) of Fig. 3.
Fig. 11
Fig. 11 The same as in Fig. 4, but for a smooth elliptical and corrugated cylinder pair as shown in panel (c) of Fig. 3.
Fig. 12
Fig. 12 The same as in Fig. 4, but for a pair of corrugated cylinder pair as shown in panel (d) of Fig. 3.
Fig. 13
Fig. 13 The same as in Fig. 4, but for a corrugated cylinder and another cylinder of arbitrary shape as shown in panel (e) of Fig. 3.
Fig. 14
Fig. 14 Panels (a)–(d) display the plots for the longitudinal and transverse radiation force functions for two perfectly conducting circular cylinders as shown in panel (a) of Fig. 2 versus the dimensionless interparticle distance kd for an angle of incidence α = 90°.
Fig. 15
Fig. 15 The same as in Fig. 14, but the plots correspond to the radiation force functions for the cylinder pair shown in panel (b) of Fig. 2.
Fig. 16
Fig. 16 The same as in Fig. 14, but the plots correspond to the radiation force functions for the cylinder pair shown in panel (c) of Fig. 2.
Fig. 17
Fig. 17 The same as in Fig. 14, but the plots correspond to the radiation force functions for the cylinder pair shown in panel (d) of Fig. 2.
Fig. 18
Fig. 18 The same as in Fig. 14, but the plots correspond to the radiation force functions for the cylinder pair shown in panel (e) of Fig. 2.
Fig. 19
Fig. 19 The same as in Fig. 14, but the plots correspond to the radiation force functions for the cylinder pair shown in panel (a) of Fig. 3.
Fig. 20
Fig. 20 The same as in Fig. 14, but the plots correspond to the radiation force functions for the cylinder pair shown in panel (b) of Fig. 3.
Fig. 21
Fig. 21 The same as in Fig. 14, but the plots correspond to the radiation force functions for the cylinder pair shown in panel (c) of Fig. 3.
Fig. 22
Fig. 22 The same as in Fig. 14, but the plots correspond to the radiation force functions for the cylinder pair shown in panel (d) of Fig. 3.
Fig. 23
Fig. 23 The same as in Fig. 14, but the plots correspond to the radiation force functions for the cylinder pair shown in panel (e) of Fig. 3.
Fig. 24
Fig. 24 Panels (a)–(d) display the plots for the longitudinal and transverse radiation force functions for the cylinder pair shown in panel (e) of Fig. 3 versus the dimensionless interparticle distance kd for different incidence angles assuming TE polarization of the incident plane wave field.
Fig. 25
Fig. 25 The same as in Fig. 24, but a TM polarized field is considered.

Equations (29)

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

A θ,1 = [ ( cosθ/ a 1 ) 2 + ( sinθ/ b 1 ) 2 ] 1/2 + d 1 cos( l 1 θ ),
A θ,2 = [ ( cosθ'/ a 2 ) 2 + ( sinθ'/ b 2 ) 2 ] 1/2 + d 2 cos( l 2 θ' ).
( n { 1,2 } × E { 1,2 } ) e { z,z' } | { r= A θ,1 ,r'= A θ,2 } =0,
n 1 = e r ( 1 A θ,1 ) d A θ,1 dθ e θ , n 2 = e r' ( 1 A θ,2 ) d A θ,2 dθ' e θ' ,
E r,1 tot ( r,θ,t )| r<d = E 0 e iωt [ n= + ( i n kr )( i n e inα J n ( kr ) + C n,1 H n ( 1 ) ( kr ) ) e inθ + n= + ( i n kr' )( C n,2 m= + J m ( kr ) H mn ( 1 ) ( kd ) e imθ ) ],
E θ,1 tot ( r,θ,t )| r<d = E 0 e iωt [ n= + ( i n e inα J n ' ( kr ) + C n,1 H n ( 1 )' ( kr ) ) e inθ + n= + ( C n,2 m= + J m ' ( kr ) H mn ( 1 ) ( kd ) e imθ ) ].
E r,2 tot ( r',θ',t )| r'<d = E 0 e iωt [ n= + ( i n kr' )( i n e inα e ikdcosα J n ( kr' ) + C n,2 H n ( 1 ) ( kr' ) ) e inθ' + n= + ( i n kr )( C n,1 m= + J m ( kr' ) H nm ( 1 ) ( kd ) e imθ' ) ],
E θ,2 tot ( r',θ',t )| r'<d = E 0 e iωt [ n= + ( i n e inα e ikdcosα J n ' ( kr' ) + C n,2 H n ( 1 )' ( kr' ) ) e inθ' + n= + ( C n,1 m= + J m ' ( kr' ) H nm ( 1 ) ( kd ) e imθ' ) ].
{ l= + [ ψ ln TE + C n,1 TE Ω ln TE + C n,2 TE Ω lnm TE ] =0, l'= + [ ψ l'n' TE + C n,1 TE Ω l'n' TE + C n,2 TE Ω l'n'm' TE ] =0,
ψ ln TE = 1 2π n= + i n e inα 0 2π [ k J n ' ( k A θ,1 )i( n A θ,1 2 ) d A θ,1 dθ J n ( k A θ,1 ) ] e i( nl )θ dθ ,
Ω ln TE = 1 2π n= + 0 2π [ k H n ( 1 )' ( k A θ,1 )i( n A θ,1 2 ) d A θ,1 dθ H n ( 1 ) ( k A θ,1 ) ] e i( nl )θ dθ ,
Ω lnm TE = 1 2π n= + m= + H ml ( 1 ) ( kd ) 0 2π [ k J m ' ( k A θ,1 )i( l A θ,1 Δ θ,1 ) d A θ,1 dθ J m ( k A θ,1 ) ] e i( mn )θ dθ ,
ψ l'n' TE = 1 2π n'= + i n' e in'α e ikdcosα 0 2π [ k J n' ' ( k A θ,2 )i( n' A θ,2 2 ) d A θ,2 dθ' J n' ( k A θ,2 ) ] e i( n'l' )θ' dθ' ,
Ω l'n' TE = 1 2π n'= + 0 2π [ k H n' ( 1 )' ( k A θ,2 )i( n' A θ,2 2 ) d A θ,2 dθ' H n' ( 1 ) ( k A θ,2 ) ] e i( n'l' )θ' dθ ',
Ω l'n'm' TE = 1 2π n'= + m'= + H l'm' ( 1 ) ( kd ) 0 2π [ k J m' ' ( k A θ,2 )i( l' A θ,2 Δ θ,2 ) d A θ,2 dθ' J m' ( k A θ,2 ) ] e i( m'n' )θ' dθ ',
( n { 1,2 } × E { 1,2 } ) e { θ,θ' } | { r= A θ,1 ,r'= A θ,2 } =0.
E z,1 tot ( r,θ,t )| r<d = E 0 e iωt [ n= + ( i n e inα J n ( kr ) + C n,1 H n ( 1 ) ( kr ) ) e inθ + n= + ( C n,2 m= + J m ( kr ) H mn ( 1 ) ( kd ) e imθ ) ],
E z,2 tot ( r',θ',t )| r'<d = E 0 e iωt [ n= + ( i n e inα e ikdcosα J n ( kr' ) + C n,2 H n ( 1 ) ( kr' ) ) e inθ' + n= + ( C n,1 m= + J m ( kr' ) H nm ( 1 ) ( kd ) e imθ' ) ].
{ l= + [ ψ ln TM + C n,1 TM Ω ln TM + C n,2 TM Ω lnm TM ] =0, l'= + [ ψ l'n' TM + C n,1 TM Ω l'n' TM + C n,2 TM Ω l'n'm' TM ] =0,
ψ ln TM = 1 2π n= + i n e inα 0 2π J n ( k A θ,1 ) e i( nl )θ dθ ,
Ω ln TM = 1 2π n= + 0 2π H n ( 1 ) ( k A θ,1 ) e i( nl )θ dθ ,
Ω lnm TM = 1 2π n= + m= + H ml ( 1 ) ( kd ) 0 2π J m ( k A θ,1 ) e i( mn )θ dθ ,
ψ l'n' TM = 1 2π n'= + i n' e in'α e ikdcosα 0 2π J n' ( k A θ,2 ) e i( n'l' )θ' dθ' ,
Ω l'n' TM = 1 2π n'= + 0 2π H n' ( 1 ) ( k A θ,2 ) e i( n'l' )θ' dθ ',
Ω l'n'm' TM = 1 2π n'= + m'= + H l'm' ( 1 ) ( kd ) 0 2π J m' ( k A θ,2 ) e i( m'n' )θ' dθ '.
Y x,1 { TE,TM } = 1 k a 1 { n= + C n,1 { TE,TM } [ C n+1,1 { TE,TM }* + i n+1 e i( n+1 )α + ( m= + C m,2 { TE,TM } H nm+1 ( kd ) ) * C n1,1 { TE,TM }* i n1 e i( n1 )α ( m= + C m,2 { TE,TM } H nm1 ( kd ) ) * ] },
Y y,1 { TE,TM } = 1 k a 1 { n= + C n,1 { TE,TM } [ C n+1,1 { TE,TM }* + i n+1 e i( n+1 )α + ( m= + C m,2 { TE,TM } H nm+1 ( kd ) ) * + C n1,1 { TE,TM }* + i n1 e i( n1 )α + ( m= + C m,2 { TE,TM } H nm1 ( kd ) ) * ] },
Y x,2 { TE,TM } = 1 k a 2 { n= + C n,2 { TE,TM } [ C n+1,2 { TE,TM }* + i n+1 e i( n+1 )α e ikdcosα + ( m= + C m,1 { TE,TM } H mn1 ( kd ) ) * C n1,2 { TE,TM }* i n1 e i( n1 )α e ikdcosα ( m= + C m,1 { TE,TM } H mn+1 ( kd ) ) * ] },
Y y,2 { TE,TM } = 1 k a 2 { n= + C n,2 { TE,TM } [ C n+1,2 { TE,TM }* + i n+1 e i( n+1 )α e ikdcosα + ( m= + C m,1 { TE,TM } H mn1 ( kd ) ) * + C n1,2 { TE,TM }* + i n1 e i( n1 )α e ikdcosα + ( m= + C m,1 { TE,TM } H mn+1 ( kd ) ) * ] },

Metrics