Abstract

Calculations of the electric field distribution within and around an infinite circular dielectric cylinder, having a relative index of refraction of 1.53 and illuminated with plane-wave radiation of wavelength λ, have been performed for size parameters ranging from 39 to 51. Results for size parameters that satisfy resonance conditions for various natural modes of oscillation of the cylinder (mode number n = 53; order numbers l = 1–5) clearly illustrate the physical significance of n and l and show that the internally reflected circumferential waves are localized near, but not confined to, the cylinder surface.

© 1981 Optical Society of America

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References

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  1. R. Fuchs, K. L. Kliewer, J. Opt. Soc. Am. 58, 319 (1968).
    [Crossref]
  2. T. P. Martin, Phys. Rev. B 15, 4071 (1977).
    [Crossref]
  3. A. B. Pluchino, Appl. Opt. 20, 531 (1981).
    [Crossref] [PubMed]
  4. G. J. Rosasco, H. S. Bennett, J. Opt. Soc. Am. 68, 1242 (1978).
    [Crossref]
  5. J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, Opt. Lett. 6, 272 (1981).
    [Crossref] [PubMed]
  6. A. Ashkin, J. M. Dziedzic, R. H. Stolen, Appl. Opt. 20, 2299 (1981).
    [Crossref] [PubMed]
  7. A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977);Appl. Opt. 20, 1803 (1981).
    [Crossref] [PubMed]
  8. R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
    [Crossref]
  9. J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang to be published.
  10. P. W. Dusel, M. Kerker, D. D. Cooke, J. Opt. Soc. Am. 69, 55 (1979).
    [Crossref]
  11. M. Gastine, L. Courtois, J. L. Dormann, IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
    [Crossref]
  12. J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, IEEE Trans. Antennas Propag. AP-28, 924 (1980).
    [Crossref]
  13. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

1981 (3)

1980 (2)

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[Crossref]

1979 (1)

1978 (1)

1977 (2)

T. P. Martin, Phys. Rev. B 15, 4071 (1977).
[Crossref]

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977);Appl. Opt. 20, 1803 (1981).
[Crossref] [PubMed]

1968 (1)

1967 (1)

M. Gastine, L. Courtois, J. L. Dormann, IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[Crossref]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, R. H. Stolen, Appl. Opt. 20, 2299 (1981).
[Crossref] [PubMed]

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977);Appl. Opt. 20, 1803 (1981).
[Crossref] [PubMed]

Barber, P. W.

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, Opt. Lett. 6, 272 (1981).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang to be published.

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

Bennett, H. S.

Chang, R. K.

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, Opt. Lett. 6, 272 (1981).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang to be published.

Cooke, D. D.

Courtois, L.

M. Gastine, L. Courtois, J. L. Dormann, IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[Crossref]

Dorain, P. B.

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang to be published.

Dormann, J. L.

M. Gastine, L. Courtois, J. L. Dormann, IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[Crossref]

Dusel, P. W.

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, R. H. Stolen, Appl. Opt. 20, 2299 (1981).
[Crossref] [PubMed]

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977);Appl. Opt. 20, 1803 (1981).
[Crossref] [PubMed]

Fuchs, R.

Gastine, M.

M. Gastine, L. Courtois, J. L. Dormann, IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[Crossref]

Kerker, M.

P. W. Dusel, M. Kerker, D. D. Cooke, J. Opt. Soc. Am. 69, 55 (1979).
[Crossref]

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Kliewer, K. L.

Martin, T. P.

T. P. Martin, Phys. Rev. B 15, 4071 (1977).
[Crossref]

Messinger, B. J.

Moser, P. J.

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[Crossref]

Murphy, J. D.

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[Crossref]

Nagl, A.

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[Crossref]

Owen, J. F.

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, Opt. Lett. 6, 272 (1981).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang to be published.

Pluchino, A. B.

Rosasco, G. J.

Stolen, R. H.

Überall, H.

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[Crossref]

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

J. D. Murphy, P. J. Moser, A. Nagl, H. Überall, IEEE Trans. Antennas Propag. AP-28, 924 (1980).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

M. Gastine, L. Courtois, J. L. Dormann, IEEE Trans. Microwave Theory Tech. MTT-15, 694 (1967).
[Crossref]

J. Opt. Soc. Am. (3)

Opt. Lett. (1)

Phys. Rev. B (1)

T. P. Martin, Phys. Rev. B 15, 4071 (1977).
[Crossref]

Phys. Rev. Lett. (2)

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977);Appl. Opt. 20, 1803 (1981).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[Crossref]

Other (2)

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang to be published.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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Figures (4)

Fig. 1
Fig. 1

Internal TE electric field intensity (E · E*) in an infinitely long dielectric cylinder with a relative index (m = 1.530) and size parameter (x = 45.6) that do not satisfy a resonance condition. To demarcate the boundary, the intensity outside the cylinder has been artifically set to zero in the figure. Results are shown from two orientations with respect to the incident beam.

Fig. 2
Fig. 2

Internal TE electric field intensity (E · E*) for a size parameter (x = 45.726) that is in resonance with mode 53,3 (n = 53, l = 3). The lower figure shows the total field intensity, as in Fig. 1, and the upper figure shows only the contribution from the resonant term (n = 53). There are 2n (106) peaks around the perimeter.

Fig. 3
Fig. 3

The average TE field intensity integrated around a circle centered at the cylinder axis [(2π)−1E(r, ϕ) · E*(r, ϕ)] as a function of the radius r of the circle. Results are shown for an off-resonance condition and for x values in resonance with modes n = 53, l = 1−5. The number of lobes in the radial direction is equal to l.

Fig. 4
Fig. 4

Same as Fig. 3 but for TM polarization. Results are shown for an off-resonance condition and for an x value that is in resonance with mode n = 53, l = 3. The averaged intensity is continuous across the cylinder boundary, in contrast to the case for TE polarization.

Equations (4)

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

E ϕ = j E 0 m n = j n c n J n ( mkr ) e j n ϕ
E r = E 0 m 2 k r n = j n n c n J n ( mkr ) e j n ϕ ,
c n = 1 J n ( m x ) [ J n ( x ) a n H n ( 2 ) ( x ) ] ,
a n = J n ( x ) J n ( m x ) m J n ( x ) J n ( m x ) H n ( 2 ) ( x ) J n ( m x ) m H n ( 2 ) ( x ) J n ( m x ) .

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