Abstract

We study the resonant scattering of light at oblique incidence by dielectric uncoated and coated cylinders. We develop a stable algorithm that permits us to calculate the resonances of a single dielectric cylinder as the tilting angle varies. This algorithm is based on semiclassical formulas for the distance between resonances. Results show that the resonances and the resonant electromagnetic energy flux near and internal to the cylindrical surface are highly sensitive to variations in the tilting angle. In addition, the coating effects are studied for scattering of light at oblique incidence by an infinite, perfect cylindrical conductor coated by a dielectric layer. In this case the resonance calculations show a peculiar similarity between this light scattering and atomic-molecular scattering. A physical interpretation for these effects is given, based on an analogy of optics and quantum mechanics.

© 1997 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. A. Serpengüzel, S. Arnold, G. Griffel, “Excitation of resonances of microsphere on optical fiber,” Opt. Lett. 20, 654–656 (1995).
    [CrossRef] [PubMed]
  3. G. Krausch, S. Wegscheider, A. Kirsch, H. Bielefeldt, J. C. Meiners, J. Mlynek, “Near field microscopy and lithography with uncoated fiber tips: a comparison,” Opt. Commun. 119, 283–288 (1995).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  8. C. Y. Ting, “Infinite cylindrical dielectric-coated antenna,” Radio Sci. 2, 325–335 (1967).
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    [CrossRef]
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    [CrossRef]
  13. L. Kai, A. D’Alessio, “Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves,” Appl. Opt. 24, 5520–5530 (1995).
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    [CrossRef]
  30. J. C. Slater, Quantum Theory of Molecules and Solids (McGraw-Hill, New York, 1963).
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    [CrossRef]
  33. T. M. Bambino, L. G. Guimarães, “Resonance of a coated sphere,” Phys. Rev. E 53, 2859–2863 (1996).
    [CrossRef]
  34. A. Cohen, P. Alpert, “Extinction efficiency of obliquely and randomly oriented infinite cylinders,” J. Appl. Phys. 50, 8262–8264 (1979).
    [CrossRef]
  35. A. Cohen, C. Acquista, “Light scattering by tilted cylinders: properties of partial wave coefficients,” J. Opt. Soc. Am. 72, 531–534 (1982).
    [CrossRef]
  36. G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand Reinhold, New York, 1966), Vol. 3.
  37. M. S. Child, “Semiclassical theory of tunneling and curve-crossing problems: a diagramatic approach,” J. Mol. Spectrosc. 53, 280–301 (1974).
    [CrossRef]
  38. H. Lefebvre-Brion, Pertubations in the Spectra of Diatomic Molecules (Academic, New York, 1986), chap. 6.
  39. B. R. Johnson, “Morphology-dependent resonances of a dielectric sphere on a conducting plane,” J. Opt. Soc. Am. A 11, 2055–2064 (1994).
    [CrossRef]
  40. K. A. Fuller, “Some novel features of morphology dependent resonances of bispheres,” Appl. Opt. 28, 3788–3790 (1989).
    [CrossRef] [PubMed]
  41. S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
    [CrossRef]
  42. J. A. Lock, “Morphology-dependent resonances of an infinitely long circular cylinder illuminated by a diagonally incident plane wave or focused Gaussian beam,” J. Opt. Soc. Am. A 14, 653–661 (1997).
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    [CrossRef]

1997 (3)

1996 (2)

1995 (4)

A. Serpengüzel, S. Arnold, G. Griffel, “Excitation of resonances of microsphere on optical fiber,” Opt. Lett. 20, 654–656 (1995).
[CrossRef] [PubMed]

N. Dubreuil, J. C. Knight, D. K. Leventhal, V. Sandoghdar, J. Hare, V. Lefèvre, “Eroded monomode optical fiber for whispering-gallery mode excitation in fused-silica microspheres,” Opt. Lett. 20, 813–815 (1995).
[CrossRef] [PubMed]

G. Krausch, S. Wegscheider, A. Kirsch, H. Bielefeldt, J. C. Meiners, J. Mlynek, “Near field microscopy and lithography with uncoated fiber tips: a comparison,” Opt. Commun. 119, 283–288 (1995).
[CrossRef]

L. Kai, A. D’Alessio, “Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves,” Appl. Opt. 24, 5520–5530 (1995).
[CrossRef]

1994 (2)

L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

B. R. Johnson, “Morphology-dependent resonances of a dielectric sphere on a conducting plane,” J. Opt. Soc. Am. A 11, 2055–2064 (1994).
[CrossRef]

1993 (2)

1992 (3)

1991 (1)

S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
[CrossRef]

1990 (1)

1989 (1)

1987 (2)

M. Barabás, “Scattering of a plane wave by a radially stratified tilted cylinder,” J. Opt. Soc. Am. A 4, 2240–2248 (1987).
[CrossRef]

D. S. Benincasa, P. W. Barber, J. Z. Zhang, W. F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 27, 1348–1356 (1987).
[CrossRef]

1986 (1)

J. R. Wait, “Impedance conditions for a coated cylindrical conductor,” Radio Sci. 21, 623–626 (1986).
[CrossRef]

1982 (1)

1981 (1)

1979 (1)

A. Cohen, P. Alpert, “Extinction efficiency of obliquely and randomly oriented infinite cylinders,” J. Appl. Phys. 50, 8262–8264 (1979).
[CrossRef]

1977 (1)

1974 (1)

M. S. Child, “Semiclassical theory of tunneling and curve-crossing problems: a diagramatic approach,” J. Mol. Spectrosc. 53, 280–301 (1974).
[CrossRef]

1970 (1)

S. N. Samaddar, “Scattering of plane electromagnetic waves by radially inhomogeneous infinite cylinders,” Nuovo Cimento B 66, 33–50 (1970).
[CrossRef]

1968 (1)

W. H. Miller, “Uniform semiclassical approximations for elastic scattering and eigenvalue problems,” J. Chem. Phys. 48, 464–467 (1968).
[CrossRef]

1967 (1)

C. Y. Ting, “Infinite cylindrical dielectric-coated antenna,” Radio Sci. 2, 325–335 (1967).

1966 (2)

1961 (1)

R. D. Kodis, “On the theory of diffraction by a composite cylinder,” J. Res. Natl. Bur. Stand. U.S., Sect. D 25, 19–33 (1961).

1955 (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–1995 (1955).
[CrossRef]

Acquista, C.

Adler, C. L.

Alpert, P.

A. Cohen, P. Alpert, “Extinction efficiency of obliquely and randomly oriented infinite cylinders,” J. Appl. Phys. 50, 8262–8264 (1979).
[CrossRef]

Armstrong, R. L.

Arnold, S.

Bambino, T. M.

T. M. Bambino, L. G. Guimarães, “Resonance of a coated sphere,” Phys. Rev. E 53, 2859–2863 (1996).
[CrossRef]

Barabás, M.

Barber, P. W.

D. S. Benincasa, P. W. Barber, J. Z. Zhang, W. F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 27, 1348–1356 (1987).
[CrossRef]

J. F. Owen, R. K. Chang, P. W. Barber, “Internal electric field distributions of a dielectric cylinder at resonance wavelengths,” Opt. Lett. 6, 540–542 (1981).
[CrossRef] [PubMed]

Benincasa, D. S.

D. S. Benincasa, P. W. Barber, J. Z. Zhang, W. F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 27, 1348–1356 (1987).
[CrossRef]

Bielefeldt, H.

G. Krausch, S. Wegscheider, A. Kirsch, H. Bielefeldt, J. C. Meiners, J. Mlynek, “Near field microscopy and lithography with uncoated fiber tips: a comparison,” Opt. Commun. 119, 283–288 (1995).
[CrossRef]

Chang, R. K.

D. S. Benincasa, P. W. Barber, J. Z. Zhang, W. F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 27, 1348–1356 (1987).
[CrossRef]

J. F. Owen, R. K. Chang, P. W. Barber, “Internal electric field distributions of a dielectric cylinder at resonance wavelengths,” Opt. Lett. 6, 540–542 (1981).
[CrossRef] [PubMed]

Child, M. S.

M. S. Child, “Semiclassical theory of tunneling and curve-crossing problems: a diagramatic approach,” J. Mol. Spectrosc. 53, 280–301 (1974).
[CrossRef]

Chýlek, P.

Cohen, A.

A. Cohen, C. Acquista, “Light scattering by tilted cylinders: properties of partial wave coefficients,” J. Opt. Soc. Am. 72, 531–534 (1982).
[CrossRef]

A. Cohen, P. Alpert, “Extinction efficiency of obliquely and randomly oriented infinite cylinders,” J. Appl. Phys. 50, 8262–8264 (1979).
[CrossRef]

Cooke, D.

D’Alessio, A.

L. Kai, A. D’Alessio, “Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves,” Appl. Opt. 24, 5520–5530 (1995).
[CrossRef]

Dubreuil, N.

Estle, T. L.

M. A. Morrison, T. L. Estle, N. F. Lane, Quantum States of Atoms Molecules and Solids (Prentice-Hall, Englewood Cliffs, N.J., 1976).

Farone, W. A.

Fernándes, G. L.

Fuller, K. A.

Greenberg, J. M.

A. C. Lind, J. M. Greenberg, “Electromagnetic scattering by obliquely oriented cylinders,” J. Appl. Phys. 37, 3195–3203 (1966).
[CrossRef]

Griffel, G.

Grober, R. D.

Gu, J.

Guimarães, L. G.

T. M. Bambino, L. G. Guimarães, “Resonance of a coated sphere,” Phys. Rev. E 53, 2859–2863 (1996).
[CrossRef]

L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

L. G. Guimarães, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

Guimarães., L. G.

L. G. Guimarães., “Theory of Mie caustics,” Opt. Commun. 103, 339–344 (1993).
[CrossRef]

Hare, J.

Harris, T. D.

Herzberg, G.

G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand Reinhold, New York, 1966), Vol. 3.

Hsieh, W. F.

D. S. Benincasa, P. W. Barber, J. Z. Zhang, W. F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 27, 1348–1356 (1987).
[CrossRef]

Jacobsen, R. A.

John, S.

S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
[CrossRef]

Johnson, B. R.

Kai, L.

L. Kai, A. D’Alessio, “Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves,” Appl. Opt. 24, 5520–5530 (1995).
[CrossRef]

Kerker, M.

Kirsch, A.

G. Krausch, S. Wegscheider, A. Kirsch, H. Bielefeldt, J. C. Meiners, J. Mlynek, “Near field microscopy and lithography with uncoated fiber tips: a comparison,” Opt. Commun. 119, 283–288 (1995).
[CrossRef]

Knight, J. C.

Kodis, R. D.

R. D. Kodis, “On the theory of diffraction by a composite cylinder,” J. Res. Natl. Bur. Stand. U.S., Sect. D 25, 19–33 (1961).

Krausch, G.

G. Krausch, S. Wegscheider, A. Kirsch, H. Bielefeldt, J. C. Meiners, J. Mlynek, “Near field microscopy and lithography with uncoated fiber tips: a comparison,” Opt. Commun. 119, 283–288 (1995).
[CrossRef]

Lam, C. C.

Lane, N. F.

M. A. Morrison, T. L. Estle, N. F. Lane, Quantum States of Atoms Molecules and Solids (Prentice-Hall, Englewood Cliffs, N.J., 1976).

Lefebvre-Brion, H.

H. Lefebvre-Brion, Pertubations in the Spectra of Diatomic Molecules (Academic, New York, 1986), chap. 6.

Lefèvre, V.

Leung, P. T.

Leventhal, D. K.

Lind, A. C.

A. C. Lind, J. M. Greenberg, “Electromagnetic scattering by obliquely oriented cylinders,” J. Appl. Phys. 37, 3195–3203 (1966).
[CrossRef]

Lindgren, G.

Lock, J. A.

Meiners, J. C.

G. Krausch, S. Wegscheider, A. Kirsch, H. Bielefeldt, J. C. Meiners, J. Mlynek, “Near field microscopy and lithography with uncoated fiber tips: a comparison,” Opt. Commun. 119, 283–288 (1995).
[CrossRef]

Merzbacher, E.

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).

Miller, W. H.

W. H. Miller, “Uniform semiclassical approximations for elastic scattering and eigenvalue problems,” J. Chem. Phys. 48, 464–467 (1968).
[CrossRef]

Mlynek, J.

G. Krausch, S. Wegscheider, A. Kirsch, H. Bielefeldt, J. C. Meiners, J. Mlynek, “Near field microscopy and lithography with uncoated fiber tips: a comparison,” Opt. Commun. 119, 283–288 (1995).
[CrossRef]

Morrison, M. A.

M. A. Morrison, T. L. Estle, N. F. Lane, Quantum States of Atoms Molecules and Solids (Prentice-Hall, Englewood Cliffs, N.J., 1976).

Nussenzveig, H. M.

L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

L. G. Guimarães, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

Olver, F. W. J.

F. W. J. Olver, Asymptotics and Special Functions (Academic, New York, 1974), Chap. 12.

Owen, J. F.

Pinnick, R. G.

Ruekgauer, T.

Rutherford, T.

Samaddar, S. N.

S. N. Samaddar, “Scattering of plane electromagnetic waves by radially inhomogeneous infinite cylinders,” Nuovo Cimento B 66, 33–50 (1970).
[CrossRef]

Sandoghdar, V.

Serpengüzel, A.

Slater, J. C.

J. C. Slater, Quantum Theory of Molecules and Solids (McGraw-Hill, New York, 1963).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1956).

Ting, C. Y.

C. Y. Ting, “Infinite cylindrical dielectric-coated antenna,” Radio Sci. 2, 325–335 (1967).

van de Hulst, H. C.

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

Wait, J. R.

J. R. Wait, “Impedance conditions for a coated cylindrical conductor,” Radio Sci. 21, 623–626 (1986).
[CrossRef]

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–1995 (1955).
[CrossRef]

Wegscheider, S.

G. Krausch, S. Wegscheider, A. Kirsch, H. Bielefeldt, J. C. Meiners, J. Mlynek, “Near field microscopy and lithography with uncoated fiber tips: a comparison,” Opt. Commun. 119, 283–288 (1995).
[CrossRef]

Xie, J. G.

Yeh, C.

Young, K.

Zhang, J. Z.

D. S. Benincasa, P. W. Barber, J. Z. Zhang, W. F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 27, 1348–1356 (1987).
[CrossRef]

Appl. Opt. (5)

L. Kai, A. D’Alessio, “Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves,” Appl. Opt. 24, 5520–5530 (1995).
[CrossRef]

D. S. Benincasa, P. W. Barber, J. Z. Zhang, W. F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 27, 1348–1356 (1987).
[CrossRef]

C. Yeh, G. Lindgren, “Computing the propagation characteristics of radially stratified fibers: an efficient method,” Appl. Opt. 16, 483–493 (1977).
[CrossRef] [PubMed]

K. A. Fuller, “Some novel features of morphology dependent resonances of bispheres,” Appl. Opt. 28, 3788–3790 (1989).
[CrossRef] [PubMed]

R. D. Grober, T. Rutherford, T. D. Harris, “Model approximation for the electromagnetic field of a near-field optical probe,” Appl. Opt. 35, 3488–3495 (1996).
[CrossRef] [PubMed]

Can. J. Phys. (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–1995 (1955).
[CrossRef]

J. Appl. Phys. (2)

A. C. Lind, J. M. Greenberg, “Electromagnetic scattering by obliquely oriented cylinders,” J. Appl. Phys. 37, 3195–3203 (1966).
[CrossRef]

A. Cohen, P. Alpert, “Extinction efficiency of obliquely and randomly oriented infinite cylinders,” J. Appl. Phys. 50, 8262–8264 (1979).
[CrossRef]

J. Chem. Phys. (1)

W. H. Miller, “Uniform semiclassical approximations for elastic scattering and eigenvalue problems,” J. Chem. Phys. 48, 464–467 (1968).
[CrossRef]

J. Mod. Opt. (1)

L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994).
[CrossRef]

J. Mol. Spectrosc. (1)

M. S. Child, “Semiclassical theory of tunneling and curve-crossing problems: a diagramatic approach,” J. Mol. Spectrosc. 53, 280–301 (1974).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (7)

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

J. Res. Natl. Bur. Stand. U.S., Sect. D (1)

R. D. Kodis, “On the theory of diffraction by a composite cylinder,” J. Res. Natl. Bur. Stand. U.S., Sect. D 25, 19–33 (1961).

Nuovo Cimento B (1)

S. N. Samaddar, “Scattering of plane electromagnetic waves by radially inhomogeneous infinite cylinders,” Nuovo Cimento B 66, 33–50 (1970).
[CrossRef]

Opt. Commun. (3)

L. G. Guimarães., “Theory of Mie caustics,” Opt. Commun. 103, 339–344 (1993).
[CrossRef]

L. G. Guimarães, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

G. Krausch, S. Wegscheider, A. Kirsch, H. Bielefeldt, J. C. Meiners, J. Mlynek, “Near field microscopy and lithography with uncoated fiber tips: a comparison,” Opt. Commun. 119, 283–288 (1995).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. E (1)

T. M. Bambino, L. G. Guimarães, “Resonance of a coated sphere,” Phys. Rev. E 53, 2859–2863 (1996).
[CrossRef]

Phys. Today (1)

S. John, “Localization of light,” Phys. Today 44, 32–40 (1991).
[CrossRef]

Radio Sci. (2)

J. R. Wait, “Impedance conditions for a coated cylindrical conductor,” Radio Sci. 21, 623–626 (1986).
[CrossRef]

C. Y. Ting, “Infinite cylindrical dielectric-coated antenna,” Radio Sci. 2, 325–335 (1967).

Other (10)

M. Kerker, The Scattering of Light and Other Electromagnetic Radiations (Academic, New York, 1969), chap. 6.

J. C. Slater, Quantum Theory of Molecules and Solids (McGraw-Hill, New York, 1963).

M. A. Morrison, T. L. Estle, N. F. Lane, Quantum States of Atoms Molecules and Solids (Prentice-Hall, Englewood Cliffs, N.J., 1976).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1956).

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

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).

G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand Reinhold, New York, 1966), Vol. 3.

H. Lefebvre-Brion, Pertubations in the Spectra of Diatomic Molecules (Academic, New York, 1986), chap. 6.

F. W. J. Olver, Asymptotics and Special Functions (Academic, New York, 1974), Chap. 12.

M. Abramowitz, I. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1968), Chap. 9.

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Figures (12)

Fig. 1
Fig. 1

For a given Lz, angular momentum eigenvalue λ, and incidence angle ϕ, the effective potential Ueff for cylinder refraction index N > 1 and positive energy k2(ϕ). The external and internal classical turning points are ρext (ϕ) and ρint (ϕ), respectively. In this framework resonances are quasi-bound states of the light.

Fig. 2
Fig. 2

For N = 1.45 and λ = 65, the resonance position β as the incidence angle ϕ varies. The symbol jnλ denotes a resonance related with polarization j, Lz angular momentum λ, and resonance order n. The dashed and solid curves, related to resonances I165 and II165, respectively, are obtained through solution of Eq. (4) by means of a numerical algorithm based on the between-resonance distance formula (see Section 3). Crosses (+) are the exact results obtained by solution of Eq. (1). Note that for both polarizations the value of the resonance position β increases as ϕ increases. Because the angle ϕ increases, the height of the effective barrier increases.

Fig. 3
Fig. 3

For N = 1.45, order n = 1, and λ = 65, the resonance width w for both polarizations I (dashed curve) and II (solid curve) as the incidence angle ϕ varies. These results are obtained with Eq. (5). Note that the resonance width decreases very quickly as ϕ increases (inset).

Fig. 4
Fig. 4

For polarization I, N = 1.45, λ = 61, and consecutive orders n = 0,…, 3, the behavior of the resonance position and width as the incidence angle ϕ varies. The left axis (dotted curves) shows the resonance positions for consecutive orders; note that in this case the distance between resonances with consecutive orders is not highly sensitive to ϕ variations. This agrees with distance formula (12) and is the goal in our algorithm for resonance calculation. The right axis (solid curves) shows ln (w); note that the resonance width of any order collapses as ϕ → 90°.

Fig. 5
Fig. 5

For resonance I361, the internal ρint (dashed line) and the external ρext (solid curve) classical turning points as the incidence angle ϕ varies. Note that ρint is very close to the cylinder radius a, so that the internal electromagnetic field has a small region to oscillate. On the other hand, for angles ϕ greater than a critical angle ϕc ≈ sin-1 [(N4 - N2 + 1)1/2 - (N2 - 1)]1/2 the external turning point ρext is greater than the cylinder radius. In this case the barrier to be tunnelled is very large. So extremely narrow resonances can be excited for angles ϕ > ϕc.

Fig. 6
Fig. 6

For resonances II361, II165 and I365, the derivative of the resonance position β in relation to incidence angle ϕ. Note that, independent of the angular momentum, resonance order, and polarization, all these derivatives have a maximum at the same point, ϕ = ϕc. The main dependence of ϕc is only on the refractive index N.

Fig. 7
Fig. 7

For several resonances, the normalized source functions Sz and S for regions internal to and near the cylinder surface. Note that for a resonance with order n, the source function has n + 1 peaks. Since the value of the resonance width increases as the order n increases, these graphics suggest that for close to normal incidence the heights of the peaks in the source function increase as the resonance width decreases.

Fig. 8
Fig. 8

(a)The left axis shows (for N = 1.45 and on-resonance II020 conditions) the internal points ρmax (circles) and ρzmax (squares), where S and Sz have maximum values. Note that these points are not highly sensitive to ϕ variations. The right scale shows the ratio Smax/Szmax (dashed curve) between maximum values of both components of the source function. Notice that this ratio increases as ϕ increases. (b) and (c) Smax and Szmax (in logarithm scale), respectively, as the incidence angle ϕ varies. Note that the values of these peaks decrease for ϕ > ϕc.

Fig. 9
Fig. 9

Effective potential Ueff for a metallic cylinder of radius b coated with a dielectric cylinder of radius a when b < ρint < a < ρext and the ratio a/b > Ñ, the resonances are similar to the resonances of a single dielectric cylinder. (b) when b = ρint < a < ρext and the ratio a/b < Ñ, reflections on the surface of the inner metallic cylinder play an important role, so that resonances in the Δ transition region are highly sensitive to variations in the layer thickness.

Fig. 10
Fig. 10

For a composite cylinder and normal incidence (ϕ = 0), several resonance positions in the range 52.5 < β < 56.5 as the ratio a/b varies. Note that many resonances present crossover points, and resonances related to I polarization have a minimum value. These resonances resemble the electronic spectrum of a diatomic molecule. On other words, resonances related to II polarization are antibonding orbitallike, and resonances related to I polarization are bonding orbitallike. The inset shows that the minimum value in resonances related with I polarization occurs for size parameters for which γ ≈ λ.

Fig. 11
Fig. 11

Extinction efficiency factor Qext as the size parameter β varies for normal incidence (ϕ = 0) and N = 1.45. Note that Qext is highly sensitive to variations in the layer thickness, so that on crossover resonance conditions (solid curve) the related peak is superimposed.

Fig. 12
Fig. 12

For nonnormal incidence (ϕ = 5°) the resonance position β for both polarizations I and II. Note that in this situation the curves do not exhibit crossing, so that in this case the resonant spectrum resembles a predissociation electronic molecular spectrum.

Equations (16)

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ΞβX˜λβZ˜λβ-λ sinϕ1v2-1u22,
X˜λβln Hλ1vv-ln Jλuu,
Z˜λβlnHλ1vv-N2ln Jλuu.
XλβZλβ=λ sinϕ1v2-1u22+Ow2,
w=2βXλ+ZλπYλ2vλ2-v2-v ln Yλv-v ln Yλv2Xλ+Zλ+81-v2/u2+Ow3,
Xλln Yλvv-ln Jλuu,
Zλln Yλvv-N2ln Jλuu,
φunj,λρintadρknj2-Ueff1/2=n+1/4π+tg-1jN˜2ϕλ2-vnj2/unj2-λ21/2, n=0, 1,  nmax-1.
wnj=βnjjN˜2ϕλ2-vnj21/2unj2-λ2cos2φunj, λ-π/4exp-2 aρextdρUeff-knj21/2,
βnλ,ϕλ tg-1M/cosϕM+n+1/4M π; nnmax,
Δβλβnjλ+1, ϕ-βnjλ, ϕβnjtg-1unj2-λ21/2/λ]unj2-λ21/2.
Δβnβn+1jλ, ϕ-βnjλ, ϕπβnjunj2-λ2.
Δβjβnj+1λ, ϕ-βnjλ, ϕβnj/unj2-λ21/2×tg-1Ñ2ϕλ2-vnj2/unj2-λ21/2-tg-1Ñ2ϕ/N2λ2-vnj2/unj2-λ21/2.
Sjρ1/2π Eincj2×02πdθEρjρ, θ2+02πdθEzjρ,θ2Sjρ+Szjρ,
Πβ=Ξβ+PβTβJλγYλγ+OJλγ/Yλγ2···=0,
β0β+PβΞ βTβJλγYλγ,

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