Abstract

Some characteristics of resonant states in obliquely illuminated cylinders are derived from a geometrical-optics point of view. A formula for the resonance shift that is due to tilted illumination is derived and predictions are compared with data from the literature.

© 1998 Optical Society of America

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References

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  1. G. C. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Prog. Energy. Combust. Sci. 22, 163–188 (1996).
    [CrossRef]
  2. L. G. Guimarães, J. P. R. Furtado de Mendonça, “Analysis of the resonant scattering of light by cylinders at oblique incidence,” Appl. Opt. 36, 8010–8019 (1997).
    [CrossRef]
  3. J. A. Lock, “Morphology-dependent resonances of an infinitely long circular cylinder illuminated by a diagonally incident plane wave or a focused Gaussian beam,” J. Opt. Soc. Am. A 14, 653–661 (1997).
    [CrossRef]
  4. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1993).
  6. Low radial mode order ν resonances. The associated rays hit the surface almost tangentially and δb ≈ π does not depend much on the actual resonator size or polarization.

1997

1996

G. C. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Prog. Energy. Combust. Sci. 22, 163–188 (1996).
[CrossRef]

Acker, W. P.

G. C. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Prog. Energy. Combust. Sci. 22, 163–188 (1996).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1993).

Chang, R. K.

G. C. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Prog. Energy. Combust. Sci. 22, 163–188 (1996).
[CrossRef]

Chen, G. C.

G. C. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Prog. Energy. Combust. Sci. 22, 163–188 (1996).
[CrossRef]

Furtado de Mendonça, J. P. R.

Guimarães, L. G.

Lock, J. A.

Mazumder, M. M.

G. C. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Prog. Energy. Combust. Sci. 22, 163–188 (1996).
[CrossRef]

Swindal, J. C.

G. C. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Prog. Energy. Combust. Sci. 22, 163–188 (1996).
[CrossRef]

van de Hulst, H. C.

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

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1993).

Appl. Opt.

J. Opt. Soc. Am. A

Prog. Energy. Combust. Sci.

G. C. Chen, M. M. Mazumder, R. K. Chang, J. C. Swindal, W. P. Acker, “Laser diagnostics for droplet characterization: application of morphology dependent resonances,” Prog. Energy. Combust. Sci. 22, 163–188 (1996).
[CrossRef]

Other

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

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1993).

Low radial mode order ν resonances. The associated rays hit the surface almost tangentially and δb ≈ π does not depend much on the actual resonator size or polarization.

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Figures (3)

Fig. 1
Fig. 1

Phase distribution within a dielectric cylinder for different angles of incidence ξ of the exciting plane wave. The rays that constitute a whispering gallery mode propagate in a region close to the cylinder surface.

Fig. 2
Fig. 2

Comparison of exact (according to Lock) and approximate resonance positions [according to Eq. (3)] as a function of the external angle of incidence.

Fig. 3
Fig. 3

Expression for the resonance shift [Eq. (8)] as a function of the external angle of incidence for different modes, polarizations, and refractive indices. Solid curves, ξ R = 0°, dashed curve, ξ R = 25°. Data taken from the literature are drawn as bullets.

Equations (8)

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k ri r = n 2 - sin 2   ξ k 0 2 r 2 - l 2 1 / 2 r , k re r = cos 2   ξ k 0 2 r 2 - l 2 1 / 2 r .
r ci = l k 0 n 2 - sin 2   ξ 1 / 2 ,   r ce = l k 0 cos   ξ .
2   r ci a   k ri ρ d ρ - π / 2 - δ b = ν - 1 2 π ,
r ci a   k ri ρ d ρ = x 2 n 2 - sin 2   ξ - l 2 1 / 2 - l   arccos l x n 2 - sin 2   ξ 1 / 2 .
δ b = 2   arctan α 2 ik re a k ri a = 2   arctan α 2 sin 2   β - sin 2   β c 1 / 2 cos   β ,
sin   β = l nx 2 + sin   ξ n 2 1 / 2 .
δ b = 2   arctan α 2 l 2 - cos 2   ξ x 2 x 2 n 2 - sin 2   ξ - l 2 1 / 2 .
x ξ = x R n 2 - sin 2   ξ R n 2 - sin 2   ξ 1 / 2 .

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