Abstract

We show that spectacular spectral changes take place in the vicinity of the dark rings of the Airy pattern formed with spatially coherent, polychromatic light diffracted at a circular aperture.

© 2002 Optical Society of America

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References

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  1. J. F. Nye, Natural Focusing and the Fine Structure of Light (Institute of Physics, Bristol, UK, 1999).
  2. A pioneering paper on this subject is by J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
    [CrossRef]
  3. A review of singular optics was recently presented by M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, p. 219.
    [CrossRef]
  4. G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2001).
    [CrossRef]
  5. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).
    [CrossRef]
  6. It follows at once from elementary geometry (in the small angle approximation) that θ and ϕ are related by the formula θ≃θc+2∊/r sin ϕ, which was used to calculate the spectrum for different values of ϕ.

2001 (1)

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2001).
[CrossRef]

1974 (1)

A pioneering paper on this subject is by J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Berry, M. V.

A pioneering paper on this subject is by J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).
[CrossRef]

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2001).
[CrossRef]

Nye, J. F.

A pioneering paper on this subject is by J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

J. F. Nye, Natural Focusing and the Fine Structure of Light (Institute of Physics, Bristol, UK, 1999).

Soskin, M. S.

A review of singular optics was recently presented by M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, p. 219.
[CrossRef]

Vasnetsov, M. V.

A review of singular optics was recently presented by M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, p. 219.
[CrossRef]

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2001).
[CrossRef]

Wolf, E.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2001).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).
[CrossRef]

Phys. Rev. Lett. (1)

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2001).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

A pioneering paper on this subject is by J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Other (4)

A review of singular optics was recently presented by M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, p. 219.
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).
[CrossRef]

It follows at once from elementary geometry (in the small angle approximation) that θ and ϕ are related by the formula θ≃θc+2∊/r sin ϕ, which was used to calculate the spectrum for different values of ϕ.

J. F. Nye, Natural Focusing and the Fine Structure of Light (Institute of Physics, Bristol, UK, 1999).

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Figures (5)

Fig. 1
Fig. 1

Illustrating the geometry and notation.

Fig. 2
Fig. 2

Gaussian spectrum (in arbitrary units) of the incident wave centered at frequency ω0=1015 s-1. The rms width of the spectral line was taken to be σ=0.01ω0.

Fig. 3
Fig. 3

Spectra (in arbitrary units) of the diffracted light in the far zone in the neighborhood of the first critical direction θc1: (a) θ=0.99θc1, (b) θ=θc1, (c) θ=1.01θc1.

Fig. 4
Fig. 4

Schematic illustration of the anomalous behavior of the spectrum in the vicinity of a critical direction θc that points toward the first zero of the Airy pattern at frequency ω0. To illustrate the effect, the angles and distances are not to scale. In particular, the circles shown by the dashed lines are in the far zone of the aperture. The spectrum of the incident light is the same as in Fig. 1.

Fig. 5
Fig. 5

Spectral changes in the neighborhood of a zero at a point P in the Airy diffraction pattern at frequency ω0 of a circular aperture, along a small circular loop of radius centered at P, which is at the distance r from the center O of the aperture. The vector OS points toward the critical direction that makes the angle θc with the z axis. The spectrum is displayed for different values of the angle ϕ. The numerical parameters are chosen so that /rθc=0.005.

Equations (2)

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Sr,θ,ωωr22J1ka sin θka sin θ2Siω.
θc10.61λ0/a.

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