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

[CrossRef]

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]

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]

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

[CrossRef]

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

[CrossRef]

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).

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]

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]

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

[CrossRef]

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]

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

[CrossRef]

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]

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).