Abstract

We describe the anomalous behavior of the spectral degree of coherence as a function of light frequency in the vicinity of phase singularities of partially spatially coherent, polychromatic wave fields. We distinguish the discovered spectral coherence anomalies from conventional spectral anomalies realized with fully spatially coherent optical fields. We also demonstrate how the previously reported spectral anomalies can be engineered in partially spatially coherent fields.

© 2013 Optical Society of America

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References

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  1. J. F. Nye, Natural Focusing and Fine Structure of Light (IOP, 1999).
  2. M. S. Soskin and M. V. Vasnetsov, Vol. 42 of Progress in Optics, E. Wolf, ed. (Elsevier, 2001), p. 219.
  3. I. Freund, A. I. Mokhun, M. S. Soskin, O. V. Angelsky, and I. I. Mokhun, Opt. Lett. 27, 545 (2002).
    [CrossRef]
  4. G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2001).
    [CrossRef]
  5. G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
    [CrossRef]
  6. S. A. Ponomarenko and E. Wolf, Opt. Lett. 27, 1211 (2002).
    [CrossRef]
  7. J. T. Foley and E. Wolf, J. Opt. Soc. Am. A 19, 2510 (2002).
    [CrossRef]
  8. M. V. Berry, New. J. Phys. 6, 66 (2002).
  9. S. A. Ponomarenko and E. Wolf, Opt. Commun. 170, 1 (1999).
    [CrossRef]
  10. S. A. Ponomarenko, J. Opt. Soc. Am. A 18, 150 (2001).
    [CrossRef]
  11. G. V. Bogatyryova, Ch. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, and E. Wolf, Opt. Lett. 28, 878 (2003).
    [CrossRef]
  12. H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
    [CrossRef]
  13. D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
    [CrossRef]
  14. G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
    [CrossRef]
  15. I. D. Maleev and G. A. Swartzlander, J. Opt. Soc. Am. B 25, 915 (2008).
    [CrossRef]
  16. T. van Dijk and T. D. Visser, J. Opt. Soc. Am. A 26, 741 (2009).
    [CrossRef]
  17. Y. Yang, M. Mazilu, and K. Dholakia, Opt. Lett. 37, 4949 (2012).
  18. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  19. F. Rahman, Opt. Photon. News 24, 26 (2013).
    [CrossRef]
  20. S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
    [CrossRef]
  21. Ch. V. Felde, A. A. Chernyshov, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, JETP Lett. 88, 418 (2008).
  22. A. A. Chernyshov, Ch. V. Felde, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, J. Opt. A 11, 094010 (2009).
    [CrossRef]
  23. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  24. P. Han, Opt. Lett. 34, 1303 (2009).
    [CrossRef]
  25. J. Pu, C. Cai, and S. Nemoto, Opt. Express 12, 5131 (2004).
    [CrossRef]
  26. P. Han, Opt. Lett. 37, 2319 (2012).
    [CrossRef]

2013 (1)

F. Rahman, Opt. Photon. News 24, 26 (2013).
[CrossRef]

2012 (2)

2009 (3)

T. van Dijk and T. D. Visser, J. Opt. Soc. Am. A 26, 741 (2009).
[CrossRef]

P. Han, Opt. Lett. 34, 1303 (2009).
[CrossRef]

A. A. Chernyshov, Ch. V. Felde, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, J. Opt. A 11, 094010 (2009).
[CrossRef]

2008 (2)

I. D. Maleev and G. A. Swartzlander, J. Opt. Soc. Am. B 25, 915 (2008).
[CrossRef]

Ch. V. Felde, A. A. Chernyshov, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, JETP Lett. 88, 418 (2008).

2005 (1)

S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

2004 (2)

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

J. Pu, C. Cai, and S. Nemoto, Opt. Express 12, 5131 (2004).
[CrossRef]

2003 (3)

2002 (5)

2001 (2)

S. A. Ponomarenko, J. Opt. Soc. Am. A 18, 150 (2001).
[CrossRef]

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

1999 (1)

S. A. Ponomarenko and E. Wolf, Opt. Commun. 170, 1 (1999).
[CrossRef]

Angelsky, O. V.

Berry, M. V.

M. V. Berry, New. J. Phys. 6, 66 (2002).

Bogatyryova, G. V.

A. A. Chernyshov, Ch. V. Felde, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, J. Opt. A 11, 094010 (2009).
[CrossRef]

Ch. V. Felde, A. A. Chernyshov, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, JETP Lett. 88, 418 (2008).

G. V. Bogatyryova, Ch. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, and E. Wolf, Opt. Lett. 28, 878 (2003).
[CrossRef]

Born, M.

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

Cai, C.

Chernyshov, A. A.

A. A. Chernyshov, Ch. V. Felde, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, J. Opt. A 11, 094010 (2009).
[CrossRef]

Ch. V. Felde, A. A. Chernyshov, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, JETP Lett. 88, 418 (2008).

Dholakia, K.

Dogariu, A.

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

Felde, Ch. V.

A. A. Chernyshov, Ch. V. Felde, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, J. Opt. A 11, 094010 (2009).
[CrossRef]

Ch. V. Felde, A. A. Chernyshov, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, JETP Lett. 88, 418 (2008).

G. V. Bogatyryova, Ch. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, and E. Wolf, Opt. Lett. 28, 878 (2003).
[CrossRef]

Foley, J. T.

Freund, I.

Gbur, G.

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
[CrossRef]

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

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

Han, P.

Maleev, I. D.

I. D. Maleev and G. A. Swartzlander, J. Opt. Soc. Am. B 25, 915 (2008).
[CrossRef]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Marathay, A. S.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Mazilu, M.

Mokhun, A. I.

Mokhun, I. I.

Nemoto, S.

Nye, J. F.

J. F. Nye, Natural Focusing and Fine Structure of Light (IOP, 1999).

Palacios, D. M.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Polyanskii, P. V.

A. A. Chernyshov, Ch. V. Felde, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, J. Opt. A 11, 094010 (2009).
[CrossRef]

Ch. V. Felde, A. A. Chernyshov, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, JETP Lett. 88, 418 (2008).

G. V. Bogatyryova, Ch. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, and E. Wolf, Opt. Lett. 28, 878 (2003).
[CrossRef]

Ponomarenko, S. A.

Popescu, G.

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

Pu, J.

Rahman, F.

F. Rahman, Opt. Photon. News 24, 26 (2013).
[CrossRef]

Roychowdhury, H.

S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

Schouten, H. F.

Soskin, M. S.

A. A. Chernyshov, Ch. V. Felde, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, J. Opt. A 11, 094010 (2009).
[CrossRef]

Ch. V. Felde, A. A. Chernyshov, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, JETP Lett. 88, 418 (2008).

I. Freund, A. I. Mokhun, M. S. Soskin, O. V. Angelsky, and I. I. Mokhun, Opt. Lett. 27, 545 (2002).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, Vol. 42 of Progress in Optics, E. Wolf, ed. (Elsevier, 2001), p. 219.

Swartzlander, G. A.

I. D. Maleev and G. A. Swartzlander, J. Opt. Soc. Am. B 25, 915 (2008).
[CrossRef]

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

van Dijk, T.

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, Vol. 42 of Progress in Optics, E. Wolf, ed. (Elsevier, 2001), p. 219.

Visser, T. D.

T. van Dijk and T. D. Visser, J. Opt. Soc. Am. A 26, 741 (2009).
[CrossRef]

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
[CrossRef]

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

Wolf, E.

S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
[CrossRef]

G. V. Bogatyryova, Ch. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, and E. Wolf, Opt. Lett. 28, 878 (2003).
[CrossRef]

S. A. Ponomarenko and E. Wolf, Opt. Lett. 27, 1211 (2002).
[CrossRef]

J. T. Foley and E. Wolf, J. Opt. Soc. Am. A 19, 2510 (2002).
[CrossRef]

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

S. A. Ponomarenko and E. Wolf, Opt. Commun. 170, 1 (1999).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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

Yang, Y.

J. Opt. A (1)

A. A. Chernyshov, Ch. V. Felde, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, J. Opt. A 11, 094010 (2009).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

Ch. V. Felde, A. A. Chernyshov, G. V. Bogatyryova, P. V. Polyanskii, and M. S. Soskin, JETP Lett. 88, 418 (2008).

New. J. Phys. (1)

M. V. Berry, New. J. Phys. 6, 66 (2002).

Opt. Commun. (2)

S. A. Ponomarenko and E. Wolf, Opt. Commun. 170, 1 (1999).
[CrossRef]

G. Gbur and T. D. Visser, Opt. Commun. 222, 117 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (7)

Opt. Photon. News (1)

F. Rahman, Opt. Photon. News 24, 26 (2013).
[CrossRef]

Phys. Lett. A (1)

S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

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

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

Other (4)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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

J. F. Nye, Natural Focusing and Fine Structure of Light (IOP, 1999).

M. S. Soskin and M. V. Vasnetsov, Vol. 42 of Progress in Optics, E. Wolf, ed. (Elsevier, 2001), p. 219.

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Figures (4)

Fig. 1.
Fig. 1.

Partially spatially coherent secondary source. The optical axis of the source is along the z axis.

Fig. 2.
Fig. 2.

Magnitude of the spectral degree of coherence as a function of the angle θ2 and frequency ω. The other angular argument, θ1=θ¯1, takes on values indicated in the figure. The aperture sizes are: (a) and (c) a1=2mm and a2=3mm; (b) and (d) a1=2mm and a2=4mm.

Fig. 3.
Fig. 3.

Frequency evolution of |μ(θ¯1,θ¯2,ω)| for two aperture sizes a2, given a1=2mm, θ¯1=2.25×104rad, and θ¯2=3.5×104rad.

Fig. 4.
Fig. 4.

(a) Engineering a spectral anomaly in the critical direction with θ*=1.91×104rad. (b) The secondary source spectral line (black solid line) is split. The primary source spectrum (red dashed line) is a Gaussian.

Equations (11)

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

U*(r1,ω)U(r2,ω)W(r1,r2,ω)δ(ωω).
μ(r1*,r2*,ω*)=0.
μ(r1,r2,ω)=W(r1,r2,ω)S(r1,ω)S(r2,ω),
U(rs,ω)keikrrΣp=1,2cp(ω)up(θ,ω).
cp*(ω)cq(ω)=S(i)(ω)δpqδ(ωω).
up(θ,ω)=2J1(kapθ)kapθ,
W(rs1,rs2,ω)S(i)(ω)r2[G(θ1,θ2,ω)θ1θ2],
G(θ1,θ2,ω)=Σp=1,2J1(kapθp)J1(kapθ3p)ap2.
S(rs,ω)W(rs,rs,ω)S(i)(ω)r2[F(θ,ω)θ2],
F(θ,ω)=Σp=1,2J12(kapθ)ap2.
μ(θ1,θ2,ω)=G(θ1,θ2,ω)F(θ1,ω)F(θ2,ω).

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