Abstract

The subject is the spectral characteristics of partially coherent light whose spectral degree of coherence satisfies or violates the scaling law in diffraction by a circular aperture. Three kinds of spectral correlations of the incident light are considered. It is shown that no matter whether the partially coherent light satisfies or violates the scaling law, a spectral switch defined as a rapid transition of spectral shifts is always found in the diffraction field. Different spectral correlations of the incident field in the aperture result in different points at which the spectral switch occurs. With an increment in the correlations, the position at which the spectral switch takes place moves toward the point at which the phase of the center frequency component ω0 becomes singular for illumination by spatially fully coherent light. For light that satisfies the scaling law, the spectral switch is attributed to the diffraction-induced spectral changes; for partially coherent light that violates the scaling law, the spectral switch is attributed to both the diffraction-induced spectral changes and the correlation-induced spectral changes.

© 2003 Optical Society of America

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References

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  1. E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett. 56, 1370–1372 (1986).
    [CrossRef] [PubMed]
  2. E. Wolf, “Non-cosmological redshifts of spectral lines,” Nature 326, 363–365 (1987).
    [CrossRef]
  3. E. Wolf, “Correlation-induced Doppler-like frequency shifts of spectral lines,” Phys. Rev. Lett. 63, 2220–2223 (1989).
    [CrossRef] [PubMed]
  4. J. T. Foley, “The effect of an aperture on the spectrum of partially coherent light,” Opt. Commun. 75, 347–352 (1990).
    [CrossRef]
  5. J. T. Foley, “Effect of an aperture on the spectrum of partially coherent light,” J. Opt. Soc. Am. A 8, 1099–1105 (1991).
    [CrossRef]
  6. K. A. Nugent, J. L. Gardner, “Radiametric measurements and correlation-induced spectral changes,” Metrologia 29, 319–324 (1992).
  7. J. Pu, H. Zhang, S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162, 57–63 (1999).
    [CrossRef]
  8. J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
    [CrossRef]
  9. J. Pu, S. Nemoto, “Spectral changes and 1×N spectral switches in the diffraction of partially coherent light,” J. Opt. Soc. Am. A 19, 339–344 (2002).
    [CrossRef]
  10. H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A Pure Appl. Opt. 3, 296–299 (2001).
    [CrossRef]
  11. H. C. Kandpal, S. Anand, J. S. Vaishya, “Experiment observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38, 336–339 (2002).
    [CrossRef]
  12. S. Anand, B. K. Yadav, H. C. Kandpal, “Experimental study of the phenomenon of 1×N spectral switch due to diffraction of partially coherent light,” J. Opt. Soc. Am. A 19, 2223–2228 (2002).
    [CrossRef]
  13. L. Pan, B. Lü, “The spectral switch of partially coherent light in Young’s experiment,” IEEE J. Quantum Electron. 37, 1388–1381 (2001).
  14. M. S. Soskin, M. V. Vasnetov, “Singular optics,” in Progress in Optics, Vol. XLII, E. Wolf, ed. (Elsevier, Amsterdam, 2001), pp. 219–276.
  15. G. Gbur, T. D. Visser, E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
    [CrossRef] [PubMed]
  16. G. Gbur, T. D. Visser, E. Wolf, “Singular behavior of the spectrum in the neighborhood of focus,” J. Opt. Soc. Am. A 19, 1694–1700 (2002).
    [CrossRef]
  17. G. Popescu, A. Dogariu, “Spectral anomalies at wavefront dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
    [CrossRef]
  18. J. T. Foley, E. Wolf, “Phenomenon of spectral switches as a new effect in singular optics with polychromatic light,” J. Opt. Soc. Am. A 19, 2510–2516 (2002).
    [CrossRef]

2002 (7)

2001 (2)

L. Pan, B. Lü, “The spectral switch of partially coherent light in Young’s experiment,” IEEE J. Quantum Electron. 37, 1388–1381 (2001).

H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A Pure Appl. Opt. 3, 296–299 (2001).
[CrossRef]

2000 (1)

J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
[CrossRef]

1999 (1)

J. Pu, H. Zhang, S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162, 57–63 (1999).
[CrossRef]

1992 (1)

K. A. Nugent, J. L. Gardner, “Radiametric measurements and correlation-induced spectral changes,” Metrologia 29, 319–324 (1992).

1991 (1)

1990 (1)

J. T. Foley, “The effect of an aperture on the spectrum of partially coherent light,” Opt. Commun. 75, 347–352 (1990).
[CrossRef]

1989 (1)

E. Wolf, “Correlation-induced Doppler-like frequency shifts of spectral lines,” Phys. Rev. Lett. 63, 2220–2223 (1989).
[CrossRef] [PubMed]

1987 (1)

E. Wolf, “Non-cosmological redshifts of spectral lines,” Nature 326, 363–365 (1987).
[CrossRef]

1986 (1)

E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett. 56, 1370–1372 (1986).
[CrossRef] [PubMed]

Anand, S.

H. C. Kandpal, S. Anand, J. S. Vaishya, “Experiment observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38, 336–339 (2002).
[CrossRef]

S. Anand, B. K. Yadav, H. C. Kandpal, “Experimental study of the phenomenon of 1×N spectral switch due to diffraction of partially coherent light,” J. Opt. Soc. Am. A 19, 2223–2228 (2002).
[CrossRef]

Dogariu, A.

G. Popescu, A. Dogariu, “Spectral anomalies at wavefront dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

Foley, J. T.

Gardner, J. L.

K. A. Nugent, J. L. Gardner, “Radiametric measurements and correlation-induced spectral changes,” Metrologia 29, 319–324 (1992).

Gbur, G.

G. Gbur, T. D. Visser, E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

G. Gbur, T. D. Visser, E. Wolf, “Singular behavior of the spectrum in the neighborhood of focus,” J. Opt. Soc. Am. A 19, 1694–1700 (2002).
[CrossRef]

Kandpal, H. C.

S. Anand, B. K. Yadav, H. C. Kandpal, “Experimental study of the phenomenon of 1×N spectral switch due to diffraction of partially coherent light,” J. Opt. Soc. Am. A 19, 2223–2228 (2002).
[CrossRef]

H. C. Kandpal, S. Anand, J. S. Vaishya, “Experiment observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38, 336–339 (2002).
[CrossRef]

H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A Pure Appl. Opt. 3, 296–299 (2001).
[CrossRef]

Lü, B.

L. Pan, B. Lü, “The spectral switch of partially coherent light in Young’s experiment,” IEEE J. Quantum Electron. 37, 1388–1381 (2001).

Nemoto, S.

J. Pu, S. Nemoto, “Spectral changes and 1×N spectral switches in the diffraction of partially coherent light,” J. Opt. Soc. Am. A 19, 339–344 (2002).
[CrossRef]

J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
[CrossRef]

J. Pu, H. Zhang, S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162, 57–63 (1999).
[CrossRef]

Nugent, K. A.

K. A. Nugent, J. L. Gardner, “Radiametric measurements and correlation-induced spectral changes,” Metrologia 29, 319–324 (1992).

Pan, L.

L. Pan, B. Lü, “The spectral switch of partially coherent light in Young’s experiment,” IEEE J. Quantum Electron. 37, 1388–1381 (2001).

Popescu, G.

G. Popescu, A. Dogariu, “Spectral anomalies at wavefront dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

Pu, J.

J. Pu, S. Nemoto, “Spectral changes and 1×N spectral switches in the diffraction of partially coherent light,” J. Opt. Soc. Am. A 19, 339–344 (2002).
[CrossRef]

J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
[CrossRef]

J. Pu, H. Zhang, S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162, 57–63 (1999).
[CrossRef]

Soskin, M. S.

M. S. Soskin, M. V. Vasnetov, “Singular optics,” in Progress in Optics, Vol. XLII, E. Wolf, ed. (Elsevier, Amsterdam, 2001), pp. 219–276.

Vaishya, J. S.

H. C. Kandpal, S. Anand, J. S. Vaishya, “Experiment observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38, 336–339 (2002).
[CrossRef]

Vasnetov, M. V.

M. S. Soskin, M. V. Vasnetov, “Singular optics,” in Progress in Optics, Vol. XLII, E. Wolf, ed. (Elsevier, Amsterdam, 2001), pp. 219–276.

Visser, T. D.

G. Gbur, T. D. Visser, E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

G. Gbur, T. D. Visser, E. Wolf, “Singular behavior of the spectrum in the neighborhood of focus,” J. Opt. Soc. Am. A 19, 1694–1700 (2002).
[CrossRef]

Wolf, E.

G. Gbur, T. D. Visser, E. Wolf, “Singular behavior of the spectrum in the neighborhood of focus,” J. Opt. Soc. Am. A 19, 1694–1700 (2002).
[CrossRef]

G. Gbur, T. D. Visser, E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

J. T. Foley, E. Wolf, “Phenomenon of spectral switches as a new effect in singular optics with polychromatic light,” J. Opt. Soc. Am. A 19, 2510–2516 (2002).
[CrossRef]

E. Wolf, “Correlation-induced Doppler-like frequency shifts of spectral lines,” Phys. Rev. Lett. 63, 2220–2223 (1989).
[CrossRef] [PubMed]

E. Wolf, “Non-cosmological redshifts of spectral lines,” Nature 326, 363–365 (1987).
[CrossRef]

E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett. 56, 1370–1372 (1986).
[CrossRef] [PubMed]

Yadav, B. K.

Zhang, H.

J. Pu, H. Zhang, S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162, 57–63 (1999).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
[CrossRef]

L. Pan, B. Lü, “The spectral switch of partially coherent light in Young’s experiment,” IEEE J. Quantum Electron. 37, 1388–1381 (2001).

H. C. Kandpal, S. Anand, J. S. Vaishya, “Experiment observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38, 336–339 (2002).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A Pure Appl. Opt. 3, 296–299 (2001).
[CrossRef]

J. Opt. Soc. Am. A (5)

Metrologia (1)

K. A. Nugent, J. L. Gardner, “Radiametric measurements and correlation-induced spectral changes,” Metrologia 29, 319–324 (1992).

Nature (1)

E. Wolf, “Non-cosmological redshifts of spectral lines,” Nature 326, 363–365 (1987).
[CrossRef]

Opt. Commun. (2)

J. T. Foley, “The effect of an aperture on the spectrum of partially coherent light,” Opt. Commun. 75, 347–352 (1990).
[CrossRef]

J. Pu, H. Zhang, S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162, 57–63 (1999).
[CrossRef]

Phys. Rev. Lett. (4)

E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett. 56, 1370–1372 (1986).
[CrossRef] [PubMed]

E. Wolf, “Correlation-induced Doppler-like frequency shifts of spectral lines,” Phys. Rev. Lett. 63, 2220–2223 (1989).
[CrossRef] [PubMed]

G. Gbur, T. D. Visser, E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef] [PubMed]

G. Popescu, A. Dogariu, “Spectral anomalies at wavefront dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

Other (1)

M. S. Soskin, M. V. Vasnetov, “Singular optics,” in Progress in Optics, Vol. XLII, E. Wolf, ed. (Elsevier, Amsterdam, 2001), pp. 219–276.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the system configuration and illustration of notation.

Fig. 2
Fig. 2

Plots of M(z, ω) (thin curve), S(0)(ω)/S0 (dashed curve), and S(z, ω) (thick curve) as a function of frequency, when z/z0=0.25. (a) Δ0, (b) Δ0=1.5, (c) Δ0=1, (d) Δ0=0.6, (e) Δ0=0.5. M(z, ω) and S(z, ω) are normalized to 4 at their maxima when the incident light is completely coherent. The unit of the transverse axis in the figures is 1015 s-1. ω0=3.2×1015 s-1, Γ=0.6×1015 s-1. The spectral degree of coherence of the incident light takes the form expressed by Eq. (2.5).

Fig. 3
Fig. 3

Spectral switches occur at (a) z/z0=0.2449 for Δ0=1 and (b) z/z0=0.2444 for Δ0=0.6. See Fig. 2 for definitions of curves, Δ0, ω0, and Γ.

Fig. 4
Fig. 4

Plots of M(z, ω) (thin curve), S(0)(ω)/S0 (dashed curve), and S(z, ω) (thick curve) as a function of frequency, when z/z0=0.25. (a) Δ0, (b) Δ0=1, (c) Δ0=0.6. ω0=3.2×1015 s-1, Γ=0.6×1015 s-1. The spectral degree of coherence of the incident light takes the form expressed by Eq. (3.3).

Fig. 5
Fig. 5

Spectral switches occur at (a) z/z0=0.2408 for Δ0=1 and (b) z/z0=0.2394 for Δ0=0.6. See Fig. 2 for definitions of curves, Δ0, ω0, and Γ.

Fig. 6
Fig. 6

Plots of M(z, ω) (thin curve), S(0)(ω)/S0 (dashed curve), and S(z, ω) (thick curve) as a function of frequency, when z/z0=0.25. (a) Δ0, (b) Δ0=1, (c) Δ0=0.6. ω0=3.2×1015 s-1, Γ=0.6×1015 s-1. The spectral degree of coherence of the incident light takes the form expressed by Eq. (3.4).

Fig. 7
Fig. 7

Spectral switches occur at (a) z/z0=0.2576 for Δ0=1 and (b) z/z0=0.2521 for Δ0=0.6. ω0=3.2×1015 s-1, Γ=0.6×1015 s-1. See Fig. 2 for definitions of curves.

Fig. 8
Fig. 8

Plots of the positions (z/z0)s where the spectral switches take place as a function of Δ0 for the spectral degree of coherence given by Eq. (2.5) (dotted curve), Eq. (3.3) (solid curve), and Eq. (3.4) (dashed curve). ω0=3.2×1015 s-1, Γ=0.6×1015 s-1.

Equations (17)

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W(0)(ρ1, ρ2, ω)=S(0)(ω)μ(0)(ρ2-ρ1, ω),
μ(0)(ρ1-ρ2, ω)=exp-(ρ2-ρ1)22σ(ω)2
S(0)(ω)=S0Γ2(ω-ω0)2+Γ2,
σ(ω)=σ0ω0/ω,
μ(0)(ρ1-ρ2, ω)=exp-[k(ρ2-ρ1)]22(σ0k0)2,
S(z, ω)=M(z, ω)S(0)(ω),
M(z, ω)=N0(z)2ωω020101×exp-r12+r222Δ(ω)2I0r1r2Δ(ω)2×exp-iπN0(z)ωω0(r12-r22)×r1r2dr1dr2
N0(z)=a2/λ0z=z0/z
z0=a2/λ0,
Δ(ω)=Δ0(ω0/ω)
N0(z)=2m(m=1, 2, 3,),
σ1(ω)=σ0(ω0/ω)2,
σ2(ω)=σ0(ω/ω0)2.
μ1(0)(ρ1-ρ2, ω)=exp-[k2(ρ2-ρ1)]22(σ0k02)2,
μ2(0)(ρ1-ρ2), ω)=exp-[k02(ρ2-ρ1)]22(σ0k2)2.
Δ(ω)=Δ1(ω)=Δ0(ω0/ω)2,
Δ(ω)=Δ2(ω)=Δ0(ω/ω0)2.

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