Abstract

We study the spectral property of a composite field superposed by a polychromatic Gaussian beam and a polychromatic Gaussian beam with an embedded mth-order vortex. It is shown that, in the overall spectral shift distribution, there exist m small areas where sharp spectral anomaly takes place, similarly and respectively, which are related with the ratio of the respective amplitudes of the two composite beams and the relative phase between them. Detailed investigation reveals that, for each small area, there exists a “main line”, along which spectral switch can be observed.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A, Pure Appl. Opt. 3(4), 296–299 (2001).
    [CrossRef]
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    [CrossRef]
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2014 (2)

2013 (1)

2012 (1)

2009 (1)

2002 (7)

J. T. Foley and E. Wolf, “Phenomenon of spectral switches as a new effect in singular optics with polychromatic light,” J. Opt. Soc. Am. A 19(12), 2510–2516 (2002).
[CrossRef] [PubMed]

H. C. Kandpal, S. Anand, and J. S. Vaishya, “Experimental observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38(4), 336–339 (2002).
[CrossRef]

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88(1), 013901 (2002).
[CrossRef] [PubMed]

J. Pu and S. Nemoto, “Spectral changes and 1×N spectral switches in the diffraction of partially coherent light by an aperture,” J. Opt. Soc. Am. A 19(2), 339–344 (2002).
[CrossRef] [PubMed]

S. A. Ponomarenko and E. Wolf, “Spectral anomalies in a Fraunhofer diffraction pattern,” Opt. Lett. 27(14), 1211–1213 (2002).
[CrossRef] [PubMed]

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88(18), 183902 (2002).
[CrossRef] [PubMed]

B. Lu and L. Pan, “Spectral switching of Gaussian-Schell model beams passing through an aperture lens,” IEEE J. Quantum Electron. 38(4), 340–344 (2002).
[CrossRef]

2001 (4)

H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A, Pure Appl. Opt. 3(4), 296–299 (2001).
[CrossRef]

L. Pan and B. Lu, “The spectral switch of partially coherent light in Young’s experiment,” IEEE J. Quantum Electron. 37(11), 1377–1381 (2001).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Progress in Optics 42, 219–276 (2001).
[CrossRef]

G. Gbur, T. D. Visser, and E. Wolf, “Singular behavior of the spectrum in the neighborhood of focus,” J. Opt. Soc. Am. A 19(8), 1694–1700 (2001).
[CrossRef] [PubMed]

2000 (1)

J. Pu and S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36(12), 1407–1411 (2000).
[CrossRef]

1999 (1)

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162(1-3), 57–63 (1999).
[CrossRef]

1974 (1)

F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[CrossRef]

Anand, S.

H. C. Kandpal, S. Anand, and J. S. Vaishya, “Experimental observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38(4), 336–339 (2002).
[CrossRef]

Berry, M. V.

F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[CrossRef]

Cai, Y. J.

Chen, C. R.

Dogariu, A.

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88(18), 183902 (2002).
[CrossRef] [PubMed]

Dong, Y.

Foley, J. T.

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88(1), 013901 (2002).
[CrossRef] [PubMed]

G. Gbur, T. D. Visser, and E. Wolf, “Singular behavior of the spectrum in the neighborhood of focus,” J. Opt. Soc. Am. A 19(8), 1694–1700 (2001).
[CrossRef] [PubMed]

Han, P.

Kandpal, H. C.

H. C. Kandpal, S. Anand, and J. S. Vaishya, “Experimental observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38(4), 336–339 (2002).
[CrossRef]

H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A, Pure Appl. Opt. 3(4), 296–299 (2001).
[CrossRef]

Liu, Y. D.

Lu, B.

B. Lu and L. Pan, “Spectral switching of Gaussian-Schell model beams passing through an aperture lens,” IEEE J. Quantum Electron. 38(4), 340–344 (2002).
[CrossRef]

L. Pan and B. Lu, “The spectral switch of partially coherent light in Young’s experiment,” IEEE J. Quantum Electron. 37(11), 1377–1381 (2001).
[CrossRef]

Nemoto, S.

J. Pu and S. Nemoto, “Spectral changes and 1×N spectral switches in the diffraction of partially coherent light by an aperture,” J. Opt. Soc. Am. A 19(2), 339–344 (2002).
[CrossRef] [PubMed]

J. Pu and S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36(12), 1407–1411 (2000).
[CrossRef]

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162(1-3), 57–63 (1999).
[CrossRef]

Nye, F.

F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[CrossRef]

Pan, L.

B. Lu and L. Pan, “Spectral switching of Gaussian-Schell model beams passing through an aperture lens,” IEEE J. Quantum Electron. 38(4), 340–344 (2002).
[CrossRef]

L. Pan and B. Lu, “The spectral switch of partially coherent light in Young’s experiment,” IEEE J. Quantum Electron. 37(11), 1377–1381 (2001).
[CrossRef]

Ponomarenko, S. A.

Popescu, G.

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88(18), 183902 (2002).
[CrossRef] [PubMed]

Pu, J.

J. Pu and S. Nemoto, “Spectral changes and 1×N spectral switches in the diffraction of partially coherent light by an aperture,” J. Opt. Soc. Am. A 19(2), 339–344 (2002).
[CrossRef] [PubMed]

J. Pu and S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36(12), 1407–1411 (2000).
[CrossRef]

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162(1-3), 57–63 (1999).
[CrossRef]

Shih, M. F.

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Progress in Optics 42, 219–276 (2001).
[CrossRef]

Vaishya, J. S.

H. C. Kandpal, S. Anand, and J. S. Vaishya, “Experimental observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38(4), 336–339 (2002).
[CrossRef]

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Progress in Optics 42, 219–276 (2001).
[CrossRef]

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88(1), 013901 (2002).
[CrossRef] [PubMed]

G. Gbur, T. D. Visser, and E. Wolf, “Singular behavior of the spectrum in the neighborhood of focus,” J. Opt. Soc. Am. A 19(8), 1694–1700 (2001).
[CrossRef] [PubMed]

Wolf, E.

Yang, Y. J.

Yeh, C. H.

Zhang, H.

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162(1-3), 57–63 (1999).
[CrossRef]

Zhao, C. L.

IEEE J. Quantum Electron. (4)

J. Pu and S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36(12), 1407–1411 (2000).
[CrossRef]

L. Pan and B. Lu, “The spectral switch of partially coherent light in Young’s experiment,” IEEE J. Quantum Electron. 37(11), 1377–1381 (2001).
[CrossRef]

B. Lu and L. Pan, “Spectral switching of Gaussian-Schell model beams passing through an aperture lens,” IEEE J. Quantum Electron. 38(4), 340–344 (2002).
[CrossRef]

H. C. Kandpal, S. Anand, and J. S. Vaishya, “Experimental observation of the phenomenon of spectral switching for a class of partially coherent light,” IEEE J. Quantum Electron. 38(4), 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(4), 296–299 (2001).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun. 162(1-3), 57–63 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. Lett. (2)

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88(1), 013901 (2002).
[CrossRef] [PubMed]

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88(18), 183902 (2002).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974).
[CrossRef]

Progress in Optics (1)

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Progress in Optics 42, 219–276 (2001).
[CrossRef]

Other (1)

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

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Figures (8)

Fig. 1
Fig. 1

Distribution of central frequency component during propagation (m = 2). (a) zn = 0.5; (b) zn = 1; (c) zn = 2; (d) zn = 10.

Fig. 2
Fig. 2

Distribution of the relative mean frequency of the spectrum (m = 2). (a) zn = 0.5; (b) zn = 1; (c) zn = 2; (d) zn = 10. The dashed line indicates the positions where spectral shift is zero.

Fig. 3
Fig. 3

Distribution of the relative mean frequency of the spectrum (m = 2, zn = 2) (a) ϕ 0 =π/2 ; (b) ϕ 0 =π . The dashed line indicates the positions where spectral shift is zero.

Fig. 4
Fig. 4

Distribution of the relative mean frequency of the spectrum (m = 2,zn = 2). (a) γ = 0.5; (b) γ = 0.63; (c) γ = 0.65; (d) γ = 0.67; (e) γ = 1.2; (f) γ = 1.48; (g) γ = 1.5; (h) γ = 1.52; (i) γ = 2. The dashed line indicates the positions where spectral shift is zero.

Fig. 5
Fig. 5

Distribution of the relative mean frequency of the spectrum (m = 5, zn = 2). (a) γ = 2.5; (b) γ = 2.73; (c) γ = 2.8; (d) γ = 4.5; (e) γ = 4.7; (f) γ = 5. The dashed line indicates the positions where spectral shift is zero.

Fig. 6
Fig. 6

Details of the distribution of the relative mean frequency of the spectrum in the vicinity of the left singularity of the central frequency component in Fig. 2(c). The dashed line indicates the positions where spectral shift is zero. The white line is the “main line”

Fig. 7
Fig. 7

Normalized spectral distribution of different observation points in the direction θ' = 0 (π). (a).r' = 0.0005mm, θ' = π; (b) r' = 0.0004mm, θ' = π; (c) r' = 0.0002mm, θ' = π; (d) r' = 0mm; (e) r' = 0.0002mm, θ' = 0; (f) r' = 0.0004mm, θ' = 0. The red curves indicate the original spectra S0(ω) and the blue curves indicate the spectra S(ω).

Fig. 8
Fig. 8

Normalized spectral distribution of different observation points in the direction θ' = 3π/2(π/2). (a).r' = 0.008mm, θ' = 3π/2; (b) r' = 0.005mm, θ' = 3π/2; (c) r' = 0.002mm, θ' = 3π/2; (d) r' = 0mm; (e) r' = 0.002mm, θ' = π/2; (f) r' = 0.005mm, θ' = π/2. The red curves indicate the original spectra S0(ω) and the blue curves indicate the spectra S(ω).

Equations (8)

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

{ E(ρ,φ,z=0)= E G (ρ,φ,z=0)+ E GV (ρ,φ,z=0) E G (ρ,φ,z=0)= E G0 exp[ ρ 2 / σ 2 ] E 0 (ω)exp[i ϕ 0 ] E GV (ρ,φ,z=0)= E GV0 (ρ/σ ) m exp[ ρ 2 / σ 2 ]exp(imφ) E 0 (ω)
E 0 (ω)= S 0 (ω) =exp[ (ω ω 0 ) 2 4 Γ 2 ]
E(r,θ,ω,z)= iω 2πzc exp[ i ωz c ] E(ρ,φ,ω,z=0)exp{ ik 2z [ (rρ) 2 ] }d ρ
E(r,θ,ω,z)= E 0 (ω)[ 1iz/ z R 1+ z 2 / z R 2 ]exp[ i ωz c (1iz/ z R ) r 2 (1+ z 2 / z R 2 ) σ 2 ] ×[ E GV0 exp(imθ) ( r σ ) m ( 1iz/ z R 1+ z 2 / z R 2 ) m + E G0 exp(i ϕ 0 ) ]
S(r,θ,ω,z)= S 0 (ω) 1+ z 2 / z R 2 exp[ 2 r 2 (1+ z 2 / z R 2 ) σ 2 ] × | E GV0 exp(imθ) ( r σ ) m ( 1iz/ z R 1+ z 2 / z R 2 ) m + E G0 exp(i ϕ 0 ) | 2
{ r= γ 1/m 1+ z n 2 σ, ( z n =z / z R0 , z R0 = ω 0 σ 2 / 2c, γ= E G0 / E GV0 ) θ=arctan(z/ z R0 )+ (π+ ϕ 0 +2nπ) /m , (n=0,1,,m1)
ω ¯ (r,θ,ω,z)= ωS(r,θ,ω,z)dω S(r,θ,ω,z)dω
Ω(r,θ,ω,z)= ω ¯ (r,θ,ω,z) ω 0 ω 0

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