Abstract

We report a phenomenon of spectral anomalies in the interference field of Young’s double-slit interference experiment. The potential applications of the spectral anomalies in the information encoding and information transmission in free space are also considered.

© 2004 Optical Society of America

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References

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IEEE J. Quantum Electron. (1)

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

J. Appl. Phys. (1)

J. Turunen, E. Tervonen, and A. T. Friberg, �??Acousto-optic control and modulation of optical coherence by electronically synthesized holographic grating,�?? J. Appl. Phys. 67, 49-59 (1990).
[CrossRef]

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

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

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]

J. Pu and S. Nemoto, �??Spectral changes and 1 �? �? spectral switches in the diffraction of partially coherent light by an aperture,�?? J. Opt. Soc. Am. A. 19, 339-344 (2002).
[CrossRef]

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

New J. Phys. (2)

M. V. Berry, �??Exploring the colors of dark light,�?? New J. Phys. 4, 74 (2002).
[CrossRef]

M. V. Berry, �??Colored phase singularities,�?? New J. Phys. 4, 66 (2002)
[CrossRef]

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, 57-63 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (2)

G. Popescu and A. Dogariu, �??Spectral anomalies at wavefront dislocations,�?? Phys. Rev. Lett. 88, 0183902 (2002).
[CrossRef]

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

Proc. R. Soc. Lond. A (1)

J. F. Nye and M. V. Berry, �??Dislocations in wave trains,�?? Proc. R. Soc. Lond. A 336, 165-190 (1974)
[CrossRef]

Prog. in Optics (1)

M. S. Soskin and M. V. Vasnetsov, �??Singular Optics,�?? Prog. in Optics, ed. E. Wolf (Amsterdam: Elsevier) 42, 219-276 (2001).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Notation relating to Young’s double-slit interference experiment

Fig. 2
Fig. 2

(color). Color-coded plot of the relative mean frequency ω̅(uN ,zN ) of the spectrum in the interference field as a function of uN and zN . The color is more red or blue as the spectrum is more redshifted or blueshifted, respectively. The parameters are chosen as ε = 0.95 ω 0 = 1015s-1 and Γ = 0.0ω 0.

Fig. 3
Fig. 3

The relative mean frequency as a function of the spectral width (Γ) of the incident light. The parameters are chosen as ε = 0.95 , ω 0 = 1015s-1 , zN = 15 and uN = 3.82 .

Fig. 4.
Fig. 4.

The spectral shifts are represented by the color marks. The more red or more blue indicates the spectrum more redshifted or more bluedshifted. (a) Γ = 0.01ω 0 (b) Γ = 0.2ω 0 . Other parameters are ε = 0.95 , ω 0 = 1015s-1, zN = 15 . The arrows indicate the positions at which the spectral detector is placed for measuring the spectra. vN = v/a.

Fig. 5
Fig. 5

The relative mean frequency as a function of the relative coherence ∆0 . Γ = 0.01ω 0 (solid curve), Γ = 0.02ω 0 (dashed curve) The parameters are chosen as ε = 0.95 , ω 0 = 1015s-1, zN = 15 and uN = 3.82 .

Fig. 6.
Fig. 6.

Illustration for the information (data) encoding and information transmission by controlling the spectral width of the incident light. The blueshift (B, in short) could be associated with a bit of information such as a “1”, and the redshift (R, in short) could be associated with “0”. The observation point is at zN = 15 and uN = 3.82. Γ is the spectral width of the incident spatial completely coherent light.

Fig. 7.
Fig. 7.

Illustration for the information (data) encoding and information transmission by modulating spatial coherence of the incident light. The blueshift (B, in short) could be associated with a bit of information such as a “1”, and the redshift (R, in short) could be associated with “0”. The observation point is at zN = 15 and uN = 3.82 . ∆0 is the normalized spatial correlation distance.

Equations (9)

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S ( 0 ) ( ω ) = exp { ( ω ω 0 ) 2 2 Γ 2 }
S ( u N , z N , ω ) = ω S ( 0 ) ( ω ) z N ω 0 E ( u N , z N , ω ) 2 ,
E ( u N , z N , ω ) = E 0 ( ω ) ( i ( ω ω 0 ) z N ) 1 / 2 { 1 ε exp [ i π ( ω ω 0 ) z N ( x 2 2 x . u N ) ] d x
+ ε 1 exp [ i π ( ω ω 0 ) z N ( x 2 2 x . u N ) ] d x } ,
ω ¯ ( u N , z N ) = ω ' S ( u N , z N , ω ' ) d ω ' S ( u N , z N , ω ' ) d ω ' .
W ( 0 ) ( x 1 , x 2 , z = 0 , ω ) = S ( 0 ) ( ω ) exp [ ( x 1 x 2 ) 2 2 σ 2 ( ω ) ] ,
σ ( ω ) = σ 0 ω 0 ω
S ( u N , z N , ω ) = S ( 0 ) ( ω ) z N ( ω ω 0 ) A A exp [ ( x 1 x 2 ) 2 2 Δ 0 2 ( ω ω 0 ) 2 ]
× exp { i π z N ( ω ω 0 ) [ x 1 2 x 2 2 2 u N ( x 1 x 2 ) ] } d x 1 d x 2 ,

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