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Spectral anomalies in Young’s double-slit interference experiment

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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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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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