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

1. Introduction

In recent years, there have been increasing interests in the points of the optical field at which the intensity has zero value, because the phase at the points becomes undetermined and the structure of the field in the neighborhood of such points has a rather complex structure, for example, exhibiting dislocations and optical vortices [1–4]. Studies of the phenomenon associated with phase singularities have gradually developed into a new branch of physical optics, referred as singular optics [4]. While most of the publications concerning with singular optics dealt with monochromatic wave, Wolf and his coworkers showed that drastic spectral changes take place in the vicinity of intensity zeros in the focal region of polychromatic scalar field [5,6], and the experimental studies of the singular behaviors around such points were also carried out [7]. More recently, it has been demonstrated that the spectral anomalies also occur in the vicinity of the dark rings of a Fraunhofer diffraction pattern [8]. The spectral anomalies seem to have a close link to the phenomena of spectral switches, which was found several years ago [9–12], and the link between the spectral anomalies and the spectral switches has been discussed in Ref. [13].

Young’s interference experiment is one of the most fundamental experiments of all physics, which is widely applied to physical optics and quantum optics. In this paper we investigate the spectral behaviors in the interference field of Young’s double-slit interference experiments illuminated by spatially completely coherent polychromatic light or partially coherent polychromatic light. It will be shown that the spectral anomalies also take place at positions located in both the near field and the far field, associated with the dark fringes for a fixed frequency. The evolution of the spectral anomalies from the near field to the far field will be investigated. The potential applications of the spectral anomalies in information encoding and information transmission in free space will be studied.

2 The spectral anomalies in the interference field

2.1 Young’s double-slit illuminated by polychromatic spatially completely coherent light

Let us first consider a spatially completely coherent light, with spectral density S (0)(ω), is incident upon double slits, as indicated in Fig. 1. The two slits have the identical width, and the inner distance and the outer distance are 2b and 2a, respectively. We define the parameter ε = b/a(1 > ε ≥ 0), for representing the width of the two slits.

It is assumed that the spectrum of the incident spatially completely coherent light consists of a single line of Gaussian profile, centered at frequency ω 0 and rms width Γ, i.e.,

S(0)(ω)=exp{(ωω0)22Γ2}

The spectrum in the interference field can be expressed as

S(uN,zN,ω)=ωS(0)(ω)zNω0E(uN,zN,ω)2,

here

E(uN,zN,ω)=E0(ω)(i(ωω0)zN)1/2{1εexp[iπ(ωω0)zN(x22x.uN)]dx
+ε1exp[iπ(ωω0)zN(x22x.uN)]dx},

here E0(ω)=S(0)(ω),zN=za2λ0,uN=ua , and λ 0 is the central wavelength of the original spectrum. Equation (3) holds if the observation distance away from the plane containing the double-slit satisfies z3π4λ[ux]max4 . We can also found from Eq. (3) that the zone zNπ in the interference field can be viewed as the far field.

 figure: Fig. 1.

Fig. 1. Notation relating to Young’s double-slit interference experiment

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The mean frequency is plotted as a function of the observation position (u and z) in Fig. 2, for ω 0 = 1015 s-1 and Γ = 0.01ω 0. The color in the Fig. 2 is more red and more blue as the spectrum is more redshifted and blueshifted, respectively. As shown in Fig. 2, there exist some positions at which the spectrum exhibits significant change, that is, at one side the spectrum is redshifted, but becomes blueshifted at the other side. It is also shown that the spectral anomalies take place in both the near field and the far field. This means that the spectrum in the interference field is redshifted at some place, and at some other place is blueshifted, and between these places the spectrum is split into two lines [6]. It has been known that this critical position, at which the spectrum exhibits drastic changes, exists just at the neighborhood of the singular point for the frequency ω 0 [5,6].

 figure: 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.

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It is found from Eq. (3) that the spectrum in the interference field is generally different from that of the incident light, and it varies with the observation position (u and z). It is also found that the spectral anomaly may take place at some position. The spectral anomaly can be characterized by the mean frequency for different observation position, which is defined as [6]

ω¯(uN,zN)=ω'S(uN,zN,ω')dω'S(uN,zN,ω')dω'.

It is found from Fig. 2 that when zN > 9 , the spectral anomaly shows the characteristic of regularity for a fixed propagation angle. This means that, along a fixed propagation direction (θcuN / zN), the spectrum is always redshifted at the angle a little smaller than θc, and always blueshifted at the angle a little larger than θc. This special characteristic may be used in the information transmission in free space. We will, in this paper, present approaches for realizing the information transmission in free space.

Now we want to investigate the variation of the spectral anomalies at the fixed point of the interference fields with some parameters. In Fig. 3, we plot the relative mean frequency at the point zN = 15 and uN = 3.82 as a function of the spectral width Γ of the incident light. We notice that when Γ < 0.066ω 0, the spectrum at this point shows redshifted, but when Γ > 0.066ω 0, the spectrum is blueshifted. Figure 4 plots the relative mean frequency near the observed point (zN = 15 and uN = 3.82), with color marks, in the cases of Γ = 0.01ω 0 (Fig. 4(a)) and Γ = 0.2ω 0 (Fig. 4(b)), respectively. It is seen that when Γ = 0.01ω 0 the spectrum at this point (uN = 3.82) is redshifted, and becomes blueshifted when the spectral width Γ of the incident light is Γ = 0.2ω 0. The reason for this spectral property may be attributed to that spectral shift at some specific point is dependent upon the spectral width Γ .

2.2 Young’s double-slits illuminated by polychromatic partially coherent light

Now we consider Young’s double-slit illuminated by partially coherent light, whose cross-spectral density in front of the two slits is given by

W(0)(x1,x2,z=0,ω)=S(0)(ω)exp[(x1x2)22σ2(ω)],

where S (0)(ω) is the spectrum of the incident light, as expressed by Eq.(1), and

σ(ω)=σ0ω0ω

is the rms spatial correlation distance of the incident partially coherent light, and σ 0 is the rms spatial correlation distance at the central frequency ω 0.

Based on the propagation law for the cross-spectral density, the spectrum in the interference field can be expressed as

S(uN,zN,ω)=S(0)(ω)zN(ωω0)AAexp[(x1x2)22Δ02(ωω0)2]
×exp{iπzN(ωω0)[x12x222uN(x1x2)]}dx1dx2,
 figure: 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 .

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 figure: 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.

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where ∆0 = σ 0 / a is the normalized spatial correlation distance for the central frequency and the integral is performed over the plane containing the two slits. It has been found that the change of the coherence gives rise to the drastic change of the spectrum of the interference field. This property can also be used for information encoding and transmission. In Fig. 5, we plot the relative mean frequency near the observation point (zN = 15 and uN = 3.82) as a function of the coherence ∆0. It is seen that when the coherence is low, the spectrum is blueshifted, and turns into the redshifted when ∆0 is larger than ten. It has been known that the spectrum in the interference is strongly dependent on the coherence. This indicates that the change of the coherence gives rise to re-distribution of the different frequency component, so that results in the drastic spectral shift at some specific point.

 figure: 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 .

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3. The potential applications of the spectral anomalies in information encoding and transmission

As shown in Section 2, the spectral anomalies take place in the interference field. Such spectral anomalies may have applications in information encoding and free-space communications, in which the blueshift could be associated with a bit of information such as a “1”, and the redshift could be associated with “0”. In Fig. 6, the information “1” is encoded by the blueshift; and the information “0” is encoded by the redshift. As the spectral width of the incident spatially completely coherent light is Γ = 0.2ω 0 , the blueshift occurs in the observation point (zN = 15 and uN = 3.82), this means an information “1” is received; when Γ = 0.01ω 0, the redshift takes place, that is, an information “0” is received.

Above results indicate that if the spectral width can be changed flexibly, the information transmission is realizable. Unfortunately this job is not easy. In the following, another scheme for information transmission by modulating spatial coherence of the incident light is presented.

 figure: 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.

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 figure: 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.

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It is also shown in Fig. 7 that the spectral shift at some observation point of the interference field can be changed by controlling the spatial coherence of the incident light. It is shown that when the coherence is low (for example, ∆0 = 3), the spectral shift at the observation point (zN = 15 and uN = 3.82) is blueshifted, but when the coherence is changed to be ∆0 = 20, the spectral shift turns into the redshift. In this sense, the information can be transferred in free space. Moreover, several approaches for modulating spatial coherence are available now [14,15]. A flexible approach for modulating spatial coherence with the responding time of the order of 1 μs has been proposed by electronically synthesized holographic grating [14]. Therefore information transmission system can be constructed by modulating the spatial coherence of the incident laser beams with spectral width Γ . The transmitted data are sent to the observation point (for example, zN = 15 and uN = 3.82) by modulating the spatial coherence of the laser beam; and a spectral detector located at the observation point receives the spectral shifts with time. If the time interval of the bits is longer than 1 μs , and the measuring for the spectral shifts is fast enough, the detected spectral shifts with time represent a set of data delivered from the double-slit. This new proposal for information transmission in free space by spectral shifts may have some advantages over traditional communication system, because in the new scheme, the information is encoded by spectral shifts, the fluctuation in the light intensity does not cause the errors in bits transmission. Moreover, due to the symmetry of the spectral shifts in the interference field along the axis uN = 0 (see Fig. 2), the information can be transmitted to two symmetrical points, at which the amount of spectral shifts is the same.

4 Conclusions and discussion

It has been shown that the spectral anomaly takes place in the interference field, both in the near field and in the far field, when the double-slit is illuminated by polychromatic completely coherent light or polychromatic partially coherent light. The spectrum in the interference field is redshifted in some position, and in some other position is blueshifted, and at the point between these positions the spectrum is split into two lines. The spectral anomalies just occur near the singular points for the frequency ω 0. Such a spectral anomaly may have applications in free-space communications, in which the blueshift could be associated with a bit of information such as a “1”, and the redshift could be associated with “0”.

As described in Section 3, for the fixed observation point (for example, zN = 15 and uN = 3.82) where a spectral detector is placed, the variation of the spectral shifts with the spectral width of the original spectrum is studied. It is found that the spectral shifts may change from the redshift to the blueshift as the spectral width of the original spectrum is changed. This characteristic may be used to information transmission, if we define the blueshift or redshift as a bit of information “1” or “0”. The detected spectral shifts in the fixed observation point represent a set of information delivered from the plane containing the double-slit.

The influence of the spatial coherence on the spectral anomalies is also investigated. Similar interesting phenomenon is found, i.e., as the coherence changes, the spectral shifts in some observation place (for example, zN = 15 and uN = 3.82) may change from the redshift to the blueshift. This specific property can also be used for information transmission, that is, due to the dependence of the spectral shifts (at the observation place) on the coherence of the incident partially coherent light, the information can be transferred from the plane containing the double-slit to the fixed observation point by modulating the coherence of the incident partially coherent light.

Acknowledgments

This study is supported by the National Natural Science Foundation of China (60477041).

References and links

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

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

3. M. V. Berry, “Colored phase singularities,” New J. Phys. 4, 66 (2002) [CrossRef]  

4. M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. in Optics , ed. E. Wolf (Amsterdam: Elsevier) 42, 219–276 (2001). [CrossRef]  

5. 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]  

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

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

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

9. 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]  

10. 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, 339–344 (2002). [CrossRef]  

11. S. Anand, B. K. Yadav, and 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]  

12. 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]  

13. 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, 2510–2516 (2002) [CrossRef]  

14. 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]  

15. D. Mendlovic, G. Shabtay, and A. W. Lohmann, “Synthesis of spatial coherence,” Opt. Lett. 24, 361–363 (1999). [CrossRef]  

References

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  1. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 165–190 (1974)
    [Crossref]
  2. M. V. Berry, “Exploring the colors of dark light,” New J. Phys. 4, 74 (2002).
    [Crossref]
  3. M. V. Berry, “Colored phase singularities,” New J. Phys. 4, 66 (2002)
    [Crossref]
  4. M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. in Optics, ed. E. Wolf (Amsterdam: Elsevier)  42, 219–276 (2001).
    [Crossref]
  5. 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]
  6. G. Gbur, T. D. Visser, and E. Wolf, “Singular behavior of the spectrum in the neighborhood of focus” J. Opt. Soc. Am. A 19, 1694–1700 (2002).
    [Crossref]
  7. G. Popescu and A. Dogariu, “Spectral anomalies at wavefront dislocations,” Phys. Rev. Lett. 88, 0183902 (2002).
    [Crossref]
  8. S. A. Ponomarenko and E. Wolf, “Spectral anomalies in a Fraunhofer diffraction pattern,” Opt. Lett. 27, 1211–1213 (2002).
    [Crossref]
  9. 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]
  10. 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, 339–344 (2002).
    [Crossref]
  11. S. Anand, B. K. Yadav, and 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]
  12. 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]
  13. 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, 2510–2516 (2002)
    [Crossref]
  14. 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]
  15. D. Mendlovic, G. Shabtay, and A. W. Lohmann, “Synthesis of spatial coherence,” Opt. Lett. 24, 361–363 (1999).
    [Crossref]

2002 (10)

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]

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

G. Popescu and A. Dogariu, “Spectral anomalies at wavefront dislocations,” Phys. Rev. Lett. 88, 0183902 (2002).
[Crossref]

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

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, 339–344 (2002).
[Crossref]

S. Anand, B. K. Yadav, and 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]

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. 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, 2510–2516 (2002)
[Crossref]

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]

2001 (1)

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. in Optics, ed. E. Wolf (Amsterdam: Elsevier)  42, 219–276 (2001).
[Crossref]

1999 (2)

D. Mendlovic, G. Shabtay, and A. W. Lohmann, “Synthesis of spatial coherence,” Opt. Lett. 24, 361–363 (1999).
[Crossref]

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]

1990 (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]

1974 (1)

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

Anand, S.

S. Anand, B. K. Yadav, and 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]

Berry, M. V.

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]

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

Dogariu, A.

G. Popescu and A. Dogariu, “Spectral anomalies at wavefront dislocations,” Phys. Rev. Lett. 88, 0183902 (2002).
[Crossref]

Foley, J. T.

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, 2510–2516 (2002)
[Crossref]

Friberg, A. T.

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]

Gbur, G.

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

Kandpal, H. C.

S. Anand, B. K. Yadav, and 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]

Lohmann, A. W.

Lu, B.

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]

Mendlovic, D.

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, 339–344 (2002).
[Crossref]

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]

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 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, 340–344 (2002)
[Crossref]

Ponomarenko, S. A.

Popescu, G.

G. Popescu and A. Dogariu, “Spectral anomalies at wavefront dislocations,” Phys. Rev. Lett. 88, 0183902 (2002).
[Crossref]

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, 339–344 (2002).
[Crossref]

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]

Shabtay, G.

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. in Optics, ed. E. Wolf (Amsterdam: Elsevier)  42, 219–276 (2001).
[Crossref]

Tervonen, E.

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]

Turunen, J.

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]

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. in Optics, ed. E. Wolf (Amsterdam: Elsevier)  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, 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, 1694–1700 (2002).
[Crossref]

Wolf, E.

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

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

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, 2510–2516 (2002)
[Crossref]

Yadav, B. K.

S. Anand, B. K. Yadav, and 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]

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, 57∆63 (1999).
[Crossref]

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 and 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×N 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×N 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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