Abstract

In this work, we offer a novel and flexible approach of spectral switches which can be handled more simply by controlling the phase of the diffracted light field of a completely spatially coherent incident beam with spectral profile from a one-dimensional phase step. This scheme has the benefit of easy implementation by simply varying the height of a one-dimensional phase step which causes spectral switches to occur when the step height reaches certain critical values without modulating any properties of the light source. To illustrate this effect, an explicit and analytical expression at an observation point corresponding to the step edge is obtained and some numerical examples are given and examined experimentally. Finally, based on the obtained results, it is shown that this method with the capability of very short response time can be easily applied to information encoding and transmission.

© 2010 Optical Society of America

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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, "Red Shifts and Blue Shifts of Spectral Lines Emitted by Two Correlated Sources," Phys. Rev. Lett. 58, 2646-2648 (1987).
    [CrossRef] [PubMed]
  3. E. Wolf, "Non-cosmological redshifts of spectral lines," Nature 326, 363-365 (1987).
    [CrossRef]
  4. M. F. Bocko, D. H. Douglass, and R. S. Knox, "Observation of Frequency Shifts of Spectral Lines Due to Source Correlations," Phys. Rev. Lett. 58, 2649-2651 (1987).
    [CrossRef] [PubMed]
  5. G. M. Morris, and D. Faklis, "Effects of source correlation on the spectrum of light," Opt. Commun. 62, 5-11 (1987).
    [CrossRef]
  6. Z. Dacic, and E. Wolf, "Changes in the spectrum of a partially coherent light beam propagating in free space," J. Opt. Soc. Am. A 5, 1118-1126 (1988).
    [CrossRef]
  7. H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, "Wolf shift and its application in spectroradiometry," Opt. Commun. 73, 169-172 (1989).
    [CrossRef]
  8. H. C. Kandpal, D. S. Mehta, K. Saxena, J. S. Vaishya, and K. C. Joshi, "Intensity distribution across a source from spectral measurements," J. Mod. Opt. 42, 455-464 (1995).
    [CrossRef]
  9. J. T. Foley, "The effect of an aperture on the spectrum of partially coherent light," Opt. Commun. 75, 347-352 (1990).
    [CrossRef]
  10. J. Turunen, E. Tervonen, and A. T. Friberg, "Acosto-optic control and modulation of optical coherence by electronically synthesized holographic gratings," J. Appl. Phys. 67, 49-59 (1990).
    [CrossRef]
  11. D. F. V. James, and E. Wolf, "Some new aspects of Young’s interference experiments," Phys. Lett. A 157, 6-10 (1991).
    [CrossRef]
  12. D. F. V. James, and E. Wolf, "Spectral changes produced in Young’s interference experiment," Opt. Commun. 81, 150-154 (1991).
    [CrossRef]
  13. J. T. Foley, "Effect of an aperture on the spectrum of partially coherent light," J. Opt. Soc. Am. A 8, 1099-1105 (1991).
    [CrossRef]
  14. J. Pu, "Spectral shifts of partially coherent light produced by passing through an annular aperture," J. Opt. (Paris) 24, 141-144 (1993).
  15. 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]
  16. M. S. Soskin, and M. V. Vasnetsov, "Singular optics," Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 2001) Vol. 42, pp. 219-276.
  17. H. C. Kandpal, "Experimental observation of the phenomenon of spectral switch," J. Opt. A, Pure Appl. Opt. 3, 296-299 (2001).
    [CrossRef]
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. S. A. Ponomarenko, and E. Wolf, "Spectral anomalies in a Fraunhofer diffraction pattern," Opt. Lett. 27, 1211-1213 (2002).
    [CrossRef]
  23. 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]
  24. T. D. Visser, and E. Wolf, "Spectral anomalies near phase singularities in partially coherent focused wave fields," J. Opt. A, Pure Appl. Opt. 5, 371-373 (2003).
    [CrossRef]
  25. 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]
  26. Y. Yang, Q. Zou, and Y. Li, "Near-field anomalous spectral behavior in diffraction of a Gaussian pulsed beam from an annular aperture," Appl. Opt. 46, 4667-4673 (2007).
    [CrossRef] [PubMed]
  27. P. DeSantis, F. Gori, G. Guattari, and C. Palma, "An example of a Collet-Wolf source," Opt. Commun. 29, 256-260 (1979).
    [CrossRef]
  28. J. Pu, C. Cai, and S. Nemoto, "Spectral anomalies in Young’s double-slit interference experiment," Opt. Express 12, 5131-5139 (2004).
    [CrossRef] [PubMed]
  29. P. Han, "Spectral switches for a circular aperture with a variable wedge," J. Opt. Soc. Am. A 26, 473-479 (2009).
    [CrossRef]
  30. P. Han, "Far-field diffraction characteristics of a Gaussian pulse incident on a sinusoidal phase grating," J. Opt. A, Pure Appl. Opt. 10, 035003 (2008).
    [CrossRef]
  31. M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, "Optical diffractometry," J. Opt. Soc. Am. A 26, 540-547 (2009).
    [CrossRef]
  32. M. Amiri, and M. T. Tavassoly, "Spectral anomalies near phase singularities in reflection at Brewster’s angle and colored catastrophes," Opt. Lett. 33, 1863-1865 (2008).
    [CrossRef] [PubMed]
  33. M. Amiri, and M. T. Tavassoly, "Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes," Opt. Commun. 272, 349-361 (2007).
    [CrossRef]
  34. M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, "Spectral modification by line singularity in Fresnel diffraction from 1D phase step," Opt. Commun. 255, 23-34 (2005).
    [CrossRef]
  35. A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom, P. G. Evans, B. Adams, and E. M. Dufresne, "Subnanosecond piezoelectric x-ray switch," Appl. Phys. Lett. 89, 021109 (2006).
    [CrossRef]

2009 (2)

2008 (2)

M. Amiri, and M. T. Tavassoly, "Spectral anomalies near phase singularities in reflection at Brewster’s angle and colored catastrophes," Opt. Lett. 33, 1863-1865 (2008).
[CrossRef] [PubMed]

P. Han, "Far-field diffraction characteristics of a Gaussian pulse incident on a sinusoidal phase grating," J. Opt. A, Pure Appl. Opt. 10, 035003 (2008).
[CrossRef]

2007 (2)

M. Amiri, and M. T. Tavassoly, "Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes," Opt. Commun. 272, 349-361 (2007).
[CrossRef]

Y. Yang, Q. Zou, and Y. Li, "Near-field anomalous spectral behavior in diffraction of a Gaussian pulsed beam from an annular aperture," Appl. Opt. 46, 4667-4673 (2007).
[CrossRef] [PubMed]

2006 (1)

A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom, P. G. Evans, B. Adams, and E. M. Dufresne, "Subnanosecond piezoelectric x-ray switch," Appl. Phys. Lett. 89, 021109 (2006).
[CrossRef]

2005 (1)

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, "Spectral modification by line singularity in Fresnel diffraction from 1D phase step," Opt. Commun. 255, 23-34 (2005).
[CrossRef]

2004 (1)

2003 (1)

T. D. Visser, and E. Wolf, "Spectral anomalies near phase singularities in partially coherent focused wave fields," J. Opt. A, Pure Appl. Opt. 5, 371-373 (2003).
[CrossRef]

2002 (7)

2001 (1)

H. C. Kandpal, "Experimental observation of the phenomenon of spectral switch," J. Opt. A, Pure Appl. Opt. 3, 296-299 (2001).
[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, 57-63 (1999).
[CrossRef]

1995 (1)

H. C. Kandpal, D. S. Mehta, K. Saxena, J. S. Vaishya, and K. C. Joshi, "Intensity distribution across a source from spectral measurements," J. Mod. Opt. 42, 455-464 (1995).
[CrossRef]

1993 (1)

J. Pu, "Spectral shifts of partially coherent light produced by passing through an annular aperture," J. Opt. (Paris) 24, 141-144 (1993).

1991 (3)

D. F. V. James, and E. Wolf, "Some new aspects of Young’s interference experiments," Phys. Lett. A 157, 6-10 (1991).
[CrossRef]

D. F. V. James, and E. Wolf, "Spectral changes produced in Young’s interference experiment," Opt. Commun. 81, 150-154 (1991).
[CrossRef]

J. T. Foley, "Effect of an aperture on the spectrum of partially coherent light," J. Opt. Soc. Am. A 8, 1099-1105 (1991).
[CrossRef]

1990 (2)

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

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

1989 (1)

H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, "Wolf shift and its application in spectroradiometry," Opt. Commun. 73, 169-172 (1989).
[CrossRef]

1988 (1)

1987 (4)

E. Wolf, "Red Shifts and Blue Shifts of Spectral Lines Emitted by Two Correlated Sources," Phys. Rev. Lett. 58, 2646-2648 (1987).
[CrossRef] [PubMed]

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

M. F. Bocko, D. H. Douglass, and R. S. Knox, "Observation of Frequency Shifts of Spectral Lines Due to Source Correlations," Phys. Rev. Lett. 58, 2649-2651 (1987).
[CrossRef] [PubMed]

G. M. Morris, and D. Faklis, "Effects of source correlation on the spectrum of light," Opt. Commun. 62, 5-11 (1987).
[CrossRef]

1986 (1)

E. Wolf, "Invariance of the Spectrum of Light on Propagation," Phys. Rev. Lett. 56, 1370-1372 (1986).
[CrossRef] [PubMed]

1979 (1)

P. DeSantis, F. Gori, G. Guattari, and C. Palma, "An example of a Collet-Wolf source," Opt. Commun. 29, 256-260 (1979).
[CrossRef]

Aalipour, R.

Adams, B.

A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom, P. G. Evans, B. Adams, and E. M. Dufresne, "Subnanosecond piezoelectric x-ray switch," Appl. Phys. Lett. 89, 021109 (2006).
[CrossRef]

Amiri, M.

M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, "Optical diffractometry," J. Opt. Soc. Am. A 26, 540-547 (2009).
[CrossRef]

M. Amiri, and M. T. Tavassoly, "Spectral anomalies near phase singularities in reflection at Brewster’s angle and colored catastrophes," Opt. Lett. 33, 1863-1865 (2008).
[CrossRef] [PubMed]

M. Amiri, and M. T. Tavassoly, "Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes," Opt. Commun. 272, 349-361 (2007).
[CrossRef]

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, "Spectral modification by line singularity in Fresnel diffraction from 1D phase step," Opt. Commun. 255, 23-34 (2005).
[CrossRef]

Anand, S.

Bocko, M. F.

M. F. Bocko, D. H. Douglass, and R. S. Knox, "Observation of Frequency Shifts of Spectral Lines Due to Source Correlations," Phys. Rev. Lett. 58, 2649-2651 (1987).
[CrossRef] [PubMed]

Cai, C.

Dacic, Z.

Darudi, A.

DeSantis, P.

P. DeSantis, F. Gori, G. Guattari, and C. Palma, "An example of a Collet-Wolf source," Opt. Commun. 29, 256-260 (1979).
[CrossRef]

Do, D.-H.

A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom, P. G. Evans, B. Adams, and E. M. Dufresne, "Subnanosecond piezoelectric x-ray switch," Appl. Phys. Lett. 89, 021109 (2006).
[CrossRef]

Douglass, D. H.

M. F. Bocko, D. H. Douglass, and R. S. Knox, "Observation of Frequency Shifts of Spectral Lines Due to Source Correlations," Phys. Rev. Lett. 58, 2649-2651 (1987).
[CrossRef] [PubMed]

Dufresne, E. M.

A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom, P. G. Evans, B. Adams, and E. M. Dufresne, "Subnanosecond piezoelectric x-ray switch," Appl. Phys. Lett. 89, 021109 (2006).
[CrossRef]

Eom, C.-B.

A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom, P. G. Evans, B. Adams, and E. M. Dufresne, "Subnanosecond piezoelectric x-ray switch," Appl. Phys. Lett. 89, 021109 (2006).
[CrossRef]

Evans, P. G.

A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom, P. G. Evans, B. Adams, and E. M. Dufresne, "Subnanosecond piezoelectric x-ray switch," Appl. Phys. Lett. 89, 021109 (2006).
[CrossRef]

Faklis, D.

G. M. Morris, and D. Faklis, "Effects of source correlation on the spectrum of light," Opt. Commun. 62, 5-11 (1987).
[CrossRef]

Foley, J. T.

Friberg, A. T.

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

Gbur, G.

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]

Gori, F.

P. DeSantis, F. Gori, G. Guattari, and C. Palma, "An example of a Collet-Wolf source," Opt. Commun. 29, 256-260 (1979).
[CrossRef]

Grigoriev, A.

A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom, P. G. Evans, B. Adams, and E. M. Dufresne, "Subnanosecond piezoelectric x-ray switch," Appl. Phys. Lett. 89, 021109 (2006).
[CrossRef]

Guattari, G.

P. DeSantis, F. Gori, G. Guattari, and C. Palma, "An example of a Collet-Wolf source," Opt. Commun. 29, 256-260 (1979).
[CrossRef]

Han, P.

P. Han, "Spectral switches for a circular aperture with a variable wedge," J. Opt. Soc. Am. A 26, 473-479 (2009).
[CrossRef]

P. Han, "Far-field diffraction characteristics of a Gaussian pulse incident on a sinusoidal phase grating," J. Opt. A, Pure Appl. Opt. 10, 035003 (2008).
[CrossRef]

James, D. F. V.

D. F. V. James, and E. Wolf, "Some new aspects of Young’s interference experiments," Phys. Lett. A 157, 6-10 (1991).
[CrossRef]

D. F. V. James, and E. Wolf, "Spectral changes produced in Young’s interference experiment," Opt. Commun. 81, 150-154 (1991).
[CrossRef]

Joshi, K. C.

H. C. Kandpal, D. S. Mehta, K. Saxena, J. S. Vaishya, and K. C. Joshi, "Intensity distribution across a source from spectral measurements," J. Mod. Opt. 42, 455-464 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, "Wolf shift and its application in spectroradiometry," Opt. Commun. 73, 169-172 (1989).
[CrossRef]

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]

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

H. C. Kandpal, D. S. Mehta, K. Saxena, J. S. Vaishya, and K. C. Joshi, "Intensity distribution across a source from spectral measurements," J. Mod. Opt. 42, 455-464 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, "Wolf shift and its application in spectroradiometry," Opt. Commun. 73, 169-172 (1989).
[CrossRef]

Karimi, E.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, "Spectral modification by line singularity in Fresnel diffraction from 1D phase step," Opt. Commun. 255, 23-34 (2005).
[CrossRef]

Khalesifard, H. R.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, "Spectral modification by line singularity in Fresnel diffraction from 1D phase step," Opt. Commun. 255, 23-34 (2005).
[CrossRef]

Kim, D. M.

A. Grigoriev, D.-H. Do, D. M. Kim, C.-B. Eom, P. G. Evans, B. Adams, and E. M. Dufresne, "Subnanosecond piezoelectric x-ray switch," Appl. Phys. Lett. 89, 021109 (2006).
[CrossRef]

Knox, R. S.

M. F. Bocko, D. H. Douglass, and R. S. Knox, "Observation of Frequency Shifts of Spectral Lines Due to Source Correlations," Phys. Rev. Lett. 58, 2649-2651 (1987).
[CrossRef] [PubMed]

Li, Y.

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]

Mehta, D. S.

H. C. Kandpal, D. S. Mehta, K. Saxena, J. S. Vaishya, and K. C. Joshi, "Intensity distribution across a source from spectral measurements," J. Mod. Opt. 42, 455-464 (1995).
[CrossRef]

Moradi, A.-R.

Morris, G. M.

G. M. Morris, and D. Faklis, "Effects of source correlation on the spectrum of light," Opt. Commun. 62, 5-11 (1987).
[CrossRef]

Nemoto, S.

Palma, C.

P. DeSantis, F. Gori, G. Guattari, and C. Palma, "An example of a Collet-Wolf source," Opt. Commun. 29, 256-260 (1979).
[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.

Pu, J.

J. Pu, C. Cai, and S. Nemoto, "Spectral anomalies in Young’s double-slit interference experiment," Opt. Express 12, 5131-5139 (2004).
[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, 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]

J. Pu, "Spectral shifts of partially coherent light produced by passing through an annular aperture," J. Opt. (Paris) 24, 141-144 (1993).

Saber, A.

Saxena, K.

H. C. Kandpal, D. S. Mehta, K. Saxena, J. S. Vaishya, and K. C. Joshi, "Intensity distribution across a source from spectral measurements," J. Mod. Opt. 42, 455-464 (1995).
[CrossRef]

Tavassoly, M. T.

M. T. Tavassoly, M. Amiri, A. Darudi, R. Aalipour, A. Saber, and A.-R. Moradi, "Optical diffractometry," J. Opt. Soc. Am. A 26, 540-547 (2009).
[CrossRef]

M. Amiri, and M. T. Tavassoly, "Spectral anomalies near phase singularities in reflection at Brewster’s angle and colored catastrophes," Opt. Lett. 33, 1863-1865 (2008).
[CrossRef] [PubMed]

M. Amiri, and M. T. Tavassoly, "Fresnel diffraction from 1D and 2D phase steps in reflection and transmission modes," Opt. Commun. 272, 349-361 (2007).
[CrossRef]

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, "Spectral modification by line singularity in Fresnel diffraction from 1D phase step," Opt. Commun. 255, 23-34 (2005).
[CrossRef]

Tervonen, E.

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

Turunen, J.

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

Vaishya, J. S.

H. C. Kandpal, D. S. Mehta, K. Saxena, J. S. Vaishya, and K. C. Joshi, "Intensity distribution across a source from spectral measurements," J. Mod. Opt. 42, 455-464 (1995).
[CrossRef]

H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, "Wolf shift and its application in spectroradiometry," Opt. Commun. 73, 169-172 (1989).
[CrossRef]

Visser, T. D.

T. D. Visser, and E. Wolf, "Spectral anomalies near phase singularities in partially coherent focused wave fields," J. Opt. A, Pure Appl. Opt. 5, 371-373 (2003).
[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, 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]

Wolf, E.

T. D. Visser, and E. Wolf, "Spectral anomalies near phase singularities in partially coherent focused wave fields," J. Opt. A, Pure Appl. Opt. 5, 371-373 (2003).
[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]

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]

D. F. V. James, and E. Wolf, "Spectral changes produced in Young’s interference experiment," Opt. Commun. 81, 150-154 (1991).
[CrossRef]

D. F. V. James, and E. Wolf, "Some new aspects of Young’s interference experiments," Phys. Lett. A 157, 6-10 (1991).
[CrossRef]

Z. Dacic, and E. Wolf, "Changes in the spectrum of a partially coherent light beam propagating in free space," J. Opt. Soc. Am. A 5, 1118-1126 (1988).
[CrossRef]

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

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Figures (10)

Fig. 1
Fig. 1

Schematic representation of the geometry and notation used for calculating the Fresnel diffraction integral and the spectral intensity at an arbitrary point on the observation plane. P0 is the projection of P onto the plane z = 0, and that P0 is taken as the coordinate origin.

Fig. 2
Fig. 2

Simulation of the FD patterns of monochromatic incident beam diffracted from 1-D reflective phase step for (a) h = λ/10 and (b) h = −λ/10 on the observation plane parallel to xy plane and at distance z = R.

Fig. 3
Fig. 3

Normalized spectra for S(0)(λ) (dashed curve), MP(0, h, λ), and S(P)(0, h, λ) for λ0 = 543 nm, σ = 70 nm, and at different normalized heights. (a) η = 0.57. (b) η = 0.885. (c) ηc+1 = 0.966276 (first spectral switch). (d) η = 1.051. (e) η = 12.

Fig. 4
Fig. 4

Plot of the normalized wavelength shift δλ/λ0 versus normalized height η for σ = 30 nm, σ = 50 nm, and σ = 70 nm. Critical normalized heights ηc±n correspond to the positions at which the spectral shifts show rapid transition (spectral switches). There exists no shift for the spectrum’s peak for the position at which Λ = 0.

Fig. 5
Fig. 5

The scheme of a set of assumed data that must be transmitted to a position P by controlling the phase of the diffracted light. The blue shift (B) and red shift (R) could be associated with a bit of information such as “1” and “0”, respectively.

Fig. 6
Fig. 6

Schematic diagram of experimental arrangement used in viewing FD pattern of monochromatic incident beam diffracted from 1-D reflective phase step for λ0 = 543 nm: L1, converging lens; PH, pin hole; L2, collimating lens; CBS, cubed beam splitter; SPS, stabilized power supply; PE, piezoelectric element; PS, phase step; CCD, CCD camera; IA, image analyzer.

Fig. 7
Fig. 7

Interference pattern of a plane incident He-Ne laser beam with λ0 = 543.5 nm, after diffraction from the phase step taken with CCD camera. The central dark fringe is produced as a result of line-singularity in the diffracted field at wavelength λ0 and hλ0/4, where the light intensity vanishes.

Fig. 8
Fig. 8

Schematic diagram of experimental arrangement used in viewing FD pattern of a Tungsten-Halogen lamp as a partial coherent source diffracted from 1-D reflective phase step for λm = 470 nm: R, reflective concave mirror; S, white-light source; NS, narrow slit; CL, cylindrical lens; CBS, cubed beam splitter; SPS, stabilized power supply; PE, piezoelectric element; PS, phase step; MC, monochromator; PMT, photo multiplier tube, IA, image analyzer.

Fig. 9
Fig. 9

Normalized spectra for S(0)(λ) (dashed curve), simulated S(P)(0,h,λ) (solid curve), and experimentally S(P)(0, h, λ) (the crosses). The experimental data for S(P)(0, h, λ) obtained for λm = 470 nm, and at step height h = 0.4λm ≈ 188 nm.

Fig. 10
Fig. 10

The colored intensity distribution recorded by CCD camera of a spatially coherent beam originated from white-light source with λm = 470 nm, after diffraction from a 1-D phase step at height step h ≈ 188 nm.

Equations (17)

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V ( x , λ , t ) = U ( x , λ ) e ickt ,
U ( x , λ ) = A ( λ ) ,
v = x 2 R λ ,
U P ( x 0 , h , λ ) = A ( λ ) 1 2 i e ikR [ 1 2 ( 1 + i ) ( 1 + e i ϕ ) + ( C 0 + i S 0 ) ( 1 e i ϕ ) ]
0 v 0 e i π v 2 2 d v = ( C 0 + i S 0 ) .
S ( P ) ( x 0 , h , λ ) = | U P ( x 0 , h , λ ) | 2 = | A ( λ ) | 2 2 [ cos 2 ( ϕ / 2 ) + 2 ( C 0 2 + S 0 2 ) sin 2 ( ϕ / 2 ) ( C 0 S 0 ) sin ϕ ] ,
S ( 0 ) ( λ ) = | A ( λ ) | 2 2 ,
M P ( x 0 , h , λ ) = [ cos 2 ( ϕ / 2 ) + 2 ( C 0 2 + S 0 2 ) sin 2 ( ϕ / 2 ) ( C 0 S 0 ) sin ϕ ] .
S ( P ) ( x 0 , h , λ ) = S ( 0 ) ( λ ) M P ( x 0 , h , λ ) .
I ( P ) ( x 0 , h ) = 0 + S ( P ) ( x 0 , h , λ ) d λ .
M P ( 0 , h , λ ) = cos 2 ( ϕ / 2 ) .
S ( 0 ) ( λ ) = S 0 exp [ ( λ λ 0 ) 2 / 2 σ 2 ] .
S ( P ) ( 0 , h , λ ) = S 0 cos 2 ( ϕ / 2 ) exp [ ( λ λ 0 ) 2 / 2 σ 2 ] .
λ ¯ ( 0 , h ) = λ S ( P ) ( 0 , h , λ ) d λ S ( P ) ( 0 , h , λ ) d λ .
h tan ( 2 π h λ ext ) = λ ext 2 ( λ ext λ 0 ) 4 π σ 2 ,
[ η c max , η c + max ] [ 2 l / λ 0 < , , 0.966276 , + 0.966276 , , < + 2 l / λ 0 ] .
Λ = δ λ / λ 0 = ( λ m λ 0 ) / λ 0 .

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