Abstract

We report on the changes in the spectrum of a femtosecond pulse originated by diffraction of the ultrashort waveform through a circularly symmetric binary diffractive optical element. The analysis is performed in the framework of the Rayleigh-Sommerfeld formulation of the diffraction, where an analytical expression for the monochromatic amplitude distribution close to the optical axis is obtained. To corroborate our results, we experimentally measure the variations of the pulse spectrum within the collecting area of a spectrometer located at the output plane. Multiple splitting of the pulse spectrum in the vicinity of a focal position and a phase singularity are shown.

© 2008 Optical Society of America

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  1. 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]
  2. G. Popescu and A. Dogariu, "Spectral anomalies at the wave-front dislocations," Phys. Rev. Lett. 88, 183902 (2002).
    [CrossRef] [PubMed]
  3. S. A. Ponomarenko and E. Wolf, "Spectral anomalies in a Fraunhofer diffraction pattern," Opt. Lett. 27, 1211-1213 (2002).
    [CrossRef]
  4. D. Ganic, J. W. M. Chon, and M. Gu, "Effect of numerical aperture on the spectral splitting feature near phase singularities of focused waves," Appl. Phys. Lett. 82, 1527-1528 (2003).
    [CrossRef]
  5. L. E. Helseth, "Spectral density of polychromatic electromagnetic waves," Phys. Rev. E 73, 026602 (2006).
    [CrossRef]
  6. Z. Liu and B. Lü, "Spectral shifts and spectral switches in diffraction of ultrashort pulsed beams passing through a circular aperture," Optik 115, 447-454 (2004).
    [CrossRef]
  7. S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski "Spectral and temporal evolutions of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
    [CrossRef]
  8. S. Jana and S. Konar, "Tunable spectral switching in the far field with a chirped cosh-Gaussian pulse," Opt. Commun. 267, 24-31 (2006).
    [CrossRef]
  9. Q. Cao and J. Jahns, "Modified Fresnel zone plates that produce sharp Gaussian focal spots," J. Opt. Soc. Am. A 20, 1576-1581 (2003).
    [CrossRef]
  10. O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, "On-axis diffraction of an ultrashort light pulse by circularly symmetrical hard apertures," Opt. Express 15, 4546-4556 (2007).
    [CrossRef] [PubMed]
  11. O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, "Focusing and spectral characteristics of periodic diffractive optical elements with circular symmetry under femtosecond pulsed illumination," J. Opt. Soc. Am. A 24, 3600-3605 (2007).
    [CrossRef]
  12. S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
    [CrossRef] [PubMed]

2007 (3)

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, "On-axis diffraction of an ultrashort light pulse by circularly symmetrical hard apertures," Opt. Express 15, 4546-4556 (2007).
[CrossRef] [PubMed]

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
[CrossRef] [PubMed]

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, "Focusing and spectral characteristics of periodic diffractive optical elements with circular symmetry under femtosecond pulsed illumination," J. Opt. Soc. Am. A 24, 3600-3605 (2007).
[CrossRef]

2006 (3)

L. E. Helseth, "Spectral density of polychromatic electromagnetic waves," Phys. Rev. E 73, 026602 (2006).
[CrossRef]

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski "Spectral and temporal evolutions of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

S. Jana and S. Konar, "Tunable spectral switching in the far field with a chirped cosh-Gaussian pulse," Opt. Commun. 267, 24-31 (2006).
[CrossRef]

2004 (1)

Z. Liu and B. Lü, "Spectral shifts and spectral switches in diffraction of ultrashort pulsed beams passing through a circular aperture," Optik 115, 447-454 (2004).
[CrossRef]

2003 (2)

D. Ganic, J. W. M. Chon, and M. Gu, "Effect of numerical aperture on the spectral splitting feature near phase singularities of focused waves," Appl. Phys. Lett. 82, 1527-1528 (2003).
[CrossRef]

Q. Cao and J. Jahns, "Modified Fresnel zone plates that produce sharp Gaussian focal spots," J. Opt. Soc. Am. A 20, 1576-1581 (2003).
[CrossRef]

2002 (3)

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]

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

Alibi, A.

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
[CrossRef] [PubMed]

Brady, D. J.

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
[CrossRef] [PubMed]

Cao, Q.

Chen, H.

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
[CrossRef] [PubMed]

Chon, J. W. M.

D. Ganic, J. W. M. Chon, and M. Gu, "Effect of numerical aperture on the spectral splitting feature near phase singularities of focused waves," Appl. Phys. Lett. 82, 1527-1528 (2003).
[CrossRef]

Climent, V.

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, "On-axis diffraction of an ultrashort light pulse by circularly symmetrical hard apertures," Opt. Express 15, 4546-4556 (2007).
[CrossRef] [PubMed]

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, "Focusing and spectral characteristics of periodic diffractive optical elements with circular symmetry under femtosecond pulsed illumination," J. Opt. Soc. Am. A 24, 3600-3605 (2007).
[CrossRef]

Dogariu, A.

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

Feller, S. D.

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
[CrossRef] [PubMed]

Fernández-Alonso, M.

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, "On-axis diffraction of an ultrashort light pulse by circularly symmetrical hard apertures," Opt. Express 15, 4546-4556 (2007).
[CrossRef] [PubMed]

Ganic, D.

D. Ganic, J. W. M. Chon, and M. Gu, "Effect of numerical aperture on the spectral splitting feature near phase singularities of focused waves," Appl. Phys. Lett. 82, 1527-1528 (2003).
[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]

Gehm, M. E.

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
[CrossRef] [PubMed]

Gu, M.

D. Ganic, J. W. M. Chon, and M. Gu, "Effect of numerical aperture on the spectral splitting feature near phase singularities of focused waves," Appl. Phys. Lett. 82, 1527-1528 (2003).
[CrossRef]

Helseth, L. E.

L. E. Helseth, "Spectral density of polychromatic electromagnetic waves," Phys. Rev. E 73, 026602 (2006).
[CrossRef]

Hsieh, C.

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
[CrossRef] [PubMed]

Jahns, J.

Jana, S.

S. Jana and S. Konar, "Tunable spectral switching in the far field with a chirped cosh-Gaussian pulse," Opt. Commun. 267, 24-31 (2006).
[CrossRef]

Konar, S.

S. Jana and S. Konar, "Tunable spectral switching in the far field with a chirped cosh-Gaussian pulse," Opt. Commun. 267, 24-31 (2006).
[CrossRef]

Lancis, J.

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, "On-axis diffraction of an ultrashort light pulse by circularly symmetrical hard apertures," Opt. Express 15, 4546-4556 (2007).
[CrossRef] [PubMed]

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, "Focusing and spectral characteristics of periodic diffractive optical elements with circular symmetry under femtosecond pulsed illumination," J. Opt. Soc. Am. A 24, 3600-3605 (2007).
[CrossRef]

Liu, Z.

Z. Liu and B. Lü, "Spectral shifts and spectral switches in diffraction of ultrashort pulsed beams passing through a circular aperture," Optik 115, 447-454 (2004).
[CrossRef]

Lü, B.

Z. Liu and B. Lü, "Spectral shifts and spectral switches in diffraction of ultrashort pulsed beams passing through a circular aperture," Optik 115, 447-454 (2004).
[CrossRef]

Mendoza-Yero, O.

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, "Focusing and spectral characteristics of periodic diffractive optical elements with circular symmetry under femtosecond pulsed illumination," J. Opt. Soc. Am. A 24, 3600-3605 (2007).
[CrossRef]

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, "On-axis diffraction of an ultrashort light pulse by circularly symmetrical hard apertures," Opt. Express 15, 4546-4556 (2007).
[CrossRef] [PubMed]

Mínguez-Vega, G.

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, "On-axis diffraction of an ultrashort light pulse by circularly symmetrical hard apertures," Opt. Express 15, 4546-4556 (2007).
[CrossRef] [PubMed]

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, "Focusing and spectral characteristics of periodic diffractive optical elements with circular symmetry under femtosecond pulsed illumination," J. Opt. Soc. Am. A 24, 3600-3605 (2007).
[CrossRef]

Momtahan, O.

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
[CrossRef] [PubMed]

Ponomarenko, S. A.

Popescu, G.

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

Veetil, S. P.

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski "Spectral and temporal evolutions of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

Vijayan, C.

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski "Spectral and temporal evolutions of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[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]

Viswanathan, N. K.

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski "Spectral and temporal evolutions of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

Wolf, E.

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]

Wyrowski, F.

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski "Spectral and temporal evolutions of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

D. Ganic, J. W. M. Chon, and M. Gu, "Effect of numerical aperture on the spectral splitting feature near phase singularities of focused waves," Appl. Phys. Lett. 82, 1527-1528 (2003).
[CrossRef]

S. P. Veetil, N. K. Viswanathan, C. Vijayan, and F. Wyrowski "Spectral and temporal evolutions of ultrashort pulses diffracted through a slit near phase singularities," Appl. Phys. Lett. 89, 041119 (2006).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

S. Jana and S. Konar, "Tunable spectral switching in the far field with a chirped cosh-Gaussian pulse," Opt. Commun. 267, 24-31 (2006).
[CrossRef]

Opt. Express. (2)

S. D. Feller, H. Chen, D. J. Brady, M. E. Gehm, C. Hsieh, O. Momtahan, and A. Alibi, "Multiple order coded aperture spectrometer," Opt. Express 15, 5625-5630 (2007).
[CrossRef] [PubMed]

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, M. Fernández-Alonso, and V. Climent, "On-axis diffraction of an ultrashort light pulse by circularly symmetrical hard apertures," Opt. Express 15, 4546-4556 (2007).
[CrossRef] [PubMed]

Opt. Lett. (1)

Optik (1)

Z. Liu and B. Lü, "Spectral shifts and spectral switches in diffraction of ultrashort pulsed beams passing through a circular aperture," Optik 115, 447-454 (2004).
[CrossRef]

Phys. Rev. E (1)

L. E. Helseth, "Spectral density of polychromatic electromagnetic waves," Phys. Rev. E 73, 026602 (2006).
[CrossRef]

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, 013901 (2002).
[CrossRef] [PubMed]

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

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Figures (4)

Fig. 1.
Fig. 1.

Definition of the diffraction (input) plane and the observation (output) plane.

Fig. 2.
Fig. 2.

Integrated output spectrum for pinholes of a) r 0=75µm, b) r 0=200µm and c) for the incoming ultrashort pulse (without pinhole).

Fig. 3.
Fig. 3.

Variation in the power spectrum with the radial coordinate at the axial positions: a) z=2.4 m (m=1) and b) z=0.87 m (n=11).

Fig. 4.
Fig. 4.

Normalized irradiance at the focal plane z 57=0.17 m, plotted by Eq. (2) (circle symbols), by Eq. (4) of Ref. [9] (box symbols) and by Eq. (1) (solid line) for a DOE with N=2 and ε=4.

Equations (4)

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U m ( z , R ) = z 2 π 0 2 π r r im om ( ik 1 ρ ( r , θ ) ) exp [ ik ρ ( r , θ ) ] ρ ( r , θ ) 2 rdrd θ .
U m ( z , R ) z exp ( ik z 2 + r im 2 ) z 2 + r im 2 J 0 ( kr im R z 2 + r im 2 ) z exp ( ik z 2 + r om 2 ) z 2 + r om 2 J 0 ( kr om R z 2 + r om 2 ) .
U m ( z , 0 ) = z exp ( ik z 2 + r im 2 ) z 2 + r im 2 z exp ( ik z 2 + r om 2 ) z 2 + r om 2 ,
S ( λ ) = S 0 ( λ ) A 0 2 π 0 r 0 I ( z , R ) RdRdφ .

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