Abstract

Results of experimental and theoretical work performed to compare diffraction patterns and focal distributions of a Fresnel zone plate illuminated by ultrashort 10  fs pulsed and cw laser beams are presented. It is shown that the foci intensities of 10  fs pulses are considerably lower than those of cw beams while the focal widths in the axial and radial directions are broadened. Calculations also indicate the spectral modulation along the center of the diffraction patterns. These phenomena are explained by the coherent superposition of the composing frequency content.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. M. Sussman, "Elementary diffraction theory of zone plates," Am. J. Phys. 28, 394-398 (1960).
    [CrossRef]
  13. R. Ashman and M. Gu, "Effect of ultrashort pulsed illumination on foci caused by a Fresnel zone plate," Appl. Opt. 42, 1852-1855 (2003).
    [CrossRef] [PubMed]
  14. Cl. Froehly, A. Lacourt, and J. Ch. Vienot, "Time impulse response and time frequency response of optical pupils: experimental confirmations and applications," Nouv. Rev. Opt. 4, 183-196 (1973).
    [CrossRef]
  15. O. Hignette, J. Santamaria, and J. Bescos, "White light diffraction patterns of amplitude and phase zone plates," J. Opt. 10, 231-238 (1979).
    [CrossRef]
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2005 (1)

2003 (4)

2001 (1)

M. K. Lebedev and Yu. A. Tolmachev, "Diffraction of an ultrashort pulse by an aperture," Opt. Spektrosk. 90, 457-463 (2001).
[CrossRef]

2000 (1)

I. É. Suleimenov, Y. A. Tolmachev, and M. K. Lebedev, "Diffraction of an ultrashort pulse by a slit," Opt. Spektrosk. 88, 104-109 (2000).
[CrossRef]

1999 (1)

1996 (2)

M. Gu and X. Gan, "Fresnel diffraction by circular and serrated apertures illuminated with an ultrashort pulsed-laser beam," J. Opt. Soc. Am. A 13, 771-778 (1996).
[CrossRef]

M. Gu and X. Gan, "Effect of an ultrashort pulse on Fresnel diffraction by a circular opaque disk," Opt. Commun. 125, 1-4 (1996).
[CrossRef]

1989 (1)

1979 (1)

O. Hignette, J. Santamaria, and J. Bescos, "White light diffraction patterns of amplitude and phase zone plates," J. Opt. 10, 231-238 (1979).
[CrossRef]

1973 (1)

Cl. Froehly, A. Lacourt, and J. Ch. Vienot, "Time impulse response and time frequency response of optical pupils: experimental confirmations and applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

1960 (1)

M. Sussman, "Elementary diffraction theory of zone plates," Am. J. Phys. 28, 394-398 (1960).
[CrossRef]

1951 (1)

O. Myers, "Studies of transmission zone plates," Am. J. Phys. 19, 359-365 (1951).
[CrossRef]

Alexander, D. R.

Ashman, R.

Bescos, J.

O. Hignette, J. Santamaria, and J. Bescos, "White light diffraction patterns of amplitude and phase zone plates," J. Opt. 10, 231-238 (1979).
[CrossRef]

Biegert, J.

Bor, Z.

De Silvestri, S.

Doerr, D. W.

Froehly, Cl.

Cl. Froehly, A. Lacourt, and J. Ch. Vienot, "Time impulse response and time frequency response of optical pupils: experimental confirmations and applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

Gan, X.

M. Gu and X. Gan, "Fresnel diffraction by circular and serrated apertures illuminated with an ultrashort pulsed-laser beam," J. Opt. Soc. Am. A 13, 771-778 (1996).
[CrossRef]

M. Gu and X. Gan, "Effect of an ultrashort pulse on Fresnel diffraction by a circular opaque disk," Opt. Commun. 125, 1-4 (1996).
[CrossRef]

Gogolak, Z.

Gu, M.

Hignette, O.

O. Hignette, J. Santamaria, and J. Bescos, "White light diffraction patterns of amplitude and phase zone plates," J. Opt. 10, 231-238 (1979).
[CrossRef]

Ichikawa, H.

Ivanov, M. Y.

Keller, U.

Lacourt, A.

Cl. Froehly, A. Lacourt, and J. Ch. Vienot, "Time impulse response and time frequency response of optical pupils: experimental confirmations and applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

Lebedev, M. K.

M. K. Lebedev and Yu. A. Tolmachev, "Diffraction of an ultrashort pulse by an aperture," Opt. Spektrosk. 90, 457-463 (2001).
[CrossRef]

I. É. Suleimenov, Y. A. Tolmachev, and M. K. Lebedev, "Diffraction of an ultrashort pulse by a slit," Opt. Spektrosk. 88, 104-109 (2000).
[CrossRef]

Li, J. C.

Morita, R.

Myers, O.

O. Myers, "Studies of transmission zone plates," Am. J. Phys. 19, 359-365 (1951).
[CrossRef]

Nisoli, M.

Oka, K.

Sansone, G.

Santamaria, J.

O. Hignette, J. Santamaria, and J. Bescos, "White light diffraction patterns of amplitude and phase zone plates," J. Opt. 10, 231-238 (1979).
[CrossRef]

Schenkel, B.

Spanner, M.

Stagira, S.

Suguro, A.

Suleimenov, I. É.

I. É. Suleimenov, Y. A. Tolmachev, and M. K. Lebedev, "Diffraction of an ultrashort pulse by a slit," Opt. Spektrosk. 88, 104-109 (2000).
[CrossRef]

Sussman, M.

M. Sussman, "Elementary diffraction theory of zone plates," Am. J. Phys. 28, 394-398 (1960).
[CrossRef]

Svelto, O.

Szabo, G.

Tadepalli, N. R.

Tolmachev, Y. A.

I. É. Suleimenov, Y. A. Tolmachev, and M. K. Lebedev, "Diffraction of an ultrashort pulse by a slit," Opt. Spektrosk. 88, 104-109 (2000).
[CrossRef]

Tolmachev, Yu. A.

M. K. Lebedev and Yu. A. Tolmachev, "Diffraction of an ultrashort pulse by an aperture," Opt. Spektrosk. 90, 457-463 (2001).
[CrossRef]

Vienot, J. Ch.

Cl. Froehly, A. Lacourt, and J. Ch. Vienot, "Time impulse response and time frequency response of optical pupils: experimental confirmations and applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

Vozzi, C.

Yamane, K.

Yamashita, M.

Zhang, H.

Zhang, Z.

Am. J. Phys. (2)

O. Myers, "Studies of transmission zone plates," Am. J. Phys. 19, 359-365 (1951).
[CrossRef]

M. Sussman, "Elementary diffraction theory of zone plates," Am. J. Phys. 28, 394-398 (1960).
[CrossRef]

Appl. Opt. (1)

J. Opt. (1)

O. Hignette, J. Santamaria, and J. Bescos, "White light diffraction patterns of amplitude and phase zone plates," J. Opt. 10, 231-238 (1979).
[CrossRef]

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

Nouv. Rev. Opt. (1)

Cl. Froehly, A. Lacourt, and J. Ch. Vienot, "Time impulse response and time frequency response of optical pupils: experimental confirmations and applications," Nouv. Rev. Opt. 4, 183-196 (1973).
[CrossRef]

Opt. Commun. (1)

M. Gu and X. Gan, "Effect of an ultrashort pulse on Fresnel diffraction by a circular opaque disk," Opt. Commun. 125, 1-4 (1996).
[CrossRef]

Opt. Lett. (4)

Opt. Spektrosk. (2)

M. K. Lebedev and Yu. A. Tolmachev, "Diffraction of an ultrashort pulse by an aperture," Opt. Spektrosk. 90, 457-463 (2001).
[CrossRef]

I. É. Suleimenov, Y. A. Tolmachev, and M. K. Lebedev, "Diffraction of an ultrashort pulse by a slit," Opt. Spektrosk. 88, 104-109 (2000).
[CrossRef]

Other (1)

M. Gu, Advanced Optical Imaging Theory (Springer Verlag, 2000).

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Figures (6)

Fig. 1
Fig. 1

Experimental setup for studying beam diffractions by a Fresnel zone plate. The laser is operated in two modes: cw mode and pulsed mode with FWHM of 10   fs . Plano–convex lens L1 and an iris combine to shape the incoming beam. Another lens L2 is placed or removed so that incoming light may be switched between parallel beam and point source.

Fig. 2
Fig. 2

(Color online) (a) Autocorrelation trace and (b) spectrum of the incoming ultrashort pulses. The pulse is calculated to be approximately 10   fs from the number of fringes in the autocorrelation trace and the width of the spectrum.

Fig. 3
Fig. 3

Calculations of radial intensity profile for parallel beams shining on the zone plate. Left and right columns are for the case of continuous and pulsed beams, respectively. The first three rows demonstrate the first three peaks, while the second three show the diffraction pattern of the near field, at a position between the first and the second peak, and at a position beyond the first peak, respectively.

Fig. 4
Fig. 4

Experimental verifications of the radial intensity profile for parallel beams shining on the zone plate. All plots are arranged the same as in Fig. 3.

Fig. 5
Fig. 5

(a) Calculated and (b) measured axial intensity profiles for cw and 10   fs laser illuminations of a Fresnel zone plate. The plano–convex lens L2 is now removed from Fig. 1.

Fig. 6
Fig. 6

Simulations of spectral modifications. The original Gaussian spectrum centered at 800 nm is shown in the first subplot of (a). The remaining subplots in (a) and (b) depict the evolution of the spectrum of the second peak to that of the third. The insets give the approximate positions associated with spectra. These locations correspond to N = 10 to N = 16 . Note that each subplot uses a different scale.

Equations (10)

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g ( λ ) = exp - [ T 2 ( ω ω 0 ) 2 / 4 ] ,
T ω 0 Δ τ ω 0 / [ ( ln 2 ) 1 / 2 ] = 5.4 π .
I ( ρ , N , λ ) = | i2 N exp ( i z 2 π / λ ) exp ( i N ρ 2 ) × m = 0 M 0 ρ m ρ m + 1 U 0 ( ρ 1 , λ ) J 0 ( 2 N ρ ρ 1 ) × exp ( i N ρ 1 2 ) ρ 1 d ρ 1 | 2
ρ m 2 = R m 2 / a 2 = m f λ / a 2 ,
N = π a 2 / λ z ,
U 0 ( ρ 1 , λ ) = C exp ( ρ 1 2 ) .
I ( ρ , N 0 ) = C 0 + ( 1 / N 0 ) | exp [ ( T 2 ω 0 2 / 4 ) × ( N / N 0 1 ) 2 ] m = 0 M 0 ρ m ρ m + 1 U 0 ( ρ 1 , ω ) × J 0 ( 2 N ρ ρ 1 ) exp ( i N ρ 1 2 ) ρ 1 d ρ 1 | 2 d N .
I 0 ( N , λ ) = | i 2 N exp ( i z 2 π / λ ) m = 0 M 0 ρ m ρ m + 1 exp ( i N d ρ 1 2 ) × U 0 ( ρ 1 , λ ) exp ( i N ρ 1 2 ) ρ 1 d ρ 1 | 2 .
I 0 ( N 0 ) = C 0 + ( 1 / N 0 ) | exp [ ( T 2 ω 0 2 / 4 ) ( N / N 0 1 ) 2 ] × m = 0 M 0 ρ m ρ m + 1 exp ( i N d ρ 1 2 ) U 0 ( ρ 1 , ω ) × exp ( i N ρ 1 2 ) ρ 1 d ρ 1 | 2 d N .
G ( λ , N 0 ) = I 0 [ N ( λ , N 0 ) , λ ] g ( λ ) = I 0 ( N 0 λ 0 / λ , λ ) × exp ( T 2 ω 0 2 / 4 ) ( N / N 0 1 ) 2 .

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