Abstract

We report on an optical arrangement capable of compensating angular dispersion of paraxial wave fields developed by diffractive optical elements (DOEs). Schematically, the system is a beam expander in which two phase-only zone plates have been inserted, remaining afocal the coupled system. The DOE, which induces a continuous set of dispersive tilted plane waves, is placed at a specific position within the proposed setup providing an output spectrum with achromatic angular deviation. A directional matching between phase fronts and pulse fronts of output wave packets is demonstrated.

© 2007 Optical Society of America

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References

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2007 (2)

2006 (3)

S. Q. Zeng, X. Lv, C. Zhan, W. R. Chen, W. H. Xiong, Q. Luo, and S. L. Jacques, Opt. Lett. 31, 1091 (2006).
[CrossRef] [PubMed]

J. Leach, G. M. Gibson, M. J. Padgett, E. Esposito, G. McConnell, A. J. Wright, and J. M. Girkin, Opt. Eng. (Bellingham) 14, 5581 (2006).

C. J. Zapata-Rodríguez, Opt. Commun. 263, 131 (2006).
[CrossRef]

2005 (1)

2004 (2)

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, V. Climent, P. Andrés, and J. Caraquitena, J. Opt. Soc. Am. A 21, 1875 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Pääkkönen, and J. Turunen, J. Mod. Opt. 51, 677 (2004).

2003 (3)

M. A. Porras and I. Gonzalo, Opt. Commun. 217, 257 (2003).
[CrossRef]

M. A. Porras, G. Valiulis, and P. D. Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

V. Iyer, B. E. Losavio, and P. Saggau, J. Biomed. Opt. 8, 460 (2003).
[CrossRef] [PubMed]

2001 (1)

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, P. Stanley, and L. E. N. Lim, Opt. Eng. 9, 200 (2001).

1997 (1)

1996 (1)

1981 (1)

Appl. Opt. (1)

J. Biomed. Opt. (1)

V. Iyer, B. E. Losavio, and P. Saggau, J. Biomed. Opt. 8, 460 (2003).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, P. Pääkkönen, and J. Turunen, J. Mod. Opt. 51, 677 (2004).

J. Opt. Soc. Am. A (4)

Opt. Commun. (2)

C. J. Zapata-Rodríguez, Opt. Commun. 263, 131 (2006).
[CrossRef]

M. A. Porras and I. Gonzalo, Opt. Commun. 217, 257 (2003).
[CrossRef]

Opt. Eng. (1)

B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, P. Stanley, and L. E. N. Lim, Opt. Eng. 9, 200 (2001).

Opt. Eng. (Bellingham) (1)

J. Leach, G. M. Gibson, M. J. Padgett, E. Esposito, G. McConnell, A. J. Wright, and J. M. Girkin, Opt. Eng. (Bellingham) 14, 5581 (2006).

Opt. Lett. (3)

Phys. Rev. E (1)

M. A. Porras, G. Valiulis, and P. D. Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Hybrid diffractive-refractive arrangement to compensate angular dispersion induced by diffraction.

Fig. 2
Fig. 2

Angular dispersion for increasing orders m of a diffraction grating of Λ = 10 μ m without (thin solid line) and with compensation (bold curves) for λ 0 = 600 nm ( A 0 = 1 ) .

Fig. 3
Fig. 3

Wavelength dependence of the angular spectrum (first row) and the wave field (second row) for a polychromatic Bessel beam (a) obtained directly from a DOE and (b) processed in the arrangement of Fig 1.

Fig. 4
Fig. 4

Instantaneous field strength for (a) a pulsed Bessel beam initiated by a DOE and (b) a X wave with compensated angular dispersion.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

θ ( ω ) = θ 0 ω 0 ω ,
U ( r 0 ) = F ( q ) exp ( i q r 0 ) d q ,
U ( r ) = ( i λ B ) 1 exp ( i k D r 2 2 B ) × U ( r 0 ) exp ( i k A r 0 2 2 B ) exp ( i k r r 0 B ) d r 0 ,
U ( r ) = A 1 F ( q ) exp ( i B q 2 2 k A ) exp ( i q r A ) d q .
θ ( ω ) = θ 0 ω 0 A 0 ω A ( ω ) ,
A 0 + ω 0 A ̇ 0 = 0 .
A ( ω ) = f Z ( ω ) d Z ( ω ) + a [ ( Z ( ω ) d ) ] ,
a = Z 0 d 2 d Z 0 .
θ θ 0 = 1 ( Δ λ λ 0 ) 2 ,
α 2 + β 2 = θ 2 ,

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