Abstract

The duality between the axial irradiance distribution originated by any circularly symmetric diffracting aperture under monochromatic illumination and its diffracted spectral intensity at a fixed on-axis point under broadband illumination is highlighted and experimentally investigated. Two applications are derived from this basic result. On the one hand, we suggest the use of a broadband source and a spectrometer for a single-shot measurement of the axial response of pupil filters. Second, we implement a spectral filter having a transmission spectrum with a fractal structure of frequencies. Experimental results and potential applications in synthetic spectra designs are provided.

© 2009 Optical Society of America

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2008 (2)

J. Gaudin, S. Rehbein, P. Guttmann, S. Godé, G. Schneider, Ph. Wernet, and W. Eberhardt, J. Appl. Phys. 104, 033112 (2008).
[CrossRef]

M. B. Sinclair, M. A. Butler, S. H. Kravitz, W. J. Zubrzycki, and A. J. Ricco, Opt. Lett. 22, 1036 (2008).
[CrossRef]

2007 (2)

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, J. Opt. Soc. Am. A 24, 3600 (2007).
[CrossRef]

A. Gürtler, J. J. Gilijamse, A. A. R. Wetzels, L. D. Noordam, E. Sali, and M. Bellini, Opt. Commun. 270, 336 (2007).
[CrossRef]

2005 (1)

M. T. Caballero, P. Andrés, A. Pons, J. Lancis, and M. Martínez-Corral, Opt. Commun. 246, 313 (2005).
[CrossRef]

2003 (1)

2002 (1)

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, Phys. Rev. E 65, 036621 (2002).
[CrossRef]

2001 (1)

U. Vogt, M. Wieland, T. Wilhein, M. Beck, and H. Stiel, Rev. Sci. Instrum. 72, 53 (2001).
[CrossRef]

1997 (1)

S. Sinzinger, V. Arrizón, and J. Jahns, Proc. SPIE 3002, 186 (1997).
[CrossRef]

1986 (1)

C. Allain and M. Coiltre, Phys. Rev. B 33, 3566 (1986).
[CrossRef]

1977 (1)

1972 (1)

Allain, C.

C. Allain and M. Coiltre, Phys. Rev. B 33, 3566 (1986).
[CrossRef]

Andrés, P.

M. T. Caballero, P. Andrés, A. Pons, J. Lancis, and M. Martínez-Corral, Opt. Commun. 246, 313 (2005).
[CrossRef]

Arrizón, V.

S. Sinzinger, V. Arrizón, and J. Jahns, Proc. SPIE 3002, 186 (1997).
[CrossRef]

Beck, M.

U. Vogt, M. Wieland, T. Wilhein, M. Beck, and H. Stiel, Rev. Sci. Instrum. 72, 53 (2001).
[CrossRef]

Bellini, M.

A. Gürtler, J. J. Gilijamse, A. A. R. Wetzels, L. D. Noordam, E. Sali, and M. Bellini, Opt. Commun. 270, 336 (2007).
[CrossRef]

Butler, M. A.

Caballero, M. T.

M. T. Caballero, P. Andrés, A. Pons, J. Lancis, and M. Martínez-Corral, Opt. Commun. 246, 313 (2005).
[CrossRef]

Climent, V.

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, J. Opt. Soc. Am. A 24, 3600 (2007).
[CrossRef]

O. Mendoza-Yero, M. Fernández-Alonso, G. Mínguez-Vega, J. Lancis, V. Climent, and J. A. Monsoriu, arXiv.org e-Print archive, arXiv:0811.0343v1, November 3, 2008, http://arXiv.org/abs/0811.0343.

Coiltre, M.

C. Allain and M. Coiltre, Phys. Rev. B 33, 3566 (1986).
[CrossRef]

Eberhardt, W.

J. Gaudin, S. Rehbein, P. Guttmann, S. Godé, G. Schneider, Ph. Wernet, and W. Eberhardt, J. Appl. Phys. 104, 033112 (2008).
[CrossRef]

Fedotowsky, A.

Fernández-Alonso, M.

O. Mendoza-Yero, M. Fernández-Alonso, G. Mínguez-Vega, J. Lancis, V. Climent, and J. A. Monsoriu, arXiv.org e-Print archive, arXiv:0811.0343v1, November 3, 2008, http://arXiv.org/abs/0811.0343.

Furlan, W. D.

Gaponenko, S. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Gaudin, J.

J. Gaudin, S. Rehbein, P. Guttmann, S. Godé, G. Schneider, Ph. Wernet, and W. Eberhardt, J. Appl. Phys. 104, 033112 (2008).
[CrossRef]

Gilijamse, J. J.

A. Gürtler, J. J. Gilijamse, A. A. R. Wetzels, L. D. Noordam, E. Sali, and M. Bellini, Opt. Commun. 270, 336 (2007).
[CrossRef]

Godé, S.

J. Gaudin, S. Rehbein, P. Guttmann, S. Godé, G. Schneider, Ph. Wernet, and W. Eberhardt, J. Appl. Phys. 104, 033112 (2008).
[CrossRef]

Gürtler, A.

A. Gürtler, J. J. Gilijamse, A. A. R. Wetzels, L. D. Noordam, E. Sali, and M. Bellini, Opt. Commun. 270, 336 (2007).
[CrossRef]

Guttmann, P.

J. Gaudin, S. Rehbein, P. Guttmann, S. Godé, G. Schneider, Ph. Wernet, and W. Eberhardt, J. Appl. Phys. 104, 033112 (2008).
[CrossRef]

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1987), p. 445.

Jahns, J.

S. Sinzinger, V. Arrizón, and J. Jahns, Proc. SPIE 3002, 186 (1997).
[CrossRef]

Keating, P. N.

Kravitz, S. H.

Lancis, J.

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, J. Opt. Soc. Am. A 24, 3600 (2007).
[CrossRef]

M. T. Caballero, P. Andrés, A. Pons, J. Lancis, and M. Martínez-Corral, Opt. Commun. 246, 313 (2005).
[CrossRef]

O. Mendoza-Yero, M. Fernández-Alonso, G. Mínguez-Vega, J. Lancis, V. Climent, and J. A. Monsoriu, arXiv.org e-Print archive, arXiv:0811.0343v1, November 3, 2008, http://arXiv.org/abs/0811.0343.

Lavrinenko, A. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Lehovec, K.

Martínez-Corral, M.

M. T. Caballero, P. Andrés, A. Pons, J. Lancis, and M. Martínez-Corral, Opt. Commun. 246, 313 (2005).
[CrossRef]

Mendoza-Yero, O.

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, J. Opt. Soc. Am. A 24, 3600 (2007).
[CrossRef]

O. Mendoza-Yero, M. Fernández-Alonso, G. Mínguez-Vega, J. Lancis, V. Climent, and J. A. Monsoriu, arXiv.org e-Print archive, arXiv:0811.0343v1, November 3, 2008, http://arXiv.org/abs/0811.0343.

Mínguez-Vega, G.

O. Mendoza-Yero, G. Mínguez-Vega, J. Lancis, and V. Climent, J. Opt. Soc. Am. A 24, 3600 (2007).
[CrossRef]

O. Mendoza-Yero, M. Fernández-Alonso, G. Mínguez-Vega, J. Lancis, V. Climent, and J. A. Monsoriu, arXiv.org e-Print archive, arXiv:0811.0343v1, November 3, 2008, http://arXiv.org/abs/0811.0343.

Monsoriu, J. A.

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, Opt. Lett. 28, 971 (2003).
[CrossRef] [PubMed]

O. Mendoza-Yero, M. Fernández-Alonso, G. Mínguez-Vega, J. Lancis, V. Climent, and J. A. Monsoriu, arXiv.org e-Print archive, arXiv:0811.0343v1, November 3, 2008, http://arXiv.org/abs/0811.0343.

Mueller, R. K.

Noordam, L. D.

A. Gürtler, J. J. Gilijamse, A. A. R. Wetzels, L. D. Noordam, E. Sali, and M. Bellini, Opt. Commun. 270, 336 (2007).
[CrossRef]

Pons, A.

M. T. Caballero, P. Andrés, A. Pons, J. Lancis, and M. Martínez-Corral, Opt. Commun. 246, 313 (2005).
[CrossRef]

Rehbein, S.

J. Gaudin, S. Rehbein, P. Guttmann, S. Godé, G. Schneider, Ph. Wernet, and W. Eberhardt, J. Appl. Phys. 104, 033112 (2008).
[CrossRef]

Ricco, A. J.

Saavedra, G.

Sali, E.

A. Gürtler, J. J. Gilijamse, A. A. R. Wetzels, L. D. Noordam, E. Sali, and M. Bellini, Opt. Commun. 270, 336 (2007).
[CrossRef]

Sandomirski, K. S.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Sawatari, T.

Schneider, G.

J. Gaudin, S. Rehbein, P. Guttmann, S. Godé, G. Schneider, Ph. Wernet, and W. Eberhardt, J. Appl. Phys. 104, 033112 (2008).
[CrossRef]

Sinclair, M. B.

Sinzinger, S.

S. Sinzinger, V. Arrizón, and J. Jahns, Proc. SPIE 3002, 186 (1997).
[CrossRef]

Stiel, H.

U. Vogt, M. Wieland, T. Wilhein, M. Beck, and H. Stiel, Rev. Sci. Instrum. 72, 53 (2001).
[CrossRef]

Vogt, U.

U. Vogt, M. Wieland, T. Wilhein, M. Beck, and H. Stiel, Rev. Sci. Instrum. 72, 53 (2001).
[CrossRef]

Wernet, Ph.

J. Gaudin, S. Rehbein, P. Guttmann, S. Godé, G. Schneider, Ph. Wernet, and W. Eberhardt, J. Appl. Phys. 104, 033112 (2008).
[CrossRef]

Wetzels, A. A. R.

A. Gürtler, J. J. Gilijamse, A. A. R. Wetzels, L. D. Noordam, E. Sali, and M. Bellini, Opt. Commun. 270, 336 (2007).
[CrossRef]

Wieland, M.

U. Vogt, M. Wieland, T. Wilhein, M. Beck, and H. Stiel, Rev. Sci. Instrum. 72, 53 (2001).
[CrossRef]

Wilhein, T.

U. Vogt, M. Wieland, T. Wilhein, M. Beck, and H. Stiel, Rev. Sci. Instrum. 72, 53 (2001).
[CrossRef]

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1987), p. 445.

Zhukovsky, S. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Zubrzycki, W. J.

Appl. Opt. (1)

J. Appl. Phys. (1)

J. Gaudin, S. Rehbein, P. Guttmann, S. Godé, G. Schneider, Ph. Wernet, and W. Eberhardt, J. Appl. Phys. 104, 033112 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

A. Gürtler, J. J. Gilijamse, A. A. R. Wetzels, L. D. Noordam, E. Sali, and M. Bellini, Opt. Commun. 270, 336 (2007).
[CrossRef]

M. T. Caballero, P. Andrés, A. Pons, J. Lancis, and M. Martínez-Corral, Opt. Commun. 246, 313 (2005).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

C. Allain and M. Coiltre, Phys. Rev. B 33, 3566 (1986).
[CrossRef]

Phys. Rev. E (1)

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Proc. SPIE (1)

S. Sinzinger, V. Arrizón, and J. Jahns, Proc. SPIE 3002, 186 (1997).
[CrossRef]

Rev. Sci. Instrum. (1)

U. Vogt, M. Wieland, T. Wilhein, M. Beck, and H. Stiel, Rev. Sci. Instrum. 72, 53 (2001).
[CrossRef]

Other (2)

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1987), p. 445.

O. Mendoza-Yero, M. Fernández-Alonso, G. Mínguez-Vega, J. Lancis, V. Climent, and J. A. Monsoriu, arXiv.org e-Print archive, arXiv:0811.0343v1, November 3, 2008, http://arXiv.org/abs/0811.0343.

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Figures (2)

Fig. 1
Fig. 1

(a) Optical device for single-shot monitoring the axial irradiance distribution generated by the binary pupils. (b) Spectral irradiance of the incident femtosecond pulse.

Fig. 2
Fig. 2

Measured spectral irradiance for (a) GZP (top) and for (b) corresponding fractal GZP (top). The axial irradiance distribution for (a) GZP predicted by Eq. (3) (bottom) and for (b) corresponding fractal GZP predicted by Eq. (4) (bottom). Scaled versions of the binary pupils are given by the insets.

Equations (4)

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

I ( z , R ) = I ( z , R , λ ) d λ ,
I ( z , R , λ ) = S 0 ( λ ) 2 π i λ z 0 t ( r ) J 0 ( 2 π λ z R r ) exp [ i π λ z r 2 ] r d r 2 = S 0 ( λ ) M ( z , R , λ ) .
M ( z , 0 , λ ) = sin 2 ( π p 2 2 ε λ z ) sin 2 ( Q π p 2 2 λ z ) sin 2 ( π p 2 2 λ z ) .
M ( u , 0 , λ ) = 4 sin 2 ( π u ( ε N ( ε 1 ) ) S ) i = 1 S sin 2 ( N ε π u ( ε N ( ε 1 ) ) i ) sin 2 ( ε π u ( ε N ( ε 1 ) ) i ) .

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