Abstract

We demonstrated a simple diffractive method to map the self-similar structure shown in squared radial coordinate of any set of circularly symmetric fractal plates into self-similar light pulses in the corresponding temporal domain. The space-to-time mapping of the plates was carried out by means of a kinoform diffractive lens under femtosecond illumination. The spatio-temporal characteristics of the fractal pulses obtained in this way were measured by means of a spectral interferometry technique assisted by a fiber optics coupler (STARFISH). Our proposal allows synthesizing suited sequences of focused fractal femtosecond pulses potentially useful for several current applications, such as femtosecond material processing, atomic, and molecular control of chemical processes or generation of nonlinear effects.

© 2012 Optical Society of America

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2010 (1)

2009 (3)

2008 (1)

2007 (3)

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, Opt. Lett. 32, 2109 (2007).
[CrossRef]

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, Appl. Phys. Lett. 90, 211113 (2007).
[CrossRef]

2006 (1)

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

2005 (1)

2004 (2)

M. Kavehrad and B. Y. Hamzeh, Proc. SPIE 5598, 144 (2004).

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef]

2003 (1)

2002 (2)

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, J. Opt. Soc. Am. B 19, 461 (2002).
[CrossRef]

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

2001 (1)

K. J. Vinoy, K. A. Jose, K. K. Varadan, and V. V. Varadan, Microwave Opt. Technol. Lett. 29, 215 (2001).
[CrossRef]

2000 (1)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

1998 (1)

1996 (1)

D. A. Hamburger-Lidar, Phys. Rev. E 54, 354 (1996).

1995 (1)

1987 (1)

C. Allain and M. Cloitre, Phys. Rev. A 36, 5751 (1987).

1979 (1)

M. V. Berry, J. Phys. A 12, 781 (1979).
[CrossRef]

Allain, C.

C. Allain and M. Cloitre, Phys. Rev. A 36, 5751 (1987).

Alonso, B.

Andrés, P.

Berry, M. V.

M. V. Berry, J. Phys. A 12, 781 (1979).
[CrossRef]

Buckley, J. R.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef]

Burge, R. E.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Calatayud, A.

Chen, X.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, Appl. Phys. Lett. 90, 211113 (2007).
[CrossRef]

Cheriaux, G.

Clark, W. G.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef]

Climent, V.

Cloitre, M.

C. Allain and M. Cloitre, Phys. Rev. A 36, 5751 (1987).

Dudley, J. M.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, J. Opt. Soc. Am. B 19, 461 (2002).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Fernández-Alonso, M.

Finot, C.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

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]

Giménez, F.

Gisbert, R.

Hamburger-Lidar, D. A.

D. A. Hamburger-Lidar, Phys. Rev. E 54, 354 (1996).

Hamzeh, B. Y.

M. Kavehrad and B. Y. Hamzeh, Proc. SPIE 5598, 144 (2004).

Harvey, J. D.

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, J. Opt. Soc. Am. B 19, 461 (2002).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Hernández-Toro, J.

Hesselink, L.

Ilday, F. Ö.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef]

Jaggard, A. D.

Jaggard, D. L.

Joffre, M.

Jose, K. A.

K. J. Vinoy, K. A. Jose, K. K. Varadan, and V. V. Varadan, Microwave Opt. Technol. Lett. 29, 215 (2001).
[CrossRef]

Kavehrad, M.

M. Kavehrad and B. Y. Hamzeh, Proc. SPIE 5598, 144 (2004).

Kruglov, V. I.

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, J. Opt. Soc. Am. B 19, 461 (2002).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Lancis, J.

Lavrinenko, A. V.

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

Lepetit, L.

Li, M.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, Appl. Phys. Lett. 90, 211113 (2007).
[CrossRef]

Lin, J.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Lu, W.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, Appl. Phys. Lett. 90, 211113 (2007).
[CrossRef]

Mandelbrot, B. B.

B. B. Mandelbrot, The Fractal Geometry of Nature, 2nd ed. (Freeman, 1982).

Matteo, J. A.

Méndez, C.

Mendoza-Yero, O.

Millot, G.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

Mínguez-Vega, G.

Monsoriu, J. A.

Peacock, A. C.

Richardson, D. J.

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

Roso, L.

Saavedra, G.

San Román, J.

Sandomirski, K. S.

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

Sola, Í. J.

Tajahuerce, E.

Tao, S. H.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Thomsen, B. C.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Varadan, K. K.

K. J. Vinoy, K. A. Jose, K. K. Varadan, and V. V. Varadan, Microwave Opt. Technol. Lett. 29, 215 (2001).
[CrossRef]

Varadan, V. V.

K. J. Vinoy, K. A. Jose, K. K. Varadan, and V. V. Varadan, Microwave Opt. Technol. Lett. 29, 215 (2001).
[CrossRef]

Varela, Ó.

Vinoy, K. J.

K. J. Vinoy, K. A. Jose, K. K. Varadan, and V. V. Varadan, Microwave Opt. Technol. Lett. 29, 215 (2001).
[CrossRef]

Wang, H.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, Appl. Phys. Lett. 90, 211113 (2007).
[CrossRef]

Wang, S. W.

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, Appl. Phys. Lett. 90, 211113 (2007).
[CrossRef]

Wise, F. W.

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef]

Yuan, X. C.

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

Zaïr, A.

Zhukovsky, S. V.

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

Appl. Phys. Lett. (2)

S. W. Wang, X. Chen, W. Lu, M. Li, and H. Wang, Appl. Phys. Lett. 90, 211113 (2007).
[CrossRef]

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 031105 (2006).
[CrossRef]

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

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

J. Phys. A (1)

M. V. Berry, J. Phys. A 12, 781 (1979).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

K. J. Vinoy, K. A. Jose, K. K. Varadan, and V. V. Varadan, Microwave Opt. Technol. Lett. 29, 215 (2001).
[CrossRef]

Nat. Phys. (1)

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, Nat. Phys. 3, 597 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (1)

C. Allain and M. Cloitre, Phys. Rev. A 36, 5751 (1987).

Phys. Rev. E (2)

D. A. Hamburger-Lidar, Phys. Rev. E 54, 354 (1996).

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

Phys. Rev. Lett. (2)

F. Ö. Ilday, J. R. Buckley, W. G. Clark, and F. W. Wise, Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef]

Proc. SPIE (1)

M. Kavehrad and B. Y. Hamzeh, Proc. SPIE 5598, 144 (2004).

Other (1)

B. B. Mandelbrot, The Fractal Geometry of Nature, 2nd ed. (Freeman, 1982).

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Figures (2)

Fig. 1.
Fig. 1.

Optical setup. Measurement of temporal-shaped, self-similar ultrashort pulses by using spatially resolved spectral interferometry assisted by a fiber optics coupler.

Fig. 2.
Fig. 2.

Spatiotemporal characteristics of the synthesized ultrashort fractal pulses. Numerical simulations (a–c) and corresponding experimental results (d–f).The FZPs are included as insets.

Equations (2)

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

uout(τ)u0(τ)[q(τ/Δt)exp(iω0τ)].
q(ς)=rect(ς1/2)Πi=0Srect[mod(ς1+pi/2,pi)pi].

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