Abstract

We present a new approach for wavefront characterization of near transform-limited intense femtosecond beams using the angular and spectral dependences of the second-harmonic generation conversion efficiency in uniaxial crystals. The method is applied to different aberrated beams and results are compared with the measurements performed with a commercial sensor, finding very good agreement. The phase retrieval dependence with different parameters (e.g. crystal thickness) is discussed. Successful application to sharpen intensity profiles is also demonstrated.

© 2011 OSA

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  1. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
    [CrossRef]
  2. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
    [CrossRef]
  3. S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. A. Mourou, and V. Yanovsky, “Generation and characterization of the highest laser intensities (1022 W/cm2),” Opt. Lett. 29(24), 2837–2839 (2004).
    [CrossRef] [PubMed]
  4. S. Ranc, G. Chériaux, S. Ferré, J.-P. Rousseau, and J.-P. Chambaret, “Importance of spatial quality of intense femtosecond pulses,” Appl. Phys. B 70, 181–187 (2000).
  5. J. M. Bueno, B. Vohnsen, L. Roso, and P. Artal, “Temporal wavefront stability of an ultrafast high-power laser beam,” Appl. Opt. 48(4), 770–777 (2009).
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    [CrossRef] [PubMed]
  7. J. Primot, “Three-wave lateral shearing interferometer,” Appl. Opt. 32(31), 6242–6249 (1993).
    [CrossRef] [PubMed]
  8. S. Velghe, J. Primot, N. Guérineau, M. Cohen, and B. Wattellier, “Wave-front reconstruction from multidirectional phase derivatives generated by multilateral shearing interferometers,” Opt. Lett. 30(3), 245–247 (2005).
    [CrossRef] [PubMed]
  9. J.-C. Chanteloup, F. Druon, M. Nantel, A. Maksimchuk, and G. Mourou, “Single-shot wave-front measurements of high-intensity ultrashort laser pulses with a three-wave interferometer,” Opt. Lett. 23(8), 621–623 (1998).
    [CrossRef] [PubMed]
  10. R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, “Ultrashort-pulse wave-front autocorrelation,” Opt. Lett. 28(23), 2399–2401 (2003).
    [CrossRef] [PubMed]
  11. E. Rubino, D. Faccio, L. Tartara, P. K. Bates, O. Chalus, M. Clerici, F. Bonaretti, J. Biegert, and P. Di Trapani, “Spatiotemporal amplitude and phase retrieval of space-time coupled ultrashort pulses using the Shackled-FROG technique,” Opt. Lett. 34(24), 3854–3856 (2009).
    [CrossRef] [PubMed]
  12. P. R. Bowlan and R. Trebino, “Using Phase Retrieval to Obtain the Complete Spatio-Temporal Intensity and Phase of Ultrashort Pulses,” in Signal Recovery and Synthesis, OSA Technical Digest (CD) (Optical Society of America, 2009), paper SWA6.
  13. areA. Marcinkevičius, R. Tommasini, G. D. Tsakiris, K. J. Witte, E. Gaižauskas, and U. Teubner, “Frequency doubling of multi-terawatt femtosecond pulses,” Appl. Phys. B 79(5), 547–554 (2004).
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  17. J.-C. Diels and W. Rudolph, Ultrashort laser pulse phenomena (Academic Press, 1996), Chap. 3.
  18. E. Sidick, A. Knoesen, and A. Dienes, “Ultrashort pulse second harmonic generation I: transformed limited fundamental pulses,” J. Opt. Soc. Am. B 12(9), 1704–1712 (1995).
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  20. E. Sidick, A. Dienes, and A. Knoesen, “Ultrashort pulse second harmonic generation II: non-transformed limited fundamental pulses,” J. Opt. Soc. Am. B 12(9), 1713–1722 (1995).
    [CrossRef]
  21. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17(1), 28–30 (1992).
    [CrossRef] [PubMed]
  22. J. P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Direct measurement of wave-front distortion induced during second-harmonic generation: application to breakup-integral compensation,” Opt. Lett. 29(8), 899–901 (2004).
    [CrossRef] [PubMed]
  23. P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann-Shack sensor in the human eye,” J. Opt. Soc. Am. A 17(8), 1388–1398 (2000).
    [CrossRef] [PubMed]
  24. G. Mínguez-Vega, C. Romero, O. Mendoza-Yero, J. R. Vázquez de Aldana, R. Borrego-Varillas, C. Méndez, P. Andrés, J. Lancis, V. Climent, and L. Roso, “Wavelength tuning of femtosecond pulses generated in nonlinear crystals by using diffractive lenses,” Opt. Lett. 35(21), 3694–3696 (2010).
    [CrossRef] [PubMed]
  25. C. Romero, Universidad de Salamanca, Pl. de la Merced s/n., E-37008 Spain, and associates are preparing a manuscript to be called “Second harmonic generation of femtosecond pulses focused on BBO with a diffractive lens.”
  26. C. Romero, R. Borrego-Varillas, A. Camino, G. Mínguez-Vega, O. Mendoza-Yero, J. Hernández-Toro, and J. R. Vázquez de Aldana, “Diffractive optics for spectral control of the supercontinuum generated in sapphire with femtosecond pulses,” Opt. Express 19(6), 4977–4984 (2011).
    [CrossRef] [PubMed]
  27. H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
    [CrossRef]

2011 (1)

2010 (1)

2009 (2)

2006 (1)

H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
[CrossRef]

2005 (2)

2004 (3)

2003 (1)

2002 (1)

2000 (3)

P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann-Shack sensor in the human eye,” J. Opt. Soc. Am. A 17(8), 1388–1398 (2000).
[CrossRef] [PubMed]

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[CrossRef]

S. Ranc, G. Chériaux, S. Ferré, J.-P. Rousseau, and J.-P. Chambaret, “Importance of spatial quality of intense femtosecond pulses,” Appl. Phys. B 70, 181–187 (2000).

1998 (2)

1995 (2)

1993 (1)

1992 (1)

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[CrossRef]

Andrés, P.

Artal, P.

Bahk, S.-W.

Bates, P. K.

Biegert, J.

Bonaretti, F.

Borrego-Varillas, R.

Brabec, T.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[CrossRef]

Bueno, J. M.

Camino, A.

Caumes, J. P.

Chalus, O.

Chambaret, J.-P.

S. Ranc, G. Chériaux, S. Ferré, J.-P. Rousseau, and J.-P. Chambaret, “Importance of spatial quality of intense femtosecond pulses,” Appl. Phys. B 70, 181–187 (2000).

Chanteloup, J.-C.

Chériaux, G.

S. Ranc, G. Chériaux, S. Ferré, J.-P. Rousseau, and J.-P. Chambaret, “Importance of spatial quality of intense femtosecond pulses,” Appl. Phys. B 70, 181–187 (2000).

Chvykov, V.

Clerici, M.

Climent, V.

Cohen, M.

DeSalvo, R.

Di Trapani, P.

Dienes, A.

Druon, F.

Faccio, D.

Ferré, S.

S. Ranc, G. Chériaux, S. Ferré, J.-P. Rousseau, and J.-P. Chambaret, “Importance of spatial quality of intense femtosecond pulses,” Appl. Phys. B 70, 181–187 (2000).

Freysz, E.

Gaižauskas, E.

areA. Marcinkevičius, R. Tommasini, G. D. Tsakiris, K. J. Witte, E. Gaižauskas, and U. Teubner, “Frequency doubling of multi-terawatt femtosecond pulses,” Appl. Phys. B 79(5), 547–554 (2004).
[CrossRef]

Goelz, S.

Griebner, U.

Grunwald, R.

Guérineau, N.

Hagan, D. J.

Hauri, C. P.

Hernández-Toro, J.

Heuck, H.-M.

H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
[CrossRef]

Hou, J.

Huang, J. Y.

Jiang, W.

Kalintchenko, G.

Kebbel, V.

Keller, U.

Knoesen, A.

Krausz, F.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[CrossRef]

Kühl, T.

H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
[CrossRef]

Lancis, J.

Ling, N.

Maksimchuk, A.

Mann, K.

Marcinkevicius, A.

areA. Marcinkevičius, R. Tommasini, G. D. Tsakiris, K. J. Witte, E. Gaižauskas, and U. Teubner, “Frequency doubling of multi-terawatt femtosecond pulses,” Appl. Phys. B 79(5), 547–554 (2004).
[CrossRef]

Marowski, G.

Méndez, C.

Mendoza-Yero, O.

Mínguez-Vega, G.

Mourou, G.

Mourou, G. A.

Nantel, M.

Neumann, U.

Neumayer, P.

H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
[CrossRef]

Planchon, T. A.

Prieto, P. M.

Primot, J.

Ranc, S.

S. Ranc, G. Chériaux, S. Ferré, J.-P. Rousseau, and J.-P. Chambaret, “Importance of spatial quality of intense femtosecond pulses,” Appl. Phys. B 70, 181–187 (2000).

Reimann, K.

Romero, C.

Roso, L.

Rousseau, J.-P.

S. Ranc, G. Chériaux, S. Ferré, J.-P. Rousseau, and J.-P. Chambaret, “Importance of spatial quality of intense femtosecond pulses,” Appl. Phys. B 70, 181–187 (2000).

Rousseau, P.

Rouyer, C.

Rubino, E.

Schaefer, B.

Sheik-Bahae, M.

Sidick, E.

Stegeman, G.

Steinmeyer, G.

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[CrossRef]

Tartara, L.

Teubner, U.

areA. Marcinkevičius, R. Tommasini, G. D. Tsakiris, K. J. Witte, E. Gaižauskas, and U. Teubner, “Frequency doubling of multi-terawatt femtosecond pulses,” Appl. Phys. B 79(5), 547–554 (2004).
[CrossRef]

Tommasini, R.

areA. Marcinkevičius, R. Tommasini, G. D. Tsakiris, K. J. Witte, E. Gaižauskas, and U. Teubner, “Frequency doubling of multi-terawatt femtosecond pulses,” Appl. Phys. B 79(5), 547–554 (2004).
[CrossRef]

Tsakiris, G. D.

areA. Marcinkevičius, R. Tommasini, G. D. Tsakiris, K. J. Witte, E. Gaižauskas, and U. Teubner, “Frequency doubling of multi-terawatt femtosecond pulses,” Appl. Phys. B 79(5), 547–554 (2004).
[CrossRef]

Van Stryland, E. W.

Vanherzeele, H.

Vargas-Martín, F.

Vázquez de Aldana, J. R.

Velghe, S.

Videau, L.

Vohnsen, B.

Wang, H.

Wattellier, B.

Witte, K. J.

areA. Marcinkevičius, R. Tommasini, G. D. Tsakiris, K. J. Witte, E. Gaižauskas, and U. Teubner, “Frequency doubling of multi-terawatt femtosecond pulses,” Appl. Phys. B 79(5), 547–554 (2004).
[CrossRef]

Wittrock, U.

H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
[CrossRef]

Wong, G. K.

Wong, K. S.

Yanovsky, V.

Zhang, J.-Y.

Zhang, Y.

Appl. Opt. (2)

Appl. Phys. B (3)

H.-M. Heuck, P. Neumayer, T. Kühl, and U. Wittrock, “Chromatic aberration in petawatt-class lasers,” Appl. Phys. B 84(3), 421–428 (2006).
[CrossRef]

S. Ranc, G. Chériaux, S. Ferré, J.-P. Rousseau, and J.-P. Chambaret, “Importance of spatial quality of intense femtosecond pulses,” Appl. Phys. B 70, 181–187 (2000).

areA. Marcinkevičius, R. Tommasini, G. D. Tsakiris, K. J. Witte, E. Gaižauskas, and U. Teubner, “Frequency doubling of multi-terawatt femtosecond pulses,” Appl. Phys. B 79(5), 547–554 (2004).
[CrossRef]

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

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

Opt. Commun. (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[CrossRef]

Opt. Express (1)

Opt. Lett. (9)

J.-C. Chanteloup, F. Druon, M. Nantel, A. Maksimchuk, and G. Mourou, “Single-shot wave-front measurements of high-intensity ultrashort laser pulses with a three-wave interferometer,” Opt. Lett. 23(8), 621–623 (1998).
[CrossRef] [PubMed]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17(1), 28–30 (1992).
[CrossRef] [PubMed]

E. Rubino, D. Faccio, L. Tartara, P. K. Bates, O. Chalus, M. Clerici, F. Bonaretti, J. Biegert, and P. Di Trapani, “Spatiotemporal amplitude and phase retrieval of space-time coupled ultrashort pulses using the Shackled-FROG technique,” Opt. Lett. 34(24), 3854–3856 (2009).
[CrossRef] [PubMed]

G. Mínguez-Vega, C. Romero, O. Mendoza-Yero, J. R. Vázquez de Aldana, R. Borrego-Varillas, C. Méndez, P. Andrés, J. Lancis, V. Climent, and L. Roso, “Wavelength tuning of femtosecond pulses generated in nonlinear crystals by using diffractive lenses,” Opt. Lett. 35(21), 3694–3696 (2010).
[CrossRef] [PubMed]

R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, “Ultrashort-pulse wave-front autocorrelation,” Opt. Lett. 28(23), 2399–2401 (2003).
[CrossRef] [PubMed]

J. P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Direct measurement of wave-front distortion induced during second-harmonic generation: application to breakup-integral compensation,” Opt. Lett. 29(8), 899–901 (2004).
[CrossRef] [PubMed]

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. A. Mourou, and V. Yanovsky, “Generation and characterization of the highest laser intensities (1022 W/cm2),” Opt. Lett. 29(24), 2837–2839 (2004).
[CrossRef] [PubMed]

S. Velghe, J. Primot, N. Guérineau, M. Cohen, and B. Wattellier, “Wave-front reconstruction from multidirectional phase derivatives generated by multilateral shearing interferometers,” Opt. Lett. 30(3), 245–247 (2005).
[CrossRef] [PubMed]

C. P. Hauri, J. Biegert, U. Keller, B. Schaefer, K. Mann, and G. Marowski, “Validity of wave-front reconstruction and propagation of ultrabroadband pulses measured with a Hartmann-Shack sensor,” Opt. Lett. 30(12), 1563–1565 (2005).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[CrossRef]

Other (5)

C. Romero, Universidad de Salamanca, Pl. de la Merced s/n., E-37008 Spain, and associates are preparing a manuscript to be called “Second harmonic generation of femtosecond pulses focused on BBO with a diffractive lens.”

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosgan, Handbook of nonlinear optical crystals (Springer, 1999).

J.-C. Diels and W. Rudolph, Ultrashort laser pulse phenomena (Academic Press, 1996), Chap. 3.

P. R. Bowlan and R. Trebino, “Using Phase Retrieval to Obtain the Complete Spatio-Temporal Intensity and Phase of Ultrashort Pulses,” in Signal Recovery and Synthesis, OSA Technical Digest (CD) (Optical Society of America, 2009), paper SWA6.

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Figures (7)

Fig. 1
Fig. 1

a) Density plot of the phase mismatch factor PM(λ, θ) for a BBO crystal of 100 μm thickness. The wavelength values satisfying the perfect phase-matching condition are marked with the dashed line. θ is the angle between the wave-vector and the optic axis of the uniaxial crystal. b) Comparison between the measured SH signal (solid line) and the estimation (dashed line) from the fundamental spectrum using Eq. (1) (see details in the text).

Fig. 2
Fig. 2

(a) General diagram for distribution of axes and angles. The beam is assumed to propagate along the z axis. k represents the wave vector at a given point of the beam wavefront; s is the unitary vector along the optic axis. The section of the beam is showed in blue. (b) Geometry in the particular case where measurements are restricted to the plane containing the optic axis.

Fig. 3
Fig. 3

Example of phase retrieval for a diverging beam using a BBO crystal (αs = 29.4°, 500 μm thick): (a) measured spectral map; (b) phase mismatch factor PM; (c) map of angles with respect to the optic axis (θ, in degrees); (d) retrieved wavefront for the central wavelength (795 nm) of the incident beam (in λ units).

Fig. 4
Fig. 4

Experimental setup. BS, beam-splitter; CF, band-pass filter; L, lenses; f, focal length of lenses; d, distance from BS to the BBO crystal and from BS to the wavefront sensor.

Fig. 5
Fig. 5

Phase retrieval for an aberrated convergent beam (see details in the text). (a) Measured spectral map. (b) Simulated spectral map. Both, experimental and simulated spectral maps, are normalized. (c) Wavefront retrieved from (a) with the proposed algorithm (blue line). For comparsion, we show the wavefront measured with the commercial sensor (red open dots). (d) Wavefront retrieved from (b) with the proposed algorithm (blue line) and wavefront measured with the commercial sensor (red open dots, same as in (c)).

Fig. 6
Fig. 6

(a) Spectral traces for 300 µm (left panel) and 1000 µm (right panel) thick BBO for 0.95λ (upper panels) and 1.84 λ (lower panels) PtV defocus and a 1 mm pupil. All the traces are normalized. (b) Experimentally retrieved wavefront (black symbols) and wavefront measured with the commercial sensor (white symbols). The order is the same as in Fig. 6a.

Fig. 7
Fig. 7

(a) Retrieved wavefront for a beam with a discontinuity in the intensity profile (black squares) compared to the theoretically calculated wavefront (white dots). (b) Beam intensity profile recorded with a CCD camera.

Tables (2)

Tables Icon

Table 1 Angular acceptance of BBO and KDP for different crystal thickness

Tables Icon

Table 2 Experimental values for R2 with different crystal (BBO) thickness values and amounts of defocus (PtV, over a 1 mm pupil).

Equations (8)

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

I 2ω = 8 d eff 2 L 2 π 2 n e ( λ 2 ,θ ) n o 2 ( λ ) ε 0 c 1 λ 2 PM( λ,θ ) I ω 2
PM( λ,θ )= [ sin( Δk( λ,θ ) L 2 ) Δk( λ,θ ) L 2 ] 2
Δk( λ,θ )= 4π λ [ n e ( λ 2 ,θ ) n o ( λ ) ]
α= α s ±θ
α 0 =arcsin( n o ( λ )sin( α ) )
ψ( x )=ψ( xΔx ) Δxtg( α 0 ) λ
R 2 =1 i=1 N ( ψ i ϕ i ) 2 i=1 N ( ψ i ψ ¯ ) 2
δθ= 2.78λ πL 1 sin( 2 θ PM ) 1 n 0 ( λ 2ω ) [ 1 n 0 2 ( λ 2ω ) n z 2 ( λ 2ω ) ] 1

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