Abstract

We present an on-shot focal-spot characterization technique based on a phase-retrieval scheme that retrieves near-field phase from multiplane focal-spot measurements in an experimental target chamber. The technique is easy to implement inside a target chamber and is demonstrated in a multiterawatt laser system. It is also found that phase retrieval can quantitatively detect residual angular dispersion coming from the pulse compressor misalignment.

© 2008 Optical Society of America

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  1. S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. A. Mourou, and V. Yanovksy, “Generation and characterization of the highest laser intensities (1022 W/cm2),” Opt. Lett. 29, 2837-2839(2004).
    [CrossRef]
  2. S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
    [CrossRef]
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    [CrossRef]
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    [PubMed]
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2008 (1)

2006 (1)

2005 (2)

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

2004 (1)

2000 (1)

1998 (1)

1996 (1)

T. F. Coleman and Y. Li, “An interior trust region approach for nonlinear minimization subject to bounds,” SIAM J. Optim. 6, 418-445 (1996).
[CrossRef]

1993 (1)

1992 (1)

1953 (1)

Bagnoud, V.

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

Bahk, S.

Bahk, S.-W.

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

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

Begishev, I.

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

Brady, G. R.

Bromage, J.

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

Chvykov, V.

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

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

Coleman, T. F.

T. F. Coleman and Y. Li, “An interior trust region approach for nonlinear minimization subject to bounds,” SIAM J. Optim. 6, 418-445 (1996).
[CrossRef]

Fienup, J. R.

Forget, N.

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

Guardalben, M.

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

Irwan, R.

Ivanov, V. Yu.

Kalintchenko, G.

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

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

Kuwabara, G.

Lane, R. G.

Le Blanc, C.

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

Li, Y.

T. F. Coleman and Y. Li, “An interior trust region approach for nonlinear minimization subject to bounds,” SIAM J. Optim. 6, 418-445 (1996).
[CrossRef]

Maksimchuk, A.

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

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

Matsuoka, S.

Mourou, G.

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

Mourou, G. A.

Planchon, T. A.

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

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

Puth, J.

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

Rousseau, P.

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

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

Sivokon, V. P.

Vorontsov, M. A.

Yamakawa, K.

Yanovksy, V.

Yanovsky, V.

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

Zuegel, J. D.

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

S.-W. Bahk, P. Rousseau, T. A. Planchon, V. Chvykov, G. Kalintchenko, A. Maksimchuk, G. Mourou, and V. Yanovsky, “Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2),” Appl. Phys. B 80, 823-832 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Opt. Express (1)

Opt. Lett. (2)

SIAM J. Optim. (1)

T. F. Coleman and Y. Li, “An interior trust region approach for nonlinear minimization subject to bounds,” SIAM J. Optim. 6, 418-445 (1996).
[CrossRef]

Other (1)

V. Bagnoud, J. Puth, I. Begishev, M. Guardalben, J. D. Zuegel, N. Forget, C. Le Blanc, and J. Bromage, “A Multiterawatt Laser Using a High-Contrast, Optical Parametric Chirped-Pulse Preamplifier,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper JFA1.
[PubMed]

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Figures (11)

Fig. 1
Fig. 1

(a) FSD-1 uses one calibration source and wavefronts are measured at two locations to calculate the transfer wavefront. (b) FSD-2 uses two calibration sources and the wavefront is measured at only one location. WFS: wavefront sensor.

Fig. 2
Fig. 2

Phase retrieval using a multiple-focal-plane intensity measurement. g ( x , y ) : near-field complex field, G k ( x , y ) : complex field at the kth focal plane, Δ z k : defocus distance, F = focal length , and λ: wavelength.

Fig. 3
Fig. 3

The test-bed setup with a geometry similar to the OMEGA EP FSD setup. BS: beam splitter, FSM: focal-spot microscope unit.

Fig. 4
Fig. 4

Summary of wavefront measurements in the test-bed setup. (a)  W s , (b)  W p , (c)  W transfer , (d) a wavefront measured at the wavefront sensor location ( W 1 ), and (e) a calculated wavefront after the paraboloidal mirror ( W 2 = W 1 + W transfer ). The wavefront units are in waves.

Fig. 5
Fig. 5

The calculated and measured focal spots for the test-bed experiment. (a) Directly measured focal spot by FSM, (b) calculated focal spot based on FSD calibration, (c) calculated focal spot from the retrieved Zernike coefficients, and (d) encircled energy comparisons and the relative R 80 errors with respect to the R 80 value of the directly measured focal spot. FSD in this figure designates the FSD-2 approach.

Fig. 6
Fig. 6

Zernike coefficients from the FSD calibrated wavefront and from phase retrieval from multi-focal-plane data agree well each other. The rms wavefront difference is 0.074 waves.

Fig. 7
Fig. 7

Experimental setup for phase-retrieval the FSD demonstration in the MTW laser system. TBWP: a mode-locked oscillator, OPCPA: parametric amplifier, GA: 15 cm thick glass amplifier (inactive), HASO: wavefront sensor, ASP: pointing sensor, GCC: compressor chamber, FSM: focal-spot microscope.

Fig. 8
Fig. 8

Horizontal (first row) and vertical (second row) line-out comparisons at each plane. The solid curves are from measurements; the dashed curves are from the phase-retrieval calculations. Distances are 500, 250, 0, 250 , and 500 μm from the left column to the right.

Fig. 9
Fig. 9

Wavefront summary of an OPCPA laser beam. (a) Wavefront measured at the wavefront sensor location; (b) wavefront after OAP reflection, from phase retrieval; (c) transfer wavefront [Eq. (3)]; (d) wavefront measured at the wavefront sensor location after the insertion of an aberrator; and (e) calibrated wavefront for the W 2 plane using the transfer wavefront. Wavefront units are in waves.

Fig. 10
Fig. 10

Linear scale comparison of the directly measured focal spot (a) in the presence of an aberrator with the calculated focal spot, (b) using the transfer wavefront obtained from phase retrieval, and (c) not using the transfer wavefront.

Fig. 11
Fig. 11

Logarithm scale comparison of the directly measured focal spot (a) in the presence of an aberrator with the calculated focal spot and (b) using the transfer wavefront obtained from phase retrieval. (c) Encircled energy comparisons show 13% of relative R 80 error.

Equations (11)

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W r 1 = W ref + W i ,
W r 2 = T ( W ref + W e ) W t ,
W transfer = W e W i = T 1 ( W r 2 + W t ) W r 1 ,
W 2 , on-shot = W 1 , on-shot + W transfer .
W s = W i , 0 + 2 W i ,
W p = T 1 ( W e , 0 ) + W e + W i ,
W transfer = W e W i = ( W p W s ) [ T 1 ( W e , 0 ) W i , 0 ] .
G k ( x , y ) = FT { g ( x , y ) exp [ π Δ z k λ F 2 ( x 2 + y 2 ) ] } , k = 1 , 2 , N . ,
g ( x , y ) = I 0 ( x , y ) exp [ i n a n ξ n ( x , y ) ] .
ε ( a 1 , a 2 , a 3 , ) = k = 1 N λ k [ | G k ( x , y ) | I k ( x , y ) ] 2 d x d y ,
ε a n = 2 Imag { IFT [ k = 1 N λ k ( G k I k e i ψ k ) ] * ξ n ( x , y ) g ( x , y ) d x d y } ,

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