Abstract

In this paper we theoretically study the spatial characteristics of optical parametric amplification (OPA) or chirped pulse OPA (OPCPA) pumped with a phase-aberrated beam. Due to the fact that pump-to-signal phase transfer caused by walk-off effect is highly gain-dependent, in a high gain OPA system the signal beam-quality will be significantly degraded even for a weak walk-off, accompanied with beam tilting and converging or diverging. It is demonstrated that an OPA configuration with walkoff-compensated crystal pair is capable of reducing the phase transfer and hence ensuring signal beam-quality, which may be of importance for designing high-energy OPCPA systems.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2007

2006

2005

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevi??ius, L. Veisz, and F. Krausz, "High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier," Appl. Phys. B 81, 753-756 (2005).
[CrossRef]

Y. Stepanenko and C. Radzewicz, "High-gain multipass noncollinear optical parametric chirped pulse amplifier," Appl. Phys. Lett. 86, 211120 (2005).
[CrossRef]

2004

2003

2002

2001

I. Jovanovic, B. J. Comaskey, and D. M. Pennington, "Angular effects and beam quality in optical parametric amplification," J. Appl. Phys. 90, 4228-4337 (2001).
[CrossRef]

2000

R. A. Snavely, M. H. Key, S. P. Hatchett,  et al., "Intense high-energy proton beams from petawatt-laser irradiation of solids," Phys. Rev. Lett. 85, 2945-2948 (2000).
[CrossRef] [PubMed]

1999

1998

1997

D. J. Armstrong, W. J. Alford, T. D. Raymond, A. V. Smith, and M. S. Bowers, "Parametric amplification and oscillation with walkoff-compensating crystals," J. Opt. Soc. Am. B 14, 460-474 (1997).
[CrossRef]

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, "The prospects for ultrashort duration and ultrahigh intensity using optical parameteric chirped pulse amplifications," Opt. Commun. 144, 125-133 (1997).
[CrossRef]

1995

1992

A. Dubietis, G. Jonušauskas, and A. Piskarskas, "Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal," Opt. Commun. 88, 437-440 (1992).
[CrossRef]

1991

A. E. Siegman, "Defining the effective radius of curvature for a nonideal optical beam," IEEE J. Quantum Electron. 27, 1146-1148 (1991).
[CrossRef]

1990

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[CrossRef] [PubMed]

Alford, W. J.

Arbore, M. A.

Arisholm, G.

Armstrong, D. J.

Bagnoud, V.

Bakker, H. J.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[CrossRef] [PubMed]

Bates, P. K.

Begishev, I.

Begishev, I. A.

Biegert, J.

Bowers, M. S.

Cerullo, G.

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
[CrossRef]

Chekhlov, O. V.

Collier, J.

Collier, J. L.

O. V. Chekhlov, J. L. Collier, I. N. Ross, P. K. Bates, M. Notley, C. Hernandez-Gomez, W. Shaikh, C. N. Danson, D. Neely, P. Matousek, and S. Hancock, "35 J broadband femtosecond optical parametric chirped pulse amplification system," Opt. Lett. 31, 3665-3667 (2006).
[CrossRef] [PubMed]

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, "The prospects for ultrashort duration and ultrahigh intensity using optical parameteric chirped pulse amplifications," Opt. Commun. 144, 125-133 (1997).
[CrossRef]

Comaskey, B. J.

I. Jovanovic, B. J. Comaskey, and D. M. Pennington, "Angular effects and beam quality in optical parametric amplification," J. Appl. Phys. 90, 4228-4337 (2001).
[CrossRef]

Danson, C. N.

De Silvestri, S.

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
[CrossRef]

Dorrer, C.

Dubietis, A.

A. Dubietis, G. Jonušauskas, and A. Piskarskas, "Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal," Opt. Commun. 88, 437-440 (1992).
[CrossRef]

Ebbers, C. A.

I. Jovanovic, J. R. Schmidt, and C. A. Ebbers, "Optical parametric chirped-pulse amplification in periodically poled KTiOPO4 at 1053 nm," Appl. Phys. Lett. 83, 4125-4127 (2003).
[CrossRef]

Fejer, M. M.

Freidman, G. I.

Fujita, H.

Galvanauskas, A.

Ginzburg, V. N.

Guardalben, M. J.

Hama, Y.

Hancock, S.

Hariharan, A.

Harimoto, T.

Harter, D.

Hatchett, S. P.

R. A. Snavely, M. H. Key, S. P. Hatchett,  et al., "Intense high-energy proton beams from petawatt-laser irradiation of solids," Phys. Rev. Lett. 85, 2945-2948 (2000).
[CrossRef] [PubMed]

Hauri, C.

Hernandez-Gomez, C.

Ishii, E.

Ishii, N.

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevi??ius, L. Veisz, and F. Krausz, "High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier," Appl. Phys. B 81, 753-756 (2005).
[CrossRef]

Izawa, Y.

Jonušauskas, G.

A. Dubietis, G. Jonušauskas, and A. Piskarskas, "Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal," Opt. Commun. 88, 437-440 (1992).
[CrossRef]

Jovanovic, I.

I. Jovanovic, J. R. Schmidt, and C. A. Ebbers, "Optical parametric chirped-pulse amplification in periodically poled KTiOPO4 at 1053 nm," Appl. Phys. Lett. 83, 4125-4127 (2003).
[CrossRef]

I. Jovanovic, B. J. Comaskey, and D. M. Pennington, "Angular effects and beam quality in optical parametric amplification," J. Appl. Phys. 90, 4228-4337 (2001).
[CrossRef]

Keegan, J.

Keller, U.

Key, M. H.

R. A. Snavely, M. H. Key, S. P. Hatchett,  et al., "Intense high-energy proton beams from petawatt-laser irradiation of solids," Phys. Rev. Lett. 85, 2945-2948 (2000).
[CrossRef] [PubMed]

Kitagawa, Y.

Kodama, R.

Kondo, K.

Krausz, F.

F. Tavella, A. Marcinkevicius, and F. Krausz, "90 mJ parametric chirped pulse amplification of 10 fs pulses," Opt. Express 14, 12822-12827 (2006).
[CrossRef] [PubMed]

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevi??ius, L. Veisz, and F. Krausz, "High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier," Appl. Phys. B 81, 753-756 (2005).
[CrossRef]

Kuipers, L.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[CrossRef] [PubMed]

Lagendijk, A.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[CrossRef] [PubMed]

Langley, A. J.

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, "The prospects for ultrashort duration and ultrahigh intensity using optical parameteric chirped pulse amplifications," Opt. Commun. 144, 125-133 (1997).
[CrossRef]

Lozhkarev, V. V.

Luo, H.

P. Yuan, L. J. Qian, H. Luo, H. Y. Zhu, and S. C. Wen, "Femtosecond optical parametric amplification with dispersion precompensation," IEEE J. Sel. Top. Quantum Electron. 12, 181-186 (2006).
[CrossRef]

Maeda, H.

Marcinkevi??ius, A.

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevi??ius, L. Veisz, and F. Krausz, "High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier," Appl. Phys. B 81, 753-756 (2005).
[CrossRef]

Marcinkevicius, A.

Matousek, P.

Mourou, G.

T. Tajima and G. Mourou, "Zettawatt-exawatt lasers and their applications in ultrastrong-field physics," Phys. Rev. ST Accel. Beams 5, 031301 (2002).
[CrossRef]

Neely, D.

New, G. H. C.

Notley, M.

Okishev, A.

Osvay, K.

Pennington, D. M.

I. Jovanovic, B. J. Comaskey, and D. M. Pennington, "Angular effects and beam quality in optical parametric amplification," J. Appl. Phys. 90, 4228-4337 (2001).
[CrossRef]

Piskarskas, A.

A. Dubietis, G. Jonušauskas, and A. Piskarskas, "Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal," Opt. Commun. 88, 437-440 (1992).
[CrossRef]

Planken, P. C. M.

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[CrossRef] [PubMed]

Puth, J.

Qian, L. J.

P. Yuan, L. J. Qian, H. Luo, H. Y. Zhu, and S. C. Wen, "Femtosecond optical parametric amplification with dispersion precompensation," IEEE J. Sel. Top. Quantum Electron. 12, 181-186 (2006).
[CrossRef]

T. Wang, T. Y. Zhan, H. Y. Zhu, and L. J. Qian, "Analysis of beam-quality degradation in nonlinear frequency conversion," J. Opt. Soc. Am. B 19, 1101-1106 (2002).
[CrossRef]

Radzewicz, C.

Y. Stepanenko and C. Radzewicz, "High-gain multipass noncollinear optical parametric chirped pulse amplifier," Appl. Phys. Lett. 86, 211120 (2005).
[CrossRef]

Raymond, T. D.

Rodriguez, S. C.

Ross, I. N.

Schlup, P.

Schmid, K.

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevi??ius, L. Veisz, and F. Krausz, "High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier," Appl. Phys. B 81, 753-756 (2005).
[CrossRef]

Schmidt, J. R.

I. Jovanovic, J. R. Schmidt, and C. A. Ebbers, "Optical parametric chirped-pulse amplification in periodically poled KTiOPO4 at 1053 nm," Appl. Phys. Lett. 83, 4125-4127 (2003).
[CrossRef]

Shaikh, W.

Siegman, A. E.

A. E. Siegman, "Defining the effective radius of curvature for a nonideal optical beam," IEEE J. Quantum Electron. 27, 1146-1148 (1991).
[CrossRef]

Smith, A. V.

Snavely, R. A.

R. A. Snavely, M. H. Key, S. P. Hatchett,  et al., "Intense high-energy proton beams from petawatt-laser irradiation of solids," Phys. Rev. Lett. 85, 2945-2948 (2000).
[CrossRef] [PubMed]

Stepanenko, Y.

Y. Stepanenko and C. Radzewicz, "High-gain multipass noncollinear optical parametric chirped pulse amplifier," Appl. Phys. Lett. 86, 211120 (2005).
[CrossRef]

Tajima, T.

T. Tajima and G. Mourou, "Zettawatt-exawatt lasers and their applications in ultrastrong-field physics," Phys. Rev. ST Accel. Beams 5, 031301 (2002).
[CrossRef]

Tavella, F.

F. Tavella, A. Marcinkevicius, and F. Krausz, "90 mJ parametric chirped pulse amplification of 10 fs pulses," Opt. Express 14, 12822-12827 (2006).
[CrossRef] [PubMed]

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevi??ius, L. Veisz, and F. Krausz, "High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier," Appl. Phys. B 81, 753-756 (2005).
[CrossRef]

Torner, L.

Torres, J. P.

Towrie, M.

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, "The prospects for ultrashort duration and ultrahigh intensity using optical parameteric chirped pulse amplifications," Opt. Commun. 144, 125-133 (1997).
[CrossRef]

Veisz, L.

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevi??ius, L. Veisz, and F. Krausz, "High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier," Appl. Phys. B 81, 753-756 (2005).
[CrossRef]

Walczak, J.

Wang, T.

Waxer, L. J.

Wen, S. C.

P. Yuan, L. J. Qian, H. Luo, H. Y. Zhu, and S. C. Wen, "Femtosecond optical parametric amplification with dispersion precompensation," IEEE J. Sel. Top. Quantum Electron. 12, 181-186 (2006).
[CrossRef]

Yamakawa, K.

Yamanaka, T.

Yoshida, H.

Yuan, P.

P. Yuan, L. J. Qian, H. Luo, H. Y. Zhu, and S. C. Wen, "Femtosecond optical parametric amplification with dispersion precompensation," IEEE J. Sel. Top. Quantum Electron. 12, 181-186 (2006).
[CrossRef]

Zhan, T. Y.

Zhu, H. Y.

P. Yuan, L. J. Qian, H. Luo, H. Y. Zhu, and S. C. Wen, "Femtosecond optical parametric amplification with dispersion precompensation," IEEE J. Sel. Top. Quantum Electron. 12, 181-186 (2006).
[CrossRef]

T. Wang, T. Y. Zhan, H. Y. Zhu, and L. J. Qian, "Analysis of beam-quality degradation in nonlinear frequency conversion," J. Opt. Soc. Am. B 19, 1101-1106 (2002).
[CrossRef]

Zuegel, J.

Zuegel, J. D.

Appl. Opt.

Appl. Phys. B

F. Tavella, K. Schmid, N. Ishii, A. Marcinkevi??ius, L. Veisz, and F. Krausz, "High-dynamic range pulse-contrast measurements of a broadband optical parametric chirped-pulse amplifier," Appl. Phys. B 81, 753-756 (2005).
[CrossRef]

Appl. Phys. Lett.

I. Jovanovic, J. R. Schmidt, and C. A. Ebbers, "Optical parametric chirped-pulse amplification in periodically poled KTiOPO4 at 1053 nm," Appl. Phys. Lett. 83, 4125-4127 (2003).
[CrossRef]

Y. Stepanenko and C. Radzewicz, "High-gain multipass noncollinear optical parametric chirped pulse amplifier," Appl. Phys. Lett. 86, 211120 (2005).
[CrossRef]

IEEE J. Quantum Electron.

A. E. Siegman, "Defining the effective radius of curvature for a nonideal optical beam," IEEE J. Quantum Electron. 27, 1146-1148 (1991).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

P. Yuan, L. J. Qian, H. Luo, H. Y. Zhu, and S. C. Wen, "Femtosecond optical parametric amplification with dispersion precompensation," IEEE J. Sel. Top. Quantum Electron. 12, 181-186 (2006).
[CrossRef]

J. Appl. Phys.

I. Jovanovic, B. J. Comaskey, and D. M. Pennington, "Angular effects and beam quality in optical parametric amplification," J. Appl. Phys. 90, 4228-4337 (2001).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

A. Dubietis, G. Jonušauskas, and A. Piskarskas, "Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal," Opt. Commun. 88, 437-440 (1992).
[CrossRef]

I. N. Ross, P. Matousek, M. Towrie, A. J. Langley, and J. L. Collier, "The prospects for ultrashort duration and ultrahigh intensity using optical parameteric chirped pulse amplifications," Opt. Commun. 144, 125-133 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, "Phase modulation in second-order nonlinear-optical processes," Phys. Rev. A 42, 4085-4101 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. A. Snavely, M. H. Key, S. P. Hatchett,  et al., "Intense high-energy proton beams from petawatt-laser irradiation of solids," Phys. Rev. Lett. 85, 2945-2948 (2000).
[CrossRef] [PubMed]

Phys. Rev. ST Accel. Beams

T. Tajima and G. Mourou, "Zettawatt-exawatt lasers and their applications in ultrastrong-field physics," Phys. Rev. ST Accel. Beams 5, 031301 (2002).
[CrossRef]

Rev. Sci. Instrum.

G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum. 74, 1-18 (2003).
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

Calculated output signal (a) and idler phase (b) in the cases with (red and blue curves) and without (black curve) walk-off. The red and blue curve correspond to two different nonlinear lengths of LNL =0.23L and LNL =0.15L respectively. Other parameters used in the simulations: Lsp=5L, L=10 mm, a=0.5, n=2, and Es(0)=10-9.

Fig. 2.
Fig. 2.

(a). The transverse distributions of signal phase after a single OPA stage with different walk-off lengths, and (b) the phase distributions of pump beam (black curve) and output signal further amplified by a second OPA. The red and blue curves correspond to Lsp/L of 5 and 100, respectively. Each OPA with the same nonlinear length LNL =0.23L, L=10 mm, a=0.5, n=2. Input signal of the first OPA is: Es(0)=10-9.

Fig. 3.
Fig. 3.

(a). Calculated output signal phase distributions with different pump phase modulation amplitudes, a=0.1, 0.5, and 2.0 correspond to the black, red and blue curves, respectively. n=2. (b) signal phase distributions with different modulation frequencies of the pump beam, n=2, 3, 5, 9 refers to the black, red, blue and green curves, respectively. a=0.5. Other parameters used in the simulations: LNL =0.23, Lsp=5L, L=10 mm, and Es(0)=10-9.

Fig. 4.
Fig. 4.

Numerical results of the output signal gain (a) and beam-quality M 2 s (b) in a single stage OPA with various walk-off in the regime of pump non-depletion (Es(0)=10-9); while graphs (c) and (d) corresponding to a strongly pump-depleted regime (Es(0)=10-2). Other parameters used in the simulations: LNL =0.15L; L=10 mm.

Fig. 5.
Fig. 5.

Calculated output signal phases for two different walk-off lengths Lsp/L. Parameters used in the simulations: M 2 p =10; LNL =0.15L; L=10 mm; Es(0)=10-9.

Fig. 6.
Fig. 6.

Calculated output signal phases for two different spatial frequencies with pump phase modulation in the form of (a) Φ(x)=(nx)2 and (b) Φ(x)=(nx)3. n=1, 2 refer to the black and red curve, respectively. Other parameters used in the simulations: LNL =0.15L; L=10 mm; Es(0)=10-9.

Fig. 7.
Fig. 7.

Calculated tilt angle of the signal with increasing interaction length in the crystal. The black and red curve correspond to Lsp=2 cm and 1.5 cm, respectively. Other parameters used in the simulations: M 2 p =10; LNL =0.15L; Es(0)=10-9.

Fig. 8.
Fig. 8.

Calculated signal beam tilt and curvature versus walk-off length at three different values of pump beam-quality. Parameters used in the simulations: LNL =0.15L; L=10 mm; Es(0)=10-9.

Fig. 9.
Fig. 9.

Calculated signal beam-quality versus walk-off length at two different pump beam intensities. Star symbol: LNL =0.15L; square symbol: LNL =0.1L. Other parameters used in the simulations: M 2 p =10; L=10 mm; Es(0)=10-9.

Fig. 10.
Fig. 10.

The schematic diagram of walkoff-compensated crystal pair.

Fig. 11.
Fig. 11.

Calculated output signal phases in a two-stage OPA system. Red curve: walkoff-compensated configuration; blue curve: ordinary two OPAs. The signal phase of the first-stage OPA (black curve) is also given. Parameters used in the simulations: M 2 p =10; LNL =0.23L; Lsp=5L; L=10 mm; Es(0)=10-9.

Fig. 12.
Fig. 12.

Calculated total OPA gain, signal beam-quality, beam tilt and curvature versus walk-off length in a two-stage OPA system with and without walkoff-compensation. Parameters used in the simulations are the same as those in Fig.11.

Equations (5)

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E S ( z , x ) z + L N L L s p E s ( z , x ) x + i L N L L 2 s 2 E S ( z , x ) 2 x = i λ p λ s E p ( z , x ) E i * ( z , x ) e i Δ k z
E i ( z , x ) z + L N L L i p E i ( z , x ) x + i L N L L 2 i 2 E i ( z , x ) 2 x = i λ p λ i E p ( z , x ) E s * ( z , x ) e i Δ k z
E p ( z , x ) z + i L N L L 2 p 2 E p ( z , x ) 2 x = i E s ( z , x ) E i ( z , x ) e i Δ k z
β = λ s ε ( s ) 2 d s ε ( s ) 2 d s
ε ( s ) = ε ( x ) exp ( i 2 π s x ) d x

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