Abstract

Quasi-parametric chirped pulse amplification (QPCPA) is a new scheme that enables the amplification of chirped signal pulses without back conversion by depleting the idler pulses. In this paper, we present a numerical study on the bandwidth, efficiency, and robustness of QPCPA. Self-locked phase among the interacting waves is found to be the underlying mechanism for the suppression of back conversion, which allows signal efficiency approaching to the quantum limit even under the phase-mismatch condition, and thus greatly increases the phase-mismatch tolerance of QPCPA. We demonstrate that QPCPA can break through the trade-off between the efficiency and bandwidth encountered in conventional optical parametric amplification, hence supporting highly efficient amplification of few-cycle pulses.

© 2017 Optical Society of America

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References

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  1. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55(6), 447–449 (1985).
  2. C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).
  3. F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010).
  4. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
    [PubMed]
  5. K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
    [PubMed]
  6. Y. Chu, Z. Gan, X. Liang, L. Yu, X. Lu, C. Wang, X. Wang, L. Xu, H. Lu, D. Yin, Y. Leng, R. Li, and Z. Xu, “High-energy large-aperture Ti:sapphire amplifier for 5 PW laser pulses,” Opt. Lett. 40(21), 5011–5014 (2015).
    [PubMed]
  7. J. H. Sung, H. W. Lee, J. Y. Yoo, J. W. Yoon, C. W. Lee, J. M. Yang, Y. J. Son, Y. H. Jang, S. K. Lee, and C. H. Nam, “4.2 PW, 20 fs Ti:sapphire laser at 0.1 Hz,” Opt. Lett. 42(11), 2058–2061 (2017).
    [PubMed]
  8. A. Vaupel, N. Bodnar, B. Webb, L. Shah, and M. Richardson, “Concepts, performance review, and prospects of table-top, few-cycle optical parametric chirped-pulse amplification,” Opt. Eng. 53(5), 051507 (2014).
  9. S. Bohman, A. Suda, T. Kanai, S. Yamaguchi, and K. Midorikawa, “Generation of 5.0 fs, 5.0 mJ pulses at 1kHz using hollow-fiber pulse compression,” Opt. Lett. 35(11), 1887–1889 (2010).
    [PubMed]
  10. G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31(2), 274–276 (2006).
    [PubMed]
  11. A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femto-second pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4−6), 437–440 (1992).
  12. D. Herrmann, L. Veisz, R. Tautz, F. Tavella, K. Schmid, V. Pervak, and F. Krausz, “Generation of sub-three-cycle, 16 TW light pulses by using noncollinear optical parametric chirped-pulse amplification,” Opt. Lett. 34(16), 2459–2461 (2009).
    [PubMed]
  13. Y. Deng, A. Schwarz, H. Fattahi, M. Ueffing, X. Gu, M. Ossiander, T. Metzger, V. Pervak, H. Ishizuki, T. Taira, T. Kobayashi, G. Marcus, F. Krausz, R. Kienberger, and N. Karpowicz, “Carrier-envelope-phase-stable, 1.2 mJ, 1.5 cycle laser pulses at 2.1 μm,” Opt. Lett. 37(23), 4973–4975 (2012).
    [PubMed]
  14. G. Andriukaitis, T. Balčiūnas, S. AliŠauskas, A. Pugžlys, A. BaltuŠka, T. Popmintchev, M-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
    [PubMed]
  15. T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
    [PubMed]
  16. H. Fattahi, H. G. Barros, M. Gorjan, T. Nubbemeyer, B. Alsaif, C. Y. Teisset, M. Schultze, S. Prinz, M. Haefner, M. Ueffing, A. Alismail, L. Vámos, A. Schwarz, O. Pronin, J. Brons, X. T. Geng, G. Arisholm, M. Ciappina, V. S. Yakovlev, D.-E. Kim, A. M. Azzeer, N. Karpowicz, D. Sutter, Z. Major, T. Metzger, and F. Krausz, “Third-generation femtosecond technology,” Optica 1(1), 45–63 (2014).
  17. B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
    [PubMed]
  18. H. Suchowski, G. Porat, and A. Arie, “Adiabatic processes in frequency conversion,” Laser Photonics Rev. 8(3), 333–367 (2014).
  19. C. R. Phillips and M. M. Fejer, “Efficiency and phase of optical parametric amplification in chirped quasi-phase-matched gratings,” Opt. Lett. 35(18), 3093–3095 (2010).
    [PubMed]
  20. P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. -Han Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
  21. J. Ma, J. Wang, P. Yuan, G. Xie, K. Xiong, Y. Tu, X. Tu, E. Shi, Y. Zheng, and L. Qian, “Quasi-parametric amplification of chirped pulses based on a Sm3+-doped yttrium calcium oxyborate crystal,” Optica 2(11), 1006–1009 (2015).
  22. J. Moses and S.-W. Huang, “Conformal profile theory for performance scaling of ultrabroadband optical parametric chirped pulse amplification,” J. Opt. Soc. Am. B 28(4), 812–831 (2011).
  23. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
  24. A. L. Oien, I. T. McKinnie, P. Jain, N. A. Russell, D. M. Warrington, and L. A. W. Gloster, “Efficient, low-threshold collinear and noncollinear β-barium borate optical parametric oscillators,” Opt. Lett. 22(12), 859–861 (1997).
    [PubMed]
  25. J. Ma, J. Wang, P. Yuan, G. Xie, and L. Qian, “Origin and suppression of back conversion in a phase-matched nonlinear frequency down-conversion process,” Chin. Opt. Lett. 15(2), 021901 (2017).
  26. O. Yaakobi, L. Caspani, M. Clerici, F. Vidal, and R. Morandotti, “Complete energy conversion by autoresonant three-wave mixing in nonuniform media,” Opt. Express 21(2), 1623–1632 (2013).
    [PubMed]
  27. I. N. Ross, P. Matousek, G. H. C. New, and K. Osvay, “Analysis and optimization of optical parametric chirped pulse amplification,” J. Opt. Soc. Am. B 19(42), 2945–2956 (2002).
  28. J. Moses, C. Manzoni, S.-W. Huang, G. Cerullo, and F. X. Kärtner, “Temporal optimization of ultrabroadband high-energy OPCPA,” Opt. Express 17(7), 5540–5555 (2009).
    [PubMed]
  29. J. Ma, J. Wang, D. Hu, P. Yuan, G. Xie, H. Zhu, H. Yu, H. Zhang, J. Wang, and L. Qian, “Theoretical investigations of broadband mid-infrared optical parametric amplification based on a La3Ga5.5Nb0.5O14 crystal,” Opt. Express 24(21), 23957–23968 (2016).
    [PubMed]
  30. R. Riedel, A. Stephanides, M. J. Prandolini, B. Gronloh, B. Jungbluth, T. Mans, and F. Tavella, “Power scaling of supercontinuum seeded megahertz-repetition rate optical parametric chirped pulse amplifiers,” Opt. Lett. 39(6), 1422–1424 (2014).
    [PubMed]
  31. N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).
  32. S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).
  33. Y. Tu, Y. Zheng, X. Tu, K. Xiong, and E. Shi, “Growth and characterization of SmxY1-xCa4O(BO3)3 single crystals for nonlinear optical applications,” CrystEngComm 15(31), 6244–6248 (2013).
  34. Y. Li, H. Zhong, J. Yang, S. Wang, and D. Fan, “Versatile backconversion-inhibited broadband optical parametric amplification based on an idler-separated QPM configuration,” Opt. Lett. 42(14), 2806–2809 (2017).
    [PubMed]
  35. J. Bromage, J. Rothhardt, S. Hädrich, C. Dorrer, C. Jocher, S. Demmler, J. Limpert, A. Tünnermann, and J. D. Zuegel, “Analysis and suppression of parasitic processes in noncollinear optical parametric amplifiers,” Opt. Express 19(18), 16797–16808 (2011).
    [PubMed]
  36. O. P. Naraniya, M. R. Shenoy, and K. Thyagarajan, “Efficient scheme for mid-infrared generation using simultaneous optical parametric oscillators and DFG processes in a double-pass pump configuration,” Appl. Opt. 54(24), 7234–7239 (2015).
    [PubMed]

2017 (4)

2016 (1)

2015 (4)

2014 (5)

A. Vaupel, N. Bodnar, B. Webb, L. Shah, and M. Richardson, “Concepts, performance review, and prospects of table-top, few-cycle optical parametric chirped-pulse amplification,” Opt. Eng. 53(5), 051507 (2014).

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

H. Suchowski, G. Porat, and A. Arie, “Adiabatic processes in frequency conversion,” Laser Photonics Rev. 8(3), 333–367 (2014).

R. Riedel, A. Stephanides, M. J. Prandolini, B. Gronloh, B. Jungbluth, T. Mans, and F. Tavella, “Power scaling of supercontinuum seeded megahertz-repetition rate optical parametric chirped pulse amplifiers,” Opt. Lett. 39(6), 1422–1424 (2014).
[PubMed]

H. Fattahi, H. G. Barros, M. Gorjan, T. Nubbemeyer, B. Alsaif, C. Y. Teisset, M. Schultze, S. Prinz, M. Haefner, M. Ueffing, A. Alismail, L. Vámos, A. Schwarz, O. Pronin, J. Brons, X. T. Geng, G. Arisholm, M. Ciappina, V. S. Yakovlev, D.-E. Kim, A. M. Azzeer, N. Karpowicz, D. Sutter, Z. Major, T. Metzger, and F. Krausz, “Third-generation femtosecond technology,” Optica 1(1), 45–63 (2014).

2013 (2)

O. Yaakobi, L. Caspani, M. Clerici, F. Vidal, and R. Morandotti, “Complete energy conversion by autoresonant three-wave mixing in nonuniform media,” Opt. Express 21(2), 1623–1632 (2013).
[PubMed]

Y. Tu, Y. Zheng, X. Tu, K. Xiong, and E. Shi, “Growth and characterization of SmxY1-xCa4O(BO3)3 single crystals for nonlinear optical applications,” CrystEngComm 15(31), 6244–6248 (2013).

2012 (2)

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Y. Deng, A. Schwarz, H. Fattahi, M. Ueffing, X. Gu, M. Ossiander, T. Metzger, V. Pervak, H. Ishizuki, T. Taira, T. Kobayashi, G. Marcus, F. Krausz, R. Kienberger, and N. Karpowicz, “Carrier-envelope-phase-stable, 1.2 mJ, 1.5 cycle laser pulses at 2.1 μm,” Opt. Lett. 37(23), 4973–4975 (2012).
[PubMed]

2011 (3)

2010 (3)

2009 (3)

2006 (1)

2003 (1)

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

2002 (1)

2001 (1)

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

1997 (2)

A. L. Oien, I. T. McKinnie, P. Jain, N. A. Russell, D. M. Warrington, and L. A. W. Gloster, “Efficient, low-threshold collinear and noncollinear β-barium borate optical parametric oscillators,” Opt. Lett. 22(12), 859–861 (1997).
[PubMed]

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).

1992 (1)

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femto-second pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4−6), 437–440 (1992).

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55(6), 447–449 (1985).

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

Ališauskas, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

G. Andriukaitis, T. Balčiūnas, S. AliŠauskas, A. Pugžlys, A. BaltuŠka, T. Popmintchev, M-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
[PubMed]

Alismail, A.

Alsaif, B.

Ando, M.

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

Andriukaitis, G.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

G. Andriukaitis, T. Balčiūnas, S. AliŠauskas, A. Pugžlys, A. BaltuŠka, T. Popmintchev, M-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
[PubMed]

Arie, A.

H. Suchowski, G. Porat, and A. Arie, “Adiabatic processes in frequency conversion,” Laser Photonics Rev. 8(3), 333–367 (2014).

Arisholm, G.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

Arpin, P.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Azzeer, A. M.

Balciunas, T.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

G. Andriukaitis, T. Balčiūnas, S. AliŠauskas, A. Pugžlys, A. BaltuŠka, T. Popmintchev, M-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
[PubMed]

Baltuška, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

G. Andriukaitis, T. Balčiūnas, S. AliŠauskas, A. Pugžlys, A. BaltuŠka, T. Popmintchev, M-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
[PubMed]

Barros, H. G.

Becker, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

-Becker, A. J.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Benavides, S.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

Bodnar, N.

A. Vaupel, N. Bodnar, B. Webb, L. Shah, and M. Richardson, “Concepts, performance review, and prospects of table-top, few-cycle optical parametric chirped-pulse amplification,” Opt. Eng. 53(5), 051507 (2014).

Bohman, S.

Boivin, M.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Brabec, T.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

Bromage, J.

Brons, J.

Brown, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Buck, A.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Calegari, F.

F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010).

Caspani, L.

Cerullo, G.

Chen, M.-C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Chen, M-C.

Chu, Y.

Ciappina, M.

Clerici, M.

Corkum, P.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

Danson, C.

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).

Demmler, S.

Deng, Y.

Dorrer, C.

Drescher, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

Dubietis, A.

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femto-second pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4−6), 437–440 (1992).

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

Fan, D.

Fattahi, H.

Fejer, M. M.

Ferrari, F.

F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010).

Flemens, N.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. -Han Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).

Gaeta, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Gan, Z.

-García, C. H.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Geissler, M.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Geng, X. T.

Gloster, L. A. W.

Gorjan, M.

Gronloh, B.

Gu, X.

Habs, D.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Hädrich, S.

Haefner, M.

-Han Hong, K.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. -Han Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).

Heinzmann, U.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

Hentschel, M.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

Herrmann, D.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

D. Herrmann, L. Veisz, R. Tautz, F. Tavella, K. Schmid, V. Pervak, and F. Krausz, “Generation of sub-three-cycle, 16 TW light pulses by using noncollinear optical parametric chirped-pulse amplification,” Opt. Lett. 34(16), 2459–2461 (2009).
[PubMed]

Hidding, B.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Hillier, D.

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).

Hopps, N.

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).

Hu, D.

Huang, S.-W.

Ibrahim, H.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Ishizuki, H.

Jain, P.

Jang, Y. H.

Jocher, C.

Jonusauskas, G.

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femto-second pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4−6), 437–440 (1992).

Jungbluth, B.

Kanai, T.

Kapteyn, H. C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

G. Andriukaitis, T. Balčiūnas, S. AliŠauskas, A. Pugžlys, A. BaltuŠka, T. Popmintchev, M-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
[PubMed]

Karpowicz, N.

Kärtner, F. X.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. -Han Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).

J. Moses, C. Manzoni, S.-W. Huang, G. Cerullo, and F. X. Kärtner, “Temporal optimization of ultrabroadband high-energy OPCPA,” Opt. Express 17(7), 5540–5555 (2009).
[PubMed]

Kato, K.

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

Kienberger, R.

Kim, D.-E.

Kobayashi, T.

Krausz, F.

Krogen, P.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. -Han Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).

Laramée, A.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Lebrun, G.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Lee, C. W.

Lee, H. W.

Lee, S. K.

Légaré, F.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Leng, Y.

Li, R.

Li, Y.

Liang, H.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. -Han Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).

Liang, X.

Limpert, J.

Lu, H.

Lu, X.

Lucchini, M.

F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010).

Ma, J.

Major, Z.

Mann, G.

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).

Mans, T.

Manzoni, C.

Marcinkevicius, A.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Marcus, G.

Matousek, P.

McKinnie, I. T.

Metzger, T.

Meyer-Ter-Vehn, J.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Midorikawa, K.

Milosevic, N.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

Morandotti, R.

Mori, Y.

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

Moses, J.

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55(6), 447–449 (1985).

Mücke, O. D.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Murnane, M. M.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

G. Andriukaitis, T. Balčiūnas, S. AliŠauskas, A. Pugžlys, A. BaltuŠka, T. Popmintchev, M-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
[PubMed]

Nam, C. H.

Naraniya, O. P.

Neely, D.

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).

New, G. H. C.

Nisoli, M.

F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010).

Nubbemeyer, T.

Oien, A. L.

Ossiander, M.

Osvay, K.

Ozaki, T.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

Pervak, V.

Phillips, C. R.

Piskarskas, A.

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femto-second pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4−6), 437–440 (1992).

Plaja, L.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Poitras, F.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Popmintchev, D.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Popmintchev, T.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

G. Andriukaitis, T. Balčiūnas, S. AliŠauskas, A. Pugžlys, A. BaltuŠka, T. Popmintchev, M-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
[PubMed]

Porat, G.

H. Suchowski, G. Porat, and A. Arie, “Adiabatic processes in frequency conversion,” Laser Photonics Rev. 8(3), 333–367 (2014).

Prandolini, M. J.

Prinz, S.

Pronin, O.

Pugzlys, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Pugžlys, A.

Qian, L.

Reider, G. A.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

Richardson, M.

A. Vaupel, N. Bodnar, B. Webb, L. Shah, and M. Richardson, “Concepts, performance review, and prospects of table-top, few-cycle optical parametric chirped-pulse amplification,” Opt. Eng. 53(5), 051507 (2014).

Riedel, R.

Ross, I. N.

Rothhardt, J.

Russell, N. A.

Sansone, G.

F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010).

Sasaki, T.

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

Schmid, K.

D. Herrmann, L. Veisz, R. Tautz, F. Tavella, K. Schmid, V. Pervak, and F. Krausz, “Generation of sub-three-cycle, 16 TW light pulses by using noncollinear optical parametric chirped-pulse amplification,” Opt. Lett. 34(16), 2459–2461 (2009).
[PubMed]

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Schmidt, B. E.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Schramm, U.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Schrauth, S. E.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Schultze, M.

Schwarz, A.

Seidel, S.

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).

Shah, L.

A. Vaupel, N. Bodnar, B. Webb, L. Shah, and M. Richardson, “Concepts, performance review, and prospects of table-top, few-cycle optical parametric chirped-pulse amplification,” Opt. Eng. 53(5), 051507 (2014).

Shenoy, M. R.

Shi, E.

J. Ma, J. Wang, P. Yuan, G. Xie, K. Xiong, Y. Tu, X. Tu, E. Shi, Y. Zheng, and L. Qian, “Quasi-parametric amplification of chirped pulses based on a Sm3+-doped yttrium calcium oxyborate crystal,” Optica 2(11), 1006–1009 (2015).

Y. Tu, Y. Zheng, X. Tu, K. Xiong, and E. Shi, “Growth and characterization of SmxY1-xCa4O(BO3)3 single crystals for nonlinear optical applications,” CrystEngComm 15(31), 6244–6248 (2013).

Shim, B.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

Son, Y. J.

Spielmann, C.

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

Stagira, S.

F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010).

Steinmeyer, G.

Stephanides, A.

Stibenz, G.

Strickland, D.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55(6), 447–449 (1985).

Suchowski, H.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. -Han Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).

H. Suchowski, G. Porat, and A. Arie, “Adiabatic processes in frequency conversion,” Laser Photonics Rev. 8(3), 333–367 (2014).

Suda, A.

Sung, J. H.

Sutter, D.

Suzuki, K.

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

Taira, T.

Takaoka, E.

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

Tautz, R.

D. Herrmann, L. Veisz, R. Tautz, F. Tavella, K. Schmid, V. Pervak, and F. Krausz, “Generation of sub-three-cycle, 16 TW light pulses by using noncollinear optical parametric chirped-pulse amplification,” Opt. Lett. 34(16), 2459–2461 (2009).
[PubMed]

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Tavella, F.

Teisset, C. Y.

Thiré, N.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Thyagarajan, K.

Tu, X.

J. Ma, J. Wang, P. Yuan, G. Xie, K. Xiong, Y. Tu, X. Tu, E. Shi, Y. Zheng, and L. Qian, “Quasi-parametric amplification of chirped pulses based on a Sm3+-doped yttrium calcium oxyborate crystal,” Optica 2(11), 1006–1009 (2015).

Y. Tu, Y. Zheng, X. Tu, K. Xiong, and E. Shi, “Growth and characterization of SmxY1-xCa4O(BO3)3 single crystals for nonlinear optical applications,” CrystEngComm 15(31), 6244–6248 (2013).

Tu, Y.

J. Ma, J. Wang, P. Yuan, G. Xie, K. Xiong, Y. Tu, X. Tu, E. Shi, Y. Zheng, and L. Qian, “Quasi-parametric amplification of chirped pulses based on a Sm3+-doped yttrium calcium oxyborate crystal,” Optica 2(11), 1006–1009 (2015).

Y. Tu, Y. Zheng, X. Tu, K. Xiong, and E. Shi, “Growth and characterization of SmxY1-xCa4O(BO3)3 single crystals for nonlinear optical applications,” CrystEngComm 15(31), 6244–6248 (2013).

Tünnermann, A.

Ueffing, M.

Umemura, N.

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

Vámos, L.

Vaupel, A.

A. Vaupel, N. Bodnar, B. Webb, L. Shah, and M. Richardson, “Concepts, performance review, and prospects of table-top, few-cycle optical parametric chirped-pulse amplification,” Opt. Eng. 53(5), 051507 (2014).

Veisz, L.

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

D. Herrmann, L. Veisz, R. Tautz, F. Tavella, K. Schmid, V. Pervak, and F. Krausz, “Generation of sub-three-cycle, 16 TW light pulses by using noncollinear optical parametric chirped-pulse amplification,” Opt. Lett. 34(16), 2459–2461 (2009).
[PubMed]

Vidal, F.

Vozzi, C.

F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010).

Wang, C.

Wang, J.

Wang, S.

Wang, X.

Warrington, D. M.

Webb, B.

A. Vaupel, N. Bodnar, B. Webb, L. Shah, and M. Richardson, “Concepts, performance review, and prospects of table-top, few-cycle optical parametric chirped-pulse amplification,” Opt. Eng. 53(5), 051507 (2014).

Xie, G.

Xiong, K.

J. Ma, J. Wang, P. Yuan, G. Xie, K. Xiong, Y. Tu, X. Tu, E. Shi, Y. Zheng, and L. Qian, “Quasi-parametric amplification of chirped pulses based on a Sm3+-doped yttrium calcium oxyborate crystal,” Optica 2(11), 1006–1009 (2015).

Y. Tu, Y. Zheng, X. Tu, K. Xiong, and E. Shi, “Growth and characterization of SmxY1-xCa4O(BO3)3 single crystals for nonlinear optical applications,” CrystEngComm 15(31), 6244–6248 (2013).

Xu, L.

Xu, Z.

Yaakobi, O.

Yakovlev, V. S.

Yamaguchi, S.

Yang, J.

Yang, J. M.

Yin, D.

Yoo, J. Y.

Yoon, J. W.

Yoshimura, M.

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

Yu, H.

Yu, L.

Yuan, P.

Zhang, H.

Zhavoronkov, N.

Zheng, Y.

J. Ma, J. Wang, P. Yuan, G. Xie, K. Xiong, Y. Tu, X. Tu, E. Shi, Y. Zheng, and L. Qian, “Quasi-parametric amplification of chirped pulses based on a Sm3+-doped yttrium calcium oxyborate crystal,” Optica 2(11), 1006–1009 (2015).

Y. Tu, Y. Zheng, X. Tu, K. Xiong, and E. Shi, “Growth and characterization of SmxY1-xCa4O(BO3)3 single crystals for nonlinear optical applications,” CrystEngComm 15(31), 6244–6248 (2013).

Zhong, H.

Zhu, H.

Zuegel, J. D.

Appl. Opt. (1)

Chin. Opt. Lett. (1)

CrystEngComm (1)

Y. Tu, Y. Zheng, X. Tu, K. Xiong, and E. Shi, “Growth and characterization of SmxY1-xCa4O(BO3)3 single crystals for nonlinear optical applications,” CrystEngComm 15(31), 6244–6248 (2013).

High Power Laser Sci. Eng. (1)

C. Danson, D. Hillier, N. Hopps, and D. Neely, “Petawatt class lasers worldwide,” High Power Laser Sci. Eng. 3, e3 (2015).

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

Jpn. J. Appl. Phys. (1)

N. Umemura, M. Ando, K. Suzuki, E. Takaoka, K. Kato, M. Yoshimura, Y. Mori, and T. Sasaki, “Temperature-insensitive second-harmonic generation at 0.5321 μm in YCa4O(BO3)3,” Jpn. J. Appl. Phys. 42(42), 5040–5042 (2003).

Laser Photonics Rev. (1)

H. Suchowski, G. Porat, and A. Arie, “Adiabatic processes in frequency conversion,” Laser Photonics Rev. 8(3), 333–367 (2014).

Nat. Commun. (1)

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[PubMed]

Nat. Photonics (2)

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. -Han Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).

F. Ferrari, F. Calegari, M. Lucchini, C. Vozzi, S. Stagira, G. Sansone, and M. Nisoli, “High-energy isolated attosecond pulses generated by above-saturation few-cycle fields,” Nat. Photonics 4, 875–879 (2010).

Nature (1)

M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001).
[PubMed]

Opt. Commun. (2)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55(6), 447–449 (1985).

A. Dubietis, G. Jonusauskas, and A. Piskarskas, “Powerful femto-second pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88(4−6), 437–440 (1992).

Opt. Eng. (1)

A. Vaupel, N. Bodnar, B. Webb, L. Shah, and M. Richardson, “Concepts, performance review, and prospects of table-top, few-cycle optical parametric chirped-pulse amplification,” Opt. Eng. 53(5), 051507 (2014).

Opt. Express (4)

Opt. Lett. (11)

D. Herrmann, L. Veisz, R. Tautz, F. Tavella, K. Schmid, V. Pervak, and F. Krausz, “Generation of sub-three-cycle, 16 TW light pulses by using noncollinear optical parametric chirped-pulse amplification,” Opt. Lett. 34(16), 2459–2461 (2009).
[PubMed]

S. Bohman, A. Suda, T. Kanai, S. Yamaguchi, and K. Midorikawa, “Generation of 5.0 fs, 5.0 mJ pulses at 1kHz using hollow-fiber pulse compression,” Opt. Lett. 35(11), 1887–1889 (2010).
[PubMed]

C. R. Phillips and M. M. Fejer, “Efficiency and phase of optical parametric amplification in chirped quasi-phase-matched gratings,” Opt. Lett. 35(18), 3093–3095 (2010).
[PubMed]

Y. Deng, A. Schwarz, H. Fattahi, M. Ueffing, X. Gu, M. Ossiander, T. Metzger, V. Pervak, H. Ishizuki, T. Taira, T. Kobayashi, G. Marcus, F. Krausz, R. Kienberger, and N. Karpowicz, “Carrier-envelope-phase-stable, 1.2 mJ, 1.5 cycle laser pulses at 2.1 μm,” Opt. Lett. 37(23), 4973–4975 (2012).
[PubMed]

G. Andriukaitis, T. Balčiūnas, S. AliŠauskas, A. Pugžlys, A. BaltuŠka, T. Popmintchev, M-C. Chen, M. M. Murnane, and H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36(15), 2755–2757 (2011).
[PubMed]

R. Riedel, A. Stephanides, M. J. Prandolini, B. Gronloh, B. Jungbluth, T. Mans, and F. Tavella, “Power scaling of supercontinuum seeded megahertz-repetition rate optical parametric chirped pulse amplifiers,” Opt. Lett. 39(6), 1422–1424 (2014).
[PubMed]

Y. Chu, Z. Gan, X. Liang, L. Yu, X. Lu, C. Wang, X. Wang, L. Xu, H. Lu, D. Yin, Y. Leng, R. Li, and Z. Xu, “High-energy large-aperture Ti:sapphire amplifier for 5 PW laser pulses,” Opt. Lett. 40(21), 5011–5014 (2015).
[PubMed]

J. H. Sung, H. W. Lee, J. Y. Yoo, J. W. Yoon, C. W. Lee, J. M. Yang, Y. J. Son, Y. H. Jang, S. K. Lee, and C. H. Nam, “4.2 PW, 20 fs Ti:sapphire laser at 0.1 Hz,” Opt. Lett. 42(11), 2058–2061 (2017).
[PubMed]

Y. Li, H. Zhong, J. Yang, S. Wang, and D. Fan, “Versatile backconversion-inhibited broadband optical parametric amplification based on an idler-separated QPM configuration,” Opt. Lett. 42(14), 2806–2809 (2017).
[PubMed]

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31(2), 274–276 (2006).
[PubMed]

A. L. Oien, I. T. McKinnie, P. Jain, N. A. Russell, D. M. Warrington, and L. A. W. Gloster, “Efficient, low-threshold collinear and noncollinear β-barium borate optical parametric oscillators,” Opt. Lett. 22(12), 859–861 (1997).
[PubMed]

Optica (2)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).

Phys. Rev. Lett. (1)

K. Schmid, L. Veisz, F. Tavella, S. Benavides, R. Tautz, D. Herrmann, A. Buck, B. Hidding, A. Marcinkevicius, U. Schramm, M. Geissler, J. Meyer-Ter-Vehn, D. Habs, and F. Krausz, “Few-cycle laser-driven electron acceleration,” Phys. Rev. Lett. 102(12), 124801 (2009).
[PubMed]

Proc. SPIE (1)

S. Seidel and G. Mann, “Numerical modeling of thermal effects in nonlinear crystal for high power second harmonic generation,” Proc. SPIE 2989, 204–214 (1997).

Science (1)

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, B. Shim, S. E. Schrauth, A. Gaeta, C. H. -García, L. Plaja, A. Becker, A. J. -Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[PubMed]

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Figures (10)

Fig. 1
Fig. 1

Schematic of three different amplification schemes. (a) CPA based on a nonparametric laser amplifier in which the medium participates in energy transfer. (b) OPCPA based on an optical parametric amplifier in which an idler pulse is generated and the nonlinear crystal doesn’t participate in energy transfer. (c) QPCPA based on a quasi-parametric amplifier in which an idler pulse is generated and then absorbed by the nonlinear crystal. The black solid (dashed) lines represent the real (virtual) energy levels.

Fig. 2
Fig. 2

Phase factor sinθ (red solid curves) and normalized signal efficiency η/ηmax (blue dashed curves) versus propagation distance z for various normalized wave-vector mismatch Δκ. Propagation distance z is normalized to the nonlinear length LNL which is defined by LNL = π/2Γ [22]. ηmax is the theoretical maximum efficiency. (a)–(c) correspond to the OPCPA cases (α = 0), and (d)–(f) correspond to the QPCPA cases (α = Γ). In (a) and (d), Δκ = 0.2. In (b) and (e), Δκ = 0.6. In (c) and (f), Δκ = 1.2. In each case, Γ = 1000 m−1, Ip0/Is0 = 106. Note that, the signal efficiency in (c) has been enlarged by 105 times for visibility.

Fig. 3
Fig. 3

Phase factor sinθ versus normalized propagation distance in QPCPA for (a) different idler absorption coefficients and (b) different nonlinear drives. In each case, Δκ = 0.6, Ip0/Is0 = 106. In (a), Γ is fixed at 1000 m−1. In (b), α is fixed at 500 m−1. Note that, although various Γ is used in (b), we adopt the same LNL as those used in panel (a) and Fig. 1.

Fig. 4
Fig. 4

Conversion efficiency as a function of normalized phase mismatch and the normalized propagation distance. (a) and (b) represent the OPCPA (α = 0) cases with Ip0/Is0 = 106 and 103, respectively. (c) and (d) represent the QPCPA (α = Γ) cases with Ip0/Is0 = 106 and 103 respectively. In each case, Γ is fixed at 1000 m−1, and the efficiency is normalized to the theoretically maximum efficiency.

Fig. 5
Fig. 5

(a) Normalized efficiency versus normalized phase mismatch Δκ at different crystal lengths for both QPCPA (α = Γ, red curves) and OPCPA (α = 0, blue curves). The normalized crystal length z/LNL has been marked near the corresponding curve. (b) Normalized efficiency versus Δκ at three crystal lengths that can support complete conversion for Δκ = 0 in OPCPA (α = 0). The plots for OPCPA and QPCPA in this figure are based on the results in Figs. 4(a) and 4(b), respectively. In each case, Γ = 1000 m−1 and Ip0/Is0 = 106.

Fig. 6
Fig. 6

Simulation results for a QPCPA system with a uniform idler absorption of α = 3 cm−1. (a) Temporal profiles of input pump (black curve), residual pump after amplification (blue curve), and amplified chirped-signal (red curve). (b) Evolution of pump-to-signal conversion efficiency within the crystal. The dashed line shows the theoretical efficiency limit. Inset shows the spectrum evolution within the crystal. (c) Input (black curve) and output (red curve) signal spectrum, and the nonlinear spectral phase imposed on the signal (blue solid curve). The blue dashed curve represents the residual nonlinear spectral phase after compensating TOD by 1.95 × 103 fs3. (d) Dechirped pulse without (black curve) and with (blue curve) TOD compensation. The Red curve represents the Fourier transform limited pulse (red curve).

Fig. 7
Fig. 7

Simulation results for a QPCPA system with a non-uniform idler absorption. (a) Gaussian absorption spectrum used in the simulation. (b) Evolution of pump-to-signal conversion efficiency within the crystal. Inset shows the spectrum evolution within the crystal. (c) Output signal spectra (black curve), and the nonlinear spectral phase imposed on the signal (blue curve). (d) Dechirped pulse (black curve) and the Fourier transform limited pulse (red curve). Other parameters used in calculations are same with those for Fig. 6.

Fig. 8
Fig. 8

Performances of QPCPA when the temperatures deviate from the reference temperature for perfect phase matching. (a) Efficiency evolutions within the crystal under a temperature increase of 100 K (black curve) and 200 K (red curve), respectively. (b) Output signal spectra (solid curve) and nonlinear spectral phases (dashed curve) under a temperature increase of 100 K (black curve) and 200 K (red curve), respectively. Other parameters used in calculations are same with those for Fig. 6.

Fig. 9
Fig. 9

Radial temperature change in the Sm:YCOB crystal. (a) Evolution of idler intensity within the crystal when the beam radius w is 0.4 cm (red curve), 0.5 cm (black curve), and 0.6 cm (blue curve), respectively. A, B, and C indicate three different crystal locations when w = 0.5 cm, corresponding to the idler intensity of 14, 7, and 1.4 GW/cm2, respectively. D and E indicate the peak idler intensities when w = 0.4 and 0.6 cm, respectively. (b) Radial temperature changes when QPCPA operates in a repetition rate of f = 100 Hz. The parameters used in the simulations are r0 = 0.6 cm, τ = 10 ps, α = 3 cm−1, κ = 2.0 W m−1 K−1. The pump energy is fixed at 400 mJ. Other parameters are same with those of Fig. 6.

Fig. 10
Fig. 10

The effect of idler-absorption profile on the conversion efficiency of QPCPA. (a) The practical absorption spectrum of Sm:YCOB crystal (black curve) and two Gaussian-profile absorption spectra (blue and red curves) adopted in the simulation. (b) Evolution of pump-to-signal conversion efficiency within the crystal for the three idler absorption profiles shown in (a). The horizontal dashed line in (b) represents the theoretical efficiency limit. The pump pulse at 515 nm has an intensity of 50 GW/cm2. The seed pulse at 820 nm has a bandwidth of 100 nm and an intensity of 50 MW/cm2.

Equations (14)

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

A p z = i ω p d eff n p c A s A i e iΔkz ,
A s z = i ω s d eff n s c A p A i * e iΔkz ,
A i z = i ω i d eff n i c A p A s * e iΔkz α 2 A i ,
g= Γ 2 + ( α 4 ) 2 ( Δk 2 ) 2 α 4 ,
g=Γ 1 ( Δκ ) 2 ,
d ρ p dz = ω p d eff n p c ρ s ρ i sinθ.
d ρ s dz = ω s d eff n s c ρ i ρ p sinθ,
d ρ i dz = ω i d eff n i c ρ s ρ p sinθ α 2 ρ i ,
n x 2 =2.80266+ 0.01559 λ 2 0.06278 0.00699 λ 2 ,
n y 2 =2.88130+ 0.02216 λ 2 0.02199 0.01037 λ 2 ,
n z 2 =2.91518+ 0.02413 λ 2 0.01151 0.01134 λ 2 ,
h 0 = τ π 2 ln2 I 0 αf,
ΔT( r )= h 0 4κ ( w 2 r 2 ) h 0 w 2 2κ ln( w r 0 ) r<w,
ΔT( r )= h 0 w 2 2κ ln( w r 0 ) rw,

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