Abstract

About 50 years ago, Sarachick and Schappert [Phys. Rev. D. 1, 2738-2752 (1970)] showed that relativistic Thomson scattering leads to wavelength shifts that are proportional to the laser intensity. About 28 years later, Chen et al. [Nature 396, 653-655 (1998)] used these shifts to estimate their laser intensity near $10^{18}$ W/cm$^2$. More recently, there have been several theoretical studies aimed at exploiting nonlinear Thomson scattering as a tool for direct measurement of intensities well into the relativistic regime. We present the first quantitative study of this approach for intensities between $10^{18}$ and $10^{19}$ W/cm$^2$. We show that the spectral shifts are in reasonable agreement with estimates of the peak intensity extracted from images of the focal area obtained at reduced power. Finally, we discuss the viability of the approach, its range of usefulness and how it might be extended to gauge intensities well in excess of $10^{19}$ W/cm$^2$.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

A. Blinne, H. Gies, F. Karbstein, C. Kohlfürst, and M. Zepf, “All-optical signatures of quantum vacuum nonlinearities in generic laser fields,” Phys. Rev. D 99(1), 016006 (2019).
[Crossref]

M. F. Ciappina, S. V. Popruzhenko, S. V. Bulanov, T. Ditmire, G. Korn, and S. Weber, “Progress toward atomic diagnostics of ultrahigh laser intensities,” Phys. Rev. A 99(4), 043405 (2019).
[Crossref]

2018 (1)

C. N. Harvey, “In situ characterization of ultraintense laser pulses,” Phys. Rev. Accel. Beams 21(11), 114001 (2018).
[Crossref]

2017 (3)

W. Yan, C. Fruhling, G. Golovin, D. Haden, J. Luo, P. Zhang, B. Zhao, J. Zhang, C. Liu, M. Chen, S. Chen, S. Banerjee, and D. Umstadter, “High-order multiphoton Thomson scattering,” Nat. Photonics 11(8), 514–520 (2017).
[Crossref]

S. Feldman, G. Dyer, D. Kuk, and T. Ditmire, “Measurement of the equation of state of solid-density copper heated with laser-accelerated protons,” Phys. Rev. E 95(3), 031201(R) (2017).
[Crossref]

W. T. Hill III and L Roso, “Probing the quantum vacuum with petawatt lasers,” J. Phys.: Conf. Ser. 869, 012015 (2017).
[Crossref]

2015 (3)

G. Tarbox, E. Cunningham, R. Sandberg, J. Peatross, and M. Ware, “Radiation from free electrons in a laser focus at 10$^{18}$18 w/cm$^2$2: modeling of photon yields and required focal conditions,” J. Opt. Soc. Am. B 32(5), 743–750 (2015).
[Crossref]

T.-C. Liu, X. Shao, C.-S. Liu, B. Eliasson, W. T. Hill, I. I. I J. Wang, and S.-H. Chen, “Laser acceleration of protons using multi-ion plasma gaseous targets,” New J. Phys. 17(2), 023018 (2015).
[Crossref]

F. Tommasino and M. Durante, “Proton Radiobiology,” Cancers 7(1), 353–381 (2015).
[Crossref]

2013 (1)

M. Roth, D. Jung, K. Falk, N. Guler, O. Deppert, M. Devlin, A. Favalli, J. Fernandez, D. Gautier, M. Geissel, R. Haight, C. E. Hamiltonand, B. M. Hegelich, R. P. Johnson, F. Merrill, G. Schaumann, K. Schoenberg, M. Schollmeier, T. Shimada, T. Taddeucci, J. L. Tybo, F. Wagner, S. A. Wender, C. H. Wilde, and G. A. Wurden, “Bright Laser-Driven Neutron Source Based on the Relativistic Transparency of Solids,” Phys. Rev. Lett. 110(4), 044802 (2013).
[Crossref]

2012 (3)

Y. Liang and A. Czarnecki, “Photon–photon scattering: a tutorial,” Can. J. Phys. 90(1), 11–16 (2012).
[Crossref]

O. Har-Shemesh and A. Piazza, “Peak intensity measurement of relativistic lasers via nonlinear Thomson scattering,” Opt. Lett. 37(8), 1352–1354 (2012).
[Crossref]

A. Paredes, D. Novoa, and D. Tommasini, “Measuring extreme vacuum pressure with ultraintense lasers,” Phys. Rev. Lett. 109(25), 253903 (2012).
[Crossref]

2009 (3)

D. Tommasini, A. Ferrando, H. Michinel, and M. Seco, “Precision tests of QED and non-standard models by searching photon-photon scattering in vacuum with high power lasers,” J. High Energy Phys. 2009(11), 043 (2009).
[Crossref]

G. V. Dunne, “New strong-field QED effects at extreme light infrastructure,” Eur. Phys. J. D 55(2), 327–340 (2009).
[Crossref]

M. Roth, I. Alber, V. Bagnoud, C. R. D. Brown, R. Clarke, H. Daido, J. Fernandez, K. Flippo, S. Gaillard, C. Gauthier, M. Geissel, S. Glenzer, G. Gregori, M. Günther, K. Harres, R. Heathcote, A. Kritcher, N. Kugland, S. LePape, B. Li, M. Makita, J. Mithen, C. Niemann, F. Nürnberg, D. Offermann, A. Otten, A. Pelka, D. Riley, G. Schaumann, M. Schollmeier, J. Schütrumpf, M. Tampo, A. Tauschwitz, and A. Tauschwitz, “Proton acceleration experiments and warm dense matter research using high power lasers,” Plasma Phys. Controlled Fusion 51(12), 124039 (2009).
[Crossref]

2008 (1)

G. M. Dyer, A. C. Bernstein, B. I. Cho, J. Osterholz, W. Grigsby, A. Dalton, R. Shepherd, Y. Ping, H. Chen, K. Widmann, and T. Ditmire, “Equation of State Measurement of Dense Plasmas Heated with Fast Protons,” Phys. Rev. Lett. 101(1), 015002 (2008).
[Crossref]

2007 (1)

K. W. D. Ledingham, W. Galster, and R. Sauerbrey, “Laser-driven proton oncology – a unique new cancer therapy?” Br. J. Radiol. 80(959), 855–858 (2007).
[Crossref]

2006 (3)

E. Lefebvre, “Numerical simulation of isotope production for positron emission tomography with laser-accelerated ions,” J. Appl. Phys. 100(11), 113308 (2006).
[Crossref]

T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, “On the observation of vacuum birefringence,” Opt. Commun. 267(2), 318–321 (2006).
[Crossref]

J. Gao, “Laser intensity measurement by Thomson scattering,” Appl. Phys. Lett. 88(9), 091105 (2006).
[Crossref]

2005 (1)

B. Jones, “Radiotherapy for the future: Protons and ions hold much promise,” BMJ 330(7498), 979–980 (2005).
[Crossref]

2004 (1)

J. Gao, “Thomson Scattering from Ultrashort and Ultraintense Laser Pulses,” Phys. Rev. Lett. 93(24), 243001 (2004).
[Crossref]

2002 (2)

X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66(3), 033402 (2002).
[Crossref]

M. Roth, A. Blazevic, M. Geissel, T. Schlegel, T. E. Cowan, M. Allen, J.-C. Gauthier, P. Audebert, J. Fuchs, J. Meyer-ter-Vehn, M. Hegelich, S. Karsch, and A. Pukhov, “Energetic ions generated by laser pulses: A detailed study on target properties,” Phys. Rev. Spec. Top.--Accel. Beams 5(6), 061301 (2002).
[Crossref]

1998 (1)

S. Chen, A. Maksimchuk, and D. Umstadter, “Experimental observation of relativistic nonlinear Thomson scattering,” Nature 396(6712), 653–655 (1998).
[Crossref]

1995 (1)

T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52(4), R2511–R2514 (1995).
[Crossref]

1993 (1)

C. I. Castillo-Herrera and T. W. Johnston, “Incoherent harmonic emission from strong electromagnetic waves in plasmas,” IEEE Trans. Plasma Sci. 21(1), 125–135 (1993).
[Crossref]

1986 (1)

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” J. Exp. Theor. Phys. 64, 1191–1194 (1986).

1970 (1)

E. S. Sarachick and G. T. Schappert, “Classical Theory of the Scattering of Intense Laser Radiation by Free Electrons,” Phys. Rev. D 1(10), 2738–2753 (1970).
[Crossref]

1936 (1)

H. Euler, “Über die Streuung von Licht an Licht nach der Diracschen Theorie (On the Scattering of Light by Light in Dirac’s Theory),” Ann. Phys. 418(5), 398–448 (1936).
[Crossref]

1935 (1)

H. Euler and B. Kockel, “Über die Streuung von Licht an Licht nach der Diracschen Theorie (The Scattering of Light by Light in the Dirac Theory),” Naturwissenschaften (1913-2014) 23(15), 246–247 (1935).
[Crossref]

1933 (1)

O. Halpern, “Scattering Processes Produced by Electrons in Negative Energy States,” Phys. Rev. 44(10), 855–856 (1933).
[Crossref]

Alber, I.

M. Roth, I. Alber, V. Bagnoud, C. R. D. Brown, R. Clarke, H. Daido, J. Fernandez, K. Flippo, S. Gaillard, C. Gauthier, M. Geissel, S. Glenzer, G. Gregori, M. Günther, K. Harres, R. Heathcote, A. Kritcher, N. Kugland, S. LePape, B. Li, M. Makita, J. Mithen, C. Niemann, F. Nürnberg, D. Offermann, A. Otten, A. Pelka, D. Riley, G. Schaumann, M. Schollmeier, J. Schütrumpf, M. Tampo, A. Tauschwitz, and A. Tauschwitz, “Proton acceleration experiments and warm dense matter research using high power lasers,” Plasma Phys. Controlled Fusion 51(12), 124039 (2009).
[Crossref]

Allen, M.

M. Roth, A. Blazevic, M. Geissel, T. Schlegel, T. E. Cowan, M. Allen, J.-C. Gauthier, P. Audebert, J. Fuchs, J. Meyer-ter-Vehn, M. Hegelich, S. Karsch, and A. Pukhov, “Energetic ions generated by laser pulses: A detailed study on target properties,” Phys. Rev. Spec. Top.--Accel. Beams 5(6), 061301 (2002).
[Crossref]

Ammosov, M.

M. Ammosov, N. Delone, and V. Krainov, “Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field,” J. Exp. Theor. Phys. 64, 1191–1194 (1986).

Amthor, K.-U.

T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, “On the observation of vacuum birefringence,” Opt. Commun. 267(2), 318–321 (2006).
[Crossref]

Audebert, P.

M. Roth, A. Blazevic, M. Geissel, T. Schlegel, T. E. Cowan, M. Allen, J.-C. Gauthier, P. Audebert, J. Fuchs, J. Meyer-ter-Vehn, M. Hegelich, S. Karsch, and A. Pukhov, “Energetic ions generated by laser pulses: A detailed study on target properties,” Phys. Rev. Spec. Top.--Accel. Beams 5(6), 061301 (2002).
[Crossref]

Bagnoud, V.

M. Roth, I. Alber, V. Bagnoud, C. R. D. Brown, R. Clarke, H. Daido, J. Fernandez, K. Flippo, S. Gaillard, C. Gauthier, M. Geissel, S. Glenzer, G. Gregori, M. Günther, K. Harres, R. Heathcote, A. Kritcher, N. Kugland, S. LePape, B. Li, M. Makita, J. Mithen, C. Niemann, F. Nürnberg, D. Offermann, A. Otten, A. Pelka, D. Riley, G. Schaumann, M. Schollmeier, J. Schütrumpf, M. Tampo, A. Tauschwitz, and A. Tauschwitz, “Proton acceleration experiments and warm dense matter research using high power lasers,” Plasma Phys. Controlled Fusion 51(12), 124039 (2009).
[Crossref]

Bandrauk, A. D.

T. Zuo and A. D. Bandrauk, “Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers,” Phys. Rev. A 52(4), R2511–R2514 (1995).
[Crossref]

Banerjee, S.

W. Yan, C. Fruhling, G. Golovin, D. Haden, J. Luo, P. Zhang, B. Zhao, J. Zhang, C. Liu, M. Chen, S. Chen, S. Banerjee, and D. Umstadter, “High-order multiphoton Thomson scattering,” Nat. Photonics 11(8), 514–520 (2017).
[Crossref]

Bernstein, A. C.

G. M. Dyer, A. C. Bernstein, B. I. Cho, J. Osterholz, W. Grigsby, A. Dalton, R. Shepherd, Y. Ping, H. Chen, K. Widmann, and T. Ditmire, “Equation of State Measurement of Dense Plasmas Heated with Fast Protons,” Phys. Rev. Lett. 101(1), 015002 (2008).
[Crossref]

Blazevic, A.

M. Roth, A. Blazevic, M. Geissel, T. Schlegel, T. E. Cowan, M. Allen, J.-C. Gauthier, P. Audebert, J. Fuchs, J. Meyer-ter-Vehn, M. Hegelich, S. Karsch, and A. Pukhov, “Energetic ions generated by laser pulses: A detailed study on target properties,” Phys. Rev. Spec. Top.--Accel. Beams 5(6), 061301 (2002).
[Crossref]

Blinne, A.

A. Blinne, H. Gies, F. Karbstein, C. Kohlfürst, and M. Zepf, “All-optical signatures of quantum vacuum nonlinearities in generic laser fields,” Phys. Rev. D 99(1), 016006 (2019).
[Crossref]

Brown, C. R. D.

M. Roth, I. Alber, V. Bagnoud, C. R. D. Brown, R. Clarke, H. Daido, J. Fernandez, K. Flippo, S. Gaillard, C. Gauthier, M. Geissel, S. Glenzer, G. Gregori, M. Günther, K. Harres, R. Heathcote, A. Kritcher, N. Kugland, S. LePape, B. Li, M. Makita, J. Mithen, C. Niemann, F. Nürnberg, D. Offermann, A. Otten, A. Pelka, D. Riley, G. Schaumann, M. Schollmeier, J. Schütrumpf, M. Tampo, A. Tauschwitz, and A. Tauschwitz, “Proton acceleration experiments and warm dense matter research using high power lasers,” Plasma Phys. Controlled Fusion 51(12), 124039 (2009).
[Crossref]

Bulanov, S. V.

M. F. Ciappina, S. V. Popruzhenko, S. V. Bulanov, T. Ditmire, G. Korn, and S. Weber, “Progress toward atomic diagnostics of ultrahigh laser intensities,” Phys. Rev. A 99(4), 043405 (2019).
[Crossref]

Castillo-Herrera, C. I.

C. I. Castillo-Herrera and T. W. Johnston, “Incoherent harmonic emission from strong electromagnetic waves in plasmas,” IEEE Trans. Plasma Sci. 21(1), 125–135 (1993).
[Crossref]

Chen, H.

G. M. Dyer, A. C. Bernstein, B. I. Cho, J. Osterholz, W. Grigsby, A. Dalton, R. Shepherd, Y. Ping, H. Chen, K. Widmann, and T. Ditmire, “Equation of State Measurement of Dense Plasmas Heated with Fast Protons,” Phys. Rev. Lett. 101(1), 015002 (2008).
[Crossref]

Chen, M.

W. Yan, C. Fruhling, G. Golovin, D. Haden, J. Luo, P. Zhang, B. Zhao, J. Zhang, C. Liu, M. Chen, S. Chen, S. Banerjee, and D. Umstadter, “High-order multiphoton Thomson scattering,” Nat. Photonics 11(8), 514–520 (2017).
[Crossref]

Chen, S.

W. Yan, C. Fruhling, G. Golovin, D. Haden, J. Luo, P. Zhang, B. Zhao, J. Zhang, C. Liu, M. Chen, S. Chen, S. Banerjee, and D. Umstadter, “High-order multiphoton Thomson scattering,” Nat. Photonics 11(8), 514–520 (2017).
[Crossref]

S. Chen, A. Maksimchuk, and D. Umstadter, “Experimental observation of relativistic nonlinear Thomson scattering,” Nature 396(6712), 653–655 (1998).
[Crossref]

Chen, S.-H.

T.-C. Liu, X. Shao, C.-S. Liu, B. Eliasson, W. T. Hill, I. I. I J. Wang, and S.-H. Chen, “Laser acceleration of protons using multi-ion plasma gaseous targets,” New J. Phys. 17(2), 023018 (2015).
[Crossref]

Cho, B. I.

G. M. Dyer, A. C. Bernstein, B. I. Cho, J. Osterholz, W. Grigsby, A. Dalton, R. Shepherd, Y. Ping, H. Chen, K. Widmann, and T. Ditmire, “Equation of State Measurement of Dense Plasmas Heated with Fast Protons,” Phys. Rev. Lett. 101(1), 015002 (2008).
[Crossref]

Ciappina, M. F.

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M. Roth, I. Alber, V. Bagnoud, C. R. D. Brown, R. Clarke, H. Daido, J. Fernandez, K. Flippo, S. Gaillard, C. Gauthier, M. Geissel, S. Glenzer, G. Gregori, M. Günther, K. Harres, R. Heathcote, A. Kritcher, N. Kugland, S. LePape, B. Li, M. Makita, J. Mithen, C. Niemann, F. Nürnberg, D. Offermann, A. Otten, A. Pelka, D. Riley, G. Schaumann, M. Schollmeier, J. Schütrumpf, M. Tampo, A. Tauschwitz, and A. Tauschwitz, “Proton acceleration experiments and warm dense matter research using high power lasers,” Plasma Phys. Controlled Fusion 51(12), 124039 (2009).
[Crossref]

Schwoerer, H.

T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, “On the observation of vacuum birefringence,” Opt. Commun. 267(2), 318–321 (2006).
[Crossref]

Seco, M.

D. Tommasini, A. Ferrando, H. Michinel, and M. Seco, “Precision tests of QED and non-standard models by searching photon-photon scattering in vacuum with high power lasers,” J. High Energy Phys. 2009(11), 043 (2009).
[Crossref]

Shao, X.

T.-C. Liu, X. Shao, C.-S. Liu, B. Eliasson, W. T. Hill, I. I. I J. Wang, and S.-H. Chen, “Laser acceleration of protons using multi-ion plasma gaseous targets,” New J. Phys. 17(2), 023018 (2015).
[Crossref]

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G. M. Dyer, A. C. Bernstein, B. I. Cho, J. Osterholz, W. Grigsby, A. Dalton, R. Shepherd, Y. Ping, H. Chen, K. Widmann, and T. Ditmire, “Equation of State Measurement of Dense Plasmas Heated with Fast Protons,” Phys. Rev. Lett. 101(1), 015002 (2008).
[Crossref]

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M. Roth, D. Jung, K. Falk, N. Guler, O. Deppert, M. Devlin, A. Favalli, J. Fernandez, D. Gautier, M. Geissel, R. Haight, C. E. Hamiltonand, B. M. Hegelich, R. P. Johnson, F. Merrill, G. Schaumann, K. Schoenberg, M. Schollmeier, T. Shimada, T. Taddeucci, J. L. Tybo, F. Wagner, S. A. Wender, C. H. Wilde, and G. A. Wurden, “Bright Laser-Driven Neutron Source Based on the Relativistic Transparency of Solids,” Phys. Rev. Lett. 110(4), 044802 (2013).
[Crossref]

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M. Roth, D. Jung, K. Falk, N. Guler, O. Deppert, M. Devlin, A. Favalli, J. Fernandez, D. Gautier, M. Geissel, R. Haight, C. E. Hamiltonand, B. M. Hegelich, R. P. Johnson, F. Merrill, G. Schaumann, K. Schoenberg, M. Schollmeier, T. Shimada, T. Taddeucci, J. L. Tybo, F. Wagner, S. A. Wender, C. H. Wilde, and G. A. Wurden, “Bright Laser-Driven Neutron Source Based on the Relativistic Transparency of Solids,” Phys. Rev. Lett. 110(4), 044802 (2013).
[Crossref]

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M. Roth, I. Alber, V. Bagnoud, C. R. D. Brown, R. Clarke, H. Daido, J. Fernandez, K. Flippo, S. Gaillard, C. Gauthier, M. Geissel, S. Glenzer, G. Gregori, M. Günther, K. Harres, R. Heathcote, A. Kritcher, N. Kugland, S. LePape, B. Li, M. Makita, J. Mithen, C. Niemann, F. Nürnberg, D. Offermann, A. Otten, A. Pelka, D. Riley, G. Schaumann, M. Schollmeier, J. Schütrumpf, M. Tampo, A. Tauschwitz, and A. Tauschwitz, “Proton acceleration experiments and warm dense matter research using high power lasers,” Plasma Phys. Controlled Fusion 51(12), 124039 (2009).
[Crossref]

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Tauschwitz, A.

M. Roth, I. Alber, V. Bagnoud, C. R. D. Brown, R. Clarke, H. Daido, J. Fernandez, K. Flippo, S. Gaillard, C. Gauthier, M. Geissel, S. Glenzer, G. Gregori, M. Günther, K. Harres, R. Heathcote, A. Kritcher, N. Kugland, S. LePape, B. Li, M. Makita, J. Mithen, C. Niemann, F. Nürnberg, D. Offermann, A. Otten, A. Pelka, D. Riley, G. Schaumann, M. Schollmeier, J. Schütrumpf, M. Tampo, A. Tauschwitz, and A. Tauschwitz, “Proton acceleration experiments and warm dense matter research using high power lasers,” Plasma Phys. Controlled Fusion 51(12), 124039 (2009).
[Crossref]

M. Roth, I. Alber, V. Bagnoud, C. R. D. Brown, R. Clarke, H. Daido, J. Fernandez, K. Flippo, S. Gaillard, C. Gauthier, M. Geissel, S. Glenzer, G. Gregori, M. Günther, K. Harres, R. Heathcote, A. Kritcher, N. Kugland, S. LePape, B. Li, M. Makita, J. Mithen, C. Niemann, F. Nürnberg, D. Offermann, A. Otten, A. Pelka, D. Riley, G. Schaumann, M. Schollmeier, J. Schütrumpf, M. Tampo, A. Tauschwitz, and A. Tauschwitz, “Proton acceleration experiments and warm dense matter research using high power lasers,” Plasma Phys. Controlled Fusion 51(12), 124039 (2009).
[Crossref]

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A. Paredes, D. Novoa, and D. Tommasini, “Measuring extreme vacuum pressure with ultraintense lasers,” Phys. Rev. Lett. 109(25), 253903 (2012).
[Crossref]

D. Tommasini, A. Ferrando, H. Michinel, and M. Seco, “Precision tests of QED and non-standard models by searching photon-photon scattering in vacuum with high power lasers,” J. High Energy Phys. 2009(11), 043 (2009).
[Crossref]

D. Tommasini, D. Novoa, and L. Roso, “Quantum vacuum polarization searches with high power lasers below the pair production regime,” in Progress in Ultrafast Intense Laser Science X, vol. 106 of Springer Series in Chemical Physics K. Yamanouchi, G. Paulus, and D. Mathur, eds. (Springer Science, 2014), pp. 137–153.

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F. Tommasino and M. Durante, “Proton Radiobiology,” Cancers 7(1), 353–381 (2015).
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X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66(3), 033402 (2002).
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M. Roth, D. Jung, K. Falk, N. Guler, O. Deppert, M. Devlin, A. Favalli, J. Fernandez, D. Gautier, M. Geissel, R. Haight, C. E. Hamiltonand, B. M. Hegelich, R. P. Johnson, F. Merrill, G. Schaumann, K. Schoenberg, M. Schollmeier, T. Shimada, T. Taddeucci, J. L. Tybo, F. Wagner, S. A. Wender, C. H. Wilde, and G. A. Wurden, “Bright Laser-Driven Neutron Source Based on the Relativistic Transparency of Solids,” Phys. Rev. Lett. 110(4), 044802 (2013).
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G. M. Dyer, A. C. Bernstein, B. I. Cho, J. Osterholz, W. Grigsby, A. Dalton, R. Shepherd, Y. Ping, H. Chen, K. Widmann, and T. Ditmire, “Equation of State Measurement of Dense Plasmas Heated with Fast Protons,” Phys. Rev. Lett. 101(1), 015002 (2008).
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M. Roth, D. Jung, K. Falk, N. Guler, O. Deppert, M. Devlin, A. Favalli, J. Fernandez, D. Gautier, M. Geissel, R. Haight, C. E. Hamiltonand, B. M. Hegelich, R. P. Johnson, F. Merrill, G. Schaumann, K. Schoenberg, M. Schollmeier, T. Shimada, T. Taddeucci, J. L. Tybo, F. Wagner, S. A. Wender, C. H. Wilde, and G. A. Wurden, “Bright Laser-Driven Neutron Source Based on the Relativistic Transparency of Solids,” Phys. Rev. Lett. 110(4), 044802 (2013).
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T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, “On the observation of vacuum birefringence,” Opt. Commun. 267(2), 318–321 (2006).
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M. Roth, D. Jung, K. Falk, N. Guler, O. Deppert, M. Devlin, A. Favalli, J. Fernandez, D. Gautier, M. Geissel, R. Haight, C. E. Hamiltonand, B. M. Hegelich, R. P. Johnson, F. Merrill, G. Schaumann, K. Schoenberg, M. Schollmeier, T. Shimada, T. Taddeucci, J. L. Tybo, F. Wagner, S. A. Wender, C. H. Wilde, and G. A. Wurden, “Bright Laser-Driven Neutron Source Based on the Relativistic Transparency of Solids,” Phys. Rev. Lett. 110(4), 044802 (2013).
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W. Yan, C. Fruhling, G. Golovin, D. Haden, J. Luo, P. Zhang, B. Zhao, J. Zhang, C. Liu, M. Chen, S. Chen, S. Banerjee, and D. Umstadter, “High-order multiphoton Thomson scattering,” Nat. Photonics 11(8), 514–520 (2017).
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X. M. Tong, Z. X. Zhao, and C. D. Lin, “Theory of molecular tunneling ionization,” Phys. Rev. A 66(3), 033402 (2002).
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W. Yan, C. Fruhling, G. Golovin, D. Haden, J. Luo, P. Zhang, B. Zhao, J. Zhang, C. Liu, M. Chen, S. Chen, S. Banerjee, and D. Umstadter, “High-order multiphoton Thomson scattering,” Nat. Photonics 11(8), 514–520 (2017).
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H. Euler and B. Kockel, “Über die Streuung von Licht an Licht nach der Diracschen Theorie (The Scattering of Light by Light in the Dirac Theory),” Naturwissenschaften (1913-2014) 23(15), 246–247 (1935).
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T. Heinzl, B. Liesfeld, K.-U. Amthor, H. Schwoerer, R. Sauerbrey, and A. Wipf, “On the observation of vacuum birefringence,” Opt. Commun. 267(2), 318–321 (2006).
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G. M. Dyer, A. C. Bernstein, B. I. Cho, J. Osterholz, W. Grigsby, A. Dalton, R. Shepherd, Y. Ping, H. Chen, K. Widmann, and T. Ditmire, “Equation of State Measurement of Dense Plasmas Heated with Fast Protons,” Phys. Rev. Lett. 101(1), 015002 (2008).
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Other (5)

D. Tommasini, D. Novoa, and L. Roso, “Quantum vacuum polarization searches with high power lasers below the pair production regime,” in Progress in Ultrafast Intense Laser Science X, vol. 106 of Springer Series in Chemical Physics K. Yamanouchi, G. Paulus, and D. Mathur, eds. (Springer Science, 2014), pp. 137–153.

National Academies of Sciences, Engineering, and Medicine, Opportunities in Intense Ultrafast Lasers: Reaching for the Brightest Light (The National Academies Press, Washington, DC, 2018).

FASTLITE, “Wizzler,” http://www.fastlite.com/en/ar824651-823532-Wizzler.html , (2019).

Schott, “BG39 Data Sheet,” https://www.sydor.com/wp-content/uploads/SCHOTT-BG39-Bandpass-Filter.pdf , (2019).

Centro de Láseres Pulsados (CLPU), https://www.clpu.es/en , (2019).

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Figures (3)

Fig. 1.
Fig. 1. (a) Cross sectional image of the focal volume and an expanded view of the central Airy disk and portions of three secondary rings. The solid (dashed) white circle indicates the extent of the pulse (central Airy disk). The signal in each image was smoothed and filtered to remove hot spots and reduce the noise, and clipped at the background count $\sim 12$. (b) Schematic of the focal region showing the orientation of both microscope objectives ($E_{\perp }$-obj and $E_{\parallel }$-obj), gas nozzle, $\vec {E}$ and $\vec {k}$ vectors. Note, the $\hat {x}$ and $\hat {y}$ axes correspond to ($\theta , \phi$) = ($\pi /2, 0$) and ($\pi /2, \pi /2$) respectively, with $\theta$ and $\phi$ being the polar and azimuthal angles respectively.
Fig. 2.
Fig. 2. Composite images (500 shots each) obtained with $E_{\perp }$-obj (a) and $E_{\parallel }$-obj (b), for $U = 2.67$ J, which includes both RTS and recombination radiation, where $L$, $h$ and $b$ are the FWHM length $\parallel$ to $\vec {k}$, multi-shot width $\perp$ to $\vec {k}$ and single-shot width $\perp$ to $\vec {k}$ (see text) respectively with values $L= 526/85\ \mu$m, $h= 66/41\ \mu$m and $b=15\ \mu$m$/$N.A. for image (a)/image (b) respectively. Composite images of the dispersed light and associated integrated profiles (c) for the prompt signal (A), obtained within a 5 ns temporal window that starts $\sim 2.5$ ns before the laser pulse, and the delayed signal (B), obtained within a 50 ns temporal window starting $\sim 2.5$ ns after the laser pulse.
Fig. 3.
Fig. 3. (a) Respectively from the top, RTS-spectral profiles (solid curves) captured by $E_{\parallel }$-obj for three values of $U$ ($2.67 \pm 0.08,\ 1.73 \pm 0.05,\ \mathrm {and}\ 0.99 \pm 0.03$ J) and the plasma recombination lines (solid curve) along with the BG39 filter transmission (dashed red curve). The red arrows in the insets indicate $\lambda ^{(2)}_{\mathrm {r}}$ as determined when the spectrum first reaches $\mathrm {Sig_{bk}}$ while the dot-dash line indicates $\lambda ^{(2)}_{\mathrm {r}}$ from the numerical fit to the shaded regions (see text). (b) Comparison between $I_{\mathrm {pk}}^{\mathrm {RTS}}$ for the $U$ values (black solid circles) and $I_{\mathrm {pk}}^{\mathrm {Im}}$ for $\Delta t = 30$ fs (blue solid line) and 60 fs (red dashed line). The shaded areas are the uncertainties in $I_{\mathrm {pk}}^{\mathrm {Im}}$ ($\sim$16.1%); the dot-dashed lines are the uncertainties in $I_{\mathrm {pk}}^{\mathrm {Im}}$ if $A_{\mathrm {pix}}$ were known exactly ($\sim$3.6%, see text). The open green triangle $I_{\mathrm {pk}}^{\mathrm {RTS}}$ point was taken at $U=2.67$ J but after the low energy points (see text).

Equations (9)

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I ( λ ( n ) , θ ; n ) = 2 π m e c 3 r 0 λ 0 2 ( 1 cos θ ) ( n λ ( n ) λ 0 1 ) ,
a 0 = e E λ 0 / 2 π m e c 2 0.855 I [ × 10 18   W / c m 2 ] λ 0 [ μ m ] ,
I p k I m = U C p k T e f f C s u m A p i x ,
I ( t , x , y ) = I 0 g ( t ) f ( x , y ) ,
U I ( t , x , y ) d t d x d y = I 0 g ( t ) d t f ( x , y ) d x d y .
T e f f = g ( t ) d t ,
f ( x , y ) d x d y i , j f ( x i , y j ) Δ x Δ y ,
i , j f ( x i , y i ) = C s u m C p k ,
U = I 0 T e f f C s u m C p k A p i x .

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