Abstract

Tight focusing of radially- or azimuthally-polarized electromagnetic waves becomes attractive because of the strong field generation in the longitudinal direction. In this paper, we investigate the strength of longitudinal electric field when a radially-polarized femtosecond PW laser pulse is tightly focused by a parabolic surface. From the calculation using the vector diffraction approach, it has been shown that the highest strength of 2.2 × 1013 V/cm can be reached for the longitudinal field with a radially-polarized 11.2-fs, 11.2-J uniform-beam-profile laser pulse. The difference in the strength of longitudinal field with different beam profile and the spectrum of a laser pulse has been also carefully examined. The propagation of a laser spot has been simulated under an extremely-tight-focusing condition (0.25 in terms of f-number) and an achievable field strength for a standing longitudinal field has been examined by colliding two radially-polarized fs PW-level laser pulses.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

L. Labate, G. Vantaggiato, and L. A. Gizzi, “Intra-cycle depolarization of ultraintense laser pulses focused by off-axis parabolic mirrors,” High Power Laser Sci. 6, e32 (2018).
[Crossref]

2017 (2)

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).
[Crossref] [PubMed]

S. V. Bulanov, T. Zh. Esirkepov, J. K. Koga, S. S. Bulanov, Z. Gong, X. Q. Yan, and M. Kando, “Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns,” J. Plasma Phys. 83(2), 905830202 (2017).
[Crossref]

2016 (1)

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

2015 (3)

2014 (1)

T. M. Jeong and J. Lee, “Femtosecond petawatt laser,” Ann. Phys. (Berlin) 526(3–4), 157–174 (2014).
[Crossref]

2013 (1)

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

2011 (1)

J.-H. Yang, R. S. Craxton, and M. G. Haines, “Explicit general solutions to relativistic electron dynamics in plane-wave electromagnetic fields and simulations of ponderomotive acceleration,” Plasma Phys. Contr. Fusion 53(12), 125006 (2011).
[Crossref]

2010 (1)

2008 (1)

2004 (2)

2002 (1)

Y. I. Salamin and C. H. Keitel, “Electron acceleration by a tightly focused laser beam,” Phys. Rev. Lett. 88(9), 095005 (2002).
[Crossref] [PubMed]

2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

2000 (3)

A. V. Nestrov and V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33(15), 1817–1822 (2000).
[Crossref]

P. Varga and P. Török, “Focusing of electromagnetic waves by paraboloid mirrors. I. Theory,” J. Opt. Soc. Am. A 17(11), 2081–2089 (2000).
[Crossref] [PubMed]

N. B. Narozhny and M. S. Fofanov, “Scattering of relativistic electrons by a focused laser pulse,” J. Exp. Theor. Phys. 90(5), 753–768 (2000).
[Crossref]

1993 (1)

1991 (1)

M. O. Scully and M. S. Zubairy, “Simple laser accelerator: Optics and particle dynamics,” Phys. Rev. A 44(4), 2656–2663 (1991).
[Crossref] [PubMed]

1939 (1)

J. Stratton and L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56(1), 99–107 (1939).
[Crossref]

April, A.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Bahk, S.-W.

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Brabec, T.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Bricchi, E.

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Bulanov, S. S.

S. V. Bulanov, T. Zh. Esirkepov, J. K. Koga, S. S. Bulanov, Z. Gong, X. Q. Yan, and M. Kando, “Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns,” J. Plasma Phys. 83(2), 905830202 (2017).
[Crossref]

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

Bulanov, S. V.

S. V. Bulanov, T. Zh. Esirkepov, J. K. Koga, S. S. Bulanov, Z. Gong, X. Q. Yan, and M. Kando, “Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns,” J. Plasma Phys. 83(2), 905830202 (2017).
[Crossref]

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

Chen, B.

Chu, L.

J. Stratton and L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56(1), 99–107 (1939).
[Crossref]

Chu, Y.

Chvykov, V.

Craxton, R. S.

J.-H. Yang, R. S. Craxton, and M. G. Haines, “Explicit general solutions to relativistic electron dynamics in plane-wave electromagnetic fields and simulations of ponderomotive acceleration,” Plasma Phys. Contr. Fusion 53(12), 125006 (2011).
[Crossref]

Esirkepov, T. Zh.

S. V. Bulanov, T. Zh. Esirkepov, J. K. Koga, S. S. Bulanov, Z. Gong, X. Q. Yan, and M. Kando, “Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns,” J. Plasma Phys. 83(2), 905830202 (2017).
[Crossref]

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

Fofanov, M. S.

N. B. Narozhny and M. S. Fofanov, “Scattering of relativistic electrons by a focused laser pulse,” J. Exp. Theor. Phys. 90(5), 753–768 (2000).
[Crossref]

Fortin, P.-L.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Fourmaux, S.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Gan, Z.

Gelfer, E.

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

Gizzi, L. A.

L. Labate, G. Vantaggiato, and L. A. Gizzi, “Intra-cycle depolarization of ultraintense laser pulses focused by off-axis parabolic mirrors,” High Power Laser Sci. 6, e32 (2018).
[Crossref]

Gong, Z.

S. V. Bulanov, T. Zh. Esirkepov, J. K. Koga, S. S. Bulanov, Z. Gong, X. Q. Yan, and M. Kando, “Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns,” J. Plasma Phys. 83(2), 905830202 (2017).
[Crossref]

Haines, M. G.

J.-H. Yang, R. S. Craxton, and M. G. Haines, “Explicit general solutions to relativistic electron dynamics in plane-wave electromagnetic fields and simulations of ponderomotive acceleration,” Plasma Phys. Contr. Fusion 53(12), 125006 (2011).
[Crossref]

Jang, Y. H.

Jeong, T. M.

Jirka, M.

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

Kalintchenko, G.

Kando, M.

S. V. Bulanov, T. Zh. Esirkepov, J. K. Koga, S. S. Bulanov, Z. Gong, X. Q. Yan, and M. Kando, “Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns,” J. Plasma Phys. 83(2), 905830202 (2017).
[Crossref]

Kawakami, S.

Kawauchi, H.

Kazansky, P. G.

Keitel, C. H.

Y. I. Salamin and C. H. Keitel, “Electron acceleration by a tightly focused laser beam,” Phys. Rev. Lett. 88(9), 095005 (2002).
[Crossref] [PubMed]

Kieffer, J.-C.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Kim, G. H.

Kimura, W. D.

Klappauf, B. G.

Klimo, O.

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

Koga, J. K.

S. V. Bulanov, T. Zh. Esirkepov, J. K. Koga, S. S. Bulanov, Z. Gong, X. Q. Yan, and M. Kando, “Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns,” J. Plasma Phys. 83(2), 905830202 (2017).
[Crossref]

Korn, G.

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

T. M. Jeong, S. Weber, B. Le Garrec, D. Margarone, T. Mocek, and G. Korn, “Spatio-temporal modification of femtosecond focal spot under tight focusing condition,” Opt. Express 23(9), 11641–11656 (2015).
[Crossref] [PubMed]

Korotkova, O.

Kozawa, Y.

Labate, L.

L. Labate, G. Vantaggiato, and L. A. Gizzi, “Intra-cycle depolarization of ultraintense laser pulses focused by off-axis parabolic mirrors,” High Power Laser Sci. 6, e32 (2018).
[Crossref]

Le Garrec, B.

Lee, C. W.

Lee, H. W.

Lee, J.

T. M. Jeong and J. Lee, “Femtosecond petawatt laser,” Ann. Phys. (Berlin) 526(3–4), 157–174 (2014).
[Crossref]

Lee, S. K.

Legare, F.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Leng, Y.

Li, R.

Liang, X.

Lu, H.

Lu, X.

Maksimchuk, A.

Marceau, V.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Margarone, D.

Mocek, T.

Mourou, G. A.

Nam, C. H.

Narozhny, N. B.

N. B. Narozhny and M. S. Fofanov, “Scattering of relativistic electrons by a focused laser pulse,” J. Exp. Theor. Phys. 90(5), 753–768 (2000).
[Crossref]

Nestrov, A. V.

A. V. Nestrov and V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33(15), 1817–1822 (2000).
[Crossref]

Niziev, V. G.

A. V. Nestrov and V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33(15), 1817–1822 (2000).
[Crossref]

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Payeur, S.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Piche, M.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Planchon, T. A.

Pu, J.

Rousseau, P.

Salamin, Y. I.

Y. I. Salamin, “Fields and propagation characteristics in vacuum of an ultrashort tightly focused radially polarized laser pulse,” Phys. Rev. A 92(5), 053836 (2015).
[Crossref]

Y. I. Salamin and C. H. Keitel, “Electron acceleration by a tightly focused laser beam,” Phys. Rev. Lett. 88(9), 095005 (2002).
[Crossref] [PubMed]

Sato, S.

Sato, T.

Schmidt, B.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Scully, M. O.

M. O. Scully and M. S. Zubairy, “Simple laser accelerator: Optics and particle dynamics,” Phys. Rev. A 44(4), 2656–2663 (1991).
[Crossref] [PubMed]

Son, Y. J.

Stratton, J.

J. Stratton and L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56(1), 99–107 (1939).
[Crossref]

Sung, J. H.

Thire, N.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Tidwell, S. C.

Török, P.

Vantaggiato, G.

L. Labate, G. Vantaggiato, and L. A. Gizzi, “Intra-cycle depolarization of ultraintense laser pulses focused by off-axis parabolic mirrors,” High Power Laser Sci. 6, e32 (2018).
[Crossref]

Varga, P.

Varin, C.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

Wang, C.

Wang, X.

Weber, S.

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

T. M. Jeong, S. Weber, B. Le Garrec, D. Margarone, T. Mocek, and G. Korn, “Spatio-temporal modification of femtosecond focal spot under tight focusing condition,” Opt. Express 23(9), 11641–11656 (2015).
[Crossref] [PubMed]

Xu, L.

Xu, Z.

Yan, X. Q.

S. V. Bulanov, T. Zh. Esirkepov, J. K. Koga, S. S. Bulanov, Z. Gong, X. Q. Yan, and M. Kando, “Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns,” J. Plasma Phys. 83(2), 905830202 (2017).
[Crossref]

Yang, J. M.

Yang, J.-H.

J.-H. Yang, R. S. Craxton, and M. G. Haines, “Explicit general solutions to relativistic electron dynamics in plane-wave electromagnetic fields and simulations of ponderomotive acceleration,” Plasma Phys. Contr. Fusion 53(12), 125006 (2011).
[Crossref]

Yanovsky, V.

Yin, D.

Yoo, J. Y.

Yoon, J. W.

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Yu, L.

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, “Simple laser accelerator: Optics and particle dynamics,” Phys. Rev. A 44(4), 2656–2663 (1991).
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Ann. Phys. (Berlin) (1)

T. M. Jeong and J. Lee, “Femtosecond petawatt laser,” Ann. Phys. (Berlin) 526(3–4), 157–174 (2014).
[Crossref]

Appl. Opt. (1)

Appl. Sci. (Basel) (1)

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P.-L. Fortin, N. Thire, T. Brabec, F. Legare, J.-C. Kieffer, and M. Piche, “Direct electron acceleration with radially polarized laser beams,” Appl. Sci. (Basel) 3(1), 70–93 (2013).
[Crossref]

High Power Laser Sci. (1)

L. Labate, G. Vantaggiato, and L. A. Gizzi, “Intra-cycle depolarization of ultraintense laser pulses focused by off-axis parabolic mirrors,” High Power Laser Sci. 6, e32 (2018).
[Crossref]

J. Exp. Theor. Phys. (1)

N. B. Narozhny and M. S. Fofanov, “Scattering of relativistic electrons by a focused laser pulse,” J. Exp. Theor. Phys. 90(5), 753–768 (2000).
[Crossref]

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

J. Phys. D (1)

A. V. Nestrov and V. G. Niziev, “Laser beams with axially symmetric polarization,” J. Phys. D 33(15), 1817–1822 (2000).
[Crossref]

J. Plasma Phys. (1)

S. V. Bulanov, T. Zh. Esirkepov, J. K. Koga, S. S. Bulanov, Z. Gong, X. Q. Yan, and M. Kando, “Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns,” J. Plasma Phys. 83(2), 905830202 (2017).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. (1)

J. Stratton and L. Chu, “Diffraction theory of electromagnetic waves,” Phys. Rev. 56(1), 99–107 (1939).
[Crossref]

Phys. Rev. A (2)

Y. I. Salamin, “Fields and propagation characteristics in vacuum of an ultrashort tightly focused radially polarized laser pulse,” Phys. Rev. A 92(5), 053836 (2015).
[Crossref]

M. O. Scully and M. S. Zubairy, “Simple laser accelerator: Optics and particle dynamics,” Phys. Rev. A 44(4), 2656–2663 (1991).
[Crossref] [PubMed]

Phys. Rev. E (1)

M. Jirka, O. Klimo, S. V. Bulanov, T. Zh. Esirkepov, E. Gelfer, S. S. Bulanov, S. Weber, and G. Korn, “Electron dynamics and γ and e-e+ production by colliding laser pulses,” Phys. Rev. E 93(2), 023207 (2016).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Y. I. Salamin and C. H. Keitel, “Electron acceleration by a tightly focused laser beam,” Phys. Rev. Lett. 88(9), 095005 (2002).
[Crossref] [PubMed]

Plasma Phys. Contr. Fusion (1)

J.-H. Yang, R. S. Craxton, and M. G. Haines, “Explicit general solutions to relativistic electron dynamics in plane-wave electromagnetic fields and simulations of ponderomotive acceleration,” Plasma Phys. Contr. Fusion 53(12), 125006 (2011).
[Crossref]

Other (2)

G. A. Mourou, G. Korn, W. Sandner, and J. L. Collier, eds., ELI-Extreme Light Infrastructure Science and Technology with Ultra-Intense Lasers WHITEBOOK (THOSS Media GmbH, 2011).

T. G. Brown, Progress in Optics (Elsevier, 2011, vol. 56, Chap. 2) and references therein.

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Figures (9)

Fig. 1
Fig. 1 Schematic diagram for focusing a radially-polarized femtosecond high-power laser pulse.
Fig. 2
Fig. 2 Distribution of squared electric fields of focal spots obtained with different polarizations under f-number of 3. Calculation window is 3 × DL in the x-direction and 3 × DL in the y-direction.
Fig. 3
Fig. 3 Distribution of squared electric fields of focal spots obtained with different polarizations under f-number of 0.25. Calculation window is 3 × DL in the x-direction and 3 × DL in the y-direction.
Fig. 4
Fig. 4 Field strength dependent on the focusing condition. The peak intensities are calculated with linearly-polarized and radially-polarized uniform-beam 11.2-fs laser pulses that deliver the energy of 11.2 J.
Fig. 5
Fig. 5 (a) Laser spectrum of fs, PW laser pulses and (b) transform-limited pulse profiles.
Fig. 6
Fig. 6 Peak intensities at different beam profiles and different laser spectrums. The focusing condition is 0.25 in terms of f-number. (a) the uniform beam profile and (b) Laguerre-Gaussian beam (LG01) profile are assumed in the calculation.
Fig. 7
Fig. 7 (a) Spectral phase and (b) wavefront map used in calculating the energy density. (c), (d), and (e) show energy density maps for radial, longitudinal, and whole fields. The wavefront aberration reduces the energy density according to the Strehl ratio. Calculation windows in (c), (d), and (e) are 3 × DL in the x-direction and 3 × DL in the y-direction.
Fig. 8
Fig. 8 Snap shots of tightly-focused radially-polarized fs laser pulse. The pulse propagates from left to right. In all figures, x-axis (vertical axis) ranges from −1.2 μm to + 1.2 μm and z-axis (horizontal-axis) ranges from −3.2 μm to + 3.2 μm.
Fig. 9
Fig. 9 (a) Tight focusing scheme for two colliding laser pulses. (b) Energy density and electric field distributions when two radially-polarized 0.5 PW fs laser pulse collide at the common focus under the f-umber of 0.6. The x-axis (vertical axis) ranges from −1.6 μm to + 1.6 μm and z-axis (horizontal axis) ranges from −4.8 μm to + 4.8 μm.

Equations (34)

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RP( δ λ ,ϕ )=[ cos( δ λ 2 )+isin( δ λ 2 )cosϕ isin( δ λ 2 )sinϕ isin( δ λ 2 )sinϕ cos( δ λ 2 )isin( δ λ 2 )cosϕ ].
RP( δ λ ,ϕ )[ E 0 0 ]=[ { cos( δ λ 2 )+isin( δ λ 2 )cosϕ } E 0 isin( δ λ 2 )sinϕ E 0 ].
[ isin( δ λ 2 )sin ϕ S E 0 { cos( δ λ 2 )+isin( δ λ 2 )cos ϕ S } E 0 ].
E i ( P )= ikf E 0 π exp( 2ikf ) 0 2π θmin π α i ( θ S , ϕ S ) 1cos θ S exp[ ikΦ( θ S , ϕ S ) ] d Ω S .
α x ( θ S , ϕ S )=icos ϕ S isin θ S 1cos θ S ( 1 1cos θ S i2kf )[ 2fsin θ S cos ϕ S x P ( 1cos θ S ) ],
α y ( θ S , ϕ S )=isin ϕ S isin θ S 1cos θ S ( 1 1cos θ S i2kf )[ 2fsin θ S sin ϕ S y P ( 1cos θ S ) ],
α z ( θ S , ϕ S )= isin θ S 1cos θ S { 1( 1 1cos θ S i2kf )[ 2fcos θ S z P ( 1cos θ S ) ] }.
H i ( P )= ikf E 0 π exp( 2ikf ) 0 2π θmin π β i ( θ S , ϕ S ) 1cos θ S exp[ ikΦ( θ S , ϕ S ) ] d Ω S .
β x ( θ S , ϕ S )=i( 1 1cos θ S i2kf ){ sin ϕ S [ 2fcos θ S z P ( 1cos θ S ) ]+ sin θ S 1cos θ S [ 2fsin θ S sin ϕ S y P ( 1cos θ S ) ] },
β y ( θ S , ϕ S )=i( 1 1cos θ S i2kf ){ cos ϕ S [ 2fcos θ S z P ( 1cos θ S ) ]+ sin θ S 1cos θ S [ 2fsin θ S cos ϕ S x P ( 1cos θ S ) ] },
β z ( θ S , ϕ S )=i( 1 1cos θ S i2kf )× { cos ϕ S [ 2fsin θ S sin ϕ S y P ( 1cos θ S ) ]+sin ϕ S [ 2fsin θ S cos ϕ S x P ( 1cos θ S ) ] } =0.
AP( δ λ ,ϕ )=[ cos( δ λ 2 )isin( δ λ 2 )sinϕ isin( δ λ 2 )cosϕ isin( δ λ 2 )cosϕ cos( δ λ 2 )+isin( δ λ 2 )sinϕ ],
AP( δ λ ,ϕ )[ E x 0 ]=[ { cos( δ λ 2 )isin( δ λ 2 )sinϕ } E x isin( δ λ 2 )cosϕ E x ],
[ isin( δ λ 2 )cos ϕ S E 0 { cos( δ λ 2 )isin( δ λ 2 )sin ϕ S } E 0 ].
α x ( θ S , ϕ S )=isin ϕ S ,
α y ( θ S , ϕ S )=icos ϕ S ,
α z ( θ S , ϕ S )=0,
β x ( θ S , ϕ S )=icos ϕ S ( 1 1cos θ S i2kf )[ 2fcos θ S z P ( 1cos θ S ) ],
β y ( θ S , ϕ S )=isin ϕ S ( 1 1cos θ S i2kf )[ 2fcos θ S z P ( 1cos θ S ) ],
β z ( θ S , ϕ S )=i( 1 1cos θ S i2kf )[ 2fsin θ S x P cos ϕ S ( 1cos θ S ) y P sin ϕ S ( 1cos θ S ) ].
τ exp = 1 c λ 2 Δλ ,
E 0 ( λ )= 2×TE×Δλ S×A× λ 2 × ε 0 | h( λ ) | 2 λ 2 .
α x ( θ S , ϕ S )=[ cos( δ λ /2 )+isin( δ λ /2 )cos ϕ S ] [ sin θ S cos ϕ S 1cos θ S cos( δ λ 2 )+ i sin θ S 1cos θ S sin( δ λ 2 ) ]( 1 1cos θ S i2kf )[ 2fsin θ S cos ϕ S x P ( 1cos θ S ) ],
α y ( θ S , ϕ S )=isin( δ λ /2 )sin ϕ S [ sin θ S cos ϕ S 1cos θ S cos( δ λ 2 )+ i sin θ S 1cos θ S sin( δ λ 2 ) ]( 1 1cos θ S i2kf )[ 2fsin θ S sin ϕ S y P ( 1cos θ S ) ],
α z ( θ S , ϕ S )= sin θ S cos ϕ S 1cos θ S [ cos( δ λ 2 )+isin( δ λ 2 )cos ϕ S ]+ sin θ S sin ϕ S 1cos θ S isin( δ λ 2 )sin ϕ S [ sin θ S cos ϕ S 1cos θ S cos( δ λ 2 )+i sin θ S 1cos θ S sin( δ λ 2 ) ]( 1 1cos θ S i2kf )[ 2fcos θ S z P ( 1cos θ S ) ],
β x ( θ S , ϕ S )=( 1 1cos θ S i2kf )× { isin( δ λ /2 )sin ϕ S [ 2fcos θ S z P ( 1cos θ S ) ]+ sin θ S 1cos θ S [ cos ϕ S { cos( δ λ 2 )+isin( δ λ 2 )cos ϕ S }+ i sin 2 ϕ S sin( δ λ 2 ) ][ 2fsin θ S sin ϕ S y P ( 1cos θ S ) ] },
β y ( θ S , ϕ S )=( 1 1cos θ S i2kf )× { [ cos( δ λ /2 )+isin( δ λ /2 )cos ϕ S ][ 2fcos θ S z P ( 1cos θ S ) ] sin θ S 1cos θ S [ cos ϕ S { cos( δ λ 2 )+isin( δ λ 2 )cos ϕ S }+ i sin 2 ϕ S sin( δ λ 2 ) ][ 2fsin θ S cos ϕ S x P ( 1cos θ S ) ] },
β z ( θ S , ϕ S )=( 1 1cos θ S i2kf )×{ [ cos( δ λ 2 )+ isin( δ λ 2 )cos ϕ S ][ 2fsin θ S sin ϕ S y P ( 1cos θ S ) ]+ isin( δ λ 2 )sin ϕ S [ 2fsin θ S cos ϕ S x P ( 1cos θ S ) ] }.
α x ( θ S , ϕ S )=[ cos( δ λ /2 )isin( δ λ /2 )sin ϕ S ] sin θ S cos ϕ S cos( δ λ 2 ) 1cos θ S ( 1 1cos θ S i2kf )[ 2fsin θ S cos ϕ S x P ( 1cos θ S ) ],
α y ( θ S , ϕ S )=isin( δ λ /2 )cos ϕ S [ sin θ S cos ϕ S 1cos θ S cos( δ λ 2 ) ]( 1 1cos θ S i2kf )[ 2fsin θ S sin ϕ S y P ( 1cos θ S ) ],
α z ( θ S , ϕ S )= sin θ S cos ϕ S 1cos θ S [ cos( δ λ 2 )isin( δ λ 2 )sin ϕ S ]+ sin θ S sin ϕ S 1cos θ S isin( δ λ 2 )cos ϕ S { sin θ S cos ϕ S 1cos θ S [ cos( δ λ 2 )isin( δ λ 2 )sin ϕ S ] +i sin θ S sin ϕ S 1cos θ S sin( δ λ 2 )cos ϕ S }( 1 1cos θ S i2kf )[ 2fcos θ S z P ( 1cos θ S ) ],
β x ( θ S , ϕ S )=( 1 1cos θ S i2kf )× { isin( δ λ /2 )cos ϕ S [ 2fcos θ S z P ( 1cos θ S ) ] sin θ S 1cos θ S × [ cos ϕ S { cos( δ λ 2 )isin( δ λ 2 )sin ϕ S }+ isin ϕ S sin( δ λ /2 )cos ϕ S ][ 2fsin θ S sin ϕ S y P ( 1cos θ S ) ] },
β y ( θ S , ϕ S )=( 1 1cos θ S i2kf )× { [ cos( δ λ 2 )isin( δ λ 2 )sin ϕ S ][ 2fcos θ S z P ( 1cos θ S ) ]+ sin θ S 1cos θ S × [ cos ϕ S { cos( δ λ 2 )isin( δ λ 2 )sin ϕ S }+ isin ϕ S sin( δ λ /2 )cos ϕ S ][ 2fsin θ S cos ϕ S x P ( 1cos θ S ) ] },
β z ( θ S , ϕ S )=( 1 1cos θ S i2kf )× { [ cos( δ λ 2 )isin( δ λ 2 )sin ϕ S ][ 2fsin θ S sin ϕ S y P ( 1cos θ S ) ]+ isin( δ λ 2 )cos ϕ S [ 2fsin θ S cos ϕ S x P ( 1cos θ S ) ] }.

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