Reflection of few cycle laser pulses from an inhomogeneous overdense plasma

S. K. Mishra; A. Andreev; M. P. Kalashinikov

doi:10.1364/OE.25.011637

Optics Express
Vol. 25,
Issue 10,
pp. 11637-11651
(2017)
•https://doi.org/10.1364/OE.25.011637

Reflection of few cycle laser pulses from an inhomogeneous overdense plasma

S. K. Mishra, A. Andreev, and M. P. Kalashinikov

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S. K. Mishra, A. Andreev, and M. P. Kalashinikov, "Reflection of few cycle laser pulses from an inhomogeneous overdense plasma," Opt. Express 25, 11637-11651 (2017)

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Related Topics
Table of Contents Category
- Ultrafast Optics
Optics & Photonics Topics
?

The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Reflection (120.5700)
- Lasers and laser optics (140.0140)
- Plasmas (350.5400)

About this Article
History
- Original Manuscript: January 13, 2017
- Revised Manuscript: March 16, 2017
- Manuscript Accepted: March 17, 2017
- Published: May 10, 2017

Abstract

The use of a plasma mirror to improve the temporal contrast of few cycle laser pulses has been considered. Pre-plasma features, prior to the main pulse, have been evaluated using an analytical model that has been verified using hydrodynamic code. The temporal/ spectral profile, reflectivity, and broadening of the reflected pulse have been parametrically analysed using an analytical formulation that describes the reflection of broadband ultra-short pulses from the plasma gradient. The analytical estimate for the pulse reflectivity is in good agreement with experimental measurements. The consistency of the analytical expressions for the collisionless case has been validated via comparison with a 1D particle in cell simulations.

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References

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Year
Author
Publication

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[Crossref]
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[Crossref]
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[Crossref]
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[Crossref]
Ch. Ziener, P. S. Foster, E. J. Divall, C. J. Hooker, M. H. R. Hutchinson, A. J. Langley, and D. Neely, “Specular reflectivity of plasma mirrors as a function of intensity, pulse duration, and angle of incidence,” J. Appl. Phys. 93(1), 768–770 (2003).
[Crossref]
P. Monot, G. Doumy, S. Dobosz, M. Perdrix, P. D’Oliveira, F. Quéré, F. Réau, P. Martin, P. Audebert, J.-C. Gauthier, and J.-P. Geindre, “High-order harmonic generation by nonlinear reflection of an intense high-contrast laser pulse on a plasma,” Opt. Lett. 29(8), 893–895 (2004).
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[Crossref] [PubMed]
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[Crossref]
Y. Shiau and R. F. H. Yang, “Distortion of a radio pulse reflected from an inhomogeneous lossy plasma,” Proc. IEEE 60(1), 142–143 (1972).
[Crossref]
M. D. Perry, T. Ditmire, and B. C. Stuart, “Self-phase modulation in chirped-pulse amplification,” Opt. Lett. 19(24), 2149–2151 (1994).
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2016 (3)

N. Khodakovskiy, M. Kalashnikov, E. Gontier, F. Falcoz, and P.-M. Paul, “Degradation of picosecond temporal contrast of Ti:sapphire lasers with coherent pedestals,” Opt. Lett. 41(19), 4441–4444 (2016).
[Crossref] [PubMed]

B. H. Shaw, S. Steinke, J. van Tilborg, and W. P. Leemans, “Reflectance characterization of tape-based plasma mirrors,” Phys. Plasmas 23(6), 063118 (2016).
[Crossref]

P. L. Poole, A. Krygier, G. E. Cochran, P. S. Foster, G. G. Scott, L. A. Wilson, J. Bailey, N. Bourgeois, C. Hernandez-Gomez, D. Neely, P. P. Rajeev, R. R. Freeman, and D. W. Schumacher, “Experiment and simulation of novel liquid crystal plasma mirrors for high contrast, intense laser pulses,” Sci. Rep. 6(1), 32041 (2016).
[Crossref] [PubMed]

2015 (1)

G. G. Scott, V. Bagnoud, C. Brabetz, R. J. Clarke, J. S. Green, R. I. Heathcote, H. W. Powell, B. Zielbauer, T. D. Arber, P. McKenna, and D. Neely, “Optimization of plasma mirror reflectivity and optical quality using double laser pulses,” New J. Phys. 17(3), 033027 (2015).
[Crossref]

2014 (3)

A. Borot, D. Douillet, G. Iaquaniello, T. Lefrou, P. Audebert, J.-P. Geindre, and R. Lopez-Martens, “High repetition rate plasma mirror device for attosecond science,” Rev. Sci. Instrum. 85(1), 013104 (2014).
[Crossref] [PubMed]

H. Liebetrau, M. Hornung, A. Seidel, M. Hellwing, A. Kessler, S. Keppler, F. Schorcht, J. Hein, and M. C. Kaluza, “Ultra-high contrast frontend for high peak power fs-lasers at 1030 nm,” Opt. Express 22(20), 24776–24786 (2014).
[Crossref] [PubMed]

T. Zh. Esirkepov, J. K. Koga, A. Sunahara, T. Morita, M. Nishikino, K. Kageyama, H. Nagatomo, K. Nishihara, A. Sagisaka, H. Kotaki, T. Nakamura, Y. Fukuda, H. Okada, A. S. Pirozhkov, A. Yogo, M. Nishiuchi, H. Kiriyama, K. Kondo, M. Kando, and S. V. Bulanov, “Prepulse and amplified spontaneous emission effects on the interaction of a PW class laser with thin solid targets,” Nucl. Instrum. Methods Phys. Res. A 745(05), 150–163 (2014).
[Crossref]

2012 (2)

M. P. Kalashnikov, K. Osvay, G. Priebe, L. Ehentraut, S. Steinke, and W. Sandner, “Temporal contrast of high intensity laser systems above 1011 with double CPA technique,” AIP Conf. Proc. 1462, 108–111 (2012).
[Crossref]

M. P. Kalashnikov, H. Schönnagel, and W. Sandner, “High temporal contrast front end with a CaF2CaF2-based XPW temporal filter for high intensity lasers,” AIP Conf. Proc. 1465, 13–17 (2012).
[Crossref]

2011 (1)

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. C. Kaluza, and G. G. Paulus, “High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude,” Appl. Phys. B 103(2), 295–302 (2011).
[Crossref]

2010 (1)

A. Sotnikov, H. Laux, and B. Stritzker, “Experimental and numerical optimization of beam shapes for short-pulse ultraviolet laser cutting processing,” Phys. Procedia 05(6), 137–146 (2010).
[Crossref]

2009 (1)

M. Kalashnikov, A. Andreev, and H. Schönnagel, “Limits of the temporal contrast for CPA lasers with beams of high aperture,” Proc. SPIE 7501, 750104 (2009).
[Crossref]

2008 (1)

N. V. Didenko, A. V. Konyashchenko, A. P. Lutsenko, and S. Y. Tenyakov, “Contrast degradation in a chirped-pulse amplifier due to generation of prepulses by postpulses,” Opt. Express 16(5), 3178–3190 (2008).
[Crossref] [PubMed]

2007 (1)

C. Thaury, F. Quéré, J.-P. Geindre, A. Levy, T. Ceccotti, P. Monot, M. Bougeard, F. Réau, P. d’Oliveira, P. Audebert, R. Marjoribanks, and Ph. Martin, “Plasma mirrors for ultrahigh-intensity optics,” Nat. Phys. 03(6), 424–429 (2007).
[Crossref]

2006 (1)

V. Chvykov, P. Rousseau, S. Reed, G. Kalinchenko, and V. Yanovsky, “Generation of 1011 contrast 50 TW laser pulses,” Opt. Lett. 31(10), 1456–1458 (2006).
[Crossref] [PubMed]

2005 (3)

M. P. Kalashnikov, E. Risse, H. Schönnagel, and W. Sandner, “Double chirped-pulse-amplification laser: a way to clean pulses temporally,” Opt. Lett. 30(8), 923–925 (2005).
[Crossref] [PubMed]

A. Jullien, O. Albert, F. Burgy, G. Hamoniaux, J.-P. Rousseau, J.-P. Chambaret, F. Augé-Rochereau, G. Chériaux, J. Etchepare, N. Minkovski, and S. M. Saltiel, “10-10 temporal contrast for femtosecond ultraintense lasers by cross-polarized wave generation,” Opt. Lett. 30(8), 920–922 (2005).
[Crossref] [PubMed]

V. A. Isakov, A. P. Kanavin, and S. A. Uryupin, “Reflection and absorption of a high-power ultra-short laser pulse heating a solid-state target,” Laser Part. Beams 23(03), 315–319 (2005).
[Crossref]

2004 (2)

P. Monot, G. Doumy, S. Dobosz, M. Perdrix, P. D’Oliveira, F. Quéré, F. Réau, P. Martin, P. Audebert, J.-C. Gauthier, and J.-P. Geindre, “High-order harmonic generation by nonlinear reflection of an intense high-contrast laser pulse on a plasma,” Opt. Lett. 29(8), 893–895 (2004).
[Crossref] [PubMed]

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J.-C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).
[Crossref] [PubMed]

2003 (1)

Ch. Ziener, P. S. Foster, E. J. Divall, C. J. Hooker, M. H. R. Hutchinson, A. J. Langley, and D. Neely, “Specular reflectivity of plasma mirrors as a function of intensity, pulse duration, and angle of incidence,” J. Appl. Phys. 93(1), 768–770 (2003).
[Crossref]

2002 (1)

I. Watts, M. Zepf, E. L. Clark, M. Tatarakis, K. Krushelnick, A. E. Dangor, R. Allott, R. J. Clarke, D. Neely, and P. A. Norreys, “Measurements of relativistic self-phase-modulation in plasma,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(3), 036409 (2002).
[Crossref] [PubMed]

2001 (1)

D. Umstadter, “Review of physics and applications of relativistic plasmas driven by ultra-intense lasers,” Phys. Plasmas 8(5), 1774–1785 (2001).
[Crossref]

1999 (1)

M. Grimes, A. Rundquist, Y. Lee, and M. Downer, “Experimental identification of vacuum heating at femtosecond-laser-irradiated metal surfaces,” Phys. Rev. Lett. 82(20), 4010–4013 (1999).
[Crossref]

1995 (2)

Z. Bor, B. Racz, G. Szabo, D. Xenakis, C. Kalpouzos, and C. Fotakis, “Femtosecond transient reflection from polymer surfaces during femtosecond UV photoablation,” Appl. Phys., A Mater. Sci. Process. 60(4), 365–368 (1995).
[Crossref]

B. Kohler, V. V. Yakovlev, K. R. Wilson, J. Squier, K. W. Delong, and R. Trebino, “Phase and intensity characterization of femtosecond pulses from a chirped-pulse amplifier by frequency-resolved optical gating,” Opt. Lett. 20(5), 483–485 (1995).
[Crossref] [PubMed]

1994 (3)

D. M. Gold, “Direct measurement of prepulse suppression by use of a plasma shutter,” Opt. Lett. 19(23), 2006–2008 (1994).
[Crossref] [PubMed]

M. D. Perry, T. Ditmire, and B. C. Stuart, “Self-phase modulation in chirped-pulse amplification,” Opt. Lett. 19(24), 2149–2151 (1994).
[Crossref] [PubMed]

M. D. Perry and G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264(5161), 917–924 (1994).
[Crossref] [PubMed]

1993 (1)

S. Backus, H. C. Kapteyn, M. M. Murnane, D. M. Gold, H. Nathel, and W. White, “Prepulse suppression for high-energy ultrashort pulses using self-induced plasma shuttering from a fluid target,” Opt. Lett. 18(2), 134–136 (1993).
[Crossref] [PubMed]

1991 (2)

H. C. Kapteyn, M. M. Murnane, A. Szoke, and R. W. Falcone, “Prepulse energy suppression for high-energy ultrashort pulses using self-induced plasma shuttering,” Opt. Lett. 16(7), 490–492 (1991).
[Crossref] [PubMed]

D. M. Gold, H. Nathel, P. R. Bolton, W. E. White, and L. D. V. Woerkom, “Short pulse high intensity lasers and applications,” Proc. SPIE 1413, 41–52 (1991).
[Crossref]

1987 (1)

F. Brunel, “Not-so-resonant, resonant absorption,” Phys. Rev. Lett. 59(1), 52–55 (1987).
[Crossref] [PubMed]

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
[Crossref]

1972 (1)

Y. Shiau and R. F. H. Yang, “Distortion of a radio pulse reflected from an inhomogeneous lossy plasma,” Proc. IEEE 60(1), 142–143 (1972).
[Crossref]

1971 (1)

K. P. Singh, P. K. Shukla, and R. N. Singh, “Propagation of an electromagnetic pulse through inhomogeneous plasmas,” Int. J. Electron. 30(03), 249–254 (1971).
[Crossref]

1969 (1)

S. Kozaki and Y. Mushiake, “Propagation of the electromagnetic pulse with Gaussian envelope in inhomogeneous ionized media,” IEEE Trans. Antenn. Propag. 17(5), 686–688 (1969).
[Crossref]

Albert, O.

Allott, R.

Andreev, A.

M. Kalashnikov, A. Andreev, and H. Schönnagel, “Limits of the temporal contrast for CPA lasers with beams of high aperture,” Proc. SPIE 7501, 750104 (2009).
[Crossref]

Arber, T. D.

Audebert, P.

Augé-Rochereau, F.

Backus, S.

Bagnoud, V.

Bailey, J.

Behmke, M.

Bolton, P. R.

D. M. Gold, H. Nathel, P. R. Bolton, W. E. White, and L. D. V. Woerkom, “Short pulse high intensity lasers and applications,” Proc. SPIE 1413, 41–52 (1991).
[Crossref]

Bor, Z.

Borot, A.

Bougeard, M.

Bourgeois, N.

Brabetz, C.

Brunel, F.

F. Brunel, “Not-so-resonant, resonant absorption,” Phys. Rev. Lett. 59(1), 52–55 (1987).
[Crossref] [PubMed]

Bulanov, S. V.

Burgy, F.

Ceccotti, T.

Chambaret, J.-P.

Chériaux, G.

Chvykov, V.

V. Chvykov, P. Rousseau, S. Reed, G. Kalinchenko, and V. Yanovsky, “Generation of 1011 contrast 50 TW laser pulses,” Opt. Lett. 31(10), 1456–1458 (2006).
[Crossref] [PubMed]

Clark, E. L.

Clarke, R. J.

Cochran, G. E.

d’Oliveira, P.

Dangor, A. E.

Delong, K. W.

Didenko, N. V.

Ditmire, T.

M. D. Perry, T. Ditmire, and B. C. Stuart, “Self-phase modulation in chirped-pulse amplification,” Opt. Lett. 19(24), 2149–2151 (1994).
[Crossref] [PubMed]

Divall, E. J.

Dobosz, S.

Douillet, D.

Doumy, G.

Downer, M.

Ehentraut, L.

Ehrt, D.

Esirkepov, T. Zh.

Etchepare, J.

Falcone, R. W.

Falcoz, F.

Foster, P. S.

Fotakis, C.

Freeman, R. R.

Fukuda, Y.

Gauthier, J.-C.

Geindre, J.-P.

Gobert, O.

Gold, D. M.

D. M. Gold, “Direct measurement of prepulse suppression by use of a plasma shutter,” Opt. Lett. 19(23), 2006–2008 (1994).
[Crossref] [PubMed]

D. M. Gold, H. Nathel, P. R. Bolton, W. E. White, and L. D. V. Woerkom, “Short pulse high intensity lasers and applications,” Proc. SPIE 1413, 41–52 (1991).
[Crossref]

Gontier, E.

Green, J. S.

Grimes, M.

Hamoniaux, G.

Heathcote, R. I.

Hein, J.

Hellwing, M.

Hernandez-Gomez, C.

Heyer, M.

Hooker, C. J.

Hornung, M.

Hutchinson, M. H. R.

Iaquaniello, G.

Isakov, V. A.

Jäckel, O.

Jullien, A.

Kageyama, K.

Kalashnikov, M.

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[Crossref]

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M. P. Kalashnikov, E. Risse, H. Schönnagel, and W. Sandner, “Double chirped-pulse-amplification laser: a way to clean pulses temporally,” Opt. Lett. 30(8), 923–925 (2005).
[Crossref] [PubMed]

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V. Chvykov, P. Rousseau, S. Reed, G. Kalinchenko, and V. Yanovsky, “Generation of 1011 contrast 50 TW laser pulses,” Opt. Lett. 31(10), 1456–1458 (2006).
[Crossref] [PubMed]

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M. P. Kalashnikov, E. Risse, H. Schönnagel, and W. Sandner, “Double chirped-pulse-amplification laser: a way to clean pulses temporally,” Opt. Lett. 30(8), 923–925 (2005).
[Crossref] [PubMed]

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V. Chvykov, P. Rousseau, S. Reed, G. Kalinchenko, and V. Yanovsky, “Generation of 1011 contrast 50 TW laser pulses,” Opt. Lett. 31(10), 1456–1458 (2006).
[Crossref] [PubMed]

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M. P. Kalashnikov, E. Risse, H. Schönnagel, and W. Sandner, “Double chirped-pulse-amplification laser: a way to clean pulses temporally,” Opt. Lett. 30(8), 923–925 (2005).
[Crossref] [PubMed]

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M. Kalashnikov, A. Andreev, and H. Schönnagel, “Limits of the temporal contrast for CPA lasers with beams of high aperture,” Proc. SPIE 7501, 750104 (2009).
[Crossref]

M. P. Kalashnikov, E. Risse, H. Schönnagel, and W. Sandner, “Double chirped-pulse-amplification laser: a way to clean pulses temporally,” Opt. Lett. 30(8), 923–925 (2005).
[Crossref] [PubMed]

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D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985).
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M. D. Perry, T. Ditmire, and B. C. Stuart, “Self-phase modulation in chirped-pulse amplification,” Opt. Lett. 19(24), 2149–2151 (1994).
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V. Chvykov, P. Rousseau, S. Reed, G. Kalinchenko, and V. Yanovsky, “Generation of 1011 contrast 50 TW laser pulses,” Opt. Lett. 31(10), 1456–1458 (2006).
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Appl. Phys., A Mater. Sci. Process. (1)

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Nat. Phys. (1)

New J. Phys. (1)

Nucl. Instrum. Methods Phys. Res. A (1)

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Fig. 1 A schematic of pulse reflection and coordinate scaling from ramp profile preformed plasma (PM).

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Fig. 2 Steepness (b) as function τ_p for I_po~10¹² Wcm⁻². The blue and black curves (with dots) correspond to analytical and hydrodynamic code estimates respectively.

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Fig. 3 Comparison of analytical results with experiment [23]: Peak reflectivity as a function of fluence for ν~10 fs⁻¹ and ~12.5 fs⁻¹; blue dots refers to measurements.

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Fig. 4 The peak reflectivity of the pulse as function of density steepness (b) for different values of τ₀ and correspond to the standard set of parameters stated in text.

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Fig. 5 Electric field profile of the reflected pulse for different values of b; the figure corresponds to ν~10 fs⁻¹ and standard set of parameters stated in text.

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Fig. 6 Electric field profile of the reflected pulse for different values of b; the figure corresponds to collisionless case (ν~0) and standard parameters stated in text.

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Fig. 7 Pulse spectrum of reflected pulse (corresponding to Fig. 5) for different values of b and figure correspond to the standard set of parameters stated in text.

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Fig. 8 The temporal width (FWHM) of the reflected pulse (τ_ref/ τ₀) as function of b for different values of τ₀; figure correspond to the standard parameters stated in text.

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Fig. 9 The peak reflectivity of the pulse as function of collision frequency (ν/ω_o) for different values of the density steepness (b).

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Fig. 10 Simulation results: Snapshot of the normalized electric filed profile of the incident (blue) and reflected (orange) pulse for three different values of the density steepness b = 10²⁴ & 10²⁶ cm⁻⁴; the simulation refers to incident pulse a_o ~0.07 (~10¹⁶ W/cm²), τ_raise ~4τ and λ_o ~800nm.

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Equations (11)

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E_{i} (y, z, t) = \int_{- \infty}^{\infty} E_{i} (ω) e x p [i {ω t - k (y \sin θ + z \cos θ)}] d ω,

E_{i} (t) = E_{o} e x p (- t^{2} / 2 τ^{2}) e x p [i (ω_{o} t + ϕ_{0})],

E_{i} (ω) = E_{o} {(2 π)}^{1 / 2} τ e x p [- (τ^{2} / 2) {(ω - ω_{o})}^{2}] .

r = e x p [- (i + η) φ_{ω} + i π / 2],

\begin{array}{l} E_{r} (y, z, t) = (1 / 2 π) \int_{- \infty}^{\infty} r E_{i} (ω) e x p {(i ω t^{'})}_{} d ω \\ = (^{2 π) - 1 / 2} e^{i π / 2} E_{o} τ [\int_{- \infty}^{\infty} e x p {[- (i + η) φ_{ω} - (τ^{2} / 2) {(ω - ω_{o})}^{2} + i ω t^{'}]}_{} d ω] \end{array}

E_{r} (y, z, t) = E_{r o} e x p (i Δ) e x p (i ω_{o} t^{'})

E_{r o} = \frac{E_{o} e x p (- η φ_{ω_{o}})}{{[χ^{2} + {(1 + χ η)}^{2}]}^{1 / 4}} e x p (- \frac{[{({φ^{'}}_{ω_{o}} - t^{'})}^{2} - {φ^{'}}_{ω_{o}}^{2} η^{2}] (1 + χ η) - 2 χ η ({φ^{'}}_{ω_{o}} - t^{'}) {φ^{'}}_{ω_{o}}}{2 τ^{2} [χ^{2} + {(1 + χ η)}^{2}]})

Δ \equiv (\frac{π}{2} - φ_{ω_{o}} - \frac{1}{2} t a n^{- 1} \frac{χ}{(1 + χ η)} + \frac{[{({φ^{'}}_{ω_{o}} - t^{'})}^{2} - {φ^{'}}_{ω_{o}}^{2} η^{2}] χ + 2 {φ^{'}}_{ω_{o}} η ({φ^{'}}_{ω_{o}} - t^{'}) (1 + χ η)}{2 τ^{2} [χ^{2} + {(1 + χ η)}^{2}]})

E_{r} (ω) = \int_{- \infty}^{\infty} E_{r} (t) e x p (j ω t) d t .

\partial n_{e} / \partial t = f_{i} (n_{o} - n_{e})

\partial T_{e} / \partial t = (\frac{e^{2} {| E_{p} |}^{2}}{m_{e} (ν^{2} + ω_{o}^{2})} - δ_{e i} (T_{e} - T_{o})) ν