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Analytical and numerical investigation of the pulse-shape effect on the longitudinal electric field of a tightly focused ultrafast few-cycle TM01 laser beam

Published online by Cambridge University Press:  05 January 2012

Harish Malav ,
K.P. Maheshwari  and
Y. Choyal
Harish Malav
Affiliation:
DST-Project, Vardhaman Mahaveer Open University, Kota, India
K.P. Maheshwari*
Affiliation:
DST-Project, Vardhaman Mahaveer Open University, Kota, India
Y. Choyal
Affiliation:
School of Physics, Devi Ahilya Vishwavidyalaya, Indore, India
*
Address correspondence and reprint requests to: K.P. Maheshwari, DST-Project, Vardhaman Mahaveer Open University, Rawatbhata road, Kota-324010, India. E-mail: malavh@yahoo.co.in
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Abstract

The effect of temporal pulse-shape on the characterization of the longitudinal electric field resulting from the tight-focusing of an ultrashort few-cycle TM01 laser beam in free space is investigated analytically and numerically. The longitudinal field is found to be sensitive to the pulse-shape of the driving field. The temporal pulse-shapes considered are Gaussian, Lorentzian, and hyperbolic secant having identical full width at half maximum of intensity. Analytical calculations are made beyond the paraxial and slowly varying envelope approximations. From the numerical results we find that due to finite duration of the signal, the evolution of the pulse envelope before the waist is faster (negative time-delay) but slowed down (positive time-delay) after the waist. This time-delay, for single-cycle pulses of wavelength λ0, and for spot-size w0f in the range 0.6λ0 > w0f > 0.25λ0, is pulse-shape dependent. The time delay is maximum for the Gaussian pulse and minimum for the Lorentzian pulse. The carrier frequency shift depends on the temporal profile of the pulse, beam spot size, axial propagating distance and also on the number of cycles in a pulse. In addition, a comparative study of the variation of the corrected axial Gouy- phase of the longitudinal electric field of single-cycle pulse (spot size w0f = 0.5λ0) with normalized retarded time shows that the phase variation is maximum for Gaussian and minimum for the Lorentzian pulse shape.

Keywords

Axial Gouy phaseCarrier frequency shiftLaser pulse-shapeTightly focused TM01 laser beam

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Type
Research Article
Information
Laser and Particle Beams , Volume 30 , Issue 1 , March 2012 , pp. 75 - 86
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Apolonski, A., Poppe, A., Tempea, G., Spielmann, Ch., Udem, Th., Holzwarth, R., Hänsch, T.W. & Krausz, F. (2000). Controlling the phase evolution of few-cycle light pulses. Phys. Rev. Lett. 85, 740–743.CrossRefGoogle ScholarPubMed
Baeva, T., Gordienko, S. & Pukhov, A. (2006). Theory of high-order harmonic generation in relativistic laser interaction with over dense plasma. Phys. Rev. E 74, 046404/1–11.CrossRefGoogle Scholar
Brabec, T. & Krausz, F. (1997). Nonlinear optical pulse propagation in the single-cycle regime. Phys. Rev. Lett. 78, 3282–3285.CrossRefGoogle Scholar
Brabec, T. & Krausz, F. (2000). Intense few-cycle laser fields: Frontier of nonlinear optics. Rev. Mod. Phys. 72, 545–591.CrossRefGoogle Scholar
Corkum, P.B. & Krausz, F. (2007). Attosecond science. Nat. Phys. 3, 281–287.CrossRefGoogle Scholar
Dorn, R., Quabis, S. & Leuchs, G. (2003). Sharper focus for a radially polarized light beam. Phys. Rev. Lett. 91, 23390/1–4.CrossRefGoogle ScholarPubMed
Dromey, B., Kar, S., Bellei, C., Carroll, D.C., Clarke, R.J., Green, J.S., Kneip, S., Markey, K., Nagel, S.R., Simpson, P.T., Willingale, L., Mckenna, P., Neely, D., Najmudin, Z., Krushelnick, K., Norreys, P. A. & Zepf, M. (2007). Bright multi-KeV harmonic generation from relativistically oscillating plasma surfaces. Phys. Rev. Lett. 99, 0850011/1–14.CrossRefGoogle ScholarPubMed
Dromey, B., Rykovanov, S.G., Adams, D., Hörlein, R., Nomura, Y., Carroll, D.C., Foster, P.S., Kar, S., Markey, K., Mckenna, P., Neely, D., Geissler, M., Tsakiris, G.D. & Zepf, M. (2009). Tunable enhancement of high harmonic emission from laser solid interactions. Phys. Rev. Lett. 102, 225002/1–4.CrossRefGoogle ScholarPubMed
Esarey, E., Scchroeder, C.B. & Leemans, W.P. (2009). Physics of laser-driven plasma–based electron accelerators. Rev. Mod. Phys. 81, 1229–1285.CrossRefGoogle Scholar
Gupta, M.K., Sharma, R.P. & Mahmoud, S.T. (2007). Generation of plasma wave and third harmonic generation at ultra relativistic laser power. Laser Part. Beams 25, 211–218.CrossRefGoogle Scholar
Krausz, F. & Ivanov, M. (2009). Attosecond physics. Rev. Mod. Phys. 81, 163–234.CrossRefGoogle Scholar
Kröll, J., Darmo, J., Dhillon, S.S., Marcadet, X., Calligaro, M., Sirtori, C. & Unterrainer, K. (2007). Phase- resolved measurements of stimulated emission in a laser. Nat. Lett. 449, 698–701.CrossRefGoogle ScholarPubMed
Lichters, R., Meyer-Ter-Vehn, J. & Pukhov, A. (1996). Short-pulse laser harmonics from oscillating plasma surfaces driven at relativistic intensity. Phys. Plasmas 3, 3425–3437.Google Scholar
Malav, H., Maheshwari, K.P. & Choyal, Y. (2011 b). Analytical and numerical investigation of pulse-shape effect on the interaction of an ultrashort, intense, few-cycle laser pulse with a thin plasma layer. Laser Part. Beams 29, 45–54.CrossRefGoogle Scholar
Malav, H., Maheshwari, K.P. & Senecha, V. (2011 a). Analytical and numerical investigation of the effect of pulse shape of intense, few-cycle TM01 laser on the acceleration of charged particles. Indian J. Pure Appl.Phys. 49, 251–256.Google Scholar
Malav, H., Maheshwari, K.P., Meghwal, R.S., Choyal, Y. & Sharma, R. (2010). Analytical and numerical investigation of diffraction effects on the nonlinear propagation of ultra-intense few-cycle optical pulses in plasmas. J. Plasma Phys. 76, 209–227.Google Scholar
Nisoli, M., Sansone, G., Stagira, S., Silvestri, S.D., Vozzi, C., Pascolini, M., Poletto, L., Villoresi, P. & Tondello, G. (2003). Effects of carrier-envelope phase differences of few-optical-cycle light pulses in single-shot high- order-harmonic spectra. Phys. Rev. Letters 91, 2139051/1–54.CrossRefGoogle ScholarPubMed
Paulus, G.G., Lindner, F., Walther, H., Baltuška, A., Gouliemakis, E., Lezius, M. & Krausz, F. (2003). Measurement of the phase of few-cycle laser pulses. Phys. Rev. Lett. 91, 253004 (1–4).Google Scholar
Porras, M.A. (2001). Pulse correction to monochromatic light-beam propagation. Opt. Lett. 26, 44–46.CrossRefGoogle ScholarPubMed
Porras, M.A. (2002). Diffraction effects in few-cycle optical pulses., Phys. Rev. E 65, 026606/1–11.CrossRefGoogle ScholarPubMed
Porras, M.A. (2009). Characterization of the electric field of focused pulsed Gaussian beams for phase –sensitive interactions with matter. Opt. Lett. 34, 1546–1548.CrossRefGoogle ScholarPubMed
Schenkel, B., Biegert, J., Keller, U., Vozzi, C., Nisoli, M., Sansone, G., Stagira, S., De Silvestri, S., & Svelto, O. (2003). Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum. Opt. Lett. 28, 1987–1989.CrossRefGoogle ScholarPubMed
Sprangle, P., Hafizi, B., Penano, J.R., Hubbard, R.F., Ting, A., Zigler, A. & Antonsen, T.M. (2000). Stable laser-pulse propagation in plasma channels for GeV electron acceleration. Phys. Rev. Lett. 85, 5110–5113.CrossRefGoogle ScholarPubMed
Varin, C. & Piché, M. (2002). Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams. Appl. Phys. B 74, S83–S88.CrossRefGoogle Scholar
Varin, C., Piché, M. & Porras, M.A. (2005). Acceleration of electron from rest to GeV energies by ultrashort transverse magnetic laser pulses in free space. Phys. Rev. E 71, 026603/1–10.Google Scholar
Varin, C., Piché, M. & Porras, M.A. (2006). Analytical calculation of the longitudinal electric field resulting from the tight focusing of an ultrafast transverse-magnetic laser beam. J. Opt. Soc. Am. A 23, 2027–2038.CrossRefGoogle ScholarPubMed
Varro, S. (2007). Linear and nonlinear absolute phase effects in interactions of ultrashort laser pulses with a metal nano-layer or with a thin plasma layer. Laser part. Beams 25, 379–390.CrossRefGoogle Scholar
Villoresi, P., Barbiero, P., Poletto, L., Nisoli, M., Cerullo, G., Priori, E., Stagira, S., De Lisco, C., Bruzzese, R. & Altucci, C. (2001). Study of few-optical-cycles generation of high-order harmonics. Laser Part. Beams 19, 41–45.CrossRefGoogle Scholar
Wittmann, T., Horvath, B., Helml, W., Schätzel, M.G., Gu, X., Cavalieri, A.L., Paulus, G.G. & Kienberger, R. (2009). Single-shot carrier-envelope phase measurement of few-cycle laser pulses. Nat. Phys. 5, 357–362.Google Scholar