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Compression of ultrashort laser pulses in planar hollow waveguides: a stability analysis C.L. Arnold1 , S. Akturk2 , M. Franco1 , A. Couairon3 and A. Mysyrowicz1 1 Laboratoire

´ d’Optique Appliquée, Ecole Nationale Supérieure des Techniques Avancées ´ Ecole Polytechnique, CNRS, F-91761 Palaiseau, France

2 Department 3 Centre

of Physics, Istanbul Technical University, Maslak 34469 Istanbul, Turkey

´ de Physique Théorique, Ecole Polytechnique, CNRS, F-91128 Palaiseau, France [email protected]

Abstract: We investigate compression of ultrashort laser pulses by nonlinear propagation in gas-filled planar hollow waveguides, using (3+1)dimensional numerical simulations. In this geometry, the laser beam is guided with a fixed size in one transverse dimension, generating significant spectral broadening, while it propagates freely in the other, allowing for energy up-scalability. In this respect the concept outperforms compression techniques based on hollow core fibers or filamentation. Small-scale selffocusing is a crucial consideration, which introduces mode deterioration and finally break-up in multiple filaments. The simulation results, which match well with initial experiments, provide important guidelines for scaling the few-cycle pulse generation to higher energies. Pulse compression down to few-cycle duration with energies up to 100 mJ levels should be possible. © 2009 Optical Society of America OCIS codes: (320.5520) Pulse compression; (320.7110) Ultrafast nonlinear optics.

References and links 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, 509–513 (2001). 2. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature 427, 817–821 (2004). 3. P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, “Attosecond angular streaking,” Nature Physics 4, 565–570 (2008). 4. M. Nisoli, S. de Silvestri, O. Svelto, R. Szipöcz, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997). 5. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004). 6. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse-compression to the single cycle limit by filamentation in a gaz with a pressure gradient,” Opt. Lett. 30, 2657–2659 (2005). 7. A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Selfcompression of ultrashort laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006). 8. A. Mysyrowicz, A. Couairon, and U. Keller, “Self-compression of optical laser pulses by filamentation,” New J. Phys. 10, 025023 (2008).

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Received 29 Apr 2009; revised 15 Jun 2009; accepted 15 Jun 2009; published 18 Jun 2009

22 June 2009 / Vol. 17, No. 13 / OPTICS EXPRESS 11122

9. A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “Generation of sub-10-fs, 5-mJ-optical pulses using a hollow fiber with a pressure gradient,” Appl. Phys. Lett. 86, 111116 (2005). 10. S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 17626–17636 (2008). 11. H. S. Chakraborty, M. B. Gaarde, and A. Couairon, “Single attosecond pulses from high harmonics driven by self-compressed filaments,” Opt. Lett. 31, 3662–3664 (2006). 12. A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814–053824 (2008). 13. F. Tavella, A. Marcinkevicius, and F. Krausz, “90 mJ parametric chirped pulse amplification of 10 fs pulses,” Opt. Express 14, 12822–12827 (2006). 14. A. Dubietis, R. Butkus, and A. P. Piskarskas, “Trends in Chirped Pulse Optical Parametric Amplification,” IEEE J. SEL. Top. Quantum Electron. 12, 163–172 (2006). 15. M. Nurhuda, A. Suda, S. Bohman, S. Yamaguchi, and K. Midorikawa, “Optical Pulse Compression of Ultrashort Laser Pulses in an Argon-Filled Planar Waveguide,” Phys. Rev. Lett. 97, 153902 (2006). 16. J. Chen, A. Suda, E. J. Takahashi, M. Nurhuda, and K. Midorikawa, “Compression of intense ultrashort laser pulses in a gas-filled planar waveguide,” Opt. Lett. 33, 2992–2994 (2008). 17. S. Akturk, C. L. Arnold, B. Zhou, and A. Mysyrowicz, “High energy ultrashort laser pulse compression in hollow planar waveguides,” Opt. Lett. 34, 1462–1464 (2009). 18. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007). 19. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997). 20. G. Tempea and T. Brabec, “Theory of self-focusing in a hollow waveguide,” Opt. Lett. 23, 762–764 (1998). 21. A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966). 22. Dalgarno and Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. Roy. Soc. London Ser. A 259, 424–429 (1966). 23. G. Fibich, S. Eisenmann, B. Ilan, Y. Erlich, M. Fraenkel, Z. Henis, A. L. Gaeta, and A. Zigler, “Self-focusing distance of very high power laser pulses,” Opt. Express 13, 5897–5903 (2005). 24. V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” Zh. Eksper. Teor. Fiz. Pis’ma 3, 471–476 (1966). [JETP Lett. 3 (1966) 307-310].

1.

Introduction

One of the main goals of today’s ultrafast nonlinear optics is the compression of ultrashort laser pulses down to the few-cycle regime. Intense few-cycle infrared (IR) laser pulses with reproducible carrier envelope offset are key ingredients in attosecond physics, serving both as driving pulses for the generation of intense coherent sources in the extreme ultraviolet (XUV) wavelengths [1] and as short intense streaking pulses in the near infrared [2, 3]. Near singlecycle pulses are commonly generated through nonlinear propagation in gas-filled hollow fibers [4] or through optical filamentation in noble gases [5, 6, 7, 8]. Due to potential damage to the fiber, the hollow fiber scheme supports pulse energies typically limited to sub-millijoules, in particular when driven at kHz-repetition rates. At low repetition rate and by using a pressure gradient along the fiber the output was recently increased to some millijoules of pulse energy [9]. Pulse compression through filamentation is limited to the same energy levels, caused by intensity clamping, inherent chirp and angular dispersion within the filament [10, 11, 12] or by the onset of multiple filaments. To date, few-cycle pulses with higher energies (up to ∼100 mJ) are mainly generated through optical parametric chirped pulse amplification (OPCPA) [13, 14]. These setups involve considerable experimental complexity and require the use of additional pump lasers. Recently, the theoretical work of Nurhuda et al. [15] suggested a compression scheme using gas-filled planar hollow waveguides, which can address the issue of energy upscalability with significantly less experimental complexity. As the beam is guided in only one transverse direction (short axis), the perpendicular direction (long axis) can be utilized to freely adjust the beam size and intensity with the objective of limiting photo ionization on the one hand, and achieving strong self-phase modulation (SPM) and spectral broadening, essential to reach the few-cycle #110742 - $15.00 USD

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regime, on the other hand. While the simulation results presented by Nurhuda et al. [15] are promising, the initial experiments by Chen et al. and Akturk et al. showed that the transverse spatial propagation dynamics imposes severe restrictions on the energy up-scalability [16, 17]. Imperfections and noise in the input spatial mode are amplified by small-scale self-focusing, resulting in output beams with complicated spatial structure and multiple filaments. Nonetheless, the planar waveguide scheme holds its promise for high energy pulse compression, but a better understanding and more practical and complete analysis of nonlinear pulse propagation inside the waveguide is needed. In this work, we present a comprehensive analysis of nonlinear propagation and pulse compression via planar hollow waveguides. In practice a planar hollow waveguide can be composed of two polished glass surfaces facing each other and separated by thin spacers. It should be noted that this structure strictly speaking is not a planar waveguide, since the modes are lossy. However, the losses are small for the thickness of the spacers considered. For simplicity we keep the term waveguide throughout the paper. We present the results of detailed (3+1)dimensional simulations of the spatio-temporal pulse dynamics in the waveguide, which provides understanding of the energy and compressibility limits of this technique, from which a practical criterion to reach the best pulse compression without compromising the spatial mode is established. Careful validation of our modeling is achieved by comparing simulated compressed pulse temporal shape and spatial mode with experimental results [17]. The model is then applied to define the conditions for the compression of very energetic pulses (>100 mJ) down to the few-cycle regime (100 mJ) to durations of sub 10 fs; and second, the compression of pulses, which already are in the few-cycle regime, to further advance to the single-cycle regime. The parameters are listed in Tab. 1. For the sake of simplicity we assume Gaussian spatial and temporal beam profiles and choose conditions, which can also be indicated in Fig. 3 (open stars). However, due to the different pulse durations only the length scale (lower axis) but not the energy scale (upper axis) is applicable. The compressed temporal output profiles for both cases are shown in Fig. 4. For the high energy pulse we calculate a compression from 40 fs duration to below 10 fs at 100 mJ output energy (left column). The short pulse can be compressed from 10 fs to below 3 fs (almost a single-cycle pulse) at energy of 15.8 mJ (right column), provided chirped mirrors of sufficient bandwidth (500 − 1200 nm) are available. The 2D plots of the compressed pulse profiles (upper row) reveal a homogeneous compression close to the axis, whereas the pulse becomes longer towards the edge of the profile due to less selfphase modulation. For the case of the 100 mJ pulse (Fig. 4, left column) about 70 % of the pulse energy falls within a duration of 1.5 times the duration at the center. Simultaneously, the compressed pulse features a phase and pulse front delay in the center. Therefore, to achieve good #110742 - $15.00 USD

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focusability, the spatial phase has to be either pre or post compensated by, e.g. adaptive optics. Table 1. Parameters used for the simulations in Fig. 1 and 2 and in Fig. 4 left and right

3.

Description

Fig. 1, Fig. 2

Fig. 4 left

Fig. 4 right

Input energy (mJ) Pulse duration (FWHM) (fs) Waveguide half separation a (μ m) Beam size guided direction wx (μ m) Beam size free direction wy (mm) Intensity at the input I0 (Wcm−2 ) Argon pressure (atm) Length of the waveguide (cm)

8.7 43 63.5 50.2 7.2 3.35 × 1013 1.5 21

107 40 63.5 50.2 95 3.35 × 1013 1.5 21

16.7 10 63.5 50.2 40 5 × 1013 1 16

Conclusion

In conclusion, we have investigated the potential of planar hollow waveguides for the compression of ultrashort laser pulses in practical experimental conditions. Stability analysis revealed that the limit of possible compression is given by a B-integral threshold determined by the input spatial beam profile. Nonetheless, within the regime of stable propagation the scheme scales up to high energies and can as well be applied to advance from the few-cycle to the single-cycle regime. In this respect a two-stage compression seems feasible, with the additional benefit of also employing the waveguide in the second stage to filter spatial noise generated within the first stage. Acknowledgements We gratefully acknowledge the funding of C.L. Arnold by the Deutsche Akademie der Naturforscher Leopoldina, Grant No. BMBF-LPD 9901/8-181.

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