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1 LASER PHYSICS LETTERS EDITORIAL BOARD W. Becker, Berlin D. Chorvat, Bratislava S. DeSilvestri, Milan M. V. Fedorov, Moscow A. Gaeta, Ithaca S. A. Gonchukov, Moscow M. Jelinek, Prague U. Keller, Zürich J. Lademann, Berlin J. T. Manassah, New York P. Meystre, Tucson R. B. Miles, Princeton P. P. Pashinin, Moscow G. Petite, Saclay L. P. Pitaevskii, Trento M. Pollnau, Enschede K. A. Prokhorov, Moscow M. Scalora, Huntsville V. M. Shalaev, West Lafayette J. E. Sipe, Toronto Ken-ichi Ueda, Tokyo I. A. Walmsley, Oxford E. Wintner, Vienna E. Yablonovitch, Los Angeles V. M. Yermachenko, Moscow I. V. Yevseyev, Moscow V. I. Yukalov, Dubna A. M. Zheltikov, Moscow REPRINT

2 Laser Phys. Lett. 8, No. 1, (211) / DOI 1.12/lapl Abstract: A systematic investigation of external focusing effect on terahertz (THz) emission from a two-color femtosecond laser-induced filament in air is demonstrated. By collecting the THz emission precisely under different external focusing conditions, an optimum external focal length around 5 cm was observed to generate stronger THz emission. The optimum dependence on the filament volume and the filament s core intensity with external focusing could be responsible for this stronger THz emission. Filament Variable metallic iris THz pulse Si filter α α max Schematic diagram of the THz divergence measurement External focusing effect on terahertz emission from a two-color femtosecond laser-induced filament in air T.-J. Wang, 1, C. Marceau, 1 S. Yuan, 1 Y. Chen, 1 Q. Wang, 1 F. Théberge, 2 M. Châteauneuf, 2 J. Dubois, 2 and S.L. Chin 1 1 Centre d Optique, Photonique et Laser (COPL) and Département de Physique, de Génie Physique et D optique, Université Laval, Québec City, Québec G1V A6, Canada 2 Defence Research and Development Canada-Valcartier, 2459 Pie-XI Blvd. North, Québec City, Québec G3J 1X5, Canada Received: 21 August 21, Revised: 5 September 21, Accepted: 8 September 21 Published online: 4 November 21 Key words: femtosecond laser filamentation; THz emission; two-color filamentation 1. Introduction Femtosecond laser filamentation [1] in gases and transparent materials finds important applications due to its novel properties such as intensity clamping, self-spatial filtering, self-stabilization, and self-steepening [2 8]. Ultra-broad bandwidth pulses generated from filaments cover from UV to microwave [9 11]. Because of its impressive application area of astrophysics, plasma physics, spectroscopy, medical imaging, biology, and communications [12], terahertz (THz) source attracts a lot of interest [13]. Compared to THz emitters based on semiconductor antennas or optical rectification in nonlinear crystals, THz emission from filaments in gases, especially in air, would provide a new prospective tool for remote THz nonlinear optics and spectroscopy [14], since the onset of the filament can be remotely controlled, in principle, by the initial laser parameters: beam diameter, divergence, and pulse duration [1]. D.J. Cook and R.M. Hochstrasser [15] reported the first intense THz emission from a filament in gas (noble gases and air) induced by a femtosecond Ti:sapphire laser pulse (fundamental wave, FW) and its second harmonic wave (SHW) in 2. A lot of research interest on the THz emission from two-color filamentation has been generated since then [16 28]. THz pulse energy from the two-color (FW and its SHW) scheme can be increased by few orders of magnitude as compared to the single FW excitation only [15]. THz electric field as high as 4 kv/cm [19] and a super-broadband THz spectrum up to 75 THz (λ =4 μm) with μj pulse energy [2,21] were reported. Several techniques based on the two-color laser-induced filamentation such as applying a DC field along two-color filaments [22], the control of multiple air plasmas [23,24], pump beam size [25] and pump pulse chirp [21] have been reported to Corresponding author: tie-jun.wang.1@ulaval.ca, tjwang27@yahoo.com

3 58 T.-J. Wang, C. Marceau, et al. : External focusing effect on terahertz emission β-bbo QWP HWP DM3 L PM DM1 CP Si PD HWP DM2 Tf W Lock-in amplifier Metallic variable attenuators Computer Figure 1 (online color at ) Schematic diagram of the experimental setup. A.1 mm thick type-i β-bbo crystal was used for the frequency doubling of the FW. DM1-DM3 are 45 dichroic mirrors, which have high reflectivity around 4 nm and a high transmission around 8 nm. QWP and HWP are quarter wave plate and half wave plate, respectively. W ultra-thin wedges, CP chopper, L lens, PM parabolic mirrors, PD pyroelectric detector, Si and Tf are silicon and Teflon filters, respectively generate stronger THz emission. The polarization of THz pulse from this bichromatic excitation has also been well interpreted based on the four-wave mixing (FWM) model by fitting the experimental observation with the theoretical prediction [26 29]. Moreover, the spatial distribution of THz emission from the bichromatic excitation has been reported by inserting a frequency-doubling crystal after a focusing lens [3]. The forward direction of the emission is more than three orders stronger than that of the sideway emission within a comparable solid angle. The forward directional emission is associated with the plasma filament length. As the length of filament increases, the divergence angle of THz emission decreases [3]. In this work, we systematically investigated external focusing effect on THz emission from a two-color femtosecond laser-induced filament in air. An optimal focusing condition was observed to generate stronger THz emission. 2. Experimental method and setup The experimental setup is illustrated in Fig. 1. A 1 khz, 8 nm, 2.2 mj, 1 mm in diameter (intensity, 1/e 2 )Tisapphire laser beam was used in the experiment. The collimated pump pulse (FW) propagated through a.1-mmthick type-i-barium borate (β-bbo) crystal to produce the SHW. In order to independently control the FW and SHW, the two-color laser pulses were separated by a 45 dichroic mirror. A translation stage and a pair of ultra-thin wedges were inserted in the SHW path to coarsely and precisely control the relative phase between the FW and SHW, respectively. Two metallic variable attenuators independently provided a precise pulse energy adjustment for each beam. Different polarization schemes could be achieved by rotating a quarter wave plate and a half wave plate in the FW path and a half wave plate in the SHW path. The two pulses were made collinear by another dichroic mirror. A plasma filament was formed in air using a focusing lens. The FW and SHW beams were rejected (absorbed and reflected) by a.5-mm-thick Si filter, which transmits the THz pulse. This Si filter also served to protect the parabolic mirrors from being damaged by the high intensity soon after the filament. Damage of the surface of the Si filter did occur but was limited to a small localized area (diameter less than one mm) whose influence on the THz transmission is negligible because of the latter s large divergence angle. The THz emission was collected and focused on a pyroelectric detector (Coherent P4-45CC) by a pair of 9 off-axis, 4 Au-coated parabolic mirrors. A lock-in amplifier (with a chopper) was used to improve the detection sensitivity. By controlling the polarizations of the FW and SHW, it was found that the strongest THz emission occurs when the polarization of FW is parallel to that of SHW, in agreement with [12]. All of the following measurements were done under the parallel polarization scheme. The THz divergence is expected to depend on the focal length of the focusing lens [3]. Therefore, for a quantitative comparison of the THz energy using different lenses, the emission was integrated over the largest possible solid angle by forming the filament as close as possible to the parabolic mirror. The following verification was

4 Laser Phys. Lett. 8, No. 1 (211) 59 (a) Filament (b) Variable metallic iris THz pulse Si filter α α max f = 1 cm f = 2 cm f = 53 cm f = 8 cm f = 1 cm 1 1 THz energy, arb. units α max FW pulse energy, mj f = 2 cm f = 53 cm f = 8 cm f = 1 cm (a) α, degree Si Si + Teflon Figure 2 (online color at ) Schematic diagram of the THz divergence measurement (a) and energy divergence of the THz emission for the 53 cm focusing lens (b). The vertical dashed line in (b) represents α max, maximum acceptance angle of the first parabolic mirror SHW pulse energy, μj 75 (b) also made. As shown in Fig. 2a, a variable metallic iris inserted between the filament and the first parabolic mirror was used to characterize the divergence of the THz emission. The iris acceptance angle α is the half-angle formed by the iris aperture to the center of the filament. Two sets of filters (.5 mm thick Si and.5 mm thick Si plus 1.6 mm thick Teflon) were used in the experiments to verify the spectrum of the THz emission. The Si and Teflon filters are low-frequency pass filters with transmission cutoffs at around 3 THz (1 μm) and 5.5 THz (55 μm), [21,31] respectively. 3. Experimental results and discussions Typical energy divergence of THz emission from the twocolor filament is shown in Fig. 2b measured with a focusing lens having a focal length of 53 cm. The THz pulse energy in both spectral ranges increases with increasing the iris aperture and then it stays at almost a constant till the maximum acceptance angle allowed by parabolic mirror, α max. The constant THz signals at larger iris acceptance angle confirms that most of the THz emission was collected. Similar divergence results were also observed for the lenses of 1, 2, 8, and 1 cm focal lengths. Figure 3 (online color at ) FW (a) and SHW (b) pump energy dependences of THz emission for different external focusing conditions. In (a), SHW pulse energy was fixed at 88 μj and in (b), FW pulse energy was fixed at 1.2 mj (1.4 mj for 2 cm focal length lens). Si filter was used in the measurements Note that in all the experiments of different lenses, pulse durations were firstly optimized by monitoring the pyroelectric signals on the oscilloscope. The same pulse duration was found, which was around the Fourier transformlimited 45 fs. Pump energy dependence of THz emission was investigated for different focusing lenses. All the pulse energies were measured after the focusing lenses. At fixed SHW pulse energy of 88 μj, THz emission from 53 cm focal length lens was stronger than that from the others when we increased the FW pulse energy, which are shown in Fig. 3a. For the cases of 1 cm and 2 cm lenses, THz signals at high FW pump energy become saturated, which could be due to the plasma absorption at the THz frequency [2]. The same phenomenon was observed for the case of SHW pump energy dependences of THz emission at the fixed FW pulse energy of 1.2 mj (1.4 mj for 2 cm lens), which

5 6 T.-J. Wang, C. Marceau, et al. : External focusing effect on terahertz emission (a) (b) 25 Delay time, ps 5 SHW pulse energy, μj f = 1 cm f = 2 cm f = 53 cm f = 8 cm f = 1 cm Si Si + Teflon Figure 4 (online color at ) (a) THz emission as a function of delay time between the FW and SHW for different focusing lenses and (b) THz emission signal as a function of focal length of the lens. A negative delay indicates that the SHW is ahead of the FW is depicted in Fig. 3b. Si filter was used for all the measurements in Fig. 3. In order to compare the THz emission from different external focusing lenses, the pump pulse energy of the FW and of the SHW were precisely controlled by two variable metallic attenuators, respectively. Hence, 1.2 mj of the FW and 88 μj of the SHW (94 μj for 1 cm lens) were combined to form a two-color filament in air. The THz emission as a function of the delay time between the FW and SHW is depicted in Fig. 4a for five different lenses. A single silicon filter was used in the THz beam path in this case. The zero delay time was assigned at the peak position of the THz emission for each lens (the lenses have slightly different thicknesses). The peak values of the THz emission as a function of the focal length are shown in Fig. 4b for two sets of filters. The THz emission was getting stronger from 1 cm to 2 cm lens and reached a maximum with the 53 cm focusing lens then decreased with the longer focal length lenses (8 cm and 1 cm). Clear peaks were observed around 5 cm focusing condition for both THz spectral ranges using the two sets of filters. For such a focal length, the THz emission is more than 3 times stronger than with 1 2 cm focal length lenses normally used in such experiments. It is interesting to note that a similar enhancement for the 5 cm focal length lens was observed in the third harmonic (TH) emission from the FW filament in air [32,33]. This dependence of the THz emission can be interpreted by the impact of the external focusing on the volume and intensity of the filament [33]. The dependence of the filament s diameter ( fil ) on the external focal length can be explained as a balance between the laser energy confinement by the external focusing, the self-focusing and the defocusing effect of the self-generated plasma. In the case of a free propagating laser beam, the filament diameter is only determined by the dynamic equilibrium between the self-focusing and the plasma defocusing. For filament generated with lenses of focal lengths between 5 cm to 1 cm in the experiment, the external focusing concentrates more laser energy on the propagation axis and the higher intensity core of the filament enlarged. [33] In this case, the diameter of the filament increases with the decrease of the focal length and reaches a maximum diameter for the 5 cm focal length lens. Beyond this point, with shorter focal length, the diameter of the filament can no longer increase because the external focusing constrains the laser energy in a smaller cross-section and the diameter of the filament decreases. For the length (l fil )ofthe filament, it diminishes with the decrease of the external focal length. On the other hand, the laser intensity in the filament core would increase for shorter focal length and are ,9 1 13, and W/cm 2 for the 1, 5, and 1 cm focal length lenses, respectively [33]. The combined effect of the filament volume, which is proportional to l fil fil 2, and the laser intensity in the filament core reached a maximum for the focusing lens with focal length around 5 cm. Such dependence has already been verified both experimentally and theoretically [32,33]. 4. Conclusion In conclusion, external focusing effect on THz emission from a two-color femtosecond laser-induced filament in air was systematically investigated. By a precise and quantitative characterization of the conical THz emission under different focusing conditions, it was observed that the THz emission was getting stronger from 1 cm to 2 cm lens and reached a maximum with the 53 cm focusing lens then decreased with the longer focal length lenses (8 cm and 1 cm). There exists an optimum focusing condition for maximum THz emission from the two-color filamentation in air. The dependence of the filament volume and the filament s core intensity with the external focusing could be responsible for the observed phenomenon. The present results demonstrate intense THz generation and also help to

6 Laser Phys. Lett. 8, No. 1 (211) 61 understand the enhancement mechanism from a two-color laser-induced filament in air with different external focusing lenses. Acknowledgements This work was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Defence Research and Development Canada in Valcartier (DRDC-Valcartier), Canada Research Chair, Canada Foundation for Innovation (CFI), Canadian Institute for Photonics Innovation (CIPI), le Fonds Québécois pour la Recherche sur la Nature et les Technologies (FQRNT). Technical support from Mr. M. Martin is also acknowledged. References [1] S.L. Chin, Femtosecond Laser Filamentation, Springer Series on Atomic, Optical, and Plasma Physics, vol. 55 (Springer Science+Business Media, LLC, New York- Dordrecht-Heidelberg-London, 21). [2] S.L. Chin, S.A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V.P. Kandidov, O.G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (25). [3] A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (27). [4] L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 7, 1633 (27). [5] J. Kasparian and J.-P. Wolf, Opt. Express 16, 466 (28). [6] V.P. Kandidov, S.A. Shlenov, and O.G. Kosareva, Quantum Electron. 39, 25 (29). [7] O.G. Kosareva, W. Liu, N.A. Panov, J. Bernhardt, Z. Ji, M. Sharifi, R. Li, Z. Xu, J. Liu, Z. Wang, J. Ju, X. Lu, Y. Jiang, Y. Leng, X. Liang, V.P. Kandidov, and S.L. Chin, Laser Phys. 19, 1776 (29). [8] J. Zhang, X. Lu, Y.Y. Ma, T.T. Xi, Y.T. Li, Z.M. Sheng, L.M. Chen, J.L. Ma, Q.L. Dong, Z.H. Wang, and Z.Y. Wei, Laser Phys. 19, 1769 (29). [9] C.M. Zhang, J.L. Wang, X.W. Chen, Y.X. Leng, R.X. Li, and Z.Z. Xu, Laser Phys. 19, 1793 (29). [1] N.I. Zhavoronkov, Laser Phys. Lett. 6, 86 (29). [11] T.-J. Wang, J.-F. Daigle, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S.L. Chin, Laser Phys. Lett. 7, 517 (21). [12] D. Dragoman and M. Dragoman, Prog. Quantum Electron. 28, 1 (24). [13] G.Kh. Kitaeva, Laser Phys. Lett. 5, 559 (28). [14] T.-J. Wang, S. Yuan, Y. Chen, J.-F, Daigle, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, H. Zeng, and S.L. Chin, Appl. Phys. Lett., accepted for publication. [15] D.J. Cook and R.M. Hochstrasser, Opt. Lett. 25, 121 (2). [16] M. Kress, T. Löffler, S. Eden, M. Thomson, and H.G. Roskos, Opt. Lett. 29, 112 (24). [17] H.G. Roskos, M.D. Thomson, M. Kreß, and T. Löffler, Laser Photon. Rev. 1, 349 (27). [18] F. Blanchard, G. Sharma, X. Ropagnol, L. Razzari, R. Morandotti, and T. Ozaki, Opt. Express, 17, 644 (29). [19] T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, Opt. Lett. 3, 285 (25). [2] K.Y. Kim, A.J. Taylor, J.H. Glownia, and G. Rodriguez, Nat. Photon. 2, 65 (28). [21] T.-J. Wang, Y.P. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S.L. Chin, Appl. Phys. Lett. 95, (29). [22] T.-J. Wang, C. Marceau, Y.P. Chen, S. Yuan, F. Théberge, M. Châteauneuf, J. Dubois, and S.L. Chin, Appl. Phys. Lett. 96, (21). [23] J.M. Dai, X. Xie, and X.-C. Zhang, Appl. Phys. Lett. 91, (27). [24] M.-K. Chen, J.H. Kim, C.-E. Yang, S.S.Z. Yin, R.Q. Hui, and P. Ruffin, Appl. Phys. Lett. 93, (28). [25] X.-Y. Peng, C. Li, M. Chen, T. Toncian, R. Jung, O. Willi, Y.-T. Li, W.-M. Wang, S.-J. Wang, F. Liu, A. Pukhov, Z.- M. Sheng, and J. Zhang, Appl. Phys. Lett. 94, 1152 (29). [26] X. Xie, J.M. Dai, and X.-C. Zhang, Phys. Rev. Lett. 96, 755 (26). [27] A. Houard, Y. Liu, B. Prade, and A. Mysyrowicz, Opt. Lett. 33, 1195 (28). [28] Y.Z. Zhang, Y.P. Chen, S.Q. Xu, H. Lian, M.W. Wang, W.W. Liu, S.L. Chin, and G.G. Mu, Opt. Lett. 34, 2841 (29). [29] D. Dietze, J. Darmo, S. Roither, A. Pugzlys, J.N. Heyman, and K. Unterrainer, J. Opt. Soc. Am. B 26, 216 (29). [3] H. Zhong, N. Karpowicz, and X.-C. Zhang, Appl. Phys. Lett. 88, (26). [31] D.J. Benford, M.C. Gaidis, and J.W. Kooi, Appl. Opt. 42, 5118 (23). [32] F. Théberge, Third-Order Parametric Processes During the Filamentation of Ultrashort Laser Pulses in Gases, PhD thesis (Université Laval, Québec City, 27), p. 38. [33] F. Théberge, W.W. Liu, P.Tr. Simard, A. Becker, and S.L. Chin, Phys. Rev. E 74, 3646 (26).