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Frequency-tunable sub-two-cycle 60-MW-peak-power free-space waveforms in the mid-infrared A. A. Lanin,1,2 A. A. Voronin,1,2 E. A. Stepanov,1,2 A. B. Fedotov,1,2 and A. M. Zheltikov1,2,3,4,* 1

Physics Department, International Laser Center, M. V. Lomonosov Moscow State University, Vorob’evy Gory, Moscow 119992, Russia 2 Russian Quantum Center, 143025 Skolkovo, Moscow Region, Russia 3

Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA 4

Kurchatov Institute National Research Center, Moscow 123098, Russia *Corresponding author: [email protected]

Received September 3, 2014; revised October 2, 2014; accepted October 2, 2014; posted October 6, 2014 (Doc. ID 222471); published November 6, 2014 A physical scenario whereby freely propagating mid-infrared pulses can be compressed to pulse widths close to the field cycle is identified. Generation of tunable few-cycle pulses in the wavelength range from 4.2 to 6.8 μm is demonstrated at a 1-kHz repetition rate through self-focusing-assisted spectral broadening in a normally dispersive, highly nonlinear semiconductor material, followed by pulse compression in the regime of anomalous dispersion, where the dispersion-induced phase shift is finely tuned by adjusting the overall thickness of anomalously dispersive components. Sub-two-cycle pulses with a peak power up to 60 MW are generated in the range of central wavelengths tunable from 5.9 to 6.3 μm. © 2014 Optical Society of America OCIS codes: (320.5520) Pulse compression; (320.7110) Ultrafast nonlinear optics. http://dx.doi.org/10.1364/OL.39.006430

Recent impressive progress in the generation of highpower ultrashort pulses in the mid-infrared [1] opens new horizons in ultrafast optical science and technologies, allowing the generation of unprecedentedly broad high-harmonic spectra [2], enabling lasing in laserinduced filaments [3], and revealing unusual phenomena and unexpected properties of materials in the midinfrared range [4,5]. One of the key challenges of ultrafast optical science in the mid-infrared that still needs to be addressed is finding the routes toward efficient generation of few- and singlecycle mid-IR pulses. Several promising techniques have been proposed to confront this challenge. Generation of subcycle pulses at a central wavelength of 3.9 μm has been demonstrated using filamentation of a twocolor laser field consisting of a powerful ultrashort near-IR pulse and its second harmonic [6]. The throughput of this method of pulse compression, however, is inevitably very low. Optical parametric amplification using periodically poled lithium tantalate has been shown to enable few-cycle pulse generation in the wavelength region from 2 to 5 μm [7]. Self-compression of midinfrared pulses with a central wavelength of 3.1 μm to a sub-three-cycle pulse width has been demonstrated using an anomalously dispersive solid dielectric [8,9]. However, pulse compression in the regime of anomalous dispersion is usually not easily scalable to higher energies and shorter pulse widths because formation of soliton transients involves a delicate balance between the phase shifts induced by dispersion and nonlinearity. Theoretical studies show that high-power sub-100-fs midIR pulses available from optical parametric chirped-pulse amplification can be compressed to few-cycle pulse widths using filamentation and gas-filled hollow waveguides [10]. These methods, however, are limited to the mid-IR range centered at approximately 4 μm, where an efficient solid-state source of high-power sub-100-fs mid-IR pulses is available. Herein, we identify a physical scenario whereby freely propagating mid-infrared pulses can be compressed to 0146-9592/14/226430-04$15.00/0

pulse widths close to the field cycle. This physical scenario involves self-focusing-assisted spectral broadening in a normally dispersive, highly nonlinear semiconductor material, followed by pulse compression in the regime of anomalous dispersion, where the dispersion-induced phase shift is finely tuned by adjusting the overall thickness of anomalously dispersive components. This approach is shown to enable the generation of tunable few-cycle pulses in the wavelength range from 4.2 to 6.8 μm, yielding field waveforms with a pulse width of less than 1.5T 0 , where T 0 is the field cycle, and a peak power up to 60 MW at a central wavelength of 5.9 μm. In the experiments, we use a frequency-tunable source of ultrashort pulses in the mid-IR [11], which involves two sequential stages of nonlinear-optical downconversion (Fig. 1). At the first stage, 65 fs, 0.8 mJ, 810 nm, 1 kHz pulses delivered by a Ti:sapphire laser consisting of a master oscillator and a multipass amplifier are used to produce a broadband seed signal through supercontinuum generation in a sapphire plate and serve as a pump for an optical parametric amplification (OPA) of the seed signal in a beta barium borate (BBO) crystal. As a result of this OPA process, ωp  ωs  ωi , the Ti:sapphire pump field at the central frequency ωp amplifies the broadband seed signal at the frequency ωs and gives rise to an idler pulse with a frequency ωi . Adjusting phase matching through a rotation of the BBO crystal, we were able to tune the signal and idler wavelengths in the ranges of 1150–1580 and 1620–2300 nm, respectively. The signal and idler pulses delivered by the OPA are characterized using the cross-correlation frequency-resolved optical gating (XFROG) technique by sum frequency mixing these pulses with the 65 fs, 810 nm Ti:sapphire laser output in a thin 50 μm BBO crystal. At the second stage (Fig. 1), the signal and idler OPA outputs were used to produce a wavelength tunable field in the mid-IR through difference–frequency generation (DFG) ωd  ωs –ωi in an AgGaS2 (AGS) crystal [12,13]. The central wavelength of the DFG signal generated as a result of this process can be tuned from 2.85 to © 2014 Optical Society of America

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Fig. 1. Experimental setup: Ti:S, mode-locked Ti:sapphire master oscillator; MPA, multipass amplifier; OPA, optical parametric amplifier; DFG, difference frequency generation unit; LPF, longpass filter; SPF, shortpass filter; L, BK7 glass lens; BFL, BaF2 lens; FWM, four-wave mixing in a gas medium; PMT, photomultiplier; LIA, lock-in amplifier.

15 μm by rotating the AGS crystal. The DFG field is separated from the signal and idler waves with a longpass filter, blocking radiation with wavelengths shorter than 2.5 μm. The spectrum of the DFG radiation is measured with the use of a pyroelectric or cooled HgCdTe detector connected with a lock-in amplifier and a homemade monochromator with replaceable 75, 150, and 300 grooves/mm gratings. The power of the DFG output was measured using a thermal power meter. Energies above 0.5 μJ were achieved for the short-pulse DFG output everywhere in the range of wavelengths from 2.7 to 13.6 μm [11]. Radial field intensity profiles in mid-IR beams were measured using a 124 × 124 pixel pyroelectric array camera (Pyrocam III, Spiricon). The DFG output, focused with a 75 mm focal length BaF2 lens, is then transmitted through a GaAs plate of variable thickness, which transforms the DFG signal into supercontinuum radiation, whose spectrum may, in certain regimes, span more than an octave in the mid-IR range (Figs. 2 and 3). The supercontinuum beam is

Fig. 2. Four-wave mixing (FWM) cross-correlation frequencyresolved optical gating (XFROG) traces of compressed mid-IR pulses behind a 7 mm GaAs plate and a pulse compressor consisting of a 3.5 mm BaF2 lens only [(a), (b)] and a 3.5 mm BaF2 lens combined with (c) a 1.5 mm BaF2 plate, (d) a 3.0 mm BaF2 plate and a 2.0 mm CaF2 plate, and (e) a 4.5 mm BaF2 plate, 2.0 mm CaF2 plate, and 2.0 mm MgF2 plate. Input pulse energy is 2.3 μJ. Input pulse widths are (a) 190 fs, (b) 140 fs, (c) 120 fs, (d) 80 fs, and (e) 170 fs.

Fig. 3. (a)–(e) Spectra (solid and dashed lines) and spectral phases (dashed–dotted lines) and (f)–(j) temporal envelopes (solid and dashed lines) and phases (dashed–dotted lines) of compressed mid-IR pulses behind a 7 mm GaAs plate and a pulse compressor consisting of a 3.5 mm BaF2 lens only [(a), (b), (f), and (g)] and a 3.5 mm BaF2 lens combined with [(c) and (h)] a 1.5 mm BaF2 plate, [(d) and (i)] a 3.0 mm BaF2 plate and a 2.0-mm CaF2 plate, and [(e) and (j)] a 4.5 mm BaF2 plate, 2.0 mm CaF2 plate, and 2.0 mm MgF2 plate: (solid blue lines) experimental results and (dashed rose lines) simulations. Spectra of the input mid-IR pulses are shown by shading with dotted contours. Input pulse energy is 2.3 μJ. Input pulse widths are [(a) and (f)] 190 fs, [(b) and (g)] 140 fs, [(c) and (h)] 120 fs, [(d) and (i)] 80 fs, and [(e) and (j)] 170 fs. Pulse widths of the compressed supercontinuum pulses are specified in the panels.

collimated with a 100 mm focal length BaF2 lens, whose central part has a thickness of 3.5 mm. Because of its anomalous dispersion, this lens can compensate phase distortions of the supercontinuum pulse produced by the GaAs plate. For a fine adjustment of dispersioninduced phase shifts, this lens is combined with BaF2 , CaF2 , and MgF2 plates of variable thickness. The use of three different materials enables an accurate tailoring of the overall composite dispersion profile in the spectral range from 4.2 to 6.8 μm, allowing high-order phase shifts to be finely tuned by varying the thicknesses of individual plates for the highest quality and minimal distortions of compressed pulses. Mid-IR pulses are characterized in our experiments using XFROG based on four-wave mixing (FWM) in a gas medium [7,11,14]. To this end, an ultrashort mid-IR pulse is combined with a reference Ti:sapphire laser pulse on

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an off-axis 100 mm focal length parabolic mirror with a hole, which focuses both pulses into a molecular or atomic gas (Fig. 1) to generate an FWM signal through the ωFWM  2ωp –ωd process. The FWM signal is then collimated with a 75 mm focal length BK7 glass lens, separated from the IR beams with a set of appropriate filters, and analyzed using a Hamamatsu H9307-02 photomultiplier tube and an Ocean Optics spectrometer. The third harmonic of the Ti:sapphire laser pump is attenuated due to absorption in the BK7 glass. For the shortest pulse widths of compressed pulses, octave-spanning supercontinua generated by a 120 fs, 5.9 μm, 2.3 μJ mid-IR DFG output in the 7-mm-thick GaAs plate were used [Fig. 3(c)]. Analysis of the radial field intensity profile across the supercontinuum beam measured behind the GaAs plate reveals intensity-dependent beam patterns [Figs. 4(a)–4(e)], suggesting that supercontinuum generation in the GaAs plate is accompanied by spatial self-action phenomena. To understand this regime of nonlinear-optical spatiotemporal field transformation, we use a numerical solution of the threedimensional time-dependent generalized nonlinear Schrödinger equation [4,15,16] for the amplitude of the field, including all the key physical phenomena, such as dispersion of the material, beam diffraction, Kerr nonlinearities, pulse self-steepening, spatial self-action phenomena, ionization-induced optical nonlinearities, and plasma loss and dispersion. The field evolution equation is solved jointly with the rate equation for the electron density, which includes photoionization and impact ionization. Simulations are performed for typical parameters of normally and anomalously dispersive materials used in experiments—a band gap of 1.4 eV for GaAs, 11.0 eV for BaF2 , 12.1 eV for CaF2 , and 11.8 eV for MgF2 —and the nonlinear refractive index n2 ≈ 3 · 10−14 cm2 ∕W for GaAs, 2.85 · 10−16 cm2 ∕W for BaF2 , 1.9 · 10−16 cm2 ∕W for CaF2 , and 0.9 · 10−16 cm2 ∕W for MgF2 . The higher-order Kerr effect (HOKE) coefficient for GaAs was taken equal to n4 ≈ 1.6 · 10−25 cm4 ∕W2 [17]. The nonlinearity of BaF2 , CaF2 , and MgF2 is more than two orders of magnitude lower than the nonlinearity of GaAs. Nonlinear effects in the compressor components are therefore of no significance for supercontinuum evolution. Dispersion of GaAs, BaF2 , CaF2 , and MgF2 was included in the model through the Sellmeier equation [18]. Simulations were performed using a message passing parallel programming interface on the Chebyshev and Lomonosov supercomputer

clusters of Moscow State University. The split-step Fourier method was implemented in our codes, with the nonlinear part solved by the implicit fifth-order Runge–Kutta method. Numerical simulations reproduce all the key features and tendencies in supercontinuum spectra [Figs. 3(a)– 3(e)], pulse shapes [Figs. 3(f)–3(j)], and beam profiles (Fig. 4) measured as functions of the initial field intensity and the initial central wavelength of the driver, demonstrating the predictive power of our model. Numerical analysis of the spatiotemporal dynamics of freely propagating mid-IR waveforms (Fig. 5) shows that spectral broadening in the GaAs plate is dominated by self-phase modulation (SPM). Pulse self-steepening becomes more significant toward the exit surface of the GaAs plate as the bandwidth approaches an octave. Self-steepening induces a spectral blue shift, suppressing the long wavelength tail of the spectrum and enhancing its highfrequency wing [Figs. 3(b) and 3(c)]. Ionization effects do not play a significant role in nonlinear field dynamics in the range of field intensities studied in this work. For typical conditions of our experiments, the electron density induced by the mid-IR driver rapidly grows toward the exit surface of the GaAs plate but remains low within the entire propagation path (exceeding 1016 cm−3 only within the last few millimeters of the plate), having virtually no influence on field evolution. The shortest pulse widths were achieved in experiments where a 3.5-mm-thick BaF2 lens was combined with a 1.5 mm BaF2 plate. As our FWM XFROG measurements show [Fig. 2(c)], the supercontinuum output of the GaAs plate in these experiments is compressed to a pulse width τc ≈ 29 fs [solid line in Fig. 3(h)], which corresponds to less than 1.5 field cycles at a central wavelength λ0 ≈ 5.9 μm. With the energy of this 29 fs pulse W 0 ≈ 1.7 μJ, its peak power is approximately 60 MW. The beam dynamics and temporal evolution of mid-IR pulses simulated for these experiments using our numerical model are presented in Figs. 5(a) and 5(b). Dispersion and diffraction, as can be seen from these simulations, tend to reduce the field intensity, lowering the efficiency of SPM. Both dispersion and diffraction lengths, lds and ldf , are of the same order as the thickness of the GaAs plate in our experiments, lds ≈ 9.0 mm and ldf ≈ 5.6 mm. Self-focusing, however, suppresses diffraction-induced beam divergence [Fig. 5(a)]. The characteristic focusing length of the nonlinear lens, estimated

Fig. 4. Radial field intensity profiles in the supercontinuum beam in the far-field zone behind the GaAs plate: (a)–(e) experiment and (f)–(k) simulations. Input field intensity is [(a) and (f)] 1 GW∕cm2 , [(b) and (g)] 16 GW∕cm2 , [(c) and (h)] 24 GW∕cm2 , [(d) and (i)] 29 GW∕cm2 , and [(e) and (k)] 38 GW∕cm2 .

Fig. 5. (a) Beam dynamics and (b) temporal evolution of the mid-IR field in the normally (GaAs) and anomalously (BaF2 ) dispersive components of the pulse compression scheme. The rms and FWHM beam radii are shown by the rose and black lines, respectively. Input spectrum and output pulse envelope are shown in Figs. 2(c) and 2(h), respectively.

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in accordance with the Marburger formula [19], is lM ≈ 4.6 mm. However, because of the HOKE, the focal length of the Kerr lens, lsf ≈ 7.3 mm, is slightly larger than the thickness of the GaAs plate. Such a nonlinear lens, whose focal length is matched with the propagation path in a nonlinear medium, keeps the field intensity high along the entire propagation path within the GaAs plate [Fig. 5(a)], enhancing SPM-induced spectral broadening. As a result, the spectrum of the mid-IR supercontinuum at the exit interface of the GaAs plate, z  7 mm in Fig 5(b), has a spectrum spanning more than an octave [Fig. 3(c)]. The FWHM pulse width of this waveform, τ ≈ 190 fs, is stretched relative to the input pulse width, τ0  120 fs [Fig. 5(b)], due to dispersion. The beam profile of supercontinuum radiation displays a pattern typical of self-focusing [Figs. 4(d) and 5(a)]. Some asymmetry observed in the radial intensity profile of the supercontinuum output [Figs. 4(a)–4(e)] is due to a slight asymmetry of the DFG output beam profile. Compression to sub-two-cycle pulse widths was implemented, at least within the range of central wavelengths from 5.9 to 6.3 μm. Generation of 35 fs pulses at λ0 ≈ 6.3 μm (τc ≈ 1.7T 0 ) using a 7 mm GaAs plate and a 3.5 mm BaF2 lens, which serves both to collimate the supercontinuum beam and compress the supercontinuum pulse, is demonstrated in Figs. 3(b) and 3(g). Within the entire tunability range, the residual phase distortions of compressed pulses [dashed–dotted lines in Figs. 3(a)– 3(e)] tend to translate into a lower intensity spike in the trailing edge of the pulse [Figs. 3(h) and 3(j)]. The ratio of the intensity of this spike to the intensity of the central pulse varies across the tunability range of sub-two-cycle pulses, changing from 0.046 for λ0 ≈ 5.9 μm [Fig. 3(h)] to 0.048 for λ0 ≈ 6.3 μm [Fig. 3(g)]. To summarize, we have identified a physical scenario whereby freely propagating mid-infrared pulses can be compressed to pulse widths close to the field cycle. Generation of tunable few-cycle pulses in the wavelength range from 4.2 to 6.8 μm has been demonstrated at a repetition rate of 1 kHz through self-focusing-assisted spectral broadening in a GaAs plate, serving as a normally dispersive, highly nonlinear material, followed by pulse compression in the regime of anomalous dispersion, where the dispersion-induced phase shift is finely tuned by adjusting the overall thickness of anomalously dispersive components. This approach is shown to enable the generation of sub-two-cycle pulses with a peak power up to 60 MW in the range of central wavelengths tunable from 5.9 to 6.3 μm. This research was supported in part by the Russian Foundation for Basic Research (Project Nos. 13-02-

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01465, 13-02-92115, and 14-02-00784) and the Welch Foundation (Grant No. A-1801). Research into the nonlinear optics in the mid-infrared has been supported by the Russian Science Foundation (Project No. 14-12-00772). The research of A. A. V. was also supported by the Dynasty Foundation. References 1. G. Andriukaitis, T. Balčiūnas, S. Ališauskas, A. Pugžlys, A. Baltuška, T. Popmintchev, M.-C. Chen, M. M. Murnane, and H. C. Kapteyn, Opt. Lett. 36, 2755 (2011). 2. T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, Science 336, 1287 (2012). 3. D. Kartashov, S. Ališauskas, G. Andriukaitis, A. Pugžlys, M. Shneider, A. Zheltikov, S. L. Chin, and A. Baltuška, Phys. Rev. A 86, 033831 (2012). 4. D. Kartashov, S. Ališauskas, A. Pugžlys, A. A. Voronin, A. M. Zheltikov, and A. Baltuška, Opt. Lett. 37, 2268 (2012). 5. E. E. Serebryannikov and A. M. Zheltikov, Phys. Rev. Lett. 113, 043901 (2014). 6. Y. Nomura, H. Shirai, K. Ishii, N. Tsurumachi, A. A. Voronin, A. M. Zheltikov, and T. Fuji, Opt. Express 20, 24741 (2012). 7. D. Brida, M. Marangoni, C. Manzoni, S. De Silvestri, and G. Cerullo, Opt. Lett. 33, 2901 (2008). 8. F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, Nat. Commun. 3, 807 (2012). 9. M. Hemmer, M. Baudisch, A. Thai, A. Couairon, and J. Biegert, Opt. Express 21, 28095 (2013). 10. A. A. Voronin and A. M. Zheltikov, Phys. Rev. A 90, 043807 (2014). 11. A. A. Lanin, A. B. Fedotov, and A. M. Zheltikov, J. Opt. Soc. Am. B 31, 1901 (2014). 12. V. Petrov, F. Rotermund, and F. Noack, J. Opt. A Pure Appl. Opt. 3, R1 (2001). 13. R. A. Kaindl, M. Wurm, K. Reimann, P. Hamm, A. M. Weiner, and M. Woerner, J. Opt. Soc. Am. B 17, 2086 (2000). 14. Y. Nomura, Y.-T. Wang, T. Kozai, H. Shrai, A. Yabushita, C.-W. Luo, S. Nakanishi, and T. Fuji, Opt. Express 21, 18249 (2013). 15. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007). 16. A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007). 17. D. Milam, M. J. Weber, and A. J. Glass, Appl. Phys. Lett. 31, 822 (1977). 18. M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. 4. 19. J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).

Frequency-tunable sub-two-cycle 60-MW-peak-power free-space waveforms in the mid-infrared.

A physical scenario whereby freely propagating mid-infrared pulses can be compressed to pulse widths close to the field cycle is identified. Generatio...
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