Phase-stable sub-cycle mid-infrared conical emission from filamentation ... · conical emission from filamentation in gases ... and J. P. Wolf, “Ultrashort filaments of light

Phase-stable sub-cycle mid-infraredconical emission from filamentation

in gases

Yutaka Nomura,1 Hideto Shirai,2 Kenta Ishii,2 Noriaki Tsurumachi, 2

Alexander A. Voronin,3,4 Aleksei M. Zheltikov,3,4,5 and Takao Fuji1,∗

1Laser Research Center for Molecular Science, Institute for Molecular Science,38 Nishigonaka, Myodaiji, Okazaki 444-8585, Japan

2Faculty of Engineering, Kagawa University, 2217-20 Hayashi-cho, Takamatsu, 761-0396,Japan

3Physics Department and International Laser Center, M.V. Lomonosov Moscow StateUniversity, 119992 Moscow, Russia

4Russian Quantum Center, 143025 Skolkovo, Moscow Region, Russia5Department of Physics and Astronomy, Texas A&M University, College Station, Texas

77843-4242, USA∗[email protected]

Abstract: Sub-single-cycle pulses in the mid-infrared (MIR) region weregenerated through a conical emission from a laser-induced filament. Fun-damental and second-harmonic pulses of 25-fs Ti:sapphire amplifier outputwere focused into argon to produce phase-stable broadband MIR pulsesin a well-focusable ring-shaped beam. The beam profile and spectrum ofthe MIR field are accurately reproduced with a simple calculation basedon a four-wave mixing process. The ring-shaped pattern of the MIR beamoriginates from a dramatic confocal-parameter mismatch between the MIRfield and the laser beams.

© 2012 Optical Society of America

OCIS codes:(320.7110) Ultrafast nonlinear optics; (190.4380) Nonlinear optics, four-wavemixing; (140.3070) Infrared and far-infrared lasers.

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1962–1964 (2010).

#174536 - $15.00 USD Received 17 Aug 2012; revised 23 Sep 2012; accepted 25 Sep 2012; published 15 Oct 2012(C) 2012 OSA 22 October 2012 / Vol. 20, No. 22 / OPTICS EXPRESS 24741

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Filamentation of powerful ultrashort laser pulses in gases [1–3] is one of the most interestingphenomena in nonlinear optics. The balance between self-focusing and plasma self-defocusingmakes the pulse propagate much longer than the Rayleigh range with a very high intensity. Itresults in a dramatic enhancement of nonlinear processes occurring in the filamentation zone.This phenomenon enables high intensity pulse compression and efficient nonlinear wavelengthconversion with gas media [2,3].

Enhanced nonlinear-optical processes in laser-induced filaments suggest a new strategy forthe generation of ultrashort pulses of long-wavelength radiation [4–11]. In particular, ultra-broadband MIR pulse generation is one of the most attractive applications of the filamentationeffect. Such MIR pulses with more than one octave at full width at half maximum are very at-tractive to be applied for molecular spectroscopy, e.g. two-dimensional infrared spectroscopy.The MIR pulse generation through filamentation was firstly demonstrated in 2007 [7], and thetechnique was followed and slightly modified by several groups [8–11]. However, the precisecharacterization of the beam profile and pulse shape of the generated MIR pulses has not beenreported so far.

In this paper, we report the detailed characterization of sub-cycle MIR pulse generationthrough a four-wave mixing (FWM) process in a filament. A full characterization of the beamprofile and pulse shape of the conically emitted MIR field shows that this field was linearlypolarized, well focusable, and its pulse duration was measured as 7.4 fs, which is much shorterthan the single-cycle period of the center wavelength (3.9µm) of the pulse. The spatial andtemporal coherence of the generated MIR pulse is so high that the light source may result ina dramatic improvement in general MIR spectroscopy. Our simple numerical simulation accu-rately reproduced the beam profile and the spectrum of the MIR pulse.

The experimental setup is shown in Fig. 1. The light source was based on a Ti:sapphiremulti-pass amplifier system (800 nm, 25 fs, 0.9 mJ at 1 kHz, Femtopower compactPro, FEM-TOLASERS). The second harmonic (SH,ω2, 25 µJ) and the fundamental (ω1, 675µJ) were


filament

τ

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BFBBO

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Fig. 1. Schematic of the system. Shaded region was purged with argon at around atmo-spheric pressure. BS: beam splitter (5% reflection), BBO:β -BaB2O4 crystal (Type 1,θ = 29◦, t = 0.1 mm), D: dichroic mirror, P: periscope, CM1:r = 1 m concave mirror,CM2: r = 0.5 m concave mirror, MH: aluminium-coated mirror with a hole (φ = 7 mm),OAP: aluminium-coated off-axis parabolic mirror, BF: bandpass filter for 335-610 nm(FGB37, Thorlabs), OMA: spectrometer for ultraviolet region.

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Fig. 2. (a) A typical spectrum of the mid-infrared pulse generated through filamentationin argon (filled curve). Sharp dips at 2400 cm−1 and at around 1600 cm−1 are due toabsorption of residual carbon dioxide and water vapor, respectively. The four-wave mixingspectra calculated with the measured fundamental and the SH spectra before (dotted curve)and after (dashed curve) the filament. (b) Fundamental spectrum measured before and afterthe filament (dotted and filled curves, respectively). The spectrum did not change when thedelay time between the fundamental and the SH pulses was adjusted. (c) SH spectra whenthe delay time between the fundamental and the SH pulses was not adjusted (solid curve)and was adjusted (filled curve).

spatially and temporally overlapped and focused into argon by a concave mirror (r = −1 m),generating a bright filament with a length of∼3 cm around the beam focus. This filament gen-erated a MIR pulse (ω0) through a FWM process (ω1+ω1−ω2 → ω0). The energy of this MIRpulse was measured as∼250 nJ by using a pyroelectric detector (J-10MB-LE, Coherent). Withthis energy level, it is possible to apply the pulses for the nonlinear spectroscopy of condensedmatter. The pulse-to-pulse intensity fluctuation was about 2.5% rms.

The spectrum of the MIR pulse was measured with a home-built Fourier transform spectrom-eter. The measured spectrum is shown as a filled curve in Fig. 2(a). The broadband spectrum,which spread over the whole MIR region (500-5000 cm−1), was due to the weak dispersion ofthe medium, with the phase-matching length (0.23 cm, evaluated including the effect of plasma


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Fig. 3. (a) Experimental and (b) simulated radial intensity distributions 250 mm after thegeneration point (on CM2 in Fig. 1) of the MIR pulses. (c) The intensity distribution at thefocal point of the MIR pulse focused with a concave mirror (r=2 m).

and nonlinear refractive index [12]) exceeding the diffraction length of the IR beam (0.12 cm).Spectra of the fundamental and SH used for MIR generation are also shown in Figs. 2(b) and

2(c), respectively. The fundamental spectrum showed significant ionization-induced blue shiftand the pulse was self-compressed down to 15 fs, whereas the SH spectrum was strongly broad-ened by cross-phase modulation. The MIR spectrum was compared with simple convolutionswith the fundamental (I1(ω)) and SHG (I2(ω)) spectra (ω2∫∫ dω ′dω ′′I1(ω ′)I1(ω ′′)I2(ω ′ +ω ′′

−ω)) before (dotted line) and after (dashed line) the filament as is shown in Fig. 2(a).The MIR spectrum is well explained with the convolution of the spectra after the filament.This means that the blue shift and broadening of the input spectra in the filament are the keyprocesses to generate shorter wavelength than terahertz. Terahertz wave generated due to thetunneling current [10], was much weaker than the signal in the MIR. According to our numeri-cal simulations, the electron density achieved in our experiments was about 3×1017 cm−3.

The beam profile of the MIR beam after ZnSe and Si filters measured with a pyroelectriccamera (Pyrocam III, Spiricon) is shown in Fig. 3(a). The shape of the beam was ring and theangle of the cone was estimated to be about 3◦. Some asymmetric shape and distortion fromideal ring pattern comes from residual pulse front tilt and/or astigmatism of the light source.The generated MIR pulse has basically pure one-direction linear polarization (>40:1) in theentire cross-section of the beam as the input pulses, which fact was confirmed with a wire gridpolarizer (NT62-774, Edmund Optics). We compare the experimental result with FWM-beamanalysis after Ref. [13], based on a straightforward integration of the FWM response over thebeam overlap region. As can be seen from Fig. 3(b), the simple approach provides an accurateagreement with the experimental result. It confirms that the ring-shaped beam profile originatesfrom a dramatic confocal-parameter mismatch between the MIR field and the laser beams.

Additionally, the∼12 mm diameter beam was focused down to 1.0 mm with ar=2 m concavemirror, indicating a reasonable focusability for a ring shaped spatial mode. The beam profile atthe focal point is shown in Fig. 3(c). Although the beam may contain some angular dispersionas was reported in Ref. [11], the dispersion is basically radially symmetric, and thus does notsignificantly deteriorate the good focusability of our MIR beam.

In order to quantitatively evaluate the temporal shape of the generated MIR pulse, we meas-ured cross-correlation frequency resolved optical gating (XFROG) [14]. We used argon againas a nonlinear medium and used FWM process (ω1+ω1−ω0 → ω2) as a nonlinear interactionbetween the test pulse (MIR pulse,Etest(t)) and the reference pulse (Eref(t)). The scheme isfree from spectral filtering caused by phase matching condition in the nonlinear interaction.The system for the XFROG measurement is also shown in Fig. 1. Small portion (∼1 µJ) ofthe fundamental 25-fs pulse was used as a reference pulse. The reference pulse and the MIR


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Fig. 4. (a) Experimental and (b) retrieved XFROG traces. The retrieved pulse in (c) timeand (d) frequency domain. The spectrum measured with Fourier transform spectrometer(brown solid curve) is also shown.

pulse (test pulse) were combined through a mirror with a hole and focused into argon withan aluminium-coated parabolic mirror (f = 50 mm). Generated blue spectra (centered around440 nm) were measured with a spectrometer (USB2000+, OceanOptics) by scanning the delaytime (τ) between the reference pulse and the MIR test pulse. The reference pulse was indepen-dently characterized with SHG-FROG, and the result was used for retrieving the MIR pulse.

The measured and retrieved XFROG traces are shown in Fig. 4(a) and 4(b). The main featureof the trace indicates that the residual chirp of the test pulse is very small. The FROG errorwas 0.0009 with 256×256 grid. The retrieved time and frequency domain pictures are shownin Fig. 4(c) and (d), respectively. The pulse width is estimated to be 7.4 fs which is 0.57 cyclesfor 3.9 µm carrier wavelength. The retrieved spectrum was nearly identical to the spectrummeasured with the Fourier-transform spectrometer, as is shown in Fig. 4(d). This indicates thatthe whole MIR spectral components were well focused and overlapped with the fundamentalbeam. Even the fine structure due to absorption line of the residual carbon dioxide was retrieved.

In theory, the carrier-envelope phase (CEP) of the generated MIR pulse is passively stabilizedin the present scheme [7,15]. This feature makes the scheme highly attractive since CEP is veryimportant physical property of sub-single cycle pulses. However, it is important to check theCEP stability experimentally since the fluctuation of the delay between the fundamental andSH pulses and some noise of the input pulse can affect the CEP stability [16–18].

The CEP stability measurement of the MIR pulses was carried out by measuring the interfer-ence between the SH of the reference pulse (ESHG(t)) and the XFROG signal (Esig(t)). The in-

terference signal is explained as a cross-term of∣

∣ESHG(t)+Esig(t)∣

∣

2, namely,E∗

SHG(t)Esig(t) =E∗

SHG(t)E2ref(t)E

∗

test(t). The phase of the interference signal is written as−φSHG+ φsig =−2φref+2φref−φtest=−φtest, whereφx denotes CEP ofEx for each subscript. From the equa-tion, it is clear that the phase drift of the interference signal reflects that of the CEP of the MIRtest pulse. This scheme is essentially the same as that described in Ref. [19].

In the experiment, a barium borate crystal (BBO,θ = 29◦, t =50µm) on a 2-mm thick fused


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Fig. 5. (a) Interference signal between the SH of the reference pulse and the XFROG signal.(b) Single shot measurement of the fringe pattern. (c) Fringe pattern change by iterativelyscanning the distance (X in Fig. 1) between the fundamental and the SH.

silica substrate was inserted behind the focus where the XFROG signal was generated. Thecrystal was placed in a way that the pulses enter from the back side, i.e., from the substrateside. This way, the XFROG signal is delayed by∼300 fs relative to the reference pulse due tothe group delay difference in the substrate before hitting the BBO crystal. A calcite polarizerwas inserted behind the crystal to optimize the intensity ratio between the SH and XFROGsignals. In Fig. 5(a) the interference fringe is shown. The fringe spacing was about 3 THz whichcorresponds to the expected delay between the reference pulse and the XFROG signal. Thephase of the fringe was reasonably stable for hours without any feedback loop. The instablilityof the phase was measured as 257 mrad rms with 100 shots (shown in Fig. 5(b)).

Due to the long wavelength cut off of the SH spectrum, the fringes were clear up to∼415 nm,which corresponded to∼900 cm−1 of the MIR pulse. Although it is rather tiny component ofthe whole spectrum, it is safe to say that the fringe corresponds to the CEP of the pulse since thespectral phase retrieved from the XFROG results were well connected and has no phase jumpin the region from 500 cm−1 to 5000 cm−1.

To demonstrate control of the CEP, the distance between fundamental and SH (X in Fig. 1)was iteratively scanned with a 5-nm resolution feedback loop translation stage and the fringewas monitored (Fig. 5(c)). The fringe changes with a period of∼400 nm, which is similarsituation as Refs. [19] and [20]. It was easy to control the CEP from 0 to 20π by changing thedelay by 4µm.

In conclusion, ultrabroadband coherent MIR spectrum which covers the entire MIR regionwas generated through conical emission from two-color filamentation. In our experiments, MIRpulses as short as 7.4 fs were generated, which corresponds to nearly half cycles of 3.9µmcenter wavelength. We have revealed that the ring-shaped pattern of the MIR beam originatesfrom a dramatic confocal-parameter mismatch between the MIR field and the laser beams.

The light source has a potential to change the situation of traditional MIR spectroscopy dra-matically. For example, the coherent broadband MIR light source enables us to obtain absorp-tion spectra through entire MIR region by single-shot with chirped pulse up-conversion tech-nique [21, 22]. The reasonable quality of the spatial mode can be useful for efficient MIR mi-croscope imaging combined with the up-conversion technique. Multi-dimensional spectroscopyfor entire MIR region to monitor vibrational coupling among very different vibrational modescan be realized with the light source.

Acknowledgments

This work was supported by NINS Program for Cross-Disciplinary Study, the Joint Studies Pro-gram (2011–2012) of the Institute for Molecular Science, MEXT/JSPS KAKENHI (24360030),


the Seventh European Framework Programme (CROSS TRAP 244068 project), and the Rus-sian Foundation for Basic Research (project nos. 11-02-92118 and 11-02-12297).


Documents

Phase-stable sub-cycle mid-infrared conical emission from filamentation ... · conical emission from filamentation in gases ... and J. P. Wolf, “Ultrashort filaments of light