Gradient enhanced third harmonic generationin a femtosecond filament

Emilia Schulz,1,2,*,† Daniel S. Steingrube,1,2,† Tobias Vockerodt,1,2 Thomas Binhammer,3

Uwe Morgner,1,2,4 and Milutin Kovačev1,2

1Leibniz Universität Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167 Hannover, Germany2QUEST, Centre for Quantum Engineering and Space-Time Research, Welfengarten 1, D-30167 Hannover, Germany

3VENTEON Laser Technologies GmbH, D-30827 Garbsen, Germany4Laser Zentrum Hannover e.V., Hollerithallee 8, D-30419 Hannover, Germany

*Corresponding author: schulz@iqo.uni‐hannover.de

Received August 18, 2011; revised October 6, 2011; accepted October 6, 2011;posted October 10, 2011 (Doc. ID 153018); published November 15, 2011

The third harmonic generated during femtosecond filamentation in air is studied. By establishing a gradient fromatmospheric pressure to vacuum conditions, we truncate the filament abruptly at defined positions. The introduc-tion of the pressure gradient leads to an enhancement of the generated third harmonic radiation by 3 orders ofmagnitude. This effect is attributed to an improved on-axis phase-matching condition. We investigate the spectralshape and the conversion efficiency of the third harmonic during the propagation in the filament. © 2011 OpticalSociety of AmericaOCIS codes: 020.4180, 190.0190, 190.4160, 320.0320, 320.5520, 320.6629.

Filamentation of ultrashort laser pulses in gaseous mediainvolves a variety of nonlinear processes [1], includingthe generation of new optical frequencies in the rangefrom the terahertz regime [2] up to the extreme-UV spec-tral domain [3]. Radiation with a UV spectrum wasproduced inside a filament by means of third harmonic(TH) generation [4,5]. Thereby, the far-field profile of theemitted TH appears on a cone that is attributed to off-axisphase-matching conditions [6]. Different methods exist inorder to enhance the on-axis conversion efficiency. Forexample, by placing a plasma string [7] or a fiber [8] in-side the filament, the on-axis conversion efficiency wasenhanced by 2 orders of magnitude. The enhancementwas recently explained for short filaments by varyingphase-matching conditions in the focus region [9]. In thisLetter, we present a novel method to achieve on-axisphase matching of TH generation. A long filament isterminated using a laser-drilled pinhole that introducesa pressure gradient from atmospheric conditions tovacuum. This allows us to investigate the TH generationprocess over the propagation distance inside the fila-ment, stopping the filament at different positions. We findan optimal on-axis conversion efficiency at a certain po-sition in the filament that is 28 dB higher than withoutintroducing the pressure gradient.The experimental setup is sketched in Fig. 1. A

Ti:sapphire chirped-pulse-amplification system (Dragon,KM-Labs Inc.) delivers 30 fs (FWHM) transform-limitedpulses centered at 780 nm with energies of 1:4mJ at arepetition rate of 3 kHz. An aperture with diameter of5:5mm is placed after the amplifier exit and transmitsabout 60% of the power. The pulses with a peak powerof 26GW exceed the critical power Pcr ¼ 3:2GW for self-focusing in 1 atm of air. They are focused with a concavesilver mirror (CM) of 2m focal length into a 1-m-long cellfilled with air at atmospheric pressure to create a singlefilament. At the end of the cell, a pressure gradient fromatmosphere down to a low background pressure of4mbars is realized by a laser-drilled pinhole (diameter<1mm) in a metal plate. After the pinhole the nonlinear

effects on the laser pulse stop, leading to a terminationof the filamentation process. This semi-infinite gas cellconcept has been applied previously for high-orderharmonic generation [10] and for tracing the pulsingdynamics inside a filament [3,11]. A delay line betweenthe entrance window and the focusing mirror allowsfor displacement of the whole filament over a range of30 cm. While moving the filament with respect to the exitpinhole of the cell, it is truncated at different lengths, andpulses from different positions inside the filament areextracted. The pulses propagate 1m in the low-pressurecell and leave through an exit window (2mm CaF2). TheTH is filtered by separating the spectral componentsusing a prism sequence and blocking the radiation of thefundamental field via a razor blade; see Fig. 1(b). Thespectra of the TH from different positions in the filamentare acquired with a spectrometer (AvaSpec, Avantes withgrating, 1200 lines=mm; slit, 10 μm) in steps of 4mm alongthe filament axis. Spatial profiles of the TH beam are re-corded behind three multilayer mirrors with high reflec-tance for the TH radiation and high transmittance for thefundamental field [Fig. 1(c)]. The fluorescence on a BK7screen, induced by the TH radiation, is monitored with adigital camera (Canon EOS 400D).

The generation of the TH inside a filament leads to theemission of UV radiation on a cone around the propaga-tion axis [6]. Figure 2(a) shows the far-field profile of anundisturbed filament, recorded after 4m of propagation,as described above. The TH beam profile consists of atiny on-axis contribution and an intense cone that con-tains 99.6% of the energy. In disturbing the filament, how-ever, using the pressure gradient to shorten the filamentlength, we observe a bright TH beam confined on the axiswith a nearly Gaussian profile in the far field, as shown inFig. 2(b). Figure 2(c) shows a cut through the intensityprofiles along the vertical axis. Obviously, the on-axisTH intensity of the truncated filament is enhanced by3 orders of magnitude (28 dB) compared to the undis-turbed filament. When disturbing the filament by a pin-hole in the absence of a pressure gradient (switching

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off the vacuum pump), the on-axis TH intensity quicklydecreases.For further investigations, we performed measure-

ments of the TH spectrum, as well as the TH conversionefficiency, versus the propagation distance in the fila-ment. Figure 3(a) reveals the spectral evolution of thegenerated TH along the filament by spectra extractedat different lengths of the filament. Figure 3(a) indicatesthat the TH intensity and its spectral bandwidth increasefor pulses that propagate further in the filament up to a

position around 245 cm behind the focusing mirror. Afterthis position, the TH intensity decreases again, while thespectral bandwidth of the TH remains relatively constant.The spectral shape at the end of the filament becomesmodulated. The spectral broadening is shown in Fig. 3(b)by means of the Fourier-limited pulse duration evaluatedfrom the measurement in Fig. 3(a). The Fourier-limitedpulse duration decreases until position 245 cm down to7 fs, where a saturation is observed. In the range from243 to 273 cm, we measured the TH conversion efficiencyat different lengths of the filament, as shown by thesolid red curve in Fig. 3(c). The conversion efficiencyincreases until reaching the maximum conversion effi-ciency of 0.02% at position 248 cm. For longer propagat-ing pulses, the conversion efficiency decreases again.The influence of the gradient is demonstrated by floodingthe vacuum chamber with air, while leaving the pinholeinstalled. The dashed curve in Fig. 3(c) shows themeasured conversion efficiency with a flooded vacuumchamber for different positions of the pinhole insidethe filament. The generated on-axis TH radiation is stillenhanced with respect to the case of an undisturbed fila-ment. However, it can be seen from Fig. 3(c) that themaximum enhancement factor is reduced by a factorof 3 compared to the case using a pressure gradient.In addition, the dependency of the conversion efficiencyon the filament length is less pronounced.

We believe that the increased on-axis intensity of theTH in case of the terminated filament stems from im-proved phase-matching conditions. In the undisturbed

Fig. 1. (Color online) Experimental setup (see text for de-tails). (a) A filament is created in a gas cell of air at 1 atmand truncated at a certain position with subsequent propagationin vacuum. (b) Setup for the measurement of the TH spectrumalong the propagation in the filament. (c) Setup for beam profileanalysis of the TH.

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Fig. 3. (Color online) (a) Spectrum of TH along thepropagation in the filament and (b) calculated Fourier limit.(c) Conversion efficiency for a filament disturbed by a metalpinhole with (solid line) and without pressure gradient (dashedline).

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Fig. 2. (Color online) Beam profiles of TH radiation. (a) THgenerated in an undisturbed filament. (b) TH radiation gener-ated with gradient imposed by a metal plate pinhole placed252 cm after the focusing mirror. (c) Cross sections of the beamprofiles from the undisturbed filament in (a) and from thefilament with gradient in (b).

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case, the phase front curvatures of the fundamental fieldand TH field match in front of the nonlinear focus, butthey differ beyond the start of the filament, which guidesthe fundamental pulse only. This geometrical phasemismatch circumvents efficient on-axis TH generation,whereas off-axis radiation might still be phase matched,leading to the observed conical beam profile. The ob-served sharp ring structure in the far field could be ex-plained considering that the TH is generated only withina confined distance from the nonlinear focus, which isconsistent with measurements of the local fundamentalintensity via high-order harmonics [12]. When disturbingthe filament with a pinhole, the guidance of the funda-mental field in the filament terminates, which would leadto phase matching beyond the nonlinear focus and thus,efficient on-axis TH generation by the still strong trans-mitted fundamental pulse. Installing a pressure gradientfurther improves the frequency conversion due to adia-batically changing phase-matching conditions [13,14].In conclusion, we have shown that introducing a pres-

sure gradient after disturbing the filament by a metalpinhole leads to an enhancement of the on-axis THgeneration in a femtosecond filament by 3 orders of mag-nitude. By measurements of the TH spectrum and its con-version efficiency, resolved over the propagation axis,we found indications that phase-matching effects aroundthe nonlinear focus are responsible for the low on-axisconversion efficiency for undisturbed filaments. Numer-ical simulations are in progress to elucidate the physicalmechanisms behind this effect. By placing a pressure gra-dient at a certain position, the conversion efficiency canbe drastically improved. Furthermore, the spectral band-width of the TH pulses inside the filament is increased.Thus, our presented method allows us to extract intenseand ultrashort UV pulses with potential durations downto 7 fs for further applications. The conversion efficiencymight be even enhanced by using a higher pressure inthe filament. By using gases with a higher nonlinear re-fractive index, we have already obtained an even larger

spectral bandwidth with a shorter Fourier-limited pulseduration.

This work was funded by Deutsche Forschungsge-meinschaft (DFG) within the Cluster of ExcellenceQUEST, Centre for Quantum Engineering and Space-Time Research.

†Equal contributions.

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