Poor man's source for sub 7 fs: a simple route to ultrashort laser pulses and their full...

Poor man’s source for sub 7 fs:a simple route to ultrashort laser pulses

and their full characterization

Bruno E. Schmidt, Waldemar Unrau, Aldo Mirabal, Shaohui Li,Marcel Krenz, Ludger Woste and Torsten Siebert∗

Institut fur Experimentalphysik, Freie Universitat Berlin,Arnimallee 14, 14195 Berlin, Germany

[email protected]

Abstract: A practicable and economic method for the generation andfull characterization of laser pulses ranging down to sub 7 fs duration withenergies spanning the full µJ domain is presented. The method utilizesa self-induced and self-guiding filamentation of titanium-sapphire based,amplified pulses in air for spectral broadening, a standard chirp mirror com-pression scheme and transient grating frequency resolved optical gating fordetermining the spectral phase over the full visible to near infrared range.In this manner, few-cycle laser pulses with a high quality in the spatialbeam profile have been generated in an robust arrangement with a minimalamount of standard optical components for their full characterization. Theoptical scheme demonstrates an uncomplicated, versatile access to thisregime of pulsed laser radiation accompanied by a comprehensive analysis.

© 2008 Optical Society of America

OCIS codes: (320.6629) Supercontinuum generation; (320.5520) Pulse compression;(320.7100) Ultrafast measurements; (190.4380) Four-wave mixing

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#97992 - $15.00 USD Received 30 Jun 2008; revised 18 Aug 2008; accepted 1 Sep 2008; published 3 Nov 2008

(C) 2008 OSA 10 November 2008 / Vol. 16, No. 23 / OPTICS EXPRESS 18910

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1. Introduction

The development of solid-state femtosecond laser technology has provided the basis for theoptical nonlinearity fundamental to generating extended coherent bandwidth and ultimately at-taining pulsed laser radiation with significantly improved time resolution and enhanced peakpower. In recent years, different strategies for improving upon these elementary attributes ofultrashort laser pulses have been pursued. One possible route to these means generally involvespropagating pulsed radiation at high field strengths over long optical pathways in a confinedvolume. This can be realized in several variations, where confinement is generally achieved inmicro-structured fibres [1], hollow core fibres [2] or via self-guiding filamentation [3, 4, 10, 11].Active processes in the spectral broadening range form self-phase modulation (SPM) [5], self-steepening [6] and pulse splitting [7], four-wave-mixing processes (FWM) [8] and coherent



Raman cascading [9] as well as light-plasma interactions [3, 10, 11]. Landmarks in the devel-opment of this general principle include initial supercontinuum generation in the solid stateand liquids [5] followed by later work in gaseous media [3]. Building on these developments,interaction lengths were increased through guiding in different forms of nonlinear media. Inthis framework, solid state micro-structured fibers allow for the generation of pulses with oc-tave spanning spectra in the nano- and recently in the lower mircojoule regime combined withthe unique and tunable propagation properties of these materials.[1, 12, 13, 14] Alternatively,the use of gaseous media in hollow core fibres and filamentation allows for high pulse ener-gies to be employed and additionally access light-plasma interactions for spectral broadeningand guiding. In this manner, octave spanning bandwidth als well as pulses with compressibilitydown to a few optical cycles can be obtained with pulse energies ranging to the mJ regimeand beyond [15]. This scheme can be extended to the terawatt regime, where white light gen-eration in filaments spanning several hundred meters can be generated with a spectral rangeextending form approximately 230 nm to 4.5 µm at altitudes beyond 10 km in the frameworkof atmospheric research with LIDAR. [16]

Accompanied with their generation, the characterization of extremely short and octave span-ning laser pulses is still a issue in current research. Established methods such as interferometricautocorrelation, frequency resolved optical gating (FROG) [17, 18, 19] and spectral phase in-terferometry for direct electric-field reconstruction (SPIDER) [20, 21] with their respectivedrawbacks and advantages are summarized in Ref [22]. While nearly single cycle, sub 4 fspulses have been correlated interferometrically via surface third harmonic generation, accessto the spectral phase over the full bandwidth still remains challenging. SPIDER posses thepowerful and unique advantage of an analytical approach in obtaining the spectral phase fromthe respective interferogram, yet the necessity of frequency mixing and pulse shearing canlimit the total pulse bandwidth that can be analyzed. FROG techniques substantially vary inthe mechanism employed for temporal gating, ranging from second order frequency mixing tothird order processes such as self-diffraction, Kerr-based polarization gating and laser inducedtransient gratings. While FROG intrinsically poses the difficulties associated with an iterative,non-analytical phase retrieval, the variations of this technique that do not rely on bandwidthlimited frequency mixing open the noteworthy prospect of a complete phase characterizationover octave spanning spectra, as will be demonstrated in this work.

In many cases, the generation, and particularly the characterization, of few cycle laser pulsesinvolve intricate optical schemes that employ non-standard optical components. With the moti-vation to makes state of the art pulse parameters readily accessible in the framework of commer-cially available solid-state femtosecond technology, this work describes a means for attainingand fully characterizing octave spanning laser pulses with compressibility in the sub 7 fs regimeand energies ranging to upper end of the µJ domain. The strategy described in the followingfull avoids complex, sensitive optical schemes and relies on an absolute minimal amount ofstandard optical components. For spectral broadening, self-induced filamentation in air is em-ployed, where the developed setup allows for pulses durations with the highest compressionfactor attained in a single filamentation process. For the characterization of the obtained pulses,it is demonstrated that transient grating, four-wave mixing based frequency gating permits thefull characterization of the spectral phase ranging an octave spanning spectrum, to the best ofour knowledge the highest bandwidth so far correlated in a FROG scenario.

2. Methodology

The general scheme for a simple and robust access to high-energy, few-cycle laser pulses inthe framework of standard Ti:Sa amplifier technology is depicted in Fig. 1. Beginning with the



SpectrometerTG FROG

Delay

SM2

I3

CM2I2

CM1

I1

SM1

1,9m~0,25m

I4L

S

0.65 - 1.5 mJ40 fs @ 800nm

FM

²Schematic View

Pulse Compression

α

k3

k1/k2k3

k1

k2

kS

kSb

kSr

Fig. 1. Experimental setup: The initial laser pulses (40 fs, 0.6-1.5 mJ) are focused withspherical mirror SM1 f = 2 m. Dispersion management is achieved by four bounces on acommercial chirped mirror pair CM1 & CM2, (Layertec) with GVD oscillation compen-sation and average negative GVD of ≈ (−)60 fs2 in wavelength range from 680-900 nm.Total reflectivity is ≥ 99.8% from 650-1000 nm at incident angle of 1◦. Within the TG-FROG, SM2 focuses the three parallel beams in a BK7 glass. k1 and k2 are horizontallyseparated and create a transient grating on which k3 is scattered. This generates the spec-trally dispersed FWM signal (kSb and kSr).

output of a commercial femtosecond laser system,1 continuum generation is attained throughfilamentation in air at atmospheric pressure by focusing the laser pulses with a spherical mirrorSM1 ( f = 2 m), as shown in upper part of Fig. 1. Through the spatial confinement and temporalmodulation resulting primarily from optical Kerr effect in competition with weak, multi-photongas ionization and thin plasma formation, this self-initiating and self-guiding process circum-vents problems of pointing stability, as well as aperture matching and the optimization of prop-agation length involved in fiber guiding. Direct filamentation in air make vacuum componentsas well as entrance and exit windows obsolete and unwanted spectral as well as spatial phasedistortions are avoided, vide infra. Assuming 1.0 mJ pulse energy, 7.2× 1013 W/cm2 at 1/e2

intensity is achieved assuming a geometric focus of the transversal mode with the correspond-ing pulse power of 25 GW. This value constitutes approximately eight times the critical powerfor self-focussing of approximately 3 GW in air [10]. Regardless of hereinafter presented inputenergies, the transmission after filamentation maintained high values of approximately 95%.An important setting is the adjustment of the beam diameter through iris I1 at 1.5 m ahead ofSM1. Reduction of the initial diameter (9.3 mm) from 10% to 30% prevents fluctuation in thefilamentation process as well as multi-filamentation in air at atmospheric pressure. In this con-figuration, the onset of filamentation can be observed through a weak fluorescence roughly 8 cm

1The Laser system consists of cw (Verdi V5, Coherent) pumped oscillator (Femtosource, Femtolasers; 80 MHz,6 nJ/pulse) which is coupled into multi-pass amplifier system (Odin C, Quantronix; 1 kHz, 0.6-1.5 mJ/pulse, 40 fs(FWHM) centered at 807 nm, ∆λ = 35 nm (FWHM).



before the geometrical focus, extending approximately 25 cm. Subsequent to spontaneous ter-mination of the filamentation, the spectrally broadened pulse propagates with a reduced beamdiameter and divergence of 2.5 mrad, which is determined by the filamentation process ratherthan the initial focusing optic SM1. An analysis of spatial, spectral and temporal behavior aswell as transmission and conversion efficiency of the initial output of the filament will be givenin the following section.

Variably, the filament output can be directed to a FROG for immediate analysis or to a setof chirped mirrors for compression with subsequent correlation, as shown in the lower part ofFig. 1. Dispersion management is achieved by four bounces on commercial available chirpedmirror pair CM1 & CM2, (Layertec) with GVD oscillation compensation and average negativeGVD of approximately -60 fs2 per bounce in the wavelength range from 700–900 nm. The totalreflectivity is > 99.8% from 650–1000 nm at incident angle of 0◦. A distance of approximately4 m is spanned between iris I2 and I3, in order to provide for the beam diameter of 6 mm onI3, necessary for the correct beam geometry for correlation. Divergence of the filament outputsketched behind iris I2 is overstated for better visualization. For characterization of the spectralphase over the complete bandwidth of the filament output, a transient grating based frequencyresolved optical gating (TG-FROG) is employed that is achieved with only eight standard op-tical components. The working principle of this TG-FROG is illustrated schematically in theinlet on the right bottom of Fig. 1, where the highly economic design is inspired by previousoptical configurations from autocorrelation scenarios of ultrashort laser pulses and transferredhere to a three beam four-wave mixing (FWM) scheme.[23] Entrance iris I3 consists of threeholes of 2 mm diameter for spatial beam separation. Considering material dispersion and theavailability of octave exceeding beam splitters necessary for the case of amplitude splitting,the advantages of this geometrical separation are evident and have been recently demonstrated[23, 24]. The illumination on iris I3 is achieved by closing I2 down to 1mm and free travel ofthe beam for 4 m. The holes for this geometric beam separation are drilled in the corners ofa square with 4 mm separation, as shown in the schematic view in Fig. 1. By passing iris I3,three phase-locked, parallel running beams with the respective wave vectors (k1, k2, k3) areobtained within 90% of 1/e2 intensity of the transversal beam profile. This arrangement con-stituting a forward folded-box configuration for a FWM scenario. Two of these subpulses (k1and k2), drawn as dashed line in Fig. 1 are separated vertically and reflected from a single flatmirror FM onto the focusing mirror SM2 with f = 250 mm. The third subpulse, k3 representedby the upper straight line in Fig. 1 is directed via a separate, movable mirror TM toward SM2,where a high resolution translation stage (MICOS, Model PLS-85) allows for variable timedelay. From SM2, the three parallel beams are focused to spot size of approx. 30 µm into acentrosymmetric dielectric medium (BK7 glass) and four-wave mixing in this beam geometryleads to, among others, a signal beam in the direction ks under the phase-matching conditionkS = k1 - k2 + k3. The two stationary beams (k1, k2) act as the gating mechanism and interactsimultaneously in the medium, while the third (k3) is swept temporally via TM for correlation.Important to note is the phase-conjugation of k1 and k2 for the detected signal direction. Thisprovides for a temporal gating mechanism via spatial phase interference that is void of temporalphase information. This translates to pure amplitude gating resulting in an unambiguous phasedetermination. The two dotted lines after broadband FWM indicate a small angular dispersionof kS, denoted with kSb and kSr, which occurs when octave spanning white light with an unsym-metric spectral profile is correlated. In order to prevent angular effects in the acquisition of thespectrum when recorded via a fiber spectrometer (Ocean optics, Model USB2000), the signalbeam is focused onto a scatterer providing for diffuse reflection that is independent of angulardispersion of kS.

At this point, two geometrical aspects concerning the distortion of the temporal measure-



ment should be discussed. First, movement of mirror TM causes a parallel spatial shift of k3

on surface of SM2. In order to minimize this shift, the incident angle β

2 on delay mirror is only1◦ which cause a parallel shift of 2 µm for a scan range of 200 fs. Since parallel shift does notchange focus position in first approximation, the shift of 2 µm is negligible. More importantis an analysis of the temporal resolution for a non-collinear interaction of three beams. Theintersection angle θ inside the medium between two k-vectors introduces a geometrical timesmearing ∆τ . Therefore, angle θ is kept small (0.6◦) by use of relatively long focal length fcombined with a small beam separation, di. Assuming Gaussian beams, the temporal smear canthus be calculated according to ref. [25] by ∆τ = ( f θλ )/(diπc) where c is speed of light andλ denotes laser wavelength. For the present TG-FROG setup, ∆τ possess a maximum valueof 0.63 fs when long wavelength of 900 nm is assumed as upper limit. ∆τ blurs the physical

value τ0 and gives a measured value τmeas =√

τ20 +ξ ∆τ2 with a scaling constant ξ which

depends on beam geometry. For three intersecting beams, ξ ≈ 5/3 in a forward box configura-tion. Based on above equations, the blurring of a 6 fs pulse results in pulse lengthening of lessthan 6% through the measurement in this beam geometry. The determination of pulse durationwas therefore carried out by evaluating the raw data obtained directly from FROG trace. TheWigner representation was projected onto the horizontal time axis and fit assuming a Gaus-sian temporal profile. Circles in Fig. 4 correspond to measured data points whereas unbrokenlines display the Gaussian fit. Different than the case of two beam correlations, the deconvolu-tion factor for Gaussian functions is

√3/2 for a three beam [25] geometry in a χ(3) process.

Retrieval of spectral phase from the FROG data was accomplished utilizing the generalizedprojection method [18, 26]. As a further advantage of employing FWM based correlation, itshould be noted that in standard correlation techniques involving frequency conversion, thecommon method for increasing phase matched bandwidth involves reducing the propagationlength through the nonlinear medium, currently down to a crystal thickness of 5-10 µm. Thus,χ(2)nonlinear processes, i.e. three wave mixing, reach physical limitation in their dimensionsas well as transparency when octave spanning spectra are gated. In contrast to this, FWM caneasily be carried out in a spectral range extending into the deep UV as will as into the IRdomain, with the only requirement being the transparency of the medium. As shown here,phase-matching of broadband spectra extending over an octave is automatically realized in thisprocess through the dispersion of the signal direction. From this, FWM mixing can be viewedas one of the most flexible nonlinear processes with respect to the spectral range and bandwidthin the correlation of pulsed laser radiation. For the experiments carried out here, standard BK7microscope objectives where employed and provided that the focus was placed at front faceof the medium, a crosscheck for varying thickness and different composition of the mediumshowed no significant change of the pulse duration when correlating few cycle laser pulses.

3. Results and discussion

In the following, an analysis of the initial filament output will be given for varying input pulseparameters with regards to the spatial beam profile as well as the efficiency and mechanism inspectral broadening. Following this, the capability to characterize the spectral phase of fem-tosecond laser pulses with bandwidths of up to 500 nm, spanning the visible to NIR rangewill be discussed. From this, the optimal filamentation conditions for obtaining few cycle laserpulses will be analyzed in view of the spectral phase retrieved form the supercontinuum pulse.Within this analysis, different filamentation conditions will be presented that allow for obtain-ing an output with a spectral phase suitable for compression of selected spectral regions to thesub 7 fs regime. Furthermore, different pulse energies in the filament output, obtained from theradial selection of the transversal mode, are compared with respect to their compressibility.



3.1. General attributes of the filament output

The transversal mode obtain from the filamentation of standard amplified pulses (1.3 mJ,40 fs @ 807 nm) is illustrated by means of a CCD camera image of the supercontinuum outputin Fig. 2b. The high radial symmetry of the intensity profile in the spatial mode generally ob-tained from plasma filamentation in gaseous media can clearly be seen from the horizontal andvertical cross section in Fig. 2a. Important to consider in the framework of filamentation is thetransversal homogeneity of spectral broadening reflected in the output mode. In order to charac-terize this quality of the filamentation, the spectral behavior is recorded at different positions byscanning a small diaphragm transversely across the mode, as shown in Fig. 2c. Within a radiusof 80% of peak intensity, all general characteristic spectral signatures remain virtually constantexcept the high frequency cut off. Particulary noteworthy in Fig. 2c is the conformity of theamplitude modulations in the spectral signature form approximately 500 to 950 nm within 25%of peak intensity of the transversal mode. An estimate of conversion efficiency toward visiblewavelengths region ranging from 450–720 nm was carried out by numerically integrating thecorresponding area in plot of Fig. 2c. Under the given conditions, typically 15%-20% of overallintensity are transferred to the visible range. Contrary to the center of the mode, the peripheralregion at 10% of maximum intensity clearly exhibits narrower bandwidth with a different spec-tral signatures and a slight red-shift.

3.2. Temporal gating of octave spanning white light

Figure 3 shows the acquired FROG trace as well as the spectral phase retrieval when the fullbandwidth obtained form filamentation is directly coupled into the TG-FROG described above.Settings of the input pulse for filamentation are chosen to demonstrate the capability of generat-ing octave exceeding spectra within single filamentation in atmospheric air as well as capabilityto characterize the spectral phase spanning this spectrum via TG-FROG. This demonstrates asimple means for the full characterization of pulsed radiation in this regime and establishes thetools for gaining new experimental insight to the fundamental mechanisms underlying filamen-

Fig. 2. Transversal mode characterization of the filament output with an input of 1.3 mJpulse energy. (a) Horizontal (light green) and vertical (black) cross section of correspondingimage in (b). (c) Spectra taken at different transverse intensities: maximum (light orange),50% (black), 25% (light green), 11% (blue) of the maximum in the transversal profile.



Fig. 3. (a) TG FROG traces and associated projection on time axis of the uncompressedbandwidth from 370-950 nm after filamentation with 1.3 mJ pulse energy. Temporallysplit and spectrally strongly modulated NIR part experiences complicated phase distor-tions whereas the VIS spectral components obey quadratic phase. (b) Phase retrieval ofwhite light spectrum from the FROG trace in (a) with the original pulse spectrum (greyline), retrieved spectral phase (green dotted line) and spectrum (black line).

tation via spectral phase analysis. Widest spectra were generated when iris I1 was nearly fullyopen, providing a pulse energy of 1.3 mJ and a prechirp of roughly 500 fs2. These settingsdenote limiting values for air at atmospheric pressure before intensity fluctuations and spatialdistortion of beam profile occur. When aiming for broadest spectra, two different sections in theFROG trace become distinguishable. The leading part of the pulse is temporally and spectrallysignificantly modulated, whereas the spectrum from 650 down to 380 nm shows a predomi-nately smooth spectral profile as well as a smooth phase profile down to 600 nm. For a simpleand qualitative interpretation of these to distinct pulse regions, a briefly summary of the current



understanding of spectral broadening through filamentation is necessary. In gas phase filamen-tation, it is primarily the competition between Kerr effect and plasma generation that causethe pulse to experience spatio-temporal modulations with the corresponding spectral modifica-tions. Propagation is influenced by self-focusing [27] and multi photon ionization [28], wherethe latter acts to arrest the collapse of beam. The balancing of both effects results in extendedself-guiding [4]. On the spectral side, Kerr induced SPM [8] accompanied by a minor red shift[30] leads initially to symmetric broadening accompanied by the respective phase distortions.Onset of plasma generation and thus lowering of the refractive index forces asymmetry of thetemporal phase and spectral envelop [8, 6], respectively. This general plasma blue-shift togetherwith the shock dynamics [29] resulting form the trailing pulse flank, give rise to asymmetricblue shift of the spectrum. Further spectral asymmetry may also be attributed to non-resonantFWM [8]. Providing sufficient intensity in nonlinear evolution, the pulse undergoes temporalsplitting [3, 31, 7].

The acquired FROG trace of the filament output in Fig. 3 together with the retrieved spectralphase distinctly reflect the different mechanism involved in the spectral broadening. The strongmodulations in the FROG trace around the laser fundamental arise when nonlinear propaga-tion through the entire filament extend beyond a symmetric SPM to complex phase distortionsmanifesting themselves in the apparent temporal splitting. The corresponding spectral phase inthe inlet of Fig. 3b retrieved form the FROG trace for this region further reflects phase distor-tions beyond SPM and its highly irregular contour clearly shows that under these filamentationconditions, compressibility with conventional methods is unpracticable. A very different pic-ture is seen in the visible part of the obtained FROG trace and the spectral phase in Fig. 3.Spectral phase retrieval for this the unmodulated part of continuum primarily obeys a smoothquadratic behavior. Here, truncation of the spectral phase function at 560 nm is caused by nu-merical unwrapping when dealing with very steep slopes as well as termination of the retrievedspectral amplitude. However, the total hight stroking over 300 radian was obtained by the re-trieval. This phase function corresponds to a GVD of approximately 900 fs2 assuming a purelylinear chirp. Considering the propagation in air amounting to 150 fs2, the remaining positivechirp is attributed to the spectral broadening mechanism in the filament. This is supported bythe observation that the phase function remains constant for a different prechirp of the inputpulse. The distinct and manageable phase function in this region clearly reveals straight for-ward compressibility. This is in contrast to the band ranging the red to NIR spectral domainunder filamentation conditions set for maximal spectral broadening.

3.3. Compression to few cycle pulses

While the compression of the visible region in the filament output has been discussed in theliterature[32], different filamentation conditions for compression of the high amplitude NIRcomponent of the continuum output will be explored in the following. The analysis includesdifferent energies and radial confinement of the input for filamentation as well as radial modeselection for different energies of the filament output. An overview of the compression undthese varying parameters is given in the series of Fig.4 a-c. Attaining the shortest pulse durationswas highly sensitive to small changes of I1, achieved when closing down to 7 mm, reducingthe input energy from 1.5 mJ to 1.0 mJ. Fine adjustment of grating separation in the amplifiercompressor was necessary for finding the shortest pulses. In general, best compressibility wasachieved with a slightly positive prechirp of 400 fs2 of the input pulse for filamentation, whichagrees with other observations by Hauri etal. [33]. Noteworthy, the total amount of positivedispersion accounts to 550 fs2 when including the optical path in air but the implemented nega-tive GVD of four bounces on chirped mirrors is only -240 fs2. It is again assumed that this is anindication of self-induced temporal changes taking place during nonlinear propagation in the



6.3 fs 7.6 fs 8.5 fs

Fig. 4. Pulse compression using chirped mirror pair with (-)60 fs2/bounce and an inputpulse energy of (a) 1.0 mJ (b) 650 µJ and (c) 760 µJ for filamentation. The obtainedfilament out is radially selected, attenuating the output in (a) from 950 to 30 µJ with atransversal mode radius of 500 µm, (b) from 620 to 20 µJ with a transversal mode radiusof 500 µm and (c) from 720 to 25 µJ full radius of the transversal mode (see Fig. 2).Circles correspond to measured data points whereas straight line displays a Gaussian fit.Highest input pulse energy in (a) causes modulation at NIR wavelengths and successivereduction of input pulse energy leads to clean temporal pulse compression in (b) and (c).1 mJ denotes threshold energy before increased temporal satellites arise. Measurements (b)and (c) compare the compressibility of the filament output for different radial selection ofthe transversal mode output of the filament.

filament. Furthermore, I2 is set to select the inner core of the filament output, reducing the fila-ment output energy form 950 approximately 30 µJ/pulse, which corresponds to a mode radiusof 500 µm in Fig. 2a. In this manner, pulse durations as short as 6.3 fs were generated with asingle filament. Figure 4a shows a representative FROG trace which displays a long term aver-age measurement. Repeatability was verified by taking 41 FROG traces during a period of 10days. The mean FWHM value for 41 measurements during this time period is 6.3±0.3 fs. Im-portant to note for this case are the satellite structures clearly evident in the FROG trace and theprojection on the time axis. The appearance of these structures can partially be understood fromthe reconstructed spectral phase for this pulse as shown in Fig. 5a. The spectral phase functionis inhomogeneous with two distinct spectral regions. While the wavelength region from 650–820 nm shows phase jumps of π or 2π , respectively, the spectral domain above 820 nm exhibitsan irregular spectral phase profile. From this, the satellite structures around the primary pulsecan be attributed to the compromise made when trying to balance these two distinct spectral re-gions with chirped mirror compression having a nearly quadratic phase correction over the fullbandwidth. In this context, it is worth mentioning that a reduced amplifier output of 1mJ and theopening of iris I1 increases the pulse width and the strength of satellite structures, i. e. not onlythe absolute amount of input energy but also the spatial beam characteristics and diffractioneffects influence the filament output. However, a fully opened iris I1 and reduced input energyof 650 µJ for filamentation enables the generation of clean temporal profiles with reduced spec-tral modulations as depicted in Fig. 4b. Again, I2 is set to select the inner core of the filamentoutput, reducing the full filament output energy from 620 to 20 µJ/pulse with a radial selectionof 500 µm in Fig. 2a. This is noteworthy, since generation of sub 10 fs with a single filament



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Fig. 5. Spectral phase retrieval of few cycle pulses generated in atmospheric air and sub-sequent compression by chirped mirrors. (a) Modulated spectral and temporal structuresappear for shortest FWHM of 6.3 fs in Fig. 4a. (b) Filamentation with 0.65 mJ results insmooth spectral broadening with linear spectral phase and clean temporal profile corre-sponding to Fig. 4b.

has previously been presented with distinctly higher energies [15] than 1 mJ. The absence ofsatellites in the FROG trace of Fig. 4b is accompanied by smoother NIR spectrum and a higherwavelength cut off around 550 nm. Furthermore, the corresponding spectral phase is mostlylinear as shown in Fig. 5b for this low energy case. In a last variation, the compressibility of thefull filament output is tested without radial selection of the output mode. Here, the input pulseis reduced from 1.4 to 0.76 mJ/pulse by closing I1. The filament output energy of 720 µJ/pulseis obtained when I2 is set to pass the full radius of the output, which is then guided to theTG-FROG via a 4 % surface reflection. Important to not is the discrimination of the outer, moreinstable region of the mode through I3 as well as the inner core corresponding to the dimensionsof I3 in the methodology section, see Fig. 2a. The FROG trace for these conditions is shownin 4c, where the shortest pulse required different dispersion compensation achieved by adjust-ing the optical pathway through air. It should also be noted that, in comparison to the previousmeasurements, correlation of the inner mode yields a pulse duration of approximately 7.6 fsfor this filament input conditions. From the FROG trace, representative pulse duration obtainedfor these conditions are at 8.5 fs. This slightly higher pulse durations for the full transversalmode correspond to theoretical predictions of radial dependency in the spectral broadening inthe filamentation process [32]. With the three measurements given above, different input andoutput conditions for pulse compression are shown for the highly practicable scenario of fila-mentation in air at atmospheric pressure and the insight gained by a full spectral phase analysisis demonstrated with the economical TG-FROG setup.

4. Conclusion

The strategy employed for the generation as well as full characterization of few cycle pulsesand octave exceeding supercontinua described above is distinguished in both cases by the easeof realization and the high economy in optical components. The white light generation via fil-amentation in atmospheric air under conventional laboratory laser conditions (0.6-1.5 mJ) anda characterization by a FWM based FROG scheme can be easily realized. The noteworthy ca-pability to frequency gate the full coherent bandwidth emitted from the filament allows for ageneral insight to the mechanism of filamentation as well as the optimal conditions for pulsecompression of different spectral regions with varying input energies and radial output selec-tion. The work presented above opens a variety of aspects for future investigations. The utiliza-



tion of a more complex phase correction provided by liquid crystal base pulse shapers opens theprospect of compressing the full bandwidth of the filament output as well as the generation ofcomplex pulse forms for spectroscopic applications [34]. Furthermore, the high quality in thespatial beam profile allows for a second filament to be ignited with the given output, bringinga higher conversion into the visible components of the spectrum and eventually compressionto shorter pulse durations. While the qualitative spectral phase retrieval presented here has pro-vided insight to the mechanism of spectral broadening and compressibility of filament output, atruly quantitative retrieval remains challenging for high bandwidths with intricate phase struc-ture. This will be approached by employing slicing techniques as well as incorporating geneticalgorithms in the iterative optimization of a quantitative spectral phase assignment. Furtherwork will also focus on a better understanding of spectral broadening via filamentation throughspectral phase analysis under varying filament conditions. The presented achievements and out-look given here aspire to establish few cycle laser pulses as a readily achievable standard forimplementation in a wide spectrum of spectroscopic applications.

Acknowledgments

The financial support provided by the Deutsche Forschungsgemeinschaft within the Sonder-forschungsbereich 450 “Analysis and Control of Ultrafast Photoinduced Reactions” and theSonderforschungsbereich 546 “Structure, Dynamics and Reactivity of Aggregates of TransitionMetal Oxides” as well as the Leibniz Graduate School for Molecular Biophysics is gratefullyacknowledged by the authors. The authors greatly appreciate the support form Dr. Daniel J.Kane for generously providing the algorithm used for the spectral phase retrieval. fruitful dis-cussion with Dr. Kamil Stelmaszczyk, Philipp Rohwetter and Dr. Estelle Salmon are gratefullyacknowledged.



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