Harmonic concatenation of 1.5-femtosecond-pulses in the deep ultraviolet
aa r X i v : . [ phy s i c s . op ti c s ] J a n Harmonic concatenation of 1.5-femtosecond-pulses in the deep ultraviolet
Jan Reislöhner, Christoph Leithold, and Adrian N. Pfeiffer
Institute of Optics and Quantum Electronics, Abbe Center of Photonics,Friedrich Schiller University, Max-Wien-Platz 1, 07743 Jena, Germany (Dated: January 24, 2019)Laser pulses with a duration of one femtosecond or shorter can be generated both in the IR-VISand in the extreme UV, but the deep UV is a spectral region where such extremely short pulseshave not yet been demonstrated. Here, a method for the synthesis of ultrashort pulses in the deepUV is demonstrated, which utilizes the temporal and spatial harmonics that are generated by twononcollinear IR-VIS pulses in a thin MgF plate. By controlling the groove-envelope phase of theIR-VIS pulses, spatial harmonics are concatenated to form deep UV waveforms with a duration of1.5 fs. Waveforms with durations short enough to probe theelectronic timescale can be generated both in the extremeUV and in the IR-VIS region of the electromagnetic spec-trum. High-order harmonic generation can be used togenerate isolated attosecond pulses and pulse trains inthe extreme UV [1], and since very recently the coherentsynthesis of optical pulses is used to generate subcycleoptical waveforms in the IR-VIS region [2]. In the deepUV (DUV), where many basic aromatic molecules absorbradiation and undergo photochemical reactions [3], pulseswith such extremely short durations have not yet beendemonstrated [4]. Exploiting nondegenerate frequencymixing in a hollow waveguide [5], in filamentation [6]or in a thin transparent solid [7], it has been possibleto generate pulses with a duration on the order of 10 fs[5]. A similar pulse duration has been achieved by achro-matic frequency doubling of visible ultrashort pulses [8].Also self-compression of DUV pulses by filamentation hasbeen demonstrated, yielding comparatively short pulsesof ∼ fs [9]. The shortest pulse duration reported todate of 2.8 fs has been achieved by frequency conversionin a gas cell [10], which, however, requires extremely short(< 4 fs) fundamental pulses in the IR-VIS.Despite these engagements of several groups in thedevelopment of pulse generation methods, spectroscopywith sub-10-fs DUV pulses has not often been reportedto date. A fundamental difficulty is rooted in the largegroup velocity dispersion of any optical component inthe DUV, causing a DUV pulse to be readily broadenedand distorted before it reaches the sample. As a rare ex-ception, it was recently demonstrated that ∼ plate yield a multifaceted emission patternof temporal and spatial harmonics. The emission angleof the harmonic orders depends on the frequency. Thisspatiotemporal coupling is exploited to concatenate twoneighboring spatial harmonics by adjusting the crossingangle of the fundamental pulses. Broadband waveformsarise, of which the lower frequency bands belong to onespatial harmonic, and the higher frequency bands be-long to the other spatial harmonic. In order to synthe-size ultrashort waveforms from these frequency bands,their phases must be adjusted. This is accomplished bycontrolling the groove-envelope phase (GEP) [13] of thefundamental pulses, which is determined by their delayon the subcycle timescale. Using temporal harmonics ofthird order, the concatenation of two spatial harmonicssynthesizes DUV pulses of 1.5 fs. A generic feature is thatthese waveforms are spatially separated from the funda-mental pulses and are therefore available for immediatespectroscopic usage without any subsequent optical ele-ments.Experimentally, two few-cycle VIS-IR pulses, labeledA and B (center wavelength λ A,B = 700 nm, pulse dura-tion t F W HMA,B = 4.8 fs, intensity I A,B = 4 TW/cm ), arefocused noncollinearly with polarization perpendicular tothe plane of incidence into a 100- µ m-thick polycrystallineMgF plate (half crossing angle α = 0 . ◦ , beam waist ∼ µ m) with variable delay τ , see Fig. 1. MgF is cho-sen because of its wide bandgap (11.3 eV) and the ratherweak group velocity dispersion in the DUV. The exper-iment is carried out in vacuum, inhibiting nonlinear in-teractions with air. A spectrometer has been constructedwith both spectral resolution and resolution in the emis-sion angle φ .A multifaceted emission pattern of temporal and spa-tial harmonics is generated through cascaded processesof frequency conversion and self-diffraction. At DUV fre-quencies, which corresponds to temporal harmonics ofthird order, several orders of self-diffraction (spatial har-monics) can be identified, see Fig. 2. The spatial har-monics with emission angle equal to one of the two fun- ABR C a m e r a τ R τ α ααααα Spectrometer
MgF FIG. 1. Experimental setup. Pulses A and B generate DUVdouble pulses. Pulse R is overlapped only for the pulse char-acterization measurements. damental pulses ( φ = ± / α ) is observed at all pulse de-lays. Within the bisector of the two generating beams( φ = ± / α ), spatial harmonics generation is restricted totemporal pulse overlap. Outside the bisector ( φ = ± / α and φ = ± / α ), spatial harmonics generation is efficientonly within a region of very small pulse delays. In be-tween the spatial harmonics, interferences arise that aredependent on the pulse delay τ on the subcycle timescale.With the restriction to 1D pulse propagation in z -direction, the DUV field E UV is given by (atomic unitsare used and the convention for Fourier transform is F{ f ( t ) } ∝ R + ∞−∞ f ( t )e − iωt d t ): E UV ( ω, z ) = − i πωcn ( ω ) e − in ( ω ) ωc z Z z dz ′ P ( ω, z ′ )e in ( ω ) ωc z ′ ) , (1)where ω is the angular frequency (resp. photon energy), c is the speed of light, n ( ω ) is the refractive index and P isthe nonlinear polarization response. Within the approx-imation that the fundamental pulses propagate linearlyand that the refractive index is constant at fundamentalfrequencies ( n ( ω IR ) = n IR ), Eq. (1) is solved by: E UV ( ω, z ) = − πP ( ω, z = 0) n ( ω ) ( n ( ω ) − n IR ) (cid:16) e − in IR ωc z − e − in ( ω ) ωc z (cid:17) . (2)Fringes appear in the spectrum | E UV | , which are ob-served in the data at all spatial harmonics (Fig. 2). Thisphenomenon is usually avoided by phase-matching meth-ods to increase the DUV pulse energy, but here the focusis on shortening the pulse duration. In time domain, thespectral fringes correspond to a DUV double pulse. Thismight be surprising, because one might expect that asingle broadened pulse is generated instead of two well-separated pulses, but the pulse splitting has been de-scribed before [14], and it directly follows from Eq. (2).At the end of the MgF plate, the leading and the trail-ing DUV pulses are well separated by ∼
36 fs. Remark-ably, only the trailing pulse (represented by e − in ( ω ) ωc z )is broadened by the strong group velocity dispersion inthe DUV. The leading pulse (represented by e − in IR ωc z )propagates at the speed of the IR-VIS pulse and remainsshort throughout the propagation with a pulse duration of t F W HMA,B / √ = 2.8 fs in the case of instantaneous third-order polarization response. -8 -7 -6 -5 -4 -3 -2 -1 tt FIG. 2. Measured DUV intensities as function of φ and ω for τ = 0 (a) and as function of φ and τ at ω = 5.4 eV (b).Spectra at φ = / α , / α , / α are shown for ϕ GEP = 0 andat φ = / α for ϕ GEP = 0 and π (c). The Fourier limit of thepulse duration is displayed in (d) in areas where the normal-ized intensity is greater 10 − . Let E A ( t, x ) = ℜ{ f A ( t, x ) exp( i ( ω t − k x x + ϕ CEP )) } and E B ( t, x ) = ℜ{ f B ( t − τ, x ) exp( i ( ω ( t − τ )+ k x x + ϕ CEP )) } bethe electric fields of laser pulses A and B respectively in-side the nonlinear medium at z = 0 . The carrier-envelopephase (CEP) ϕ CEP determines the temporal position ofthe carrier wave underneath the temporal envelope. TheCEP is not stabilized from shot-to-shot, but is identicalfor A and B in each shot. At temporal pulse overlap,an intensity grating (laser induced grating) appears withgroove spacing π/k x ≈ µ m. The GEP ϕ GEP = ω τ isthe phase between the grooves of the intensity gratingand the spatial envelope of the beams [13]. The GEP isadjusted by the pulse delay τ , where a delay of one op-tical cycle translates into a GEP shift of 2 π . The GEPis the spatial analogue to the CEP: The CEP determinesthe interference of converted temporal frequencies (mul-tiples of ω ), while the GEP determines the interferenceof converted spatial frequencies (multiples of k x ) [13]. Inorder to observe CEP dependence, the spectral widthmust be large enough for spectral overlap of neighbour-ing temporal harmonics (for example in an f -2 f interfer-ometer, where a pulse with an octave-spanning spectruminterferes with a frequency-doubled replica). In order toobserve GEP dependence, the divergence of the spatialharmonics must be large enough for overlap of neighbour-ing spatial harmonics. This is adjusted by the crossingangle and beam waist.For close-to-collinear configurations, the intensity grat-ing consists of only a few grooves, and phenomena of non-linear optics yield subcycle-dependent (GEP-dependent)signals. Recently it has been demonstrated that a close-to-collinear geometry can be exploited to achieve subcy-cle resolution in probe retardation measurements [15] andself-diffraction [13]. Self-diffraction denotes that A and B(or waves that are generated by A and B) are diffractedon the laser induced grating. A detailed discussion of thetiming of the diffraction orders was presented in Ref. [13].If the GEP is shifted by δ , then the phase of the DUVlight (temporal harmonics of third order) in spatial har-monic φ = / α is shifted by δ , in spatial harmonic φ = - / α by δ , and in spatial harmonic φ = - / α by δ . Thisscheme continues outside the bisector.Harmonic concatenation exploits that the harmonic or-ders exhibit spatiotemporal couplings: the emission an-gle depends on the frequency. For light in between twospatial harmonics, for example at φ = / α , the lowerfrequency band belongs to harmonic φ = / α , whereasthe higher frequency band belongs to harmonic φ = / α ,see Fig. 2. The spectral bandwidth at φ = / α is muchbroader than at the spatial harmonics. Whereas the spec-tra of the spatial harmonics depend only very weakly onthe GEP, the GEP dependence is very pronounced in be-tween the orders. At φ = / α , the spectral content at thecenter frequency can be tuned from constructive interfer-ence at ϕ GEP = 0 to destructive interference at ϕ GEP = π .In order to exploit the broad bandwidth for the synthesisof a short waveform, the frequency bands of the spatialharmonics must be concatenated by adjusting the cross-ing angle and the GEP. A first glimpse on achievablepulse durations is provided by the Fourier limit (Fouriertransforms of the spectra with the assumption of a flatphase) after removal of the spectral fringes, see Fig. 2(d).The broadest bandwidths and potentially shortest pulsesare located in between the spatial harmonics.In order to scrutinize the mechanism of harmonic con-catenation, simulations are employed similar as describedin Refs. [13, 16–18]. The unidirectional pulse propaga-tion equation (UPPE) is integrated numerically usingthe split-step method. One transverse dimension (the x -dimension) is included to account for the noncollineargeometry. The electric field is treated as scalar field, be-cause all pulses are polarized perpendicular to the planeof incidence. To initialize the fundamental fields A and Bat the beginning of the MgF plate, the pulse retrieval ofthe data (described in the next paragraph) is employed:for all fundamental fields, the cube root of the complexenvelope of the leading pulse in spatial harmonic φ = / α is used. The pulse duration of the fundamental pulsesis 4.8 fs, which was additionally confirmed with a third-order harmonic FROG [19]. Numerical refractive indexdata is used for the linear response, and the nonlinearresponse is calculated assuming instantaneous responsewith χ (3) = 0 .
82 au , corresponding to a nonlinear refrac-tive index n = 0.057 cm /PW [20]. Subsequent to thesample propagation, linear propagation into the far fieldis performed. The UPPE simulations reproduce the ex-perimental data very well, see Fig. 3(a)-(c). In addition to the spectral intensities, the time-domain representa-tion of the fields can be extracted from the simulation.At all emission angles, well-separated double pulses arefound, in accordance with the 1D propagation describedby Eq. (2). At spatial harmonics φ = / α , / α , / α ,the pulses are independent on the GEP and the lead-ing pulses have a pulse duration of ∼ φ = / α , the case of de-structive interference ( ϕ GEP = π , respectively τ = 1.3 fs)leads to a pulse that is distorted. The reason is that thefrequency bands of the spatial harmonics are not concate-nated with a GEP that is ideal for the synthesis of a shortwaveform. Better suited for ultrafast spectroscopy is thepulse that is generated in the case of constructive inter-ference ( ϕ GEP = 0 , respectively τ = 0). Here, the pulseis only very weakly distorted, is well-separated from thetrailing pulse and has a duration of only 1.5 fs. -8 -7 -6 -5 -4 -3 -2 -1 FIG. 3. Panels (a)-(c) are extracted from the simulation andcorrespond to the respective panels in Fig. 2. For the spectrashown in (c), the intensity envelopes of the leading pulse aredepicted in (d). The result of the pulse characterization isshown in (e) for the measured data (red) and for the simula-tion (blue). The values for φ and τ in (c)-(e) are indicated onthe right in (e). For a further validation of the simulation results, theDUV waveforms are characterized with the recently de-veloped method cross-phase modulation scans [16]. Spec-tra | E UV | are recorded, while a further VIS-IR pulse, la-beled R, is overlapped at a variable delay τ R , see Fig. 1.The pulse characterization is performed both experimen-tally and on synthetic data, which is generated usingthe UPPE simulation where all three pulses A, B andR are initialized. The variant center is used, where thephase of the leading DUV pulse is shifted via cross-phasemodulation. As a preparation for the pulse retrieval, thespectra | E UV | at each τ R are inverse Fourier transformed,the alternating component (side peak) is selected andshifted to zero frequency, and thereafter Fourier trans-formed. The basis for pulse retrieval is the data trace Y c ( ω, ω R ) , which is calculated by subtraction of the non- τ R -dependent background, followed by Fourier transformfrom τ R to ω R . The pulse retrieval from Y c ( ω, ω R ) isanalytic, and the fidelity of the retrieval is checked bycomparing the complex-valued data trace with the re-trieved trace (Fig. 4). The retrieved pulses are depictedin Fig. 3(e) for both the experimental and the syntheticdata. The pulse shapes predicted by the simulation(Fig. 3(d)) are reasonably well reproduced both apply-ing the retrieval to the synthetic data (Fig. 3(e), blue)and to the experimental data (Fig. 3(e), red). -1 0 14567 -1 0 14567 -1 0 14567 -1 0 14567 -0 FIG. 4. Magnitudes (a), (b) and phases (c), (d) of experimen-tally measured (a), (c) and retrieved (b), (d) traces Y c ( ω, ω R ) used for the pulse characterization at φ = / α and τ = 0(depicted in Fig. 3(e)). Phase values are only shown wherethe normalized magnitudes are greater than 0.01 in both themeasured and retrieved traces. A distinct advantage of harmonic concatenation is thatthe generated waveforms are spatially separated from the fundamental pulses. The generated waveforms are notwell suited to act as pump pulses, because they are veryweak and the spatiotemporal coupling prevents refocus-ing. They are, however, excellently suited to act as probepulses. A sample to be investigated can be placed directlyafter the generation medium, where a pump pulse can beoverlapped. In this scheme, the probe pulses generatedby harmonic concatenation are available for immediatespectroscopic usage without any subsequent optical el-ements, which have previously been the main obstaclefor DUV spectroscopy in the sub-10-fs range [3]. As thetrailing pulse is well separated with a large inter-pulse de-lay, it may enable simultaneous transient absorption anddispersion measurements. If the trailing pulse should besuppressed, for example when a process with a decay timelarger than the inter-pulse delay is studied, this could bedone by deflecting it with the aid of a spatially shapedpulse. In the present setup, pulse R could be shaped tohave an intensity gradient extending over the beam pro-files of A and B and be temporally overlapped with thetrailing pulse. Cross-phase modulation would induce aspatial gradient in the phase of the trailing pulse, effec-tively deflecting the trailing pulse.In conclusion, harmonic concatenation is a method forthe synthesis of short waveforms in the DUV. It requirestwo noncollinear IR-VIS pulses that trigger cascaded pro-cesses of frequency conversion and self-diffraction in athin dielectric. The spatiotemporal coupling of the tem-poral and spatial harmonics is exploited to concatenatetwo neighboring spatial harmonics. This requires adjust-ing the crossing angle of the fundamental pulses and theirGEP. Using temporal harmonics of third order generatedin a 100- µ m-MgF plate by 4.8 fs-pulses, the concatena-tion of two spatial harmonics synthesizes DUV pulses of1.5 fs. FUNDING.
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