The generation of THz radiation from ionizing two-color femtosecond pulses
propagating in metallic hollow waveguides filled with Ar is numerically
studied. We observe a strong reshaping of the low-frequency part of the
spectrum. Namely, after several millimeters of propagation the spectrum is
extended from hundreds of GHz up to ~150 THz. For longer propagation distances,
nearly single-cycle near-infrared pulses with wavelengths around 4.5 um are
obtained by appropriate spectral filtering, with an efficiency of up to 0.25%.Comment: 6 pages, 3 figure

Babushkin, I.

Herrmann, J.

Skupin, S.

Optics Express

English

arXiv

The generation of THz radiation from ionizing two-color femtosecond pulses propagating in metallic hollow waveguides filled with Ar is numerically studied. We observe a strong reshaping of the low-frequency part of the spectrum. Namely, after several millimeters of propagation the spectrum is extended from hundreds of GHz up to $\sim 150$~THz. For longer propagation distances, nearly single-cycle near-infrared pulses with wavelengths around 4.5~$\mu$m are obtained by appropriate spectral filtering, with an efficiency of up to 0.25~\%

Babushkin, Ihar

Skupin, Stefan

Herrmann, Joachim

Publications Server of the Weierstrass Institute for Applied Analysis and Stochastics

Weierstraß-Institutfür Angewandte Analysis und Stochastikim Forschungsverbund Berlin e.V.Preprint ISSN 0946 – 8633Generation of terahertz radiation from ionizingtwo-color laser pulses in Ar filled metallic hollowwaveguidesI. Babushkin1, S. Skupin2, and J. Herrmann3submitted: 23. Feb. 20101 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany,E-mail: babushkin@wias-berlin.de2 Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany;Friedrich Schiller University, Institute of Condensed Matter Theory and Optics,Fröbelstieg 1, 07742 Jena, Germany.3 Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Str. 2A, 12489,Berlin, Germany.No. 1483Berlin 20102000 Mathematics Subject Classification. 78A60, 35Q61, 35Q60.Key words and phrases. THz light generation, Photoionization, Ultrashort optical pulse prop-agation.1999 Physics and Astronomy Classification Scheme. 42.65.Tg, 32.80.Fb, 42.65.-k.Edited byWeierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)Mohrenstraße 3910117 BerlinGermanyFax: + 49 30 2044975E-Mail: preprint@wias-berlin.deWorld Wide Web: http://www.wias-berlin.de/AbstractThe generation of THz radiation from ionizing two-color femtosecond pulsespropagating in metallic hollow waveguides filled with Ar is numerically stud-ied. We observe a strong reshaping of the low-frequency part of the spectrum.Namely, after several millimeters of propagation the spectrum is extended fromhundreds of GHz up to ∼ 150 THz. For longer propagation distances, nearlysingle-cycle near-infrared pulses with wavelengths around 4.5 µm are obtainedby appropriate spectral filtering, with an efficiency of up to 0.25 %.1 IntroductionIn recent years, the range of wavelengths where coherent radiation can be generatedhas grown dramatically into both high and low frequency domain. Remarkably,most of the methods to obtain radiation at extreme frequencies use, in one or theother way, nonlinear processes in laser-induced plasma. One prominent exampleis high harmonic generation (HHG) where frequencies thousand times larger thanthe frequency of the pump pulse are excited, exploiting the recollision dynamics ofelectrons ionized by the intense light pulses. More recently it was demonstrated thata two-color fs beam allows generation of new frequencies just in the opposite partof the spectrum, namely in the THz range, hundreds times smaller than the opticalpump frequency. To this end, a short two-color pulse of fundamental frequencyand second harmonic is strongly focused into a plasma spot [1–12] The observedTHz emission generated in this scheme has been attributed to the laser-inducedplasma current in the asymmetric two-color field [7,8]. Using such scheme generationof strong THz radiation was reported, with a spectrum which can be as broadas 70 THz [8]. Such broad-band coherent radiation can allow new applicationsproviding the possibility to probe complex molecules or as an analytical and imagingtool in a broad range of fields.In this article we consider a modification of the above described focusing geometryin a bulk gas by using a metallic hollow waveguide with a cladding from aluminumto guide both THz and optical radiation. The use of a waveguide prevents thediffraction of light for all wavelengths involved. In addition, such setup allows torealize nearly single-mode operation for a wide range of frequencies. High thresholdintensities for ionization-induced processes in the range larger than 100 TW/cm2have been already realized in the context of HHG schemes in hollow waveguides[13, 14]. We will show that during propagation a dramatic spectral broadening ofthe low-frequency part of the spectrum occurs, caused by only modest changes in1the fundamental and second harmonic fields. In particular, ultrashort pulses of 10 fsduration lead to the formation of low-frequency spectrum extended from severalhundreds of GHz to approximately 150 THz. Upon further propagation we reportthe generation of nearly single-cycle pulses with central wavelengths around 4.5 µmand efficiency of the order of 0.25 %.2 The modelIn the previous works, THz emission by two-color fields in gases has been interpretedby four-wave mixing rectification [1–5]. In contrast, later studies attributed THzemission to the laser-induced plasma-current in the asymmetric two-color field [7–12]described by the local quasi-classical model of the electron current in the laserfield without taking into account propagation effects. As an alternative approach,particle-in-cell simulations were used [9,10]. Those methods are, however, computa-tionally very expensive, and propagation effects have been taken into account overdistances of a few micrometers only. In such models the microscopic current is de-scribed as a sum over contributions from all electrons, born at discrete times tn.The ”continuous” analog of this approach is given by ( [7, 8, 11])J(t) = qt∫−∞v(t, t0)ρ̇(t0)dt0, (1)where q is the electron charge. The current density J(t) at the time t is obtained byintegrating over all impacts from different ionization times t0: v(t, t0) is the velocityof electrons at time t which were born at time t0, and δρ(t0) = ρ(t0 + δt) − ρ(t0) ≈ρ̇(t0)δt is the density of electrons born at time t01. This approach was utilized inthe previous works of Kim and coauthors [7, 8, 11].The additional integration over the variable t0 increases the numerical effort, but onecan eliminate the microscopic velocity distribution v(t, t0) and derive a differentialequation for the macroscopic current density J(t). Assuming no interaction withother particles and zero velocity of new-born electrons, the equation for the electronvelocity can be written as v(t, t0) =qme∫ tt0E(τ)dτ (where E is the electric field,me is the electron mass). With the simple additive property of integrals we canrewrite it as v(t, t0) = v(t,−∞) − v(t0,−∞). Substituting this into Eq. (1) anddifferentiating with respect to t we obtain J̇(t) = qv̇(t)ρ(t). It is easy to see thatby introducing new variables v′ = v exp(−νet), J′ = J exp(−νet) (where νe is theelectron-ion collision rate) and proceeding analogously we can include collisionaleffects as well, and finally obtainJ̇(t) + νeJ(t) =q2meE(t)ρ(t). (2)1We use the convention ḟ ≡ ∂f∂t.2Indeed, Eq. (2) coincides with the well known (and very commonly used) equationfor the current in plasmas [15, 16].In the present article, the static model for the tunneling ionization [17] is used:ρ̇(t) = WST[E(t)][ρat − ρ(t)], WST [E(t)] = αEaE(t)exp{−βEaE(t)}. (3)Here, ρat is the neutral atomic density, and Ea ≈ 5.14 × 1011 Vm−1 the atomicfield; the coefficients α = 4ωar5/2H and β = (2/3)r3/2H are defined through the ratioof ionization potentials of argon and hydrogen atoms rH = UAr/UH , UAr = 15.6 eV,UH = 13.6 eV, and ωa ≈ 4.13 × 1016 s−1 [6, 17].To describe the light propagation, we use the so called forward Maxwell equation(FME) for the fast oscillating optical field E(r, z, t) in the waveguide with the opticalaxis along z direction [18]:∂Ẽ(r, z, ω)∂z= ik(ω)Ẽ(r, z, ω) +i2k(ω)∆⊥Ẽ(r, z, ω) +iµ0ωc2n(ω)P̃nl(r, z, ω), (4)where r = {x, y}, ∆⊥ = ∂xx+∂yy, n(ω) is the refractive index of Ar, k(ω) = n(ω)ω/c.Ẽ(r, z, ω) and P̃nl(r, z, ω) are the Fourier transforms of E(r, z, t), Pnl(r, z, t) withrespect to time, Pnl is the nonlinear polarization, which includes both the Kerr(PKerr = ε0χ(3)|E|2E) nonlinearity and the plasma contribution: P̃nl = P̃Kerr +iJ̃/ω + iJ̃loss/ω, where Jloss = WST(ρat − ρ)UAr/E is a loss term accounting forphoton absorption during ionization; “division by a vector” means the component-wise division [17]. Decomposing the field into a series of linear eigenmodes of thewaveguide {Fj(r), j = 1, . . . ∞} with corresponding propagation constants βj(ω),we obtain the following set of equations for the amplitudes of the eigenmodes Ej ,coupled through the nonlinear polarization term P(j)nl =∫FjPnldr:∂Ẽj(z, ω)∂z= iβj(ω)Ẽj(z, ω) + icµ0ω22k(ω)P̃(j)nl (z, ω). (5)3 Numerical simulationsIn our simulations, we assume a dielectric waveguide with aluminum coating of theinner walls and diameter d = 100 µm. Such waveguides can be routinely produced(see, e.g., [19]). The main purpose of the waveguide is not to modify the dispersionrelation but to confine both pump and THz radiation (especially the latter, becauseit quickly spreads out otherwise as a result of diffraction [25]). Taking into accountthat THz as well as fundamental and second harmonic frequencies undergo strongabsorption due to plasma generation a long waveguide is not useful. Therefore, werestrict our simulations to distances ≤ 1 cm.The linearly-polarized waveguide mode EH11 has no cut-off at low frequencies, andthe fundamental and second-harmonic frequencies can be coupled into the waveguide3Figure 1: (a) Scheme for THz generation considered in this article. A short pulsewith center frequency ν0 = 375 THz (corresponding to wavelength λ = 800 nm)and its second harmonic are focused into an aluminum coated hollow waveguide.The THz emission is detected at the exit of the waveguide. (b) Losses α (red solidline) and refractive index change δn = kc/ω (green dashed line) induced by theAl waveguide with the diameter d = 100 µm for the mode EH11 versus frequencyΩ = ω/2π.with almost 100 % efficiency from the free-space propagating laser mode. Thedispersion and losses for the mode EH11 of the 100-µm waveguide are shown inFig. 1(b) in low-frequency range. Both quantities are calculated using the directsolution of the corresponding boundary value problem [20], Drude model for thedispersion in aluminum [21] as well as Sellmeier formula for the dispersion in argon[22]. One can see that the losses are relatively large only in the small frequencyrange corresponding to wavelengths of the order of the waveguide diameter. Thealuminum coating was chosen because then the modeling of linear dispersion andlosses in the whole frequency range from sub-THz to sub-PHz is straight forwardusing the Drude model [21]. In contrast, for dielectric coatings (such as fused silica)such simple description for the whole spectral region of interest fails. Nevertheless,we expect even weaker losses than for the metallic waveguide.Results from simulations of ultrashort pulses with 10 fs duration and frequenciesν0 = 375 THz (corresponding to the wavelength λ = 800 nm) and 2ν0 , havingintensities Iω = 1014 W/cm2 and I2ω = 2 × 1013 W/cm2 correspondingly are shownin Fig. 2. We checked that the transverse field distribution consists predominantlyof the fundamental and few higher order modes. At the initial stage of propagation,broadband THz radiation is generated from approximately 0.5 THz to 80 THz (seeFig. 2(a) and (b)). With further propagation (up to 2 mm) the low-frequency partof the spectrum grows in the direction to higher frequencies (up to 150 THz). Atthe same time, the spectral intensity around 10 THz degrades because of the stronglosses of the waveguide mode. From 2 mm up to ∼ 7 mm the long-wavelength part ofthe spectrum shifts continuously towards higher frequencies. Finally, starting from7 mm the spectrum does not change considerably anymore, except for its decreasedue to losses. At this propagation distance, the long-wavelength part of the spectrum410-610-510-410-310-2 1  10  100I(λ) (arb. units)Ω (THz)(b)-100 -50  0  50  100E(t) (arb. units)t, fs(c)10-610-510-410-310-210-1100 0  200  400  600  800  1000I(λ) (arb. units)Ω (THz)(a)Figure 2: Evolution of the THz spectrum upon propagation for a waveguide withdiameter d = 100 µm, input intensities Iω = 1014 W/cm2, I2ω = 2×1013 W/cm2 andpulse duration 10 fs. (a) The spectrum and (b) low-frequency part of spectrum (notethe logarithmic scale of y-axis in (a) and both axes in (b)) for z = 0.5, 2, and 10 mmof propagation (black dashed, green dotted and red solid lines). (c) Pulses obtainedby filtering the long-wavelength part of the spectrum below 250 THz. Propagationdistances, color coding and line styles are the same as in (a).is localized around 60-80 THz, with the center around 66 THz (corresponding to awavelength ∼ 4.5 µm). The observed efficiency of this ”frequency down-conversion”reaches 0.25 percent.The electric field obtained by filtering the long-wavelength part of the spectrum fordifferent propagation distances is shown in Fig. 2(c). One can see that despite thestrong reshaping of the spectrum, the envelope of the obtained THz pulses doesnot change significantly. The amplitude of the pulse grows considerably duringpropagation, from approximately 1 % of the pump amplitude at z = 0.5 mm (whichcorrespond to the conversion efficiency ∼ 10−4) to about 5 % at z = 10 mm (whichcorrespond to the conversion efficiency ∼ 2.5 × 10−3).Fig. 2(a) reveals that in contrast to the strong reshaping of the low frequency compo-nents, the spectrum in the range of the pump frequencies remains almost unchanged.Nevertheless, the spectrum of the pump broadens slightly upon propagation. Due toplasma-induced refraction index change the maximum frequency of the fundamen-tal pulse is slightly shifted to the blue [23, 24]. In our case the shift is small, onlyabout 10 THz. As elaborated in [25], even small changes in the pump fields can af-fect dramatically the spectral shape of the generated low-frequency radiation. Suchchanges affect significantly the temporal positions of the ionization events. Contri-butions from the electrons born in different ionization events are superimposed, andinterference effects lead to a reshaping the THz spectra.The situation is qualitatively similar for other pulse durations (see Fig. 3). Ingeneral, the efficiency of the THz generation is larger for shorter pulse durations (inFig. 3, spectra are normalized to unity at their maxima, so the efficiencies can bedirectly compared). This observation can be explained by the additional asymmetryin the current which is introduced by the finite pulse duration and therefore morepronounced for short pulses.510-610-510-410-310-210-1100101 0  200  400  600  800  1000I(λ) (arb. units)Ω (THz)(a)10-610-510-410-310-2 0  50  100  150  200I(λ) (arb. units)Ω (THz)(b)Figure 3: Spectra for different input pulse durations (25, 50 and 1000 fs are shown byred solid, green dashed and blue dotted lines, respectively) for 1 cm of propagation.In (a) and (b) the full spectra and their low-frequency parts are shown, respectively.Spectra are normalized to their maximum value, so that efficiencies can be compared.4 ConclusionIn conclusion, we studied THz generation by plasma currents through noble gasionization in strong asymmetric laser fields. We have shown that the mechanismallows the relatively simple generation of extremely wide range of frequencies, start-ing from THz to near infrared. By using hollow waveguides we overcome the strongdiffraction of the generated low-frequency generation. We report that dependingon the length of the waveguide either THz supercontinuum or almost single-cyclenear-infrared pulses can be produced at output with ∼ 0.25 % efficiency. We believethat our findings may open new intriguing possibilities to control the spectral andtemporal shape of low-frequency radiation generated by the ionization dynamics inintense optical fields.References[1] D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-waverectification in air,” Opt. Lett. 25, 1210 (2000).[2] T. Bartel et al., “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805 (2005).[3] X. Xie, J. Dai, and X.-C. Zhang, “Coherent Control of THz Wave Generationin Ambient Air,” Phys. Rev. Lett. 96, 075005 (2006).[4] J. Dai, X. Xie, and X.-C. Zhang, “Detection of Broadband Terahertz Waveswith a Laser-Induced Plasma in Gases,” Phys. Rev. Lett. 97, 103903 (2006).[5] K. Reimann, Rep. Prog. Phys. “Table-top sources of ultrashort THz pulses,”70, 1597 (2007).6[6] M. D. Thomson, M. Kreß, T. Löffler, H. G. Roskos, “Broadband THz emissionfrom gas plasmas induced by femtosecond optical pulses: From fundamentalsto applications,” Laser & Photon. Rev. 1, 349 (2007).[7] K.-Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emissionfrom ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15,4577 (2007).[8] K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control ofterahertz supercontinuum generation in ultrafast laser-gas interactions,”, Nat.Photon. 2, 605 (2008).[9] T. D. Wang, Z.-M. Sheng, H.-C. Wu, M. Chen, C. Li, J. Zhang, and K. Mima,“Strong terahertz pulse generation by chirped laser pulses in tenuous gases,”Opt. Express 16, 16999 (2008).[10] M. Chen, A. Pukhov, X.-Y. Peng, and O. Willi, “Theoretical analysis and sim-ulations of strong terahertz radiation from the interaction of ultrashort laserpulses with gases,” Phys. Rev. E 78, 046406 (2008).[11] K.-W. Kim, “Generation of coherent terahertz radiation in ultrafast laser-gasinteractions,” Phys. Plasma 16, 056706 (2009).[12] J. Dai, N. Karpowicz, and X.-C. Zhang, “Coherent Polarization Control ofTerahertz Waves Generated from Two-Color Laser-Induced Gas Plasma,” Phys.Rev. Lett. 103, 023001 (2009).[13] C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. H. Murnane, and H. C.Kapteyn, “Phase Matching of High-Order Harmonics in Hollow Waveguides,”Phys. Rev. Lett. 83, 2187 (1999).[14] E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P.Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H.C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science, 302, 95 (2003).[15] P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laserpulses and electromagnetic pulse generation in air and on dielectric surfaces,”Phys. Rev. E 69, 066415 (2004).[16] L. Bergé, S. Skupin, R. Nuter, J. Kasparian and J.-P. Wolf, “Ultrashort fila-ments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys.70, 1633 (2007).[17] L. D. Landau, and E. M. Lifshitz, Quantum Mechanics (Pergamon, New York,1965), 2nd ed., p. 276.[18] A. V. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-OrderSolitons by Fission in Photonic Crystal Fibers,” Phys. Rev. Lett. 87, 203901(2001).7[19] P. Tzankov, O. Steinkellner, J. Zheng, M. Mero, W. Freyer, A. Husakou, I.Babushkin, J. Herrmann and Frank Noack, “High-power fifth-harmonic genera-tion of femtosecond pulses in the vacuum ultraviolet using a Ti:sapphire laser,”Opt. Express 15, 6389 (2007).[20] E. A. V. Markatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveg-uides for long distance optical transmission and lasers,” Bell Sys. Tech. J. 431784 (1964).[21] Handbook of Optics, ed. by M. Bass, McGraw-Hill, (1994).[22] P. J. Leonard, “Refractive indices, Verdet constants and polarizabilities for inertgases,” Atom. data nucl. data tables 14, 21 (1974).[23] W. M. Wood, C. W. Siders, and M. C. Downer, “Measurement of femtosec-ond ionization dynamics of atmospheric density gases by spectral blueshifting,”Phys. Rev. Lett. 67, 3523 (1991).[24] S.C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectralblueshifting,” Phys. Rev. A 46, 1084 (1992).[25] I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M.Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatio-temporal dynamicsof terahertz generation by ionizing two-color femtosecond pulses in gases,” inpreparation.8

Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides

MPG.PuRe

The generation of THz radiation from ionizing two-color femtosecond pulses propagating in metallic hollow waveguides filled with Ar is numerically studied. We observe a strong reshaping of the low-frequency part of the spectrum. More precisely, after several millimeters of propagation the spectrum is extended from hundreds of GHz up to ~ 150 THz. For longer propagation distances, nearly single-cycle near-infrared pulses with wavelengths around 4.5 μm are obtained by appropriate spectral filtering, with an efficiency of 0.1–1%

The generation of THz radiation from ionizing two-color femtosecond
pulses propagating in metallic hollow waveguides filled with Ar is
numerically studied. We observe a strong reshaping of the low-frequency part
of the spectrum. Namely, after several millimeters of propagation the
spectrum is extended from hundreds of GHz up to  150 THz. For longer
propagation distances, nearly single-cycle near-infrared pulses with
wavelengths around 4.5 μm are obtained by appropriate spectral filtering,
with an efficiency of up to 0.25 %

Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides

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