Abstract

Combined optical nonlinearity of bound and free electrons in a fast-ionizing medium driven by ultrashort, mid-infrared (mid-IR) pulses gives rise to a vast variety of ultrafast nonlinear-optical scenarios, producing bright, broadband radiation in spectral ranges as different as ultraviolet (UV) and terahertz (THz). Given its enormous bandwidth, a quantitative experimental analysis of this type of nonlinear response is anything but simple. Here, we confront this challenge by ultrabroadband spectral measurements performed across the spectral range from the UV to the millimeter-wave (MMW) band jointly with beam profile analysis in the THz-to-MMW band and direct time-domain field waveform characterization. As one of the most striking results, the nonlinear response of a fast-ionizing gas driven by a two-color field, consisting of a high-peak-power sub-100-fs mid-IR pulse and its second harmonic, is shown to provide a source of a bright multiband supercontinuum (SC) radiation, whose spectrum spans over about 14 octaves, stretching from below 300 nm all the way beyond 4.3 mm. The MMW-to-THz part of this SC is emitted, as direct measurements show, in the form of half-cycle field waveforms that can be focused to yield a field strength of $ {\approx}{5}\;{\rm MV/cm}$. At least 1.5% of the MMW–THz supercontinuum energy is emitted in the MMW range, giving rise to MMW field strengths up to 100 kV/cm in the beam waist region.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Combined nonlinear-optical response of bound and free electrons in gases and solids is a powerful resource of ultrafast optical science. Multioctave, high-energy supercontinuum (SC) generation in various frequency bands [13] is one of the most prominent cutting-edge applications of this type of optical nonlinearity, which helps expand the potential of short-pulse laser technologies beyond the inevitable bandwidth limitations of laser gain media [4], paving the ways toward petahertz optoelectronics [5] and providing much-needed bandwidth for frequency-comb technologies [6], subcycle light wave engineering [7], and novel methods of ultrafast spectrochronography [3,8,9]. Generation of bright supercontinua extending to the terahertz (THz) range has been demonstrated [1014] through a suitably designed interaction of intense ultrashort near-infrared (IR) laser pulses with gas targets.

Stretching beyond the THz range is the millimeter-wave (MMW) frequency band—the region of particular interest and significance for radio astronomy, remote sensing, as well as telecommunication, medical, and security screening applications [15]. Central to fully unleashing the potential of SC generation and, more generally, extending the concepts and approaches of broadband optics to new frequency ranges, including the MMW band, is the development of methods whereby ultrafast optical nonlinearities of bound and free electrons could be accurately characterized within the entire pertinent frequency range—from the ultraviolet (UV) to the THz band and beyond. With such an enormous bandwidth to explore, a quantitative experimental analysis of this nonlinear response is anything but simple. Here, we confront this challenge by performing an ultrabroadband, UV-to-MMW-band spectral analysis jointly with direct time-domain field waveform characterization based on electro-optical sampling and autocorrelation analysis. Central to our experimental approach is the idea of using a two-color field consisting of a high-peak-power mid-IR pulse and its second harmonic as a driver for the broadband nonlinear response of a gas system. Providing a rationale for shifting the driver wavelength $ \lambda_{0}$ to the mid-IR range is the strong enhancement of the THz yield attainable with longer-$ \lambda_{0}$ laser drivers [16,17]. As one of the most striking results, our experiments demonstrate that, when driven by such a field, the nonlinear response of a fast-ionizing gas can provide a source of a bright multiband SC radiation, spanning over about 14 octaves, stretching from below 300 nm in the UV all the way beyond 4.3 mm in the MMW band.

A laser system used in our experiments [18] consists of a solid-state ytterbium laser with an amplifier, a three-stage optical parametric amplifier (OPA), a grating–prism stretcher, a Nd:YAG pump laser, a three-stage optical parametric chirped-pulse amplifier (OPCPA), and a grating compressor. The 1 kHz, 200 fs, 1030 nm amplified output of the ${\rm Yb}:{{\rm CaF}_2}$ laser system pumps the three-stage OPA, which delivers 1460 nm pulses at its output. These pulses are stretched with a grism stretcher and seed a three-stage OPCPA, pumped by 100 ps, 20 Hz Nd:YAG-laser pulses with energies 50, 250, and 700 mJ. The stretched-pulse idler-wave OPCPA output at a central wavelength ${\lambda _0}\;\approx\;{3.9}\;\unicode{x00B5}{\rm m}$ is compressed with a grating compressor, yielding pulses with a pulse width ${\tau _0}\;{\approx}\;{80}\;{\rm fs}$ and an energy up to ${E_0}\;{\approx}\;{35}\;{\rm mJ}$ [18].

 

Fig. 1. Experimental setup: PM1, PM2, PM3, off-axis parabolic mirrors; ${{\rm CaF}_2}$, entrance window of the gas cell; AGS, ${{\rm AgGaS}_2}$ crystal for second-harmonic (SH) generation; PFM, parabolic flip mirror; I1, I2, iris diaphragms; F1, F2, polypropylene filters; F3, F4, filters for the analysis of the mid-IR-to-UV and THz-to-MMW parts of the SC output, respectively; PMH, off-axis parabolic mirror with a through hole; GaP, gallium phosphide crystal; P, polarizer, DL, delay line; L, lenses; $\lambda /{2}$, half-wave plates; WP, Wollaston prism; BD, balance detector.

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The 80 fs, 3.9 µm OPCPA output is focused into a gas cell with an off-axis parabolic mirror (PM1 in Fig. 1). The focal length $f$ of this mirror is varied in experiments from 50 to 100 cm. A 0.5-mm-thick ${{\rm AgGaS}_2}$ crystal (AGS in Fig. 1), placed right behind the ${{\rm CaF}_2}$ gas cell entrance window, is used for second-harmonic generation (SHG). The SC output is highly sensitive to the orientation of the AGS crystal. Adjusting this crystal for optimal SHG phase matching is critical for the generation of multidecade-spanning supercontinua. The focused two-color field, consisting of the 3.9 µm OPCPA output and its second harmonic, drives a gas target, giving rise to broadband radiation, which exits the gas cell to be subjected to a spectral, temporal, and beam profile analysis (Fig. 1). Spectral analysis of the mid-IR part of this SC is performed with a homebuilt scanning monochromator coupled to a cryogenically cooled HgCdTe detector. Spectral measurements in the 300–1100 nm range are carried out using an OceanOptics HR4000 spectrometer, while the spectra in the 900–2200-nm range are measured with a NIRQuest spectrometer. A broad overlap between the spectral ranges covered by these spectrometers facilitates a reliable cross calibration of piecewise spectral measurements. Mid-IR-to-UV spectral measurements are resolved across the SC beam using an adjustable iris diaphragm (I1 in Fig. 1) placed on a high-precision two-dimensional translation stage.

 

Fig. 2. (a) and b) On-axis (wine line) and off-axis (blue line) spectra of the near-IR-to-UV part of SC radiation from atmospheric air driven by a two-color laser driver with ${\lambda _0}\;{\approx}\;{3.9}\;\unicode{x00B5}{\rm m}$, ${\tau _0}\; {\approx}\;{80}\;{\rm fs}$, (a) ${E_0}\; {\approx}\;{4.0}\;{\rm mJ}$ and (b) 8.5 mJ focused by a parabolic mirror with (a) $f\; {\approx}\;{50}\;{\rm cm}$ and (b) 100 cm. Gray shading is the second-harmonic spectrum. (c) The spectrum of the MMW-to-UV supercontinuum: (solid line) mid-IR-to-UV (wine line) and THz-to-MMW (blue and pink lines) parts of the SC spectrum measured in air with a two-color laser driver with ${\lambda _0}\approx{3.9}\;\unicode{x00B5}{\rm m}$, ${\tau _0}\; {\approx}\;{80}\;{\rm fs}$, ${E_0}\; {\approx}\;{6.0}\;{\rm mJ}$, $f\; {\approx}\;{50}\;{\rm cm}$, and the input spectrum as shown by gray shading, (blue shading) calculations using the photoionization current model, (green and pink dashed line) calculations using the nonlinear polarization model in the mid-IR-to-UV (pink line) and THz-to-MMW (green line, note a ${{10}^3}$ multiplier). (d) Electro-optic sampling and (e) autocorrelation traces of the waveforms of the THz−MMW field. (f) The MMW-to-THz part of the SC spectrum: (solid line) Fourier transform of the EOS (pink line) and autocorrelation (blue line) experimental traces, (blue shading) calculations using the photoionization current model, and (dotted line) an ${\omega ^2}$ asymptote.

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Pulse characterization in the THz and MMW ranges [Figs. 2(a)2(f)] is performed in our studies using two techniques—autocorrelation measurements and electro-optic sampling (EOS). In the EOS scheme, multioctave radiation that exits the gas cell is reflected off a 2-inch-diameter, 15-cm-focal-length off-axis parabolic flip mirror (PFM in Fig. 1) and is transmitted through a 3 mm polypropylene filter (F1 in Fig. 1), which blocks the UV-to-mid-IR part of the SC spectrum. The THz-to-MMW part of the SC transmitted through the polypropylene filter is combined with a 1.03 µm, 120 fs reference pulse, delivered by the Yb laser, on a 2-inch-diameter, 10-cm-focal-length off-axis parabolic mirror with a through hole (PMH in Fig. 1). The THz-to-MMW field waveform is then sampled using sum-frequency generation in a 250-µm-thick GaP crystal. The sum-frequency output of this crystal is collimated with a 15-cm-focal-length spherical lens and transmitted through a quarter-wave plate and a Wollaston prism to be detected with a balance detector (BD in Fig. 1). The beam focusability of the THz-to-MMW SC is analyzed by filtering the THz-to-MMW field out of the SC radiation generated by a two-color driver with a polypropylene filter (F2 in Fig. 1), collimating the THz−MMW beam with a 2-inch-diameter, 15-cm-focal-length off-axis parabolic mirror (PM2 in Fig. 1), and focusing this beam onto a ${{\rm LiTaO}_3}$ pyroelectric camera with a 2-inch-diameter, 10-cm-focal-length parabolic mirror (PM3 in Fig. 1).

In the autocorrelation analysis scheme, the mid-IR-to-UV part of the SC is filtered out with a 0.4-mm-thick iron disc. The THz-to-MMW beam is then split into two replicas using a silicon beam splitter. One of these replicas is delayed with respect to the other with a movable mirror. Both replicas are then combined on the same silicon beam splitter. The power of the combined signal is measured with a ${{\rm LiTaO}_3}$ pyroelectric power meter as a function of the delay time between the replicas to yield the autocorrelation trace of the THz-to-MMW field waveform. Fourier transform of the autocorrelation trace enables an accurate retrieval of the high-frequency part of the THz-to-MMW SC spectrum (with frequencies $\nu $ above $ {\approx}{2}\;{\rm THz}$). This spectral region is not easily accessible to EOS because of the limited bandwidth of the reference pulse used in the EOS scheme. EOS, on the other hand, provides a higher signal-to-noise ratio at low frequencies (below $ {\approx}{0.1}\;{\rm THz}$), lost in autocorrelation measurements because of the transfer function of the silicon beam splitter.

On- and off-axis spectra of the near-IR-to-UV part of SC radiation generated by the two-color laser driver in air are presented in Figs. 2(a) and 2(b). This part of the SC spectrum is dominated by the peaks centered at frequencies $m{\omega _0}$, with $m$ being a positive integer. Observed as well-resolved spectral peaks at low driver intensities, these features tend to broaden, eventually forming a continuous spectrum stretching from 350 to 2200 nm for ${E_0}$ above $ {\approx}{5}\;{\rm mJ}$ [Figs. 2(a)2(c)]. This tendency correlates well with the Kerr-effect-induced spectral broadening of the 3.9 µm pulse itself [Fig. 3(a)], showing that the merger of $m{\omega _0}$ peaks in the SC output is mainly due to the nonlinear phase shift of the driver transferred to the nonlinear output [a dip centered at $ {\approx}{4.3}\;\unicode{x00B5}{\rm m}$ in Fig. 3(a) is due to the absorption by atmospheric ${{\rm CO}_2}$].

 

Fig. 3. (a) Spectra of the mid-IR part of the driver field broadened by interaction with atmospheric air with $f\; {\approx}\;{50}\;{\rm cm}$ and energy ${E_0}$ as shown in the plot. (b) The THz-to-MMW output energy measured as a function of the gas pressure $p$ for different gases (as specified in the plot) driven by the two-color laser driver with ${\lambda _0}\;{\approx}\;{3.9}\;\unicode{x00B5}{\rm m}$, ${\tau _0}\; {\approx}\;{80}\;{\rm fs}$, ${E_0}\; {\approx}\;{6.0}\;{\rm mJ}$, $f\; {\approx}\;{50}\;{\rm cm}$, and the energy of the second harmonic of $ {\approx}{0.2}\;{\rm mJ}$. (c)−(e) Transverse field intensity distribution in the THz−MMW SC from air: (c) 2D beam profile and (d) $x$ and (e) $y$ cuts of this profile.

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In Fig. 3(b), we present the THz-to-MMW output energy measured behind the polypropylene filter as a function of the gas pressure $p$ for a variety of gases (He, Ar, ${{\rm N}_2}$, air, and Kr) driven by the two-color laser driver. As a general tendency, clearly observed in Fig. 3(b), gases with a lower ionization potential provide a higher THz−MMW yield. With the energy of the 3.9 µm pulse set at ${E_0}\; {\approx}\;{6.0}\;{\rm mJ}$, corresponding to a field intensity of $ {\approx}{{10}^{14}}\;{\rm W}/{{\rm cm}^2}$, the highest energy of the THz−MMW output, ${E_{\rm THz}}\; {\approx}\;{24}\;\unicode{x00B5} {\rm J}$, is achieved in experiments with Kr [blue line in Fig. 3(b)], whose ionization potential is $ {\approx}{14}\;{\rm eV}$.

THz−MMW yields of several microjoules are achieved in these experiments at gas pressures as low as a few millibars. With ${\lambda _0}\;{\approx}\;{3.9}\;\unicode{x00B5}{\rm m}$, ${E_0}\; {\approx}\;{6.0}\;{\rm mJ}$, and ${\tau _0}\; {\approx}\;{80}\;{\rm fs}$, no filamentation is possible in this range of gas pressures as the peak power of the laser driver, $P$, is orders of magnitude lower than the critical power of self-focusing, ${P_{\rm cr}}$. For Kr, the gas with a highest nonlinear refractive index among all the gases studied here, $P/{P_{\rm cr}}\; {\approx}\;{0.003}$ at $p\; = \;{2}\;{\rm mbar}$. Yet, the THz−MMW yield for such a pressure of krypton is as high as ${E_{\rm THz}}\; {\approx}\;{5}\;\unicode{x00B5} {\rm J}$ [Fig. 3(b)], showing that no filamentation is needed for efficient THz−MMW SC generation in our experimental conditions. Moreover, as the gas pressure reaches the level at which ${P_{\rm cr}}$ becomes comparable with the laser driver peak power $P$ [$p\; {\approx}\;{600}\;{\rm mbar}$ for krypton in Fig. 3(b)], the THz−MMW yield ceases to grow and starts to rapidly lower as a function of the gas pressure [Fig. 3(b)], thus showing, in agreement with earlier studies [19], that even moderate self-action effects and related nonlinear phase shifts are detrimental for SC generation in this regime.

In Figs. 2(d) and 2(e), we present typical EOS and autocorrelation traces of THz−MMW field waveforms with an energy of ${E_{\rm THz}}\; {\approx}\;{18}\;\unicode{x00B5} {\rm J}$ generated by the two-color laser driver in air. The spectrum of this part of the SC, found through a Fourier transform of the EOS and autocorrelation traces, is shown by pink and blue lines in Figs. 2(c) and 2(f). The spectrum of the THz−MMW field, ${I_{\rm THz}}(\omega )$, is seen to peak at ${\nu _m}\; {\approx}\;{1}\;{\rm THz}$, or ${\lambda _m}\; {\approx}\;{300}\;\unicode{x00B5}{\rm m}$. At low ${E_0}$, an $f\; = \;{50}\;{\rm cm}$ mirror used in this experiment focuses a 5-mm-diameter OPCPA output into a 250-µm-diameter beam waist. With ${E_0}\; {\approx}\;{6.0}\;{\rm mJ}$, however, ionization-induced defocusing increases the driver beam waist diameter ${D_0}\; {\approx}\;{330}\;{\rm - }\;{400}\;\unicode{x00B5}{\rm m}\gtrsim{\lambda _m}$. The THz−MMW SC spectrum extends from $ {\approx}{70}\;{\rm GHz}$ to $ {\approx}{55}\;{\rm THz}$, where it meets the mid-IR part of SC radiation [Figs. 3(c) and 3(d)]. The pulse width of the MMW−THz field waveform, estimated from its autocorrelation trace as ${\tau _{\rm THz}}\; {\approx}\;{70}\;{\rm fs}$, corresponds to approximately half the cycle of a field with a central frequency ${\omega _{\rm THz}}\; = \;[\int \omega {I_{\rm THz}}(\omega )d\omega ]/[\int {{I_{\rm THz}}} (\omega )d\omega ]\; {\approx}\;{6.7}\;{\rm THz}.$ The central wavelength of this waveform is $\lambda{_{\rm THz}} \approx {45}\;\unicode{x00B5}{\rm m}\; \ll \;{D_0}$. When focused with a 10-cm-focal-length parabolic mirror (PM3 in Fig. 1), this MMW−THz output exhibits a transverse beam waist profile [Figs. 3(c)3(e)] that closely follows a Gaussian fit with an FWHM beam radius ${r_0}\; {\approx}\;{1.3}\;{\rm mm}$ [dashed line in Figs. 3(d) and 3(e)]. With ${E_{\rm THz}}\; {\approx}\;{20}\;\unicode{x00B5} {\rm J}$ and ${\tau _{\rm THz}}\; {\approx}\;{70}\;{\rm fs}$, the on-axis field strength in the focused MMW−THz beam is ${F_{\rm THz}}\; {\approx}\;{5}\;{\rm MV/cm}$.

To calibrate the spectral intensity of 0.07−900 THz supercontinua [Fig. 2(c)], we employ the above-described apparatus (Fig. 1) to directly measure radiation energy within three frequency bands: MMW-to-mid-IR ($ {\approx}{0.07 - 60}\;{\rm THz}$), mid-IR-to -near-IR ($ {\approx}{60 - 120}\;{\rm THz}$), and near-IR-to-UV ($ {\approx}{120 - 900}\;{\rm THz}$). With ${E_0}\; {\approx}\;{6}\;{\rm mJ}$, radiation energies within these bands are $ {\approx}{18}\;\unicode{x00B5} {\rm J}$, 4.5 mJ, and 0.15 µJ, respectively.

For a quantitative analysis of radiation power distribution in the MMW−THz part of ultrabroadband radiation generated by the two-color mid-IR driver, the SC output is first transmitted through the 3 mm polypropylene filter, which blocks the IR-to-UV part of the SC. The MMW−THz part of the SC field that passes through these filters is transmitted through carefully precalibrated filters whose materials and thicknesses are chosen in such a way as to provide a transfer function with a well-defined high-frequency edge ${\nu _c}$: ${\nu _c}\; {\approx}\;{14}\;{\rm THz}$ (a 180-µm-thick teflon film), 4.0 THz (a 5.5 mm teflon film), 2.4 THz (a 10 mm teflon film), 2.1 THz (a 0.19 mm sheet of ${100}\;{{\rm g/m}^2}$ paper), 0.7 THz (a 4.0 cm teflon block), and 330 GHz (a 10 mm PMMA plate). The signal transmitted through these filters is detected with a pyroelectric ${{\rm LiTaO}_3}$ detector with a detection range from $ {\approx}{0.05}$ to 30 THz. These measurements show that 85% of MMW−THz radiation power is emitted within a frequency band with ${\nu _c}\; {\approx}\;{14}\;{\rm THz}$, 72% of this power is radiated within the band with ${\nu _c}\; {\approx}\;{4.0}\;{\rm THz}$, 15% is at frequencies below ${\nu _c}\; {\approx}\;{2.4}\;{\rm THz}$, and 8% is at frequencies below ${\nu _c}\; {\approx}\;{0.7}\;{\rm THz}$. Measurements with a 10-mm PMMA filter show that, with a total MMW−THz radiation energy of $ {\approx}{25}\;\unicode{x00B5} {\rm J}$ per pulse, at least 1.5% of this energy, that is, over 0.4 µJ per pulse, is emitted in the MMW frequency range, that is, at frequencies below 300 GHz. When focused into a beam waist radius ${r_0}\; {\approx}\;{1.3}\;{\rm mm}$ [Figs. 3(c)3(e)] a pulse with such an energy yields an on-axis MMW field strength of $ {\approx}{100}\;{\rm kV/cm}$.

Two mechanisms may account for the generation of SC as observed in experiments. One of these mechanisms involves perturbative wave-mixing processes enabled by the relevant nonlinear polarization [20]. In particular, the third-order nonlinear polarization driven by a two-color, ${\omega _0} - {2}{\omega _0}$ laser field gives rise to a variety of signals, including a signal at the ${3}{\omega _0}$ frequency, via ${2}{\omega _0}\;{ + }\;{2}{\omega _0}\; - \;{\omega _0}$ four-wave mixing (FWM), as well as a low-frequency, THz, or sub-THz signal, via ${\omega _0}\;{ + }\;{\omega _0}\; - \;{2}{\omega _0}$ optical-rectification-type FWM. In the second scenario, laser-induced tunneling leads to a rapid, almost stepwise buildup of the electron density [19]. The resulting ultrafast modulation of the photoelectron current $j(\eta )$ provides a source of optical nonlinearity [1016,19,21,22], giving rise to radiation within a broad spectral range.

Calculations performed with the use of standard models of nonlinear polarization and laser-driven photoelectron current (see Supplement 1) show that SC generation with such an extraordinarily broad bandwidth becomes possible due to the joint effect of nonlinear polarization and photoelectron current. In the near-IR-to-UV range, FWM and photoionization current give rise to $m\omega_{0}$ peaks with similar spectra and close intensity [cf. dashed lines and blue shading in Fig. 2(c)], both playing a significant role in SC generation. In the THz-to-MMW part of the spectrum, however, the photocurrent model alone is seen to provide a fairly accurate description of the experimental THz-to-MMW SC spectra [cf. blue shading and solid line in Figs. 2(c) and 2(f)], with the nonlinear signal due to wave mixing being orders of magnitude weaker [dashed line in Figs. 2(c) and 2(f)]. These results suggest that the generation of the THz-to-MMW part of the SC in our experiments is mainly due to the photoionization-current nonlinearity.

The benefits of a longer-${\lambda _0}$ driver for THz–MMW SC generation in this regime are manifold: (i) To the first-order approximation, the photoelectron current follows the $\propto$ ${\lambda _0}$ scaling of the electron quiver velocity [16]. When coupled to a strong ${\lambda _0}$ dependence of beam focusing and phase matching, this leads to a rapid, $\propto$ $\lambda _0^q$ growth of the THz/sub-THz radiation yield with $q\; \gg \;{1}$ [16,17]. (ii) Due to the $\propto$ $\lambda _0^2$ scaling of the self-focusing threshold ${P_{\rm cr}}$, driver pulses with much higher peak powers can be used in mid-IR experiments without causing beam filamentation, which tends to be detrimental, as shown above, for THz–MMW SC generation. (iii) Dispersion of the refractive index of a gas in the mid-IR range is typically much weaker than in the near-IR, reducing the relative phase acquired by the ${\omega _0}$ and ${2}{\omega _0}$ components of a two-color laser driver within the nonlinear-interaction region (see Supplement 1, Fig. S2a). (iv) Since the amplitude of the electron quiver motion increases with the driver wavelength, the size ${d_s}$ of the photoelectron current source of MMW–THz radiation rapidly increases with ${\lambda_0}$. Photoelectrons generated near the peaks of field intensity (Fig. S3a) can catch the phase of the field that drives them well outside the beam waist region (see Supplement 1). For the parameters of our experiments, the displacement that such photoelectrons reach within a typical collision time ${\tau _e}\;\sim\;{1}\;{\rm ps}$ can be as large as ${x_m}\; {\approx}\;{4}\;{\rm mm}$ (Figs. S3b). This value of ${x_m}$ provides a simple, yet meaningful upper-bound estimate for the THz–MMW source size ${d_s}$ that is consistent with a typical low-frequency cutoff, ${\lambda _{\rm off}}\;\sim\;{3} -{4}\;{\rm mm}$, in SC spectra observed in our experiments [Fig. 2(f)].

The photocurrent model used in our analysis does not include any propagation effects. However, the radiation source term in this model, $\partial{j}(\eta )/\partial \eta $, is overall consistent with a canonical picture of diffraction in the far-field [23] and helps reproduce important signatures of far-field diffraction. Indeed, the Fourier transform of the field radiated by $j(\eta ),\;{E_j}(\eta )\propto{\partial j}(\eta )/\partial \eta $, leads to an intensity spectrum $\vert E_{j}(\omega)\vert^{2} \propto \vert\omega j(\omega)\vert^{2}$ with a signature ${\omega ^2}$ factor, typical of far-field radiation spectra [24]. That $\vert E_{j}(\omega)\vert^{2}$ decreases toward lower frequencies and vanishes at $\omega \; = \;{0}$ is consistent with dc-field no-propagation—another signature result of diffraction theory. It is pleasing that the low-frequency wing of the experimental SC spectra [pink line in Figs. 2(c) and 2(f)] agrees well with predictions of the photocurrent model [blue shading in Figs. 2(c) and 2(f)]. In particular, at very low $\omega $, experimental spectra closely follow the ${\omega ^2}$ scaling [dotted line in Fig. 2(f)], in full agreement with diffraction theory.

To summarize, the nonlinear response of a fast-ionizing gas provides a source of bright multiband SC radiation, spanning over about 14 octaves, from below 300 nm in the UV all the way beyond 4.3 mm in the MMW band. The MMW-to-THz part of this SC is emitted in the form of half-cycle field waveforms that can be focused to yield field strengths of $ {\approx}{5}\;{\rm MV/cm}$, with MMW field strengths up to 100 kV/cm.

Funding

Russian Foundation for Basic Research (18-29-20031, 18-02-40034, 18-02-40031, 19-02-00473, 17-02-01131); Russian Science Foundation (17-12-01533 - ultrafast spectrochronography, 19-72-10054 - nonlinear optics in the mid-infrared); Welch Foundation (A-1801-20180324).

Acknowledgment

Fruitful collaboration with A. Baltuška and A. Pugžlys is gratefully acknowledged.

 

See Supplement 1 for supporting content.

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13. S. Tzortzakis, G. Méchain, G. Patalano, Y.-B. André, B. Prade, M. Franco, A. Mysyrowicz, J.-M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, “Coherent subterahertz radiation from femtosecond infrared filaments in air,” Opt. Lett. 27, 1944–1946 (2002). [CrossRef]  

14. K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007). [CrossRef]  

15. S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013). [CrossRef]  

16. M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013). [CrossRef]  

17. A. Nguyen, K. J. Kaltenecker, J.-C. Delagnes, B. Zhou, E. Cormier, N. Fedorov, R. Bouillaud, D. Descamps, I. Thiele, S. Skupin, P. U. Jepsen, and L. Bergé, “Wavelength scaling of terahertz pulse energies delivered by twocolor air plasmas,” Opt. Lett. 44, 1488–1491 (2019). [CrossRef]  

18. A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015). [CrossRef]  

19. I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011). [CrossRef]  

20. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210–1212 (2000). [CrossRef]  

21. A. Nguyen, P. González de Alaiza Martínez, J. Déchard, I. Thiele, I. Babushkin, S. Skupin, and L. Bergé, “Spectral dynamics of THz pulses generated by two-color laser filaments in air: the role of Kerr nonlinearities and pump wavelength,” Opt. Express 25, 4720–4740 (2017). [CrossRef]  

22. M. D. Thomson, M. Kreß, T. Lëoffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1, 349–368 (2007). [CrossRef]  

23. O. D. Jefimenko, Electricity and Magnetism (Appleton, 1966).

24. S. A. Akhmanov and S. Y. Nikitin, Physical Optics (Clarendon, 1997).

References

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  1. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
    [Crossref]
  2. R. Alfano, ed. The Supercontinuum Laser Source: The Ultimate White Light (Springer, 2016).
  3. D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
    [Crossref]
  4. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
    [Crossref]
  5. M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
    [Crossref]
  6. N. Picqué and T. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13, 146–157 (2019).
    [Crossref]
  7. E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
    [Crossref]
  8. M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
    [Crossref]
  9. A. A. Lanin, E. A. Stepanov, A. V. Mitrofanov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “High-order harmonic analysis of anisotropic petahertz photocurrents in solids,” Opt. Lett. 44, 1888–1891 (2019).
    [Crossref]
  10. K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605–609 (2008).
    [Crossref]
  11. M. D. Thomson, V. Blank, and H. G. Roskos, “Terahertz white-light pulses from an air plasma photo-induced by incommensurate two-color optical fields,” Opt. Express 18, 23173–23182 (2010).
    [Crossref]
  12. T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
    [Crossref]
  13. S. Tzortzakis, G. Méchain, G. Patalano, Y.-B. André, B. Prade, M. Franco, A. Mysyrowicz, J.-M. Munier, M. Gheudin, G. Beaudin, and P. Encrenaz, “Coherent subterahertz radiation from femtosecond infrared filaments in air,” Opt. Lett. 27, 1944–1946 (2002).
    [Crossref]
  14. K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
    [Crossref]
  15. S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
    [Crossref]
  16. M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
    [Crossref]
  17. A. Nguyen, K. J. Kaltenecker, J.-C. Delagnes, B. Zhou, E. Cormier, N. Fedorov, R. Bouillaud, D. Descamps, I. Thiele, S. Skupin, P. U. Jepsen, and L. Bergé, “Wavelength scaling of terahertz pulse energies delivered by twocolor air plasmas,” Opt. Lett. 44, 1488–1491 (2019).
    [Crossref]
  18. A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
    [Crossref]
  19. I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
    [Crossref]
  20. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210–1212 (2000).
    [Crossref]
  21. A. Nguyen, P. González de Alaiza Martínez, J. Déchard, I. Thiele, I. Babushkin, S. Skupin, and L. Bergé, “Spectral dynamics of THz pulses generated by two-color laser filaments in air: the role of Kerr nonlinearities and pump wavelength,” Opt. Express 25, 4720–4740 (2017).
    [Crossref]
  22. M. D. Thomson, M. Kreß, T. Lëoffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1, 349–368 (2007).
    [Crossref]
  23. O. D. Jefimenko, Electricity and Magnetism (Appleton, 1966).
  24. S. A. Akhmanov and S. Y. Nikitin, Physical Optics (Clarendon, 1997).

2019 (3)

2018 (1)

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

2017 (1)

2016 (2)

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref]

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
[Crossref]

2015 (1)

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

2013 (3)

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref]

2011 (1)

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

2010 (1)

2008 (2)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref]

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605–609 (2008).
[Crossref]

2007 (3)

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

M. D. Thomson, M. Kreß, T. Lëoffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1, 349–368 (2007).
[Crossref]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[Crossref]

2002 (1)

2000 (1)

1986 (1)

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov and S. Y. Nikitin, Physical Optics (Clarendon, 1997).

Ališauskas, S.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

Ambacher, O.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

André, Y.-B.

Andriukaitis, G.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

Antes, J.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Apolonski, A.

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref]

Babushkin, I.

A. Nguyen, P. González de Alaiza Martínez, J. Déchard, I. Thiele, I. Babushkin, S. Skupin, and L. Bergé, “Spectral dynamics of THz pulses generated by two-color laser filaments in air: the role of Kerr nonlinearities and pump wavelength,” Opt. Express 25, 4720–4740 (2017).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

Balciunas, T.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Baltuška, A.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

Beaudin, G.

Bergé, L.

Blank, V.

Boes, F.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Bouillaud, R.

Cabrera-Granado, E.

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

Caspani, L.

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref]

Cavalieri, A. L.

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

Chen, M.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Clerici, M.

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref]

Cook, D. J.

Corkum, P. B.

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
[Crossref]

Cormier, E.

Couairon, A.

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref]

Déchard, J.

Delagnes, J.-C.

Descamps, D.

Dollar, F.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Encrenaz, P.

Faccio, D.

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref]

Fan, G.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Fedorov, N.

Fedotov, A. B.

A. A. Lanin, E. A. Stepanov, A. V. Mitrofanov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “High-order harmonic analysis of anisotropic petahertz photocurrents in solids,” Opt. Lett. 44, 1888–1891 (2019).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
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A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
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Franco, M.

Freude, W.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
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D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
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M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
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M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
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Giguère, M.

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
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K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605–609 (2008).
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K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
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González de Alaiza Martínez, P.

Goulielmakis, E.

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
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M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
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E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
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M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
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D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
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M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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Hochstrasser, R. M.

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
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I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
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Kallfass, I.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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Kapteyn, H. C.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
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M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
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Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref]

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

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T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605–609 (2008).
[Crossref]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
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E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
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M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
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E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
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E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
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M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
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Lanin, A. A.

Légaré, F.

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
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M. D. Thomson, M. Kreß, T. Lëoffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1, 349–368 (2007).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
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M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
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M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
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Mancuso, C. A.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
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Miaja-Avila, L.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
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T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
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A. A. Lanin, E. A. Stepanov, A. V. Mitrofanov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “High-order harmonic analysis of anisotropic petahertz photocurrents in solids,” Opt. Lett. 44, 1888–1891 (2019).
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A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
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M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
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Moulet, A.

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
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Mücke, O. D.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
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Murnane, M. M.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
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D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
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Oh, T. I.

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
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M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
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Palmer, R.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
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Peccianti, M.

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
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Pervak, V.

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
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E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
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Picqué, N.

N. Picqué and T. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13, 146–157 (2019).
[Crossref]

Popmintchev, D.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Popmintchev, T.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Prade, B.

Pugzlys, A.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Pugžlys, A.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

Raskazovskaya, O.

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
[Crossref]

Rodriguez, G.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605–609 (2008).
[Crossref]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[Crossref]

Rolland, C.

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
[Crossref]

Rosenthal, E. W.

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

Roskos, H. G.

M. D. Thomson, V. Blank, and H. G. Roskos, “Terahertz white-light pulses from an air plasma photo-induced by incommensurate two-color optical fields,” Opt. Express 18, 23173–23182 (2010).
[Crossref]

M. D. Thomson, M. Kreß, T. Lëoffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1, 349–368 (2007).
[Crossref]

Schmidt, B.

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref]

Schmogrow, R.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref]

Shalaby, M.

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref]

Shaw, J. M.

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

Sidorov-Biryukov, D. A.

A. A. Lanin, E. A. Stepanov, A. V. Mitrofanov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “High-order harmonic analysis of anisotropic petahertz photocurrents in solids,” Opt. Lett. 44, 1888–1891 (2019).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

Skupin, S.

Srinivasan-Rao, T.

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
[Crossref]

Stepanov, E. A.

A. A. Lanin, E. A. Stepanov, A. V. Mitrofanov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “High-order harmonic analysis of anisotropic petahertz photocurrents in solids,” Opt. Lett. 44, 1888–1891 (2019).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

Taylor, A. J.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605–609 (2008).
[Crossref]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[Crossref]

Tessmann, A.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Thiele, I.

Thomson, M. D.

M. D. Thomson, V. Blank, and H. G. Roskos, “Terahertz white-light pulses from an air plasma photo-induced by incommensurate two-color optical fields,” Opt. Express 18, 23173–23182 (2010).
[Crossref]

M. D. Thomson, M. Kreß, T. Lëoffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1, 349–368 (2007).
[Crossref]

Tzortzakis, S.

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref]

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

Voronin, A. A.

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref]

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

You, Y. S.

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

Zhan, M.

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref]

Zheltikov, A. M.

A. A. Lanin, E. A. Stepanov, A. V. Mitrofanov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “High-order harmonic analysis of anisotropic petahertz photocurrents in solids,” Opt. Lett. 44, 1888–1891 (2019).
[Crossref]

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
[Crossref]

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

Zhokhov, P.

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
[Crossref]

Zhou, B.

Zwick, T.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Laser Photon. Rev. (1)

M. D. Thomson, M. Kreß, T. Lëoffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser Photon. Rev. 1, 349–368 (2007).
[Crossref]

Nat. Photonics (3)

N. Picqué and T. Hänsch, “Frequency comb spectroscopy,” Nat. Photonics 13, 146–157 (2019).
[Crossref]

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605–609 (2008).
[Crossref]

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7, 977–981 (2013).
[Crossref]

Nature (2)

M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Klostermann, A. Guggenmos, and E. Goulielmakis, “Multi-petahertz electronic metrology,” Nature 538, 359–363 (2016).
[Crossref]

M. T. Hassan, T. T. Luu, A. Moulet, O. Raskazovskaya, P. Zhokhov, M. Garg, N. Karpowicz, A. M. Zheltikov, V. Pervak, F. Krausz, and E. Goulielmakis, “Optical attosecond pulses and tracking the nonlinear response of bound electrons,” Nature 530, 66–70 (2016).
[Crossref]

New J. Phys. (2)

T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal, H. M. Milchberg, and K. Y. Kim, “Intense terahertz generation in two-color laser filamentation: energy scaling with terawatt laser systems,” New J. Phys. 15, 075002 (2013).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controlling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. Lett. (3)

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268–2271 (1986).
[Crossref]

D. Popmintchev, B. R. Galloway, M. Chen, F. Dollar, C. A. Mancuso, A. Hankla, L. Miaja-Avila, G. O’Neil, J. M. Shaw, G. Fan, S. Ališauskas, G. Andriukaitis, T. Balčiunas, O. D. Mücke, A. Pugzlys, A. Baltuška, H. C. Kapteyn, T. Popmintchev, and M. M. Murnane, “Near- and extended-edge X-ray-absorption fine-structure spectroscopy using ultrafast coherent high-order harmonic supercontinua,” Phys. Rev. Lett. 120, 093002 (2018).
[Crossref]

M. Clerici, M. Peccianti, B. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength Scaling of Terahertz Generation by Gas Ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref]

Sci. Rep. (1)

A. V. Mitrofanov, A. A. Voronin, D. A. Sidorov-Biryukov, A. Pugžlys, E. A. Stepanov, G. Andriukaitis, T. Flöry, S. Ališauskas, A. B. Fedotov, A. Baltuška, and A. M. Zheltikov, “Mid-infrared laser filaments in the atmosphere,” Sci. Rep. 5, 8368 (2015).
[Crossref]

Science (2)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320, 1614–1617 (2008).
[Crossref]

E. Goulielmakis, V. S. Yakovlev, A. L. Cavalieri, M. Uiberacker, V. Pervak, A. Apolonski, R. Kienberger, U. Kleineberg, and F. Krausz, “Attosecond control and measurement: lightwave electronics,” Science 317, 769–775 (2007).
[Crossref]

Other (3)

R. Alfano, ed. The Supercontinuum Laser Source: The Ultimate White Light (Springer, 2016).

O. D. Jefimenko, Electricity and Magnetism (Appleton, 1966).

S. A. Akhmanov and S. Y. Nikitin, Physical Optics (Clarendon, 1997).

Supplementary Material (1)

NameDescription
» Supplement 1       Ultraviolet-to-millimeter-band supercontinua

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Figures (3)

Fig. 1.
Fig. 1. Experimental setup: PM1, PM2, PM3, off-axis parabolic mirrors; ${{\rm CaF}_2}$, entrance window of the gas cell; AGS, ${{\rm AgGaS}_2}$ crystal for second-harmonic (SH) generation; PFM, parabolic flip mirror; I1, I2, iris diaphragms; F1, F2, polypropylene filters; F3, F4, filters for the analysis of the mid-IR-to-UV and THz-to-MMW parts of the SC output, respectively; PMH, off-axis parabolic mirror with a through hole; GaP, gallium phosphide crystal; P, polarizer, DL, delay line; L, lenses; $\lambda /{2}$, half-wave plates; WP, Wollaston prism; BD, balance detector.
Fig. 2.
Fig. 2. (a) and b) On-axis (wine line) and off-axis (blue line) spectra of the near-IR-to-UV part of SC radiation from atmospheric air driven by a two-color laser driver with ${\lambda _0}\;{\approx}\;{3.9}\;\unicode{x00B5}{\rm m}$, ${\tau _0}\; {\approx}\;{80}\;{\rm fs}$, (a) ${E_0}\; {\approx}\;{4.0}\;{\rm mJ}$ and (b) 8.5 mJ focused by a parabolic mirror with (a) $f\; {\approx}\;{50}\;{\rm cm}$ and (b) 100 cm. Gray shading is the second-harmonic spectrum. (c) The spectrum of the MMW-to-UV supercontinuum: (solid line) mid-IR-to-UV (wine line) and THz-to-MMW (blue and pink lines) parts of the SC spectrum measured in air with a two-color laser driver with ${\lambda _0}\approx{3.9}\;\unicode{x00B5}{\rm m}$, ${\tau _0}\; {\approx}\;{80}\;{\rm fs}$, ${E_0}\; {\approx}\;{6.0}\;{\rm mJ}$, $f\; {\approx}\;{50}\;{\rm cm}$, and the input spectrum as shown by gray shading, (blue shading) calculations using the photoionization current model, (green and pink dashed line) calculations using the nonlinear polarization model in the mid-IR-to-UV (pink line) and THz-to-MMW (green line, note a ${{10}^3}$ multiplier). (d) Electro-optic sampling and (e) autocorrelation traces of the waveforms of the THz−MMW field. (f) The MMW-to-THz part of the SC spectrum: (solid line) Fourier transform of the EOS (pink line) and autocorrelation (blue line) experimental traces, (blue shading) calculations using the photoionization current model, and (dotted line) an ${\omega ^2}$ asymptote.
Fig. 3.
Fig. 3. (a) Spectra of the mid-IR part of the driver field broadened by interaction with atmospheric air with $f\; {\approx}\;{50}\;{\rm cm}$ and energy ${E_0}$ as shown in the plot. (b) The THz-to-MMW output energy measured as a function of the gas pressure $p$ for different gases (as specified in the plot) driven by the two-color laser driver with ${\lambda _0}\;{\approx}\;{3.9}\;\unicode{x00B5}{\rm m}$, ${\tau _0}\; {\approx}\;{80}\;{\rm fs}$, ${E_0}\; {\approx}\;{6.0}\;{\rm mJ}$, $f\; {\approx}\;{50}\;{\rm cm}$, and the energy of the second harmonic of $ {\approx}{0.2}\;{\rm mJ}$. (c)−(e) Transverse field intensity distribution in the THz−MMW SC from air: (c) 2D beam profile and (d) $x$ and (e) $y$ cuts of this profile.

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