1. Introduction

Ultrashort laser pulses with durations down to the few femtosecond scale (1 fs = 10⁻¹⁵ s) have created a revolution in science and technology [1]. In particular, the availability of high energy, ultrashort pulses has been instrumental in the emergence of the field of attosecond science. Promising to unravel the complexity of electron dynamics in atoms, molecules and solids, attosecond science has experienced tremendous growth over the past years and is one of the most exciting and rapidly developing areas of modern physics [2–4].

The key technological advance that has led to the emergence of attosecond science is the generation of attosecond pulses (1 as = 10⁻¹⁸ s) in the extreme ultraviolet (XUV) range of the electromagnetic spectrum through the generation of high-order harmonics of a near infrared (NIR) or visible source of ultrashort laser pulses. In the high-order harmonic generation (HHG) process, bursts of XUV light with sub-fs duration are emitted during each half cycle of the driver laser. In order to produce isolated attosecond pulses, the process must be driven by few-cycle laser pulses while controlling the waveform of the driving pulse via the carrier-envelope phase (CEP). The few-cycle pulse duration limits the number of attosecond pulses that are generated, and in combination with CEP control ensures that the XUV generation can be confined to a single half-cycle of the driving pulse utilizing one of a number of gating techniques. However, most gating techniques can only be used at the expense of a substantial reduction in the HHG conversion efficiency [5]. Consequently, for the most efficient generation of isolated attosecond pulses direct amplitude gating using a near single-cycle driving pulse is preferable [6, 7]. In doing so, the driver laser wavelength should be as short as possible, in order to counteract the λ⁵ − λ⁶ scaling of the single-atom response [8].

Most experimental setups for attosecond science to date are based on Ti:Sapphire Chirped Pulse Amplification (CPA) systems that can generate NIR pulses with a few mJ of energy with pulse durations typically limited to approximately 25 fs, due to bandwidth limitations in the Ti:Sapphire gain medium. Compression to pulse durations of only a few fs is achieved using spectral broadening in gas-filled hollow core fibers [9]. Using Ti:Sapphire technology, the repetition rate of experiments combining isolated attosecond XUV pulses with a few-cycle NIR field is typically one or a few kHz, and limited to a maximum repetition rate of 10 kHz [10]. The limitation in repetition rate is imposed by thermal effects in the Ti:Sapphire amplifiers utilized.

There are many reasons why attosecond technology needs to be extended to substantially higher repetition rates than available up to now. In gas phase (atomic or molecular) attosecond experiments, coincident momentum-resolved measurements of all charged particles (electrons and ions) that are produced in an attosecond pump-probe sequence are desirable to facilitate the often challenging interpretation of the experimental results. Such a coincident detection of electrons and ions is possible in a reaction microscope or cold target recoil ion momentum spectroscopy (COLTRIMS) apparatus [11]. However the technique requires that at most one atom or molecule is ionized per laser shot, in order to ensure that the detected ions and electrons can be assigned to a common ionization event. As a result, data acquisition is only possible at a small fraction of the laser repetition rate and high repetition rate (≥100 kHz) laser sources are required to ensure that statistically significant data sets can be acquired in a reasonable time, while retaining laser pulse energies (≥100 µJ) that are compatible with the intensity requirements of the high harmonic generation process and producing a sufficiently large number of photons per pulse. Note that the first experiments using isolated attosecond laser pulses were conducted using few-cycle driver lasers with pulse energies of a few hundred µJ [12, 13]. Note in addition, that CEP effects and evidence towards isolated attosecond pulse generation utilizing high repetition rate, few-cycle pulses with ∼10 µJ of energy per pulse have been reported in the literature [14, 15]. However the number of XUV photons per pulse reported for these sources is considerably lower than the typical number of photons per pulse required for experiments in attosecond science in the gas phase. Similar considerations apply in many proposed attosecond condensed phase experiments (although in this case, the requirements on the number of XUV photons per pulse is more relaxed), such as attosecond time-resolved surface photoemission, in particular when performed in combination with detection using energy-resolving photoelectron electron emission microscopy (PEEM) [16]. In these experiments the number of photoelectrons that can be extracted from a surface or nano-structure per laser shot is severely limited by space-charge effects, as well as possible damage threshold limitations of the sample. High repetition rates also promise significant advances in (attosecond) transient absorption spectroscopy experiments, which are developing into one of the most popular implementations of pump-probe spectroscopy, based on their relative experimental simplicity and their unique ability for obtaining dynamical information with atomic specificity [17]. So far, however, the sensitivity that is achieved in these experiments, as defined by the minimum differential absorption that can be measured, remains orders of magnitude removed from the sensitivity that is achieved in transient absorption experiments in the visible or infrared domain [18]. Substantially higher repetition rates than available up to now promise to alleviate this situation.

In order to enable the use of high repetition rates in attosecond experiments, amplification of ultra-short laser pulses in noncollinear optical parametric chirped pulse amplifiers (NOPCPAs) has been proposed, as well as more recently, the direct post-compression of pulses from fiber amplifiers in gas-filled hollow-core fibers [19]. NOPCPAs allow amplifying CEP-stable, few-cycle pulses from laser oscillators to high average powers [20–23]. In particular, a high power NOPCPA at 800 nm, capable of generating 7 fs long CEP-stable pulses with 190 µJ of energy at a repetition rate of 100 kHz has been developed at the Max Born Institute [24]. With these specifications, this NOPCPA permits the generation of isolated attosecond laser pulses by polarization gating [25]. Still, for optimal attosecond pulse generation, the pulse duration of well over 2 optical cycles is too long, and limits the efficiency of isolating an attosecond pulse. Hence, it is highly attractive to combine the NOPCPA with some form of pulse post-compression.

Recently, a novel technique has been developed to efficiently increase the bandwidth of high energy multi-cycle laser pulses, exploiting the nonlinear interaction of the intense laser pulses with a solid sample [26, 27]. When a strong laser pulse is focused into bulk material, the nonlinear index of refraction induced by the intense field leads to several effects such as self-phase modulation (SPM), self-focusing and pulse self-steepening. Eventually the high intensities lead to ionization, plasma formation and the subsequent formation of filaments and/or dielectric material damage. By properly limiting the sample thickness and placing multiple thin plates in selected locations around the focal region of the laser, the formation of filaments can be avoided. Consequently the combined action of SPM, self-focusing and self-steepening leads to a dramatic bandwidth increase. The technique has been labeled multiple-plate supercontinuum generation (MPC). Utilizing 25 fs, 250 µJ pulses at 1 kHz and 800 nm from a Ti:Sapphire amplifier, the generation of a broad coherent spectrum supporting sub-3 fs pulses has been reported [26]. Compression to near-single-cycle pulse duration of 2.9 fs [28] and to 2 cycles of 5.4 fs [29] have been demonstrated for 1 kHz systems. Recently a number of techniques have been proposed or demonstrated for pulse compression in solids of high repetition rate and high average power systems. These include the use of multiple cells [30–32], and extensions of the MPC [33, 34]. However, pulses produced in these reports were either too long in duration or too weak in energy to be of interest for efficient generation of isolated attosecond XUV pulses. Compared to other nonlinear techniques for spectral broadening, MPC can support supercontinuum generation over a very broad range of input parameters. In particular, the technique can be implemented for sub-100 fs input pulse durations with energies spanning a broad range from sub-100 µJ to the multi-mJ level. The relatively low required input power and MPC’s immunity to beam pointing fluctuations makes its implementation in high repetition rate and high average power systems extremely attractive. This motivates the current investigation of the use of the MPC scheme in conjunction with sources of few-cycle pulses for the purpose of obtaining single-cycle pulses that are optimal for isolated attosecond pulse generation. It is worth mentioning that the technique has also been extended to work with pulses at longer wavelengths [34–36].

In this work reduction of the pulse duration from a high energy, high repetition rate NOPCPA down to the single-cycle limit is reported. By utilizing a very compact, simple, and cost-effective setup, it is shown that CEP-stable pulses with a high average power of almost 10 W, a repetition rate of 100 kHz, and a 3.7 fs duration are achievable, with excellent wavefront characteristics. To the best of our knowledge, this is the first laser system with the potential to combine the challenging requirements regarding repetition rate (100 kHz), pulse energy (100 µJ), pulse duration (< 4 fs) and CEP-stability that are needed for next-generation attosecond experiments, at the shortest wavelength where such a performance may be achievable in the foreseeable future.

2. Experimental setup

A sketch of the experimental setup is shown in Fig. 1. Compressed pulses from the high power NOPCPA described in [24] operated in these experiments with an energy per pulse of 140 µJ and 7 fs duration, were loosely focused with a 75 cm focal length spherical mirror to an approximate intensity of ∼ 3×10¹³ W/cm². At the focal plane, a 50 µm quartz plate was placed in Brewster angle configuration. Due to the nonlinear interaction of the pulses with the plate, a second focal plane arises a few cm downstream from the first plate. A second 50 µm-thick quartz plate was placed behind the first plate and its position was optimized to obtain an octave-spanning spectrum. At this point the spatial profile of the pulse evolves into a central spot that contains most of the energy and additional conical emission (rings) with higher divergence (see inset in Fig. 1) [27].

 

Fig. 1 Experimental setup: Two thin plates of quartz placed around the focal plane of the loosely focused beam from the high power NOPCPA extend the pulse spectrum to more than a full octave. Compression is achieved with chirped mirrors and thin fused silica wedges. The inset shows a photograph of the resulting beam with octave-spanning spectrum.

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The conical emission was filtered out by placing an iris in the beam path (not shown in Fig. 1)). It is important to remark, that the formation of filaments was avoided at all times throughout the experiments. Pulse characterization can not be performed at the 10 W level. Therefore, an uncoated wedge was placed approximately 41 cm behind the last focal plane in the MPC setup, where the beam size had already increased to an approximate diameter of 1.5 mm. The beam reflected off of the uncoated wedge was then collimated to a beam diameter of 2.5 mm by a spherical mirror (f = 75 cm). The pulses were compressed utilizing 4 pairs of bounces on chirped mirrors (Ultrafast Innovations PC-70) in combination with material dispersion in air and thin fused silica wedges. We checked by numerical propagation of our pulses that placing the wedge before or after the chirped mirrors does not affect the results. At full power the B-integral through the entire compressor is less than 0.19 π-radians).

3. Spectral characteristics

The spectral content of the output pulses was measured before the chirped mirrors utilizing an integrating sphere (Ocean Optics FOIS-1) fiber-coupled to a spectrometer (Ocean Optics Flame-VIS-NIR). The spectrum was recorded for a different number of plates and in the absence of plates, in order to distinguish the effect of SPM in air. As observed in Fig. 2, there is significant enhancement in the spectral content even without the plates due to the interaction of the intense pulses with air in the focal region of the input beam. Note however that this measured spectrum reflects the nonlinear interaction of the pulses with air as they propagate through the entire focal region and, as such, does not correspond to the pulse spectrum entering the first quartz plate, since the first plate is placed at the center of the focal volume. Therefore the actual spectral broadening entering the first plate is smaller. Nevertheless, due to this nonlinear interaction with air, a determination of the actual intensity incident on the first plate is quite challenging. The intensity quoted in the previous section is an estimation based on the measured beam profile and pulse duration of the NOPCPA at the position of the first plate, under conditions where most of the energy is first dumped utilizing a variable power attenuator, so that the nonlinear interaction with air is suppressed.

 

Fig. 2 Output spectra for a different number of plates in (a) linear and (b) logarithmic scale. When no plates are present the spectrum is already broadened compared to the spectrum produced in the NOPCPA due to the interaction of the intense pulses with air. With two 50 µm-thick quartz plates the spectrum extends well beyond a full octave.

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As observed in Fig. 2, the addition of a single plate is sufficient to expand the original spectrum of the NOPCPA pulses, spanning the range 680 nm–1050 nm (−20 dB point), to beyond a full octave. Furthermore, the interaction of the NOPCPA pulses with two plates extends the −20 dB width of the spectrum to more than 550 nm. The determination of the −20 dB point on the long wavelength side of the spectrum is hindered by the upper detection limit in the spectrometer. Assuming that the spectrum does not extend beyond 1050 nm, the transform-limited pulse duration supported by the spectrum is 2.31 fs, which for a central wavelength of 821 nm (center of the intensity weighted-spectrum) corresponds to 0.85 optical cycles. It was found that for the initial 7 fs pulses, the introduction of further plates only broadened the spectral content marginally while reducing the efficiency.

These observations represent a departure from the typical behavior in MPC with multi-cycle pulses. As has been previously reported [26, 27, 36], the spectral broadening in MPC with multi-cycle pulses, where the total number of plates is typically between 4 and 7, is characterized by a step-wise bandwidth increase with each additional plate, driven mostly by SPM for the first few plates, and followed by the rapid formation of a plateau-like structure towards the high frequency side of the spectrum. Following the formation of the plateau, additional plates only contribute to the formation of a hump-like structure right before the high-frequency cut-off, and the spectral broadening saturates. The formation of the plateau has been assigned to pulse self-steepening, i.e. the enhancement of the trailing edge of the pulse in a self-focusing beam [37]. The phenomenon of self-steepening arises from a correction to the nonlinear Schrödinger equation for few-cycle pulses, for which the slowly-varying-envelope approximation is no longer valid [38]. The effect is usually understood as the result of an intensity dependent group velocity shifting energy from the peak of the pulse towards its side [39]. In the multi-plate technique, the shifting in energy happens between the plates [27]. For MPC with few-cycle pulses, the situation is changed. This is because the relative contribution to spectral broadening by SPM for pulses of different temporal widths is approximately given by the ratio of the incident pulse widths [40]. Hence the broadening due to SPM for a 7 fs pulse would be a factor of ≈3.6 larger than for a 25 fs pulse, as used in [26]. Thus, for few-cycle pulses, SPM can become the dominant mechanism for spectral broadening. This explains the measured spectra in Fig. 2 where after the first plate inside which only SPM has occurred the pulse spectrum has already reached to 480 nm at the -20 dB intensity level, and becomes nearly saturated after the second plate. Evidently in this few-cycle case, pulse-steepening starts to show up in the second plate but plays a minor role in the overall broadening scheme. It is significant that when SPM is being more dominant the half-width of the generated spectrum is broader. This is highly beneficial as it means that successful compression to the transform limit will result in more (> 90 %) of the pulse energy residing in the main lobe of the envelope, with small side lobes. This translates into higher peak powers. In order to better understand the physical processes leading to the spectral broadening of the few-cycle pulses from the NOPCPA, nonlinear propagation simulations have been carried out. The simulations were performed utilizing an unidirectional propagation equation, written directly for the electric field without using the slowly varying envelope approximation (see e.g. [41]). Linear dispersion to all orders, Kerr effect including self-steepening, second-order nonlinearity in air and SiO₂ plates, as well as ionization of the media were included in the simulation. Propagation in air, followed by SiO₂ plates, followed by air has been simulated, according to the experimental setup. The spectrum and spectral phase retrieved by a SEA-F-SPIDER device were utilized to generate the input field at the initial intensity quoted before (3×10¹³ W/cm²). Fig. 3 shows the input spectrum, together with the simulated spectra resulting from nonlinear propagation in air, propagation in air plus one 50 µm plate of quartz, two plates, etc. The simulated spectra are qualitatively in good agreement with the experimental results. There is significant spectral broadening in air, but the addition of quartz plates leads to the extension of the bandwidth significantly over one octave. Moreover the simulations suggest that the -20 dB point extends beyond 1200 nm at the long wavelength end of the spectrum. The amount of energy in this spectral region (λ > 1050 nm) can be estimated to be 11 % of the total pulse energy for the case of two plates, which is consistent with the losses measured in the compressor (see section 4). The origin of the oscillations visible in the simulated spectra in the 400–500 nm range is the SPM process itself, which typically results in periodically modulated spectra. In the current simulations, only on-axis propagation was considered, therefore well-defined minima in this spectral region are predicted. On the contrary, in the experiment the output spectra are formed by radiation propagating at different angles with correspondingly different minima. Therefore, these oscillations are averaged out in the measured spectra. In addition, the simulated temporal shapes of the electric fields corresponding to propagation through different number of plates, show that in general the profiles are symmetric except for the case of propagation through three and four plates, for which a steep profile is observed in the leading edge of the pulse. However, the asymmetry observed is not a signature of self-steepening which would lead to a steep profile in the trailing edge of the pulse. Instead, linear dispersion plays a dominant role in the asymmetry of the pulses. From the temporal profiles of the electric fields and from the symmetry of the simulated spectra shown in Fig. 3 it is concluded that self-phase modulation is the main mechanism of spectral broadening.

 

Fig. 3 Simulated spectra for a different number of plates in logarithmic scale.

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4. Output power

Figure 4 shows the power out of the MPC setup before the chirped mirror compressor for the case when two plates are utilized and the input power from the NOPCPA was 14.4 W. The output power was measured after filtering out the conical emission with an iris. The resultant power of 11.5 W represents 80 % of the input power. Accordingly the conversion efficiency of the MPC process is approximately 1.5 times higher compared to the case where 25 fs input pulses were used [26]. The output power was recorded over a period of 1 hour utilizing a thermopile with an acquisition time of 1 second. At the intensity reported here, no damage was observed in the plates. The throughput of the chirped-mirror compressor amounts to 85 %, which would result in compressed pulses with an average power of 9.7 W, or 97 µJ of energy per pulse. The inset in Fig. 4 shows a histogram of the power measurements. The standard deviation of the average power is only 0.5 % of the mean value, showing the excellent long term stability of the system. The pulse-to-pulse energy fluctuations were characterized simultaneously for the NOPCPA and the MPC output utilizing two fast photodiodes and an oscilloscope. The pulse energy and standard deviation were recorded for several series of measurements, each series consisting of 2500 measurements taken over a time span of 5 minutes. In all series of measurements and for both, the NOPCPA and the MPC pulses, the retrieved standard deviation represented 2 % of the mean value and was determined by the stability of the NOPCPA.

 

Fig. 4 Output power before compression showing excellent stability over one hour. The inset shows a histogram of the power measurement.

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5. Spectrally resolved spatial characterization

The spatial distribution and the wavefront uniformity are important signatures that define how tightly a beam can be focused and therefore, determine the achievable peak intensity, which is crucial for many applications. Since the spectrum of the MPC covers more than one octave and most beam and wavefront analysis techniques are designed for monochromatic fields, an accurate characterization calls for performing spectrally resolved measurements. For that reason, a series of images of the beam profile were acquired at different wavelengths. The broadband spatio-spectral distribution was filtered utilizing band-pass filters with a spectral width of 10 nm (Thorlabs FB-λ-10, with λ the specific central wavelength in nm). In addition, for the spectrally filtered distributions, the wavefronts were characterized utilizing a Shack-Hartmann sensor (Thorlabs WFS150-5C). The measurements were performed after the chirped mirror compressor. The beam size was reduced by a factor of two utilizing a Galilean telescope, in order to fit the beam into the area of the detectors. Figure 5 shows the spectrally resolved MPC beam profiles and wavefronts. Figs. 5(a)–(h) show the spectrally integrated beam profile and the spectrally resolved beam profiles at 500, 550, 600, 700, 800, 900 and 1000 nm respectively. Fig. 5(i) illustrates the spectral location of the filters, represented by lilac vertical stripes, while Figs. 5(j)–(p) show the reconstructed wavefronts at the individual wavelengths. The magenta circles on Figs. 5(a)–(h) illustrate the approximate area over which the respective wavefronts were measured. As clearly seen in Figs. 5(b)–(h), the spectrally filtered beam profile depends on which part of the spectrum is analyzed. The main characteristic of the series of images is the dependence of the beam size on the wavelength. The spatial distribution is smallest around the spectral range of the input pulses and gets larger towards the wings of the spectrum. The spatial distributions at 700 nm breaks with this trend, but it is significantly distorted. By comparing the input and output spectra it could be noted that a significant portion of the spectral power density had shifted away from the region around 700 nm. It has been observed that depending on the exact input parameters, distortions in the spatial distribution can also be observed around 800 and 900 nm. In the case of the input pulses from the NOPCPA (measurements not shown here), the spatial distribution depends only weakly on the wavelength. Therefore, the wavelength dependent nature of the spatial distribution originates from the nonlinear propagation. In the absence of a guiding mechanism during the nonlinear propagation, the most intense part of the beam, (i.e. the center of the spatial distribution) is where the broadest spectrum is generated. As the beam propagates the spatial distribution gets wider towards the edges of the spectrum, where new frequency components have been generated. Similar observations have recently been reported elsewhere [33].

 

Fig. 5 MPC beam and wavefront characterization.(a)–(h) Spectrally integrated and spectrally resolved beam profiles at 500, 550, 600, 700, 800, 900 and 1000 nm respectively. (i) Pulse spectrum. The vertical stripes indicate the location of the filters in the spectral domain. (j)–(p) Spectrally resolved wavefront reconstruction.

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Figs. 5(j)–(p) show the retrieved wavefronts expressed in units of wavelengths. In each case the wavefront was calculated for the corresponding spectrally filtered beam profile, over the area indicated by the magenta dashed line, shown in the figure to the left. For the wavefront reconstruction at the individual wavelengths, the measured wavefront distortions were fitted to a Zernike polynomial expansion [42], utilizing in all cases the first 28 terms of the expansion. Since the Zernike polynomials are defined over the unit circle, the XY axes in Figs. 5(j)–(p) are dimensionless and run from −1 to 1, but in all cases the wavefronts were calculated over the areas illustrated by the dashed circles in Figs. 5(j)–(p). In the wavefront reconstructions shown in Figs. 5(j)–(p), the term responsible for homogeneous focusing has been arbitrarily set to zero in order to highlight asymmetrical wavefront aberrations. The wavefront characterization shows well-behaved wavefronts and only a slight dependence on the wavelength. The wavefront distortion across the full beam is limited in all cases to less than λ/4 and is mostly due to astigmatism and coma. The input NOPCPA pulses show very similar wavefront characteristics (measurements not shown).

In order to quantify the amount of wavefront distortions and their impact on potential applications, a Strehl ratio can be calculated directly from the coefficients of the polynomial expansion to quantify how much the intensity at focus will get reduced due to the wavefront distortions as compared to a perfectly flat wavefront. Following the analysis of [42], first the rms wavefront error σ of a circular pupil for a particular wavelength λ can be defined in terms of the coefficients multiplying the Zernike polynomials in the polynomial expansion. From the wavefront error, the Strehl ratio for a monochromatic beam can be estimated as

The previous analysis focuses solely on the wavefront and does not take into account the near field spatial distributions or the fact that different spectral components can focus at different positions (i.e. chromatic aberrations). Additional insight can be gained by analyzing spectrally resolved images of the beam in the far field. Fig. 6 shows the spectrally integrated and spectrally resolved images of the MPC output at the focal plane of a 1 m focal length spherical mirror. The spectrally integrated beam profile shown in Fig. 6(a) has a small deformation from a perfectly round beam. Figs. 6(b)–(d) show slightly smaller beams at 500, 550 and 600 nm. On the contrary, the beams at 800, 900, and 1000 nm are similar in size to the spectrally integrated beam. However it can be observed that towards 1000 nm the spatial distribution gets smaller. This is a consequence of the different sizes in the near field in combination with a slight chromatic aberration. On top of that, the spatial distribution at 700 and 800 nm, where most of the energy in the input pulses was contained, suffer the strongest distortions.

 

Fig. 6 Beam images in the far field. (a)–(h) Spectrally integrated and spectrally resolved beam profiles at 500, 550, 600, 700, 800, 900 and 1000 nm respectively.

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From the beam profiles in Fig. 6 it can be concluded that at the center of the focal volume, where the beam is most intense, all spectral components are present. An estimation can be made of the percentage of the total energy contained in the central part of the focal volume, where all spectral components contribute to the formation of a short pulse. For that purpose, the fraction of energy F contained in an area A corresponding to the beam size at 500 nm is calculated at each wavelength. In order to determine the area A, the 1/e² beam half widths (ω_x and ω_y) of the beam profile measured at 500 nm were calculated. Assuming a Gaussian beam, more than 99% of the energy should be contained in the area A inside the ellipse given by x²/a² + y²/b² = 1, with a = πω_x/2 and b = πω_y/2 [43]. Once the ellipse of integration is determined, the fraction of energy inside this area was determined for each spectrally resolved spatial distribution according to

Integral 4 is calculated over the bandwidth of the bandpass filters utilized for the measurements (vertical lilac stripes in Fig. 5(i)). The fraction of the total energy at focus that can be utilized in a particular application, is then estimated as 53 %. Similarly, integrating the spectrally integrated beam from Fig. 6(a) over the selected area A results in a fractional energy of 44 %. The agreement is notable considering that for the first calculation, only the spectral windows of the band-pass filters are considered, while in the second calculation, the spectral response of neutral density filters or the CCD were not considered. Note that the calculated percentage gives information about what fraction of the total energy is contained in the focal volume where the spectral content is maximum. This is not to be confused with the Strehl ratio introduced before, which only considered the wavefront distortions to quantify how much the peak intensity degrades for a given spatial distribution.

6. Spatio-temporal characterization

Spatio-temporal couplings alter the temporal and spatial composition of the pulse, potentially degrading the achievable peak intensities and therefore have a strong impact on the efficiency of highly nonlinear processes. As a consequence, it is extremely important to perform spatially resolved measurements of the compressed pulses from the MPC setup. In order to characterize the compressed pulses, the SEA-F-SPIDER technique was employed [44] together with the implementation of a multiple-shearing algorithm [45], which is essential to faithfully reconstruct the spectral phase across the dips that are invariably present in the strongly modulated spectra of few-cycle pulses [46]. Fig. 7 shows the measured spatio-spectral and reconstructed spatio-temporal distributions of the pulses from the MPC setup after compression with chirped mirrors along the walk-off plane (i.e. the plane on which the pump and seed beams cross in the NOPCPA) and the perpendicular plane.

 

Fig. 7 Spatio-spectral and spatio-temporal characterization of the compressed output pulses with SEA-F-SPIDER.(a) Spatio-spectral reconstruction in the walk-off plane. (b) Spatio-temporal reconstruction in the walk-off plane. (c) Spatio-spectral reconstruction in the perpendicular plane. (b) Spatio-temporal reconstruction in the perpendicular plane. (e) Spatially-integrated spectra and (f) pulse shapes. The blue traces correspond to the measurements in the walk-off plane, while the red traces correspond to the measurements in the perpendicular plane. OC: Optical Cycles.

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The upper panels of Fig. 7 show the spatio-spectral [Fig. 7(a)] and spatio-temporal [Fig. 7(b)] distributions across the walk-off plane. The spatio-spectral distribution in the walk-off plane shows a slight spatial chirp, particularly towards higher frequencies [Fig. 7(a)] at the focal plane of the SPIDER device, an indication that the MPC pulses have a small degree of angular dispersion. In the temporal domain a small degree of pulse front tilt is also detected [Fig. 7(b)]. Along the perpendicular plane the spectrum is fairly homogeneous [Fig. 7(c)], as is the spatio-temporal distribution, within the full-width at half-maximum (FWHM) of the spatial distribution, indicated by two horizontal dashed lines [Fig. 7(d)]. Note that the width of the spatial distribution is frequency dependent along both directions [Figs. 7(a) and 7(c)]. Both distributions are narrower towards the edges of the spectrum, in agreement with the results of the previous section.

For a quantitative characterization of the spatio-temporal distortions the attention is focused on first-order couplings in the x-ω and y-ω planes, and also the x-t and y-t planes. x is the spatial coordinate of the beam within the walk-off plane, while y is the spatial coordinate perpendicular to the walk-off plane, ω is the angular frequency and t is the time. From the distribution in Fig. 7(a), the normalized spatial chirp ρ_xω defined in [47] was calculated according to

The same calculations were performed along the perpendicular y coordinate. The normalized spatial chirp for the x and y directions calculated from Figs. 7(a) and 7(c) are −0.04 and 0.003 respectively. As a reference, according to [47] the pulses from a typical chirped pulse amplification system are characterized by a normalized spatial chirp in the order of 0.05–0.2. Hence the magnitude of the spatial chirp at focus of the compressed pulses is relatively small. However, the normalized chirp along the x direction is an order of magnitude stronger than in the y direction. Although the input NOPCPA pulses are expected to have stronger couplings in the walk-off plane (i.e., along the x direction), additional measurements confirmed that the residual angular dispersion (or spatial chirp in the focal plane), is related to the Brewster angle geometry of the plates in the MPC setup. Indeed, by repeating the measurements with the quartz plates arranged at normal incidence to the input beam, normalized spatial chirp values of −0.0025 and 0.0099 were found along the x and y coordinates respectively, at the focal plane of the SPIDER device. Moreover the spatio-spectral distributions look very similar in this case. Hence it is first and foremost the Brewster angle geometry that increases the couplings along the x coordinate. Along this direction the spectral components of the incident pulse get angularly dispersed as they cross the interface from air to quartz and angular dispersion is corrected when the pulse exits the plates back to air. However, the additional frequency components formed during the non-linear propagation in the plates propagate parallel to the fundamental field inside the plates, and therefore, as these new frequency components emerge from the plates they carry a certain degree of angular dispersion along the x coordinate.

A similar analysis of linear couplings can be performed in the x-t and y-t planes. In this case, the normalized pulse front tilts retrieved from the distributions in Figs. 7(b) and 7(d) are −0.06 and −0.07 respectively. The magnitude of the pulse front tilt is very similar and relatively small in both cases. Nevertheless, the presence of pulse front tilt will make the spatially integrated pulse shape longer than the pulse shape at any given point in the distribution. Still the main conclusion remains that despite the obvious presence of couplings along the walk-off plane (or x axis), the retrieved spatio-temporal distribution is not highly distorted.

The lower panels show the spatially integrated spectra reconstructed in the SEA-F-SPIDER [Fig. 7(e)] and the spatially integrated pulse shapes [Fig. 7(f)], with the blue traces corresponding to the walk-off plane and the red traces to the perpendicular plane. The spectrum of the compressed pulses is restricted by the utilized chirped mirrors. The designed spectral range of these mirrors extends from 500 nm to 1050 nm, and therefore the compressed pulse spectrum is cut at both ends, causing the transform-limited pulse duration to stretch to slightly below 3.5 fs along both transverse directions. The integration of the spatio-temporal distribution was performed within the FWHM of the spatial distribution. The pulse duration was 3.64 fs in the walk-off plane and 3.72 fs in the perpendicular plane, corresponding to approximately 1.45 and 1.55 optical cycles respectively. This pulse duration combined with the achievable pulse energy after compression results in a peak power of 26 GW. Each distribution and trace shown in Figs. 7(a)–(e) represents an average over ten different measurements, with each measurement integrating over 50 ms (i.e. 5000 shots). In Fig. 7(f) multiple traces corresponding to the different measurements are plotted together to illustrate the repeatability of the measurement. The error bars reported for the pulse duration were calculated as one standard deviation from the mean over the series of ten spatially-integrated measurements. The retrieved pulse duration represents, to the best of our knowledge, the shortest pulse duration reported to date for high average power, high repetition rate (≥100 kHz) pulses.

7. CEP stability

To characterize the CEP stability spectral fringes were measured as a function of time utilizing a common path f-to-2f interferometer [48]. Since the spectrum from the MPC setup covers a full octave, the interferometer merely consists of second harmonic generation in a BBO crystal, a cube polarizer beam splitter to mix the two interfering waves and a spectrometer (Ocean Optics Flame). Fig. 8 shows the results of a measurement over 35 minutes, where the retrieved phase from the spectral fringes was used to generate a correction signal that feeds a modulation input in the controller of the locking system of the oscillator. Fig. 8(a) shows the spectral fringes as a function of time while Fig. 8(c) shows the retrieved CEP. Due to the minimum integration time in the spectrometer, each spectrum is integrated over 100 shots. In addition, the acquisition rate in the spectrometer was limited to 100 Hz, which set the limit for the detection bandwidth. As a consequence, the retrieved residual phase noise of 95 mrad from the histogram of Fig. 8(d) represents an underestimation of the actual residual phase noise. Nevertheless an integration over the temporal coordinate [Fig. 8(b)] shows a high degree of modulation in selected parts of the spectrum, an indication that within the 1 ms integration time the CEP must have remained rather stable. In future, single-shot CEP measurements will be undertaken using the stereo-ATI technique [49].

 

Fig. 8 CEP stability. Fig. 8(a) shows the measured spectral fringes as a function of time. Fig. 8(b) shows an integration over the temporal coordinate. Fig. 8(c) provides the retrieved phase as a function of time from the data in Fig. 8(a). Fig. 8(d) shows the histogram over all the retrieved phase values.

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8. Conclusion

In this work it has been demonstrated that the combination of a NOPCPA and the multi-plate compression technique is an effective and simple arrangement to produce CEP-stable, near single-cycle coherent light pulses with high average power and high repetition rate. It has been observed that for the case of few-cycle laser pulses the spectral broadening in MPC is dominated by self-phase modulation. The spectrally resolved spatial characterization of the resultant ultrashort pulses shows a strong wavelength dependence of the spatial distribution in the near field. Nevertheless, a Strehl ratio analysis and far field images show that the ability to focus the beam is not compromised and high intensities, crucial for most applications, can be achieved. It has also been shown that CEP stability is conserved during the nonlinear interaction of the intense input pulses with the thin quartz plates. The spatio-spectral and spatio-temporal distributions of the compressed pulses have been characterized, showing compression of the pulses down to 1.5 optical cycles. The demonstrated pulse duration of 3.7 fs represents, to the best of our knowledge, the shortest pulse duration reported to date for pulses with high average power and high repetition rate. The achievable 26 GW peak power is unprecedented for these type of sources. The ultrashort high power pulses will be suitable for the generation of bright attosecond pulses for many applications in the XUV and soft X-ray region. Further compression to sub-cycle pulse duration should be feasible with the implementation of chirped mirrors with a broader bandwidth.