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Abstract
We report that high-conversion efficiency of nearly 50% has been realized by combining a commercially available Ti:Sapphire femtosecond, 1 kHz laser system and an optical parametric amplifier (OPA). For an input energy of 2.2 mJ/pulse at 1 kHz and 35 fs duration, the total OPA output energy of the signal plus idler pulses is 1.09 mJ/pulse at a signal wavelength of 1310 nm. We found that the output beam profile is almost flat-top due to high gain saturation in the OPA. Using the signal pulse, we generate high-harmonics in gases and measure the velocity map images of photoelectrons ionized from argon gas as a function of the signal wavelength. We observe that in a particular range of the high-harmonic photon energy, a four-fold photoelectron angular structure is observed in the low kinetic energy region. Our results indicate that the output pulses with the high-conversion efficiency OPA and super Gaussian beam profile can be used for experiments requiring generation of tunable high-harmonics in the extreme ultra-violet region.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Attosecond, high-harmonic emission is generated by ionization and electron re-collision processes in a gas medium with intense, infrared laser pulses [1]. The photon energy of high-harmonics is extended to the extreme ultra-violet or soft-x ray region by using mid-infrared fundamental pulses [2,3]. Since the maximum photon energy of high-harmonics, referred to as the cut-off energy, is proportional to the square of the laser wavelength, a longer wavelength fundamental pulse is advantageous to generating higher photon energies [4]. An intense, infrared pulse can be produced by: an optical parametric amplifier (OPA) pumped by a femtosecond Ti:Sapphire laser, an optical parametric chirped pulse amplifier (OPCPA), Dual-Chirped OPA (DC-OPA), or Frequency domain Optical Parametric Amplification (FOPA) [5–16]. The optical set-up of an OPA is simpler than that of an OPCPA, DC-OPA or FOPA. The conversion efficiency of an OPA pumped by 25 fs to 40 fs laser pulses with a kHz system is typically ∼30-43% [13–15], though a conversion of ∼45% with a 10 Hz system was reported [16]. Thus, the generation of infrared laser pulses with a high-peak power and with high-repetition rate is beneficial for attosecond experiments in the soft-X ray region [17].
Here we report that a conversion efficiency of nearly 50% is obtained by combining a commercially available 1 kHz laser system. In general, achieving a higher conversion efficiency may come at the expense of the beam profile quality or the pulse duration, that may prevent us from applying the OPA output pulse to an actual ultra-fast application. In contrast, we demonstrate that the output pulse produced with nearly 50% conversion efficiency is effectively utilized for the generation of tunable XUV pulses and subsequent photoionization experiments. We found that the spatial beam profile of the signal output pulse from the OPA is a super-Gaussian while the pulse duration is slightly increased from 35 fs to 46 fs at a signal wavelength of 1320 nm. We discuss the focusability of the output pulse by estimating the diameter of the beam in which the high-harmonics are generated, and comparing it with the one evaluated by assuming a transform-limited pulse. As an application of this system, by scanning the high-harmonic photon energy, we measured the velocity map images of photoelectrons ionized from argon gas to find a resonance state during the ionization.
It has been reported that a super-Gaussian or top-hat beam profile is advantageous to obtain a high-conversion efficiency in an OPA in the few hundred femtoseconds region [18,19]. On the other hand, a Gaussian mode is often used for better beam propagation and focusing conditions while the conversion efficiency of OPA to produce the Gaussian mode output is lower than that of the super-Gaussian mode [11,20]. Our experimental results and analysis indicate that in spite of using the super-Gaussian mode for the fundamental pulse, the tunable high-harmonics can be generated efficiently and used for applications such as photoionization.
2. Experimental set-up
Figure 1 shows the optical diagram and experimental set-up. We use a dual-stage, multi-pass amplifier system to generate 35 fs, 1 kHz, 790 nm laser pulses (carrier-envelope phase-stabilized, Komodo-Dragon from KMlabs). The system in pumped by two 20 mJ, 1 kHz Nd:YLF lasers (Evolution 30, Coherent). We replaced one of the compressor gratings from the originally installed ruled grating with a holographic grating (Spectragon) to improve the quality of the spatial mode. At the same time, the pulse energy decreased to 4.2 mJ/pulse from 5.7 mJ/pulse because the grating blaze angle is not optimized for our existing compressor grating set-up. (If the grating blaze angle is optimized, then we expect more output energy.) About 50% of the pulse energy is directed to the optical parametric amplifier (OPA, TOPAS-C, Light Conversion). The beam size is reduced from 12 mm to 8 mm by a telescope consisting of two silver-coated mirrors with a ROC of -2500 mm and + 1500 mm, respectively. The OPA electronics allows us to set the output wavelength within the range of 1100 nm to 2600 nm. In this experiment we didn’t use the carrier-envelope phase stabilization options.
Fig. 1. A schematic diagram of the experimental set up. OPA-TOPAS - optical parametric amplifier. Gas jet A - pulsed gas jet for generating high-harmonic emission. Gas jet B - pulsed gas jet for ionizing sample gas. VMI - velocity map imaging apparatus. The inset shows the optical diagram for measuring the spatial profile of the signal pulse. Filter A - long-pass filter (>900 nm), lens - 500 mm focal length lens, filter B - narrow band pass filter (650 nm ± 5 nm).
We select the signal pulse to generate high-harmonics using a wavelength separator to remove the idler wavelength. After enlarging the beam size by a second telescope, we focus the pulse into an argon gas jet to produce high-harmonics. The high-harmonic emission is separated from the fundamental beam by multiple grazing-angle reflections on germanium mirrors. The beam is re-focused by a gold-coated toroidal mirror with 270 mm focal length and with 1:1 magnification condition (ARW Optical Corporation) into a second gas jet B inside a vacuum chamber designed for photoionization experiments. The momentum distribution of the photoelectrons is measured by a velocity map imaging (VMI) apparatus [21–23]. The high-harmonic spectrum is measured by two spectrometers A and B (Fig. 1). For each spectrometer, the high-harmonics are dispersed by a flat-field grating and the spectrum is imaged on a micro-channel plate with a phosphor screen. The image is captured by a CCD camera and recorded in a computer. The first spectrometer A measures the spectrum just after the high-harmonic generation source (jet A), and the second spectrometer B measures the spectrum after propagation through the germanium and toroidal mirrors setup. The high-harmonic spectrum is simultaneously measured with the VMI image on a CCD camera (Fig. 1).
3. Results and discussion
3.1 Pulse energy
Figure 2(a) shows the typical output energy of the signal plus idler (S + I) pulses (black square points) and the signal pulse (red circle). The conversion efficiency (right axis) is calculated with an input energy of 2.20 mJ/pulse. In the wavelength range from 1250 nm to 1450 nm, the total conversion efficiency is larger than 45%. The maximum efficiency of 49.5% was observed at a signal wavelength of 1310 nm where the signal pulse energy was 1.09 mJ. In order to obtain the same output energy with a typical conversion efficiency of ∼30%, the input pulse energy would have to be 3.3 mJ/pulse. For the signal pulse only, the maximum efficiency is greater than 30%. Figure 2(b) shows the idler pulse energy evaluated by subtracting the signal pulse energy from the total (signal plus idler) pulse energy. From 1700 nm to 2000 nm, the conversion efficiency exceeds 20% and the energy is more than 0.4 mJ/pulse.
Fig. 2. (a) OPA output energy (left axis) and conversion efficiency (right axis) for the total output signal + idler pulses (black squares) and for the signal pulse only (red dots). (b) The idler pulse energy (left axis, open circles). The OPA pump pulse energy is 2.20 mJ at 790 nm.
3.2 Spatial distribution of the pulses
We investigate the beam profile of the input and output beams from the OPA with a CCD camera (DataRay DM2DU-50 with WinCam software) at a signal wavelength of 1300 nm, close to the wavelength where the maximum conversion efficiency is observed. A small fraction of the pulse is taken after the telescope A by reflecting on a fused silica plate for the measurement of the spatial distribution of the input beam. Furthermore, the beam size is reduced to fit the size of the CCD. For the measurement of the OPA output beam, we use an optical set-up shown in the inset of Fig. 1. After isolating the signal beam from the idler by a wavelength separator and a long-pass filter (900 nm), we double the frequency of the pulse by a β-BBO crystal. Then after a narrow bandpass filter (650 nm ± 5 nm) we reduce the beam size by 50% with a 500 mm focal length lens to fit the size of the CCD camera. The band pass filter removes the stray light and possible harmonics generated by the OPA.
Figure 3 shows the beam profile of the pump beam from the amplifier and the output beam profile from the OPA at 1300 nm signal wavelength. The input energy is set to 2.0 mJ/pulse which generates a signal pulse energy of 0.61 mJ/pulse at this wavelength. The upper and right panel of the main panel shows the vertical and horizontal beam profiles obtained by integration of the signal counts in vertical (top trace) and horizontal (left trace) directions, respectively. A small asymmetry is related to small misalignment of the 5 passes in the second stage of the Ti:Sapphire amplifier. The output beam from the OPA has a more flat-top intensity distribution compared to the input beam profile. We note that the measured image plotted in Fig. 3(b) is slightly modified from the original beam profile because of the use of second harmonic generation. Typically, one would reduce the pump energy in the last stage of the OPA to reduce depletion of the gain in the center of the beam in order to keep the Gaussian profile while the overall system efficiency is around 30-40% [11,20]. This would help in beam propagation through the rest of the system and in keeping the beam profile Gaussian at the focus spot. In our OPA we kept the pump energy high and observed a super-Gaussian beam profile at the output of the OPA system. Propagation of such beam and focusing it depends on the sharpness of the beam edge and may generate high frequency modulation that may affect the quality of the focus at the sample [24]. However, in our case we do not see any evidence of such effects and have an efficient high harmonic generation process as shown later. This is probably due to smooth super-Gaussian beam profile and high nonlinearity of the high harmonic generation process.
Fig. 3. The measured near-field beam profile for the OPA pump pulse (a) and the OPA output pulse (b). The beam profiles plotted in the top and left panels are the integrated signal counts over the vertical or horizontal directions of the main panel, respectively. The pump energy is 2.0 mJ and the OPA signal output pulse energy is 0.61 mJ at the signal wavelength of 1300 nm. Note that the output image (b) is measured via second harmonic generation followed by filtering with a narrow bandpass filter.
3.3 Pulse duration
Next, we measure the pulse duration of the OPA pump and the OPA output pulses by a single-shot autocorrelator (Light Conversion, TiPA). For the OPA pump pulse, we take a small fraction of the beam after telescope A. The measured input pulse duration is 35 fs. Figure 4(a) shows the measured pulse duration for the output pulse over the selected signal wavelength range. We plot representative auto-correlation traces measured at 1240 nm and 1320 nm in (b) and (c). The temporal pulse shape is estimated as a Gaussian distribution. As was shown in Fig. 2, the maximum pulse energy is achieved around 1300 nm to 1360 nm. The pulse duration at 1320 nm is 46 fs, which is slightly longer than the input pulse duration of 35 fs from the Ti:Sapphire system.
Fig. 4. (a). The measured pulse duration over the OPA tuning range. Auto-correlation traces at (b) 1240 nm and (c) 1320 nm.
3.4 High-harmonic generation
Using the OPA signal pulse, we generate high-harmonics from argon gas and measure the spectra using the first spectrometer A. Figure 5(a) shows the high-harmonic spectra as a function of the signal wavelength of the OPA. Each harmonic order is continuously tuned over ∼7 eV when the OPA signal wavelength is changed from 1140 nm to 1520 nm.
Fig. 5. (a) The high-harmonic spectra as a function of the OPA signal wavelength. (b) The cut-off region on the high-harmonic spectra plotted on a logarithmic color scale. The signal intensity for each high-harmonics is normalized to unity. The white dots show the estimated cut-off energy. (c) The total high-harmonic generation yield. The maximum signal count in the curve is normalized to unity. (d) The black squares show the pulse energy of the OPA signal pulse entering the gas jet (right axis). The red circles show the estimated peak intensity of the OPA signal pulse (left axis). (e) The estimated beam diameter at the gas jet A position where the high harmonics are generated. The black squares are the estimation from the beam focusing condition; the red circles are the data obtained from the cut-off values of high-harmonic spectra (see text). The dotted lines in (c) and (d) represent the range where a focal spot is estimated.
Figure 5(b) plots the cut-off region of the high-harmonic spectra on a logarithmic scale. The signal intensity is normalized to unity for each high-harmonic spectrum. We estimated the cut-off energy for each harmonic using an approach similar to that shown in [14,25]. We extrapolated the falling part of the spectrum plotted on a logarithmic scale with a sigmoidal function. Then we regarded the photon energy at which the curve intersects with 10−3 of the highest peak intensity as the cut-off energy. We plot the measured cut-off energy as white dots in Fig. 5(b).
Figure 5(c) plots the total yield of the high-harmonic spectra as a function of the signal wavelength. To obtain the total yield curve, we integrated all signal counts of the spectrum along the photon energy at a given OPA wavelength. The maximum intensity is normalized to unity. The black square data points in Fig. 5(d) represent the signal pulse energies after the focusing mirror just before the gas jet. These values take into account the reflection losses (38%) in the beam steering optics and the telescope mirrors.
We now discuss the focusability of the signal pulse by estimating the focal spot diameter in which the high-harmonics are generated in the gas jet. The cut-off energy (Ec) of the high-harmonics is related to the peak intensity I of the fundamental pulse using the following equation [3]
where Up is the ponderomotive energy and Ip is the ionization potential of argon gas, both in eV. The value of Up is given by where I [1014 W/cm2] is the peak intensity and λ [µm] is the wavelength of the fundamental pulse. Using Eqs. (1) and (2), we estimate the peak intensity, I, as a function of the signal wavelength from the cut-off energy plotted in Fig. 5(b). The results are plotted as red circles in Fig. 5(d). The high-harmonic generation yield shown in Fig. 5(c) decreases with increasing driving wavelength. This is due to two factors. (1) The driving intensity is decreasing (Fig. 5(d)), largely due to the increasing focal spot diameter, and (2) the single-atom response in high-harmonic generation scales very strongly with driving laser wavelength, on the order of λ−5 [26].The peak intensity, I, is given by
From Eq. (3), using the measured pulse energy, pulse duration and the estimated value of I, we infer the value of d as a function of the signal wavelength and plot them as red circles in Fig. 5(e). The value of d increases as the wavelength is longer from 102 µm (at 1200 nm) to 162 µm (at 1380 nm).Alternatively, we can estimate the beam diameter in a gas jet A using the measured beam parameters: wavelength, focal length (F) and the beam diameter (D) on the focusing mirror. For a diffraction-limited beam, the focused beam diameter d* is
We plot d* as square data points in Fig. 5(e). Though the use of convex and concave mirrors to enlarge the beam size potentially modifies the beam profile slightly by their aberrations, we assume a flat-top beam profile. The factor of 1.22 is characteristic of a diffraction-limited beam with a uniform illumination at the focusing lens. For a pure Gaussian beam, which is usually the desired shape for OPA output, this factor is 1.27 and is close to the factor in Eq. (4). For super-Gaussian beams and a flat-top beam profile, this factor is even larger by the beam quality factor M2 which can be close to 2.5 for high order super-Gaussian beams [27,28]. The beam diameter estimated from the high-harmonic cut-off is approximately 1.4 to 1.9 times larger than the focus size d* estimated for the diffraction-limited beam. The slope of the wavelength dependence curve for d is larger than that of d*. The difference between the d and d* indicates that the OPA output does not focus as well as a diffraction-limited pulse. In spite of this, our result indicates that our OPA output beam has good focusability with relatively low M2 factor.We estimate a possible error for the value of d caused by inaccurate estimation of the cut-off energy. If the cut-off energy is changed by −1.0 eV at the signal wavelength 1300 nm, then the estimated peak intensity and the value of d change by −0.02 × 1014 W/cm2 and + 2 µm, respectively.
3.5 Photoionization
Next, using the high-harmonics generated by the OPA signal pulse, we ionize argon gas in gas jet B, and measure the velocity map images of the ejected photoelectrons as a function of the signal wavelength. In addition to the high-harmonic emission, some of the OPA signal pulse also reaches the argon gas due to incomplete rejection of the signal wavelength on the germanium mirrors [22] which were optimized for 800 nm rejection. In Fig. 6, we present an example of VMI images measured at a signal wavelength of (a) 1255 nm and at (b) 1300 nm, respectively. Figure 6(c) is the expansion of (a) in the low kinetic energy region. The polarization direction of the laser is vertical in the plane of the image. In the VMI measurement, photoelectrons with larger kinetic energy are detected in the outer region of the MCP [21,22]. Since the first ionization energy of argon is 15.78 eV, the innermost photoelectron ring in (a) is produced by the one-photon ionization with harmonic 17. The second innermost ring is due to the ionization by harmonic 19.
Fig. 6. Velocity map images (VMI) of photoelectrons from argon ionized by the high-harmonics that are generated by (a) 1255 nm and (b) 1300 nm, respectively. (c) The low kinetic energy region of the VMI image (a). (d) Ionization diagram for argon. The dark area seen in the left part of images is due to the low efficiency of the micro-channel plate.
Figure 7(a) show the kinetic energy distribution of photoelectrons emitted parallel to the polarization axis as a function of the signal wavelength. At each wavelength, we integrate the photoelectron signal counts along the Kx axis in a small range around the zero momentum of Kx in the VMI images. Then we plot the integrated signal counts along Ky as a function of the fundamental wavelength. We compare the photoelectron kinetic energy distribution with the high-harmonic spectra measured by the XUV spectrometer B simultaneously with the VMI images (Fig. 7(b)). It is clearly seen that, with the decrease of the photon energy of high-harmonics, the photoelectron kinetic energy of each photoelectron rings decreases except near the zero kinetic energy region.
Fig. 7. (a) The kinetic energy distribution of photoelectrons emitted parallel to the polarization axis and (b) the corresponding high-harmonic spectra as a function of the fundamental wavelength. In (a), the dotted line indicates zero-kinetic energy. The horizontal red dotted line in (b) indicates the first ionization energy of argon, IP = 15.78 eV. The vertical green dotted lines indicate the wavelength region where the low-kinetic energy structure appears (see text).
We found that a four-fold structure appears below the kinetic energy of 0.1 eV in the particular range of the signal wavelength from 1235 nm to 1270 nm. As seen in Figs. 6(a) and 6(c), the photoelectron angular distribution in the low kinetic energy region has both parallel and small perpendicular components relative to the laser beam polarization direction. Different from the outer photoelectron ring, the radial distribution is almost independent of the fundamental wavelength. The dotted line in Fig. 7(b) indicates the wavelength range where the four-fold structure appears.
The four-fold structure is generated by two-photon resonant ionization with the 15th harmonic plus one fundamental OPA signal photon through the Rydberg manifolds of argon. The 15th harmonic energy at which the low energy peak appears ranges from 15.0 eV to 14.65 eV. In this energy region, the 6s (J = 3/2, 14.85 eV) and 4d (J = 3/2, 14.86 eV) manifolds can be resonantly populated by the 15th harmonic [29]. Furthermore, one photon ionization from these states with the fundamental pulse generates photoelectrons with kinetic energy from 0.084 eV to 0.056 eV for the 6s state, and from 0.074 eV to 0.046 eV for the 4d state, respectively. The estimated energy is consistent with the observed kinetic energy of the low energy structure. On the other hand, when the 15th harmonic energy is off-resonant with the 4s or 6s state, then the low energy structure can disappear because the non-resonant ionization has relatively low transition probability.
Figure 6(d) shows a simple transition diagram. Initially, the 15th harmonic populates the 6s or 4d states. The one-photon transition from the 6s state generates a p-wave with m = 0 in the ionization continuum. The angular distribution of the p-wave with m = 0 is parallel to the polarization axis (vertical in the VMI image plane). For one-photon ionization from the 4d states, p-wave with both m = 0 and m=±1 can be generated. The m=±1 component of the p-wave can generate a component perpendicular to the polarization axis (horizontal in the VMI image plane). Since the observed photoelectron distribution has no significant six-fold structure, the contribution of f-wave generated from the 4d state must be small.
4. Summary
In summary, we have achieved a high-conversion efficiency of nearly 50% from an OPA pumped by a Ti:Sapphire femtosecond amplifier. The OPA output beam has a super-Gaussian spatial profile and can be efficiently used for high-harmonic generation in gases. A Gaussian mode is not necessary to generate high-harmonics with good efficiency. With a relatively low pump power system, we can generate high-harmonics using mid-infrared pulses.
We confirm that the signal output pulse can generate tunable high-harmonics and that the photoelectron momentum distribution can be measured using high-harmonic emission. This turnability of high harmonic energy allows us to find a particular resonant state of atoms and molecules.
In the future, we plan to use the high-conversion efficiency OPA pulse as a seed pulse for further parametric amplification. By adding an additional amplification stage, we can generate a few-mJ infrared pulse from relatively low energy of 800 nm femtosecond pulse system. It opens the possibility that, using a relatively simple optical set-up compared to other methods, e.g., OPCPA, intense infrared pulse for the production of the tunable, soft-X-ray pulses is possible.
Funding
Japan Society for the Promotion of Science (18H03903).
Acknowledgments
The authors acknowledge the support from NRC-Japan collaboration program and technical support from R. Kroeker at the National Research Council of Canada.
Disclosures
The authors declare no conflicts of interest.
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