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Abstract
We generate tunable extreme ultraviolet emission through high-order frequency mixing between a strong near-infrared field and a weak shortwave-infrared pulse whose wavelength can be adjusted. In this two-color driving scheme, new harmonics appear in between the single-color harmonics at energies which are linear combinations of photons from the two pulses. We demonstrate the utility of tunable two-color harmonics by employing them for XUV transient absorption spectroscopy and time-resolved photoelectron spectroscopy. We show that the two-color harmonics can be used to address the dynamics associated with excited states in Helium and Oxygen which are inaccessible using single-color harmonics. Specifically, we show the ability to switch between excitation of 3p and 4p states in Helium, control of transitions to the light induced states, observe new four-wave-mixing emissions, and selectively address different principal and vibrational quantum numbers associated with Oxygen Rydberg states.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the last two decades, ultrashort extreme ultraviolet (XUV) pulses created through high-harmonic generation (HHG) have powered the development of spectroscopic techniques which have enabled the study of atomic and molecular dynamics with femtosecond to attosecond temporal resolution. These techniques include ultrafast photoelectron and photoion spectroscopies [1–4], attosecond and femtosecond XUV transient absorption spectroscopy [5–7], and four-wave mixing spectroscopy [8–10].
Most ultrafast XUV spectroscopic techniques make use of one ultrashort XUV pulse and one or more intense ultrashort near-infrared (NIR) pulses. Typically, a replica of the NIR pulse is focused into a gas where it undergoes HHG to create an XUV attosecond pulse train (APT) or isolated attosecond pulse (IAP). To probe the dynamics of specific atomic or molecular excited states, the XUV spectrum has to be resonant with the transitions of interest. When an XUV APT is used as a pump, the excitation is caused by discrete odd harmonics which are separated by multiple electron volts, which limits the resonances that can be targeted. Experiments often have to be chosen based on which states can be addressed with the available harmonics. The resonances which fall in between the odd harmonics of the driving field are inaccessible for APTs. When an IAP pump is used, the XUV spectrum is a broadband continua spanning 10’s of eV or more, which simultaneously addresses a large set of states. However, when the goal is to excite only a few specific states and track their dynamics in isolation, e.g. in the case of Rydberg electronic wave packets or vibrational wave packets, an intermediate excitation scheme is required. Here, we demonstrate one such approach where the XUV photons are produced by the high-order frequency mixing between NIR and shortwave-infrared (SWIR) driving fields. This generates additional XUV spectral components and allows tuning and tailoring of the spectrum to probe the states of interest. This approach offers significant benefits over the harmonic source driven by the NIR pulse alone, opening new investigative opportunities in ultrafast XUV spectroscopy.
While APTs generated from a single-color (SC) NIR pulse are made up of only the odd harmonics of the driving field, it is possible to generate additional XUV components by adding a second color to the pulse. For example, when the second harmonic of the driving field is added, both odd and even harmonics of the driving field are generated [11,12]. When a non-commensurate field is added, new frequency components are generated through high-order frequency mixing which are not harmonics of either pulse [13–15]. The additional components of two-color (TC) harmonics can be used to access resonances in between the SC harmonics. In this work, we demonstrate the utility of this technique by applying it to velocity map imaging (VMI) and XUV transient absorption spectroscopy (XTAS). We show that TC harmonics can be used to excite to energy levels which are inaccessible to SC harmonics. Additionally, by adjusting the frequency of one of the pulses, we can control our harmonic spectrum to excite to certain states while avoiding other nearby states.
2. Experimental methods
The experimental setup is shown in Fig. 1(a). A Ti:sapphire laser amplifier produces $\sim$40 fs, $\sim$2 mJ NIR pulses which are centered at 780 nm wavelength. The output of the amplifier is split into three pulses. 45% of the pulse is used as an intense driving pulse for HHG. 50% of the NIR pulse is sent through an optical parametric amplifier (OPA), which produces weak tunable SWIR pulses with wavelengths between 1.2 and 1.6 $\mu$m and pulse energies of up to 50 $\mu$J. The driving pulse and tunable pulse are combined using a longpass dichroic mirror, and the delay between them is adjusted so that they overlap in time. The TC pulse is focused using a 50 cm mirror into a semi-infinite gas cell which is backed by $\sim$10 torr of Xenon, where it drives high-order XUV mixing processes. The remaining 5% of the NIR pulse is used as a probe pulse for photoelectron and transient absorption spectroscopy. The XUV and probe pulses are combined using a mirror with a hole and sent towards the VMI and XTAS experimental chambers.
Fig. 1. (a) Experimental setup for two-color harmonic generation and application. BS: beamsplitter; DM: dichroic mirror; SIGC: semi-infinite gas cell for HHG; TM: toroidal mirror; HM: holed mirror; DS: delay stage; S: shutter; VMI: velocity-map imaging spectrometer; GC: gas cell; G: grating. The blue, red, and green colors represent the XUV pulse, 780 nm NIR pulse, and tunable SWIR pulse, respectively. (b) Typical SC harmonic spectrum created with the NIR pulse only. (c) TC harmonic spectrum created with a strong NIR pulse and weak tunable SWIR pulse.
The first experimental chamber houses a VMI apparatus [16] for photoelectron spectroscopy. Gas is introduced as an effusive jet through the electrostatic repeller plate where it interacts with the XUV pulse train and time-delayed IR pulse. The electrons produced via XUV/IR ionization are imaged by using a set of electrodes such that electrons with identical velocity vectors hit the MCP plate at the same location, independent of their spatial origin in the focal volume. The phosphor screen behind the MCP is imaged by a CCD camera to record the energy and angular distribution of electrons. The cylindrical symmetry of the system allows one to inverse Abel transform the resulting 2-D image to extract the full momentum distribution. The voltages on the electrostatic lens can be adjusted to optimize spectral resolution and range.
The second experimental chamber is for XTAS experiments. The XUV and NIR pulses are sent through a 1 cm thick gas cell backed by Helium or Oxygen gas, where some of the XUV photons interact with the gas and can be absorbed. The transmitted XUV spectrum is reflected off of a curved grating and focused onto a CCD camera. XUV spectra are measured with both pulses present and with the XUV pulse alone. The change in optical density is calculated from these two spectra using $\Delta {\textrm {OD}}=-\log (I_{\textrm {XUV}+{\textrm {NIR}}}/I_{\textrm {XUV}})$, where $I_{\textrm {XUV}}$ and $I_{\textrm {XUV+NIR}}$ are the XUV spectra taken with the XUV pulse alone and with both pulses, respectively. This measurement is repeated for different time delays between the XUV and NIR pulses.
3. Intensity and wavelength dependence of two-color harmonics
Figure 1(b) shows typical harmonics generated in Xenon using a SC pulse. The peak intensity of the driving pulse is $\sim$200 TW/cm$^{2}$ and the spectrum contains the 13th, 15th, 17th, and 19th harmonics. Because the SC XUV pulse has limited tunability, there are broad spectral regions in between the odd harmonics which are not accessible. In Fig. 1(c), we use the same driving pulse but add the tunable SWIR pulse using a wavelength of 1.2 $\mu$m and peak intensity of $\sim$8 TW/cm$^{2}$. When the SWIR pulse is added, the spectrum changes dramatically as several prominent XUV emissions appear in between the harmonics of the SC pulse. These emissions result from high-order XUV wave-mixing processes, and each emission is a linear combination of photons from the driving and tunable pulses. Additionally, the cutoff energy of the harmonics is significantly increased for the TC pulse, similar to what has previously been shown [17,18]. The presence of the tunable SWIR pulse not only increases the ponderomotive energy of the field, but the irregular shape of the TC field creates possibilities for electron trajectories which have more kinetic energy than the classical limit for SC pulses. The tailoring of electron trajectories, and hence the attosecond temporal structure of the pulse, potentially offers interesting opportunities that will be explored elsewhere. In the present work, we focus on the new femtosecond studies enabled by the TC XUV harmonics and the spectral properties of this source.
In Fig. 2(a), HHG spectra are plotted for different intensities of the SWIR pulse obtained from the OPA. The peak intensity I$_1$ of the driving pulse is 200 TW/cm$^{2}$ and the peak intensity I$_2$ of the tunable SWIR pulse is varied. We label each of the TC harmonic emissions as a sum of photons from the driving pulse ($\omega _1$) and the tunable pulse ($\omega _2$). For example, the emission centered at 23.2 eV corresponds to 14 driving photons plus 1 tunable photon, and is therefore labeled as the $14\omega _1+\omega _2$ emission. We found that very little intensity (less than 1% of the NIR pulse) is required from the tunable pulse to efficiently produce TC harmonic emissions. At the intensity of 0.4 TW/cm$^{2}$, emissions involving 1 tunable photon are visible while higher orders appear at the intensity of 1.2 TW/cm$^{2}$. This shows that the two-color scheme allows one to dramatically increase the bandwidth of the XUV while sacrificing a very small amount of energy ($\sim$5%) from the NIR pulse to generate tunable SWIR. The three spectra in Fig. 2(a) were plotted using the same vertical scale, showing that this method does not sacrifice HHG conversion efficiency, unlike the polarization gating techniques used in IAP generation.
Fig. 2. (a) Intensity dependence of the harmonic spectra created with one- and two-color fields. The spectra were generated using I$_1$ = 200 TW/cm$^{2}$ and I$_2$ = 0.4, and 1.2 TW/cm$^{2}$ for the blue, red, and green curves, respectively. The XUV flux for the three spectra are plotted on the same scale. The harmonic orders for the SC and TC harmonics are labeled. (b) TC harmonic spectra created using different wavelengths of the tunable pulse. All of the spectra were generated using I$_1$ = 190 TW/cm$^{2}$ and I$_2$ = 7 TW/cm$^{2}$. The dashed lines indicate the positions of different harmonic orders as a function of wavelength.
Figure 2(b) shows TC harmonic spectra using different wavelengths of the tunable SWIR pulse between 1.2 and 1.6 $\mu$m. The NIR and SWIR intensities used for generating these spectra were I$_1$ = 190 TW/cm$^{2}$ and I$_2$ = 7 TW/cm$^{2}$, respectively. As one would expect, the positions of the TC harmonics shift according to the change in $\omega _2$. This wavelength dependence can be exploited to extend the range of energies that is accessible by the TC harmonics. When one combines the tunability of the pulse from the OPA with the limited tunability of a typical Ti:sapphire laser amplifier, it is relatively easy to use the TC harmonics to access any desired XUV photon energy that falls within the range of the SC harmonics.
4. Pump-probe photoelectron spectroscopy with two-color harmonics
In this section, we will demonstrate the use of TC harmonics in photoelectron spectroscopy using Helium as a prototypical system. The energy level diagram for this experiment is shown in Fig. 3(a). We use SC or TC harmonics to populate Helium Rydberg states, and then use a delayed NIR probe pulse to ionize the Rydberg electrons. We used a tunable pulse set to 1.5 $\mu$m for the TC harmonic generation. The intensities used for the driving NIR, tunable SWIR, and probe NIR pulses for this experiment are approximately 200, 10, and 2 TW/cm$^{2}$, respectively. We measured the photoelectron yield as a function of kinetic energy using the VMI spectrometer.
Fig. 3. (a) Energy level diagram for the XUV + NIR Rydberg ionization process in Helium. The XUV harmonics populate the Helium Rydberg levels and the NIR pulse ionizes the excited electrons. (b) Rydberg photoelectron spectrum generated from SC harmonics (blue curve) and TC harmonics (red curve). The SC harmonics primarily populate the 4p state in Helium while the TC harmonics can be used to reduce the 4p population while creating a strong 3p excitation, which is not possible with our SC harmonics.
The photoelectron spectra generated using SC and TC harmonics are shown in Fig. 3(b). For the SC harmonics, we observe a single peak centered near 0.75 eV. When we switch from SC to TC harmonics, we observe that two new features appear at 0.15 eV and 1.1 eV, while the 0.75 eV feature diminishes greatly. We can identify the Rydberg states associated with each photoelectron peak by calculating the kinetic energy of the free electron after two-photon absorption through different intermediate Rydberg states. The kinetic energy is given by $K.E.=E_{np}+\omega _{\textrm{NIR}} -I.P.$, where $E_{np}$ is the energy of the Rydberg state, $\omega _{\textrm{NIR}}$ is the NIR photon energy, and $I.P.$ is the Helium ionization potential. Using this equation, we find that the 0.15 eV, 0.75 eV, and 1.1 eV features are associated with the 3p, 4p, and 5p states of Helium, respectively.
When the SC harmonics are used, the only resonant state in Helium is the 4p Rydberg state, which is driven by the $15\omega _1$ harmonic. Therefore, only a single photoelectron peak appears at 0.75 eV. When the TC harmononics are used, the $14\omega _1+\omega _2$ excites the 3p state and the $16\omega _1-\omega _2$ harmonic excites the 5p state, leading to two new photoelectron peaks. Additionally, the intensity of the $15\omega _1$ harmonic is reduced as XUV flux goes to the other TC harmonics, leading to a reduction in the 4p signal. These results show that TC harmonics can be used to selectively switch excitation pathways on and off.
5. XUV transient absorption with two-color harmonics
5.1 Helium experiments
In this section, we will demonstrate how TC harmonics can be used to expand the scope of XTAS experiments. Our first experiment is in Helium, a prototypical system that has been used in many XTAS studies. Figure 4(a) shows transient absorption spectrograms generated in Helium using SC harmonics. Because the XUV pulse bandwidth is limited to odd harmonics of the NIR pulse, only a few states are excited by the XUV. The 15th harmonic is resonant with the 4p state, leading to strong XUV absorption at 23.74 eV. Weaker absorption features are visible at the 3p and 5p-8p lines, while the 2p line is barely visible at all due to the lack of XUV flux at that energy.
Fig. 4. XTAS spectra in Helium measured using (a) SC harmonics and (b) TC harmonics. The left side of each plot shows the change in optical density, while the right side shows the XUV spectrum used in each scan, plotted on a log scale. Relevant real and virtual states are labeled on the side of each spectrogram.
In Fig. 4(b), a TC pulse composed of the driving pulse and a 1.2 $\mu$m tunable pulse from the OPA is used to drive HHG. The XUV spectrum contains emissions which are not present in the SC harmonics, allowing many additional states to be excited. The 2p state is excited by the $14\omega _1-\omega _2$ emission which is centered at 21.2 eV, while the 3p state is excited by the $14\omega _1+\omega _2$ emission centered at 23.2 eV. Both states are much more prominent than they are in the SC data because of the expanded XUV bandwidth. It is not possible to resonantly excite both the 2p and 3p states using SC harmonics because they are separated by 1.87 eV, while neighboring SC harmonics are separated by $\sim$3.2 eV.
Additionally, several absorption features appear in between the 2p and 3p states where there are no real states in Helium. These features correspond to light induced states (LISs) [19–21], which are intermediate virtual states from a two-photon XUV-NIR transition to an optically dark state. LISs appear one IR photon ($\sim$1.6 eV) above or below an optically dark state. Because LISs are virtual, they only appear when the XUV and NIR pulses are temporally overlapped. Features corresponding to the 3s$^{-}$, 3d$^{-}$, and 2s$^{+}$ virtual states are visible using TC harmonics. Because these states fall midway between the 13th and 15th harmonics of a Ti:sapphire laser, they have previously only been studied using broadband IAPs, which are relatively hard to produce. In contrast, our wideband tunable TC harmonic approach provides an easy route to targeting a variety of resonances, including the light induced states. Additionally, a negative OD feature appears at 24.4 eV, just below the Helium continuum. We believe that this feature corresponds to an XUV + 2 NIR four-wave mixing emission through the 2p state. This negative OD feature has not been reported in any previous XTAS studies.
5.2 Oxygen experiments
Next, we demonstrate XTAS in Oxygen molecules using SC and TC harmonics. Previous studies [7,22] have investigated Rydberg states converging to the c$^{4}\Sigma _u^{-}$ ionic state, which are accessed by the XUV excitation of an inner-shell $2\sigma _u$ electron. Energetically, these neutral states lie above the X$^{2}\Pi _g$, a$^{4}\Pi _u$, A$^{2}\Pi _u$, b$^{4}\Sigma _g^{-}$, and B$^{2}\Sigma _g^{-}$ ionic states. As a result, they quickly autoionize to several continua, which leads to complicated non-Lorentzian structures in the spectrum. The left plot of Fig. 5(a) shows transient absorption spectrograms using SC harmonics. In this data, the spectrum of the 15th harmonic overlaps with the $\nu =0$ and $\nu =1$ vibrational levels of the 4d$\sigma _g$ and 5s$\sigma _g$ states. The 13th harmonic shows a feature with strong negative OD at $\sim$20.6 eV. This is interesting because it is below the $\nu =0$ and $\nu =1$ vibrational levels of the 3s$\sigma _g$ state, which are visible as faint red structures at 20.85 and 21.05 eV, respectively. One possible explanation for the strong negative OD are 20.6 eV is the ladder-type four-wave mixing emission. In this scenario, the 15th harmonic excites to the 4d/5s$\sigma _g$ states, followed by 2 NIR photon transitions downward, leading to emission near 20.6 eV. The delay dependence and shape of the negative feature OD feature looks very similar to that of the 4d/5s series at 23.7 eV. As we discuss below, the Rydberg vibrational series associated with B$^{2}\Sigma _g^{-}$ state also extends to the energy range of the negative OD feature, and could be contributing to this process.
Fig. 5. (a) XTAS spectrograms in Oxygen using SC harmonics (left plot) and TC harmonics (right plot). The TC spectrum accesses nl$\sigma _g$ Rydberg states of the c$^{4}\Sigma _u^{-}$ ionic state, which we have labeled. We also indicate an unknown feature near 20.6 eV and features near 20 eV corresponding to B$^{2}\Sigma _g^{-}$ Rydberg states. The right side of each plot shows the XUV spectrum plotted on a log scale. (b) XTAS spectrograms in Oxygen covering the spectrum of the TC $12\omega _1 + \omega _2$ harmonic emission with the tunable pulse set to 1.2 $\mu$m (left), 1.4 $\mu$m (center), and 1.6 $\mu$m (right). The spectrum overlaps with np$\sigma _u$ Rydberg states of the B$^{2}\Sigma _g^{-}$ ionic state. The right side of each plot shows the XUV spectrum plotted on a linear scale.
The right plot of Fig. 5(a) shows an XTAS spectrogram taken using TC harmonics. For this data, the tunable pulse was set to 1.4 $\mu$m, and the resulting XUV spectrum is shown on the right of the plot. In this data, we see the same three features as the SC data as well as some additional features. The $14\omega _1+\omega _2$ emission excites the $\nu =0$ (22.86 eV) and $\nu =1$ ($\sim$23.1 eV) vibrational levels of the 3d$\sigma _g$ state, as well as the $\nu =0$ (23.08 eV) vibrational level of the 4s$\sigma _g$ state. In addition, another series of absorption features appears near 20 eV from the $12\omega _1+\omega _2$ emission. We identify these features as coming from the Rydberg series converging to the B$^{2}\Sigma _g^{-}$ ionic state. We will examine these features more closely in part (b) of Fig. 5.
In Fig. 5(b), we show transient absorption spectra for the $12\omega _1 + \omega _2$ emission with the tunable pulse wavelength set to 1.2 $\mu$m (left), 1.4 $\mu$m (center), and 1.6 $\mu$m (right). At this energy range, we access Rydberg levels of the B$^{2}\Sigma _g^{-}$ ionic state, which were previously identified in static absorption studies [23]. By adjusting the wavelength of the tunable pulse, we are able to shift our $12\omega _1+\omega _2$ emission to select levels with different principal and vibrational numbers. The $12\omega _1 + \omega _2$ emission accessed the 6p$\sigma _u$ $\nu =1$ (19.95 eV), 5p$\sigma _u$ $\nu =2$ (19.83 eV), and 5p$\sigma _u$ $\nu =1$ (19.70 eV) Rydberg states using tunable pulses set to 1.2 $\mu$m, 1.4 $\mu$m, and 1.6 $\mu$m, respectively. This ability to select an individual transition while avoiding other nearby transitions can help to simplify the analysis of the data. This is especially true for experiments with photoelectrons or photoions, where charged particles from different pathways can overlap and congest the spectrum.
6. Conclusions
We have shown that TC harmonics can overcome the limited bandwidth of SC harmonics by introducing emissions in between the odd harmonics of a SC APT. Even a weak SWIR pulse generated by using 5$\%$ of the NIR to pump the OPA is sufficient to produce strong TC harmonics. It is easy to tune the TC harmonics by changing the wavelength of SWIR pulses obtained from the OPA and thus address transitions of choice in atoms and molecules. This two-color approach is quite efficient and cost-effective compared to driving the harmonics directly with tunable high-energy laser pulses.
We demonstrated control and selectivity in excitation of atomic and molecular systems by conducting photoelectron spectroscopy and transient absorption spectroscopy in Helium and Oxygen. In Helium, we were able to switch between 4p and 3p excitation, and access new light induced states. In the case of Oxygen, we were able to access additional Rydberg states, and FWM emissions associated with c$^{4}\Sigma _u^{-}$ Rydberg states. We also showed the ability to selectively address the vibrational levels of B$^{2}\Sigma _g^{-}$ Rydberg states.
Our approach utilizes the standard Ti:Sapphire amplifier and OPA, an economical configuration that is present in many labs. We show that these two can be easily combined to produce an XUV source that can create new spectral components on demand, to address states that are not accessible with single-color harmonics. This approach will have immediate benefits in femtosecond XUV spectroscopy of materials and molecules [24–26], where specific absorption edges or electronic/vibrational states need to be targeted. Thus, the tunability, efficiency, and economy of TC harmonics makes them a very strong candidate for new investigations in ultrafast XUV science.
Funding
U.S. Department of Energy, Office of Science, Basic Energy Sciences (DE-SC0018251).
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