Generation of Energetic Highly Elliptical Extreme Ultraviolet Radiation

Abstract

In this study, the generation of energetic coherent extreme ultraviolet (XUV) radiation with the potential for controlled polarization is reported. The XUV radiation results from the process of high harmonic generation (HHG) in a gas phase atomic medium, driven by an intense two-color circularly polarized counter-rotating laser field, under loose focusing geometry conditions. The energy of the XUV radiation emitted per laser pulse is found to be of the order of ~100 nJ with the spectrum spanning from 17 to 26 eV. The demonstrated energy values (along with tight XUV focusing geometries) are sufficient to induce nonlinear processes. Our results challenge current perspectives regarding ultrafast investigations of chiral phenomena in the XUV spectral region.

1. Introduction

Coherent XUV laser-driven sources based on HHG processes have been extensively explored and used for a variety of applications in ultrafast science [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. Furthermore, many HHG-based experimental strategies have been implemented in the production and characterization of intense attosecond light sources [15,18,19,20,21,22,23,24,25,26,27,28]. However, these pulsed sources, which are typically bright enough to induce non-linear processes and temporally short enough to map electronic motion, are mostly limited to emit only linearly polarized radiation (being driven by linearly polarized fundamental laser fields). Circularly polarized (CP) XUV light pulses have proven to be a valuable tool and have attracted a keen interest in the scientific community for a broad range of investigations such as chirality-sensitive light-matter interactions, angle-resolved photoemission spectroscopy, and magnetic circular dichroism spectroscopy. Novel approaches for producing CP XUV radiation pulses can be found in the literature ([29,30,31] and references therein) but all campaigns so far have led only to moderate pulse energies.

Nowadays, table-top laser-driven HHG-based sources offer strategies to generate and manipulate the polarization state of highly elliptical/CP XUV light. A key idea underlying several of these methods is to break the symmetry of the system (i.e., to either break the symmetry of the emitting medium or the symmetry of the driving field) [32,33,34]. Experimental approaches proposed for the generation of CP XUV radiation involve the exploitation of crossed driving laser beams [35], resonant HHG in elliptical laser fields [36], orthogonally-polarized two-color laser fields [37], bichromatic counter-rotating elliptically polarized drivers [38], circularly polarized counter-rotating fields [39,40,41], or co-rotating bichromatic laser fields [42]. In particular, by implementing counter rotating ω/2ω laser fields, an innovative experimental work in 1995 reported the generation of polarization-dependent high-order harmonics [43]. In this case, the polarization state of the higher order harmonics can be fully controlled without significantly reducing the conversion efficiency of the HHG process [33,34]. The generated HHG spectrum then results in the generation of pairs of harmonics with opposite helicity. The spectral location of the harmonic orders depends on the wavelength of the fundamental and the second harmonic components. The synthesized driving laser field exhibits a threefold spatiotemporal symmetry. Hence, the 3n-order (where n is a positive integer) harmonics are forbidden in isotropic media, as in the case of an atomic gas phase medium [39,40,44]. The helicity of the 3n+1 and 3n−1 harmonics are the same as those of the fundamental and second harmonic, respectively, and are opposite to each other due to the conservation of spin angular momentum. With respect to the time domain, the electric field resulted by the superposition of the harmonics synthesizes an attosecond pulse train in which each pulse is linearly polarized and the polarization axis rotates by 120° from pulse to pulse [33,41,45].

While the existing literature on the generation of highly elliptical or CP XUV radiation is extensive, the energy content of the experimentally generated pulses is so far limited to pJ regimes [34,46], mostly due to the focusing geometry used for the HHG. In this work, we apply a bichromatic counter rotating circularly polarized laser field to drive HHG in Argon (Ar) atoms under loose focusing conditions, demonstrating the production of ~100 nJ highly elliptical polarized XUV radiation in the spectral range of ≈20 eV.

2. Methods

In producing a bi-circular field for circular polarized HHG a compact MAch-ZEhnder-Less for Threefold Optical Virginia spiderwort-like (MAZEL-TOV-like [47]) scheme is used. A schematic illustration of it is sketched in Figure 1. The experimental investigations were carried out exploiting the MW beamline of the Attosecond Science and Technology Laboratory (AST) at FORTH-IESL. The experiment utilizes a 10 Hz repetition rate Ti:Sapphire laser system delivering pulses up to 400 mJ/pulse energy at τ_L = 25 fs duration and a carrier wavelength at 800 nm. The experimental set-up consists of three chambers: the focusing and MAZEL-TOV-like [47] device chamber, the harmonic generation chamber and the detection chamber. All chambers are under vacuum. A laser beam of 3 cm outer diameter and energy of ≈20 mJ/pulse is passing through a 3 m focal-length lens with the MAZEL-TOV-like device positioned 1.25 m downstream. The apparatus consists of a beta-phase barium borate crystal (BBO), a calcite plate and a super achromatic quarter waveplate (Figure 1). A fraction of the energy of the linear p-polarized fundamental pulse, is converted into a perpendicular (s-polarized) second harmonic field (410 nm) in a BBO (0.2 mm, cutting angle 29.2° for type I phase matching). The conversion efficiency of the BBO crystal was maximized and it was found ≈30%. The run-out introduced by the BBO crystal for the SHG of 800 nm was determined to be 38.6 fs. It is noted that by placing the BBO after the focusing lens ensures that the wavefronts of the converging fundamental laser beam are reproduced into that of the second harmonic field. Therefore, the foci (placed close to a pulsed gas jet filled with Ar) of the ω and 2ω fields coincide along the propagation axis. Additionally, the beam passes through a calcite plate at almost normal incidence (AR coated, group velocity delay (GVD) compensation range 310–450 fs), which pre-compensates group delays introduced by the BBO crystal and the super achromatic quarter waveplate. The super achromatic waveplate converts the two-color linearly polarized pump into a bi-circular field, consisting of the fundamental field and its second harmonic, accumulating at the same time a group delay difference of 253 fs between the 410 nm and 800 nm wavelengths. Assuming Gaussian optics, the intensity at the focus for the two components of the bicircular polarized field is estimated to be I_ω≈ I_2ω ≈ 1 × 10¹⁴ W/cm². After the jet, the produced XUV co-propagates with the bicircular driving fields towards a Si plate, which is placed at 75° reducing the p-polarization component of the fundamental and the second harmonic radiation while reflecting the harmonics [48] towards the detection area. Directly after the Si plate, a pair of 5 mm diameter apertures were placed in order to block the outer part of the ω and 2ω beams, while letting essentially the entire XUV through. A 150 nm thick Sn filter is attached to the second aperture, not only for the spectral selection of the XUV radiation, but also to eliminate the residual bicircular field. A calibrated XUV photodiode (XUV PD) was introduced into the beam path in order to measure the XUV pulse energy. The transmitted beam enters the detection chamber, where the spectral characterization of the XUV radiation takes place. The characterization is achieved by recording the products of the interaction between the XUV generated beam and the gas phase Ar atoms introduced by a pulsed gas jet valve. The electrons produced by the interaction of Ar atoms with the unfocused XUV radiation were detected by a μ-metal shielded time-of-flight (TOF) spectrometer. The spectral intensity distribution of the XUV radiation is obtained by measuring the single-photon ionization photo-electron (PE) spectra induced by the XUV radiation with photon energy higher than the I_p of Ar (I_pAr = 15.76 eV).

3. Results

Exploiting a MAZEL–TOV-like device, the generated HHG spectrum changes from a spectrum which contains only the odd harmonics to a spectrum containing 3n ± 1, n = 1,2,3… harmonic orders. It is well established in the literature, and verified experimentally and theoretically, that this is a typical spectral signature of highly elliptical polarized HHG radiation in counter rotating ω/2ω laser fields [33,34,39,40,41,45,47]. Figure 2a and the inset show the recorded HHG spectrum of the highly elliptical XUV radiation generated in Ar gas when no metal filter is used. Additionally, Figure 2b shows the spectra of the XUV radiation transmitted through a 150 nm thick Sn filter and the purpose of presenting this spectral region (selected by the Sn filter) is the application of this energetic highly elliptical XUV radiation in two-photon multi-color single or double ionization of rare gases and in relevant circular dichroism experiments in atoms. Although, in this work no ellipsometry measurements have been performed, the presence of highly elliptical XUV radiation is deduced from the appearance of 3n ± 1 order harmonics in the spectrum discussed above, as is often the case in similar studies [33,34,47]. Furthermore, it should be noted that other effects that could have resulted these specific observed spectral features have been ruled out. Nonadiabatic short pulse effects at the focus are excluded due to our long driving pulse of 25-fs pulse duration. Any plasma induced frequency shifts of the driver can also be considered being negligible. This is due to the fact that there is lower ionization rate when a bi-chromatic counter rotating circularly polarized laser field interacts with gas phase rare atoms to drive HHG compared to the one of one color linearly polarized drivers, since the time dependent ellipticity (ε) inside the pulse is mostly ε > 0 assuming perfect spatiotemporal overlap of these fields. Thus, this results in limited plasma formation. Spectral features originating from the interference between long and short trajectories that can lead to a shift and/or splitting of the harmonic peaks can be also excluded. This is evidenced by the theoretical framework that governs the HHG processes by bicircular polarized fields and detailed analysis of it, which can be found elsewhere [40], based on strong field approximation [49] adapted in the case of bicircular bichromatic driving electric fields and the saddle point analysis (SPA). Here it should be stressed that due to the threefold electric field synthesized by the superposition of the bicircular electric fields, only one trajectory exists during the process of HHG, in contrast to the case of linear monochromatic drivers where two trajectories contribute to harmonic emission [40,41], excluding any quantum phase interference effects.

At this point, as expressed in [50], it should be noted that single photon ionization is a linear process and ionization by highly elliptically polarized fields can be interpreted as the sum of two ionization channels opened by the two perpendicular linearly polarized field of the elliptical laser field. Therefore, the ionization cross section of Argon is assumed to be the same as in the case of linearly polarized light [50]. The red (blue) circular arrow in Figure 2 indicates the rotation direction of the polarization of the fundamental (second harmonic) used for HHG and the transferred helicity to each harmonic.

The highest harmonic order observed was the 17th for Ar exploited as a generating medium. According to the cut-off law, for equal intensities of the ω and 2ω laser field components (I_ω = I_2ω), the highest XUV photon energy emitted is given by the expression: E_max = 1.2 I_p + $\frac{1}{\sqrt{2}}$ 3.17 U_p, where U_p = U_pω+U_p2ω ([34,51,52]). Therefore, in the present experimental conditions the cutoff photon energy is expected to be around the 23rd harmonic. This deviation is attributed to the macroscopic response of the medium and selective phase matching conditions [34,53] which depend on the relative position of the focus of the driving field and the gas jet. Additionally, due to the p character of the ground state of the Ar gas, the harmonics of one helicity are stronger than the harmonics of the opposite one [54]. Finally, the collection efficiency of the TOF spectrometer is lower (compared to the case of linear polarization) when highly elliptical ionizing radiation is applied [55,56], restricting the highest possible observable harmonic orders.

It should be stressed that there is an uncertainty considering the degree of circular polarization of the driving laser shaped by the achromatic quarter waveplate, due to the deviation from an ideal waveplate both in retardation and in the crystal axis. Therefore, the symmetry of the superimposed electric field deviated from the threefold symmetry. Thus, the 12th and 15th harmonics are still weakly observed in the spectra. The appearance of the 3n harmonic orders can be induced by the driving fields’ imperfect overlap [57] or by the anisotropy of the generating medium [58,59], a case which is not probable in this experimental investigation since noble gasses are exploited as the generating media and due to the collinear configuration of the MAZEL–TOV like device. Lou Barreau and colleagues [60] showed that by solving the TDSE, breaking can occur (even for perfectly circular driving fields and in an isotropic medium) when the strong-field interaction resulting to the harmonic emission presents sub-ω cycle modulations due to (i) a fast temporal variation of the driving laser fields on the envelope rising and falling edges, causing temporal variations of the harmonic dipole vector and (ii) ionization of the medium, resulting in a fast decay of the induced dipole strength with time.

Moreover, emphasis should be given to the possibility of controlling the harmonic ellipticity and helicity at the source by simply rotating the fast axis of the super achromatic waveplate [33]. This is based on the conservation of spin angular momentum in the HHG process [33]. Considering the formulation described in [33], the equation characterizing the ellipticity for the emitted harmonics allowed by the selection rules (as a function of the angle α of the fast axis of the super achromatic waveplate in the case of a MAZEL–TOV-like device) can be extracted from: ${\epsilon }_{n_1,n_2}=\frac{1-\sqrt{1-{\left(n_1-n_2\right)}^2{\sin }^2\left(2\alpha \right)}}{\left(n_1-n_2\right)\sin \left(2\alpha \right)}$ where ${\epsilon }_{n_1,n_2}$ is the ellipticity of the $(n_1,n_2)$ harmonic channel and $n_2=n_1\pm 1$. The equation is valid for an ideal overlap of the two foci and when the generation is by an isotropic medium. Figure 3a presents the estimated harmonic ellipticity ${\epsilon }_{n_1,n_2}$ as a function of the rotation angle α of the super achromatic waveplate in our MAZEL–TOV-like device installed in the MW beamline of AST at FORTH–IESL. Figure 3b shows the normalized experimental spectra as a function of the angle α of the fast axis of the waveplate in the case of Ar as generating medium. The spectral features demonstrated in Figure 3b can be interpreted theoretically by the model described in [33] and in particular for angles 0° < α < 10° (an area out of our interest), were also verified experimentally in [47]. The area for angles α ≥ 40° is the desirable area of our studies where it is well known from the literature that represents the generation of highly elliptical radiation in the XUV region. It is also observed that the energy content within this area is approximately the same, with a small deviation (within the experimental error) to the energy measurement discussed in the next subsection.

Energy Content Estimation

The estimation of the energy content of the highly elliptical XUV radiation emitted per pulse is discussed in detail in this section. The estimation is enabled at a first step by measuring the linearly polarized XUV pulse energy by means of the XUV photodiode. Then, by comparing the HHG spectra depicted in the measured photoelectron spectrum of Ar atoms upon interaction with highly elliptically and linearly polarized XUV light, respectively, we can deduce the energy per pulse of the highly elliptical XUV emission.

The linearly polarized HHG signal recorded with the calibrated XUV photodiode (Opto Diode AXUV100G) placed on the XUV beam path after the Sn filter is fed to an oscilloscope with 50 Ω input impedance and the measured trace was integrated. In Figure 4a a typical measurement of the p-polarized XUV radiation energy is presented. The photodiode signal was measured with the harmonic generation gas jet ON and OFF. This signal was accumulated for 200 averaged shots. The measured signal when the jet was OFF originates from the residual IR radiation and is subtracted from the signal measured when the generation gas was ON. In this way, one can measure the neat XUV pulse energy. For determining the energy of the harmonic radiation produced at the source one has to consider also the filter transmission as well as the Si reflectivity. Here is the ~3% transmission of the Sn filter in this spectral region measured by recording the harmonic spectrum of linear p-polarized harmonics (with the MAZEL–TOV-like device out of the beam path) with and without filter. The main reason that p-polarized XUV radiation was chosen for the calibration of the Sn filter is the higher signal it results with and without the filter thus minimizing the error of the measurement. The reflectivity of the Si plate is approximately 60% [48]. Under optimal generation conditions, the maximum energies at the source were found to be in the range of 1 μJ. These values concern the emitted 11th, 13th, 15th, 17th, and 19th harmonics laying in the plateau spectral region. Therefore, the energy content per harmonic pulse is ~200 nJ at the source for Ar.

A similar measurement for the highly elliptically polarized radiation has a high degree of uncertainty since the difference of the two signals (gas jet ON—gas jet OFF) is rather small. This is due to the fact that when the MAZEL–TOV-like device is introduced in the beam path, the significantly increased amount of light of the fundamental as well as of the second harmonic frequencies reflected from the Si plate, in the case of non-p-polarized fields, prevents an accurate measurement of the highly elliptical XUV using the XUV PD.

In order to deduce an estimation of the energy per pulse of the highly elliptical XUV light in the present configuration, it is necessary to perform measurements of the Ar single photon ionization PE spectra induced by linear p-polarized and highly elliptical XUV radiation (at the same detection conditions), and directly compare both cases after the optimization of harmonic emission. Figure 5 depicts typical PE spectra in the case of both linear and highly elliptical polarization for Ar gas.

Having determined the energy values in the case of linear polarized XUV field and having deduced also the ratios of the harmonic integral values in the case of p-polarization and highly elliptical XUV radiation, by the recordings of the PE spectra, one can extract the energy content of the latter. The typical ratios of the integral values $I_q^{highlyelliptical}/I_q^{linear}$, (where q is the harmonic order) deduced from the systematic measurements have been determined for the 11th, 13th, 14th, 16th, and 17th harmonic, respectively, with variations of the order of 50% from day-to-day measurements (within the experimental error). This ratio of the integral values of the two different PE spectra (highly elliptical vs linearly polarized) is equal to the ratio of the energy content of the (per harmonic order) generated XUV radiation. $I_q^{highlyelliptical}/I_q^{linear}=E_q^{highlyelliptical}/E_q^{linear}$ in both polarizations and has to be divided by the correction parameter ~0.6 introduced by the different percentage of the total photoelectons’ number entering the TOF spectrometer. This consideration has to be taken into account due to the different angular photoelectron distributions resulting from the single photon ionization by the two polarization’s states (linear, circular) [55,56]. After this correction, the energy per laser pulse emitted in the case of highly elliptical radiation was then estimated to be $E_{Ar}^{highly elliptical}$ ≈ 100 nJ. Conclusively, the energy of highly elliptically polarized XUV radiation is ~10 times less compared to the linearly polarized XUV radiation at the same spectral region under conditions where the yield was optimized in both cases.

The estimated energy content of $E_{Ar}^{highly elliptical}$ ≈ 100 nJ at the source, per driving laser pulse, in conjunction with the implementation of broadband optical elements and tight focusing configurations, is sufficient to induce nonlinear phenomena at the target’s area. More specifically, the Si plate used in these experimental investigations can be substituted with custom built multilayers mirrors offering reflectivity up to ~75% in a broad spectral region. A 100 nm thick Al filter can provide transmission of ~80% to the spectral region >17 eV. Finally, a set of gold coated toroidal mirrors, in a Wolter configuration [61] to minimize the coma aberration, can provide high reflectivity (~80%) and a focal spot ~3 μm. The combination of the above-mentioned optical elements and arrangements can result in intensity up to ~10¹³ W/cm² at the focus.

Reducing the ellipticity of the generated radiation (by varying the fast axis of the super-achromatic waveplate) higher pulse energies were measured. This is a counterplay between the generated energy and the ellipticity of the harmonics.

4. Conclusions

By exploiting the implemented linearly polarized megawatt XUV beamline at FORTH-IESL, we report a method to produce energetic highly elliptical XUV light. The approach is based on gas-phase HHG driven by an intense two-color circularly polarized counter-rotating driving laser field, produced by a MAZEL–TOV-like device when introduced in the linear MW XUV beamline, under loose focusing conditions. The energy content for the highly elliptical XUV light is deduced by direct comparison between the linear and highly elliptical XUV spectra measured in the photoelectron spectra of Ar atoms (once the energy content of the linearly polarized XUV light is determined). The energy per driving laser pulse in the spectral region between 17 to 26 eV, is found to be in the range of ~100 nJ. Tight focusing of this light in conjunction with appropriately broadband optical elements is anticipated to lead to ~10¹³ W/cm² intensity in the focal area. This intensity would be sufficient to induce nonlinear phenomena in chiral systems in the XUV spectral region.