Generation of energetic highly elliptical extreme ultraviolet radiation

In this study the generation of energetic coherent extreme ultraviolet (XUV) radiation with 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 focusing geometries is sufficient to induce nonlinear processes and challenges the perspectives for ultrafast investigations of chiral phenomena in the XUV spectral region.

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 [31 -33].
Experimental approaches proposed for the generation of CP XUV radiation involve the exploitation of crossed driving laser beams [34], resonant HHG in elliptical laser fields [35], orthogonally-polarized two-color laser fields [36], bichromatic counter-rotating elliptically polarized drivers [37], circularly polarized counter-rotating fields [38][39][40] or corotating bichromatic laser fields [41,42]. In particular, by implementing counter rotating ω/2ω laser fields, an innovative experimental work back in 1995 reported the generation of polarization dependent high-order harmonics [43]. In this case the polarization state of higher order harmonics can be fully controlled without significantly reducing the conversion efficiency of the HHG process [32,33]. The generated HHG spectrum then results in the generation of a pair of harmonics with opposite helicity. The spectral location of the harmonic orders depends on the wavelength of the fundamental and the second harmonic component. 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, like in the case of an atomic gas phase medium [38,39,44]. 3 The helicity of the 3n+1 and 3n-1 harmonics are the same to those of the fundamental and second harmonic, respectively, and are opposite to each other because of the conservation of spin angular momentum. In the time domain the electric field resulted by the superposition of the harmonics, synthesize an attosecond pulse train in which each pulse is linearly polarized and the polarization axis is rotating by 120 o from pulse to pulse [32,40,45].
Albeit the rich existing literature on the generation of highly elliptical or CP XUV radiation, the energy content of the experimentally generated pulses is so far limited to pJ regime [33,46], 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 and demonstrate the production of ~100 nJ highly elliptical polarized XUV radiation in the spectral range of  20 eV.

Experimental section
In producing a bi-circular field for circular polarized HHG a compact MAch-  (Fig. 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 0 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 twocolor 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 Iω≈ I2ω ≈ 1x10 14 W/cm 2 . After the jet, the produced XUV co-propagates with the bicircular driving fields towards a Si plate, which is placed at 75 o 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. Α 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 Ip of Ar (IpAr=15.76 eV). 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. This is a typical spectral signature of highly elliptical polarized HHG radiation [29,32,33]. Figures 2 (a) and inset, show the recorded HHG spectrum of the highly elliptical XUV radiation generated in Ar gas when no metal filter is used.
Additionally, Figure 2 (b) shows the spectra of the XUV radiation transmitted through a 150 nm thick Sn filter. At this point it should be perceived that single photon ionization is a linear process and ionization by highly elliptical polarization can be understood as a simple sum of ionization from two perpendicular linear components of the polarized laser fields. Therefore, the ionization cross section for Argon is assumed to be the same as in the case of linear polarized light [49]. 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 17 th for Ar exploited as generating medium. According to the cut-off law, for equal intensities of the ω and 2ω laser field components (Iω=I2ω), the highest XUV photon energy emitted is given by the expression:  ( 1 − 2 ) sin (2 ) where 1 , 2 is the ellipticity of the ( 1 , 2 ) harmonic channel where 2 = 1 ± 1. The equation is valid for ideal overlap of the two foci and the generation by isotropic medium. Figure   3(a) presents the estimated harmonic ellipticity 1 , 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 3

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   4 (a) 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. The measured signal when the jet was OFF comes from the residual IR radiation and is subtracted from the signal measured when the generation gas was ON. The pulse energy is given by = ∑ where q is the harmonic order, ne is the number of produced photoelectrons, w is the statistical weight of the qth harmonic, hq is the harmonic photon energy, q is the photodiode quantum efficiency [60] and e is the electron charge. 9 The photoelectron number is given by = − • where ST is the total time integrated photodiode signal, is the time integrated photodiode signal when the harmonic generation is OFF, e is the electron charge and R is the oscilloscope impedance. The quantum efficiency of the photodiode as a function of the photon energy is provided by the manufacturing company and it is presented in Figure 4(b). 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. Then the produced XUV energy E emitted per laser pulse at the harmonic generation source is given by = ∑ 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 callibration of the Sn filter is the higher signal it results with and without the filter thus minimizing the error of the measurement. = 50% − 60% is the reflectivity of the Si plate [48]. Under optimal generation conditions the maximum energies at the source were found to be in the range ≈ 1μJ. These values concern the emitted 11 th ,13 th ,15 th ,17 th and 19 th 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 because the difference of the two signals (gas jet ONgas 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-ppolarized fields, prevents an accurate measurement of the highly elliptical XUV using the XUV PD. photoelectons' number entering the TOF spectrometer. This consideration has to be taken into acount due to the different angular photoelectron destributions resulting from the single photon ionization by the two polarization's states (linear, circular) [54,55]. After this correction, the energy per laser pulse emitted in the case of highly elliptical radiation was then estimated to be ℎ ℎ ≈100 nJ. It has to be pointed out that most of the energy is almost equally distributed between 11 th and 13 th harmonics and only a small percentage in 14 th and 16 th harmonics. Conclusively, the enegy of highly elliptically polarized XUV radiation is ~ 10 times less as compared to linearly polarized XUV radiation at the same spectral region under conditions where the yield was optimized in both cases. 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, at 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 to intensities up to ~10 13 W/cm 2 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.

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 ~10 13 W/cm 2 intensities in the focal area. Such intensities would be sufficient to induce nonlinear phenomena in chiral systems in the XUV spectral region.