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Abstract
Monochromatic elliptically polarized (CP) ultrashort extreme ultraviolet (EUV) light source with higher ellipticity than 0.80 is developed for the investigation of molecular chirality and electromagnetic phenomena. Elliptically polarized 47-nm high harmonic (HH) is monochromatized from the comb spectrum of HHs by a time-delay compensated monochromator (TDCM) consisting of a pair of Pt-coated toroidal gratings. The ellipticity of EUV light, which is higher than 0.10 at high harmonic generation, is compensated by the anisotropies of the diffraction efficiency and of the phase shift of the toroidal gratings. The degree of polarization is also improved by the diffraction on the gratings. Prior to the polarization compensation, the unknown optical parameters of the toroidal grating at 47 and 50 nm were determined using CP light source and Mueller matrices. The optical parameters were found to be close to those of coated substance Pt. The single-order CP HH light source will be versatile both for spectroscopy and for diffractive imaging.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Circularly polarized (CP) light is required to investigate the magnetic properties and chirality of materials. Extreme ultraviolet (EUV) light, which has a high photon energy, allows element selective probing. Accordingly, CP EUV light enables the investigation of element selective electromagnetic and chiral phenomena [1]. High harmonics (HHs) of ultrashort laser pulses [2,3] are promising for such investigations owing to their spatial and temporal coherence transferred from the driving laser. The electromagnetic fields of HHs are well polarized, and the temporal width of the HH pulses breaks into the attosecond regime [4–8].
The polarization conversion from linear to circular polarization was demonstrated by a reflective polarizer, although the conversion efficiency was ∼4% [1]. Recently, the generation scheme of CP HHs directly driven by laser field was established [9–14]. The driving laser field synthesized by two-color CP light fields with counter-rotating circular polarizations enables the efficient generation of CP HHs, while the one-color single beam CP laser field does not generate HHs, underlain by the three-step model of HH generation [15] and by the conservation of the spin angular momentum of photons. For example, when two beams are collinearly overlapped and have different colors, ω (800 nm) and 2ω (400 nm), the HH spectrum has the following features: i) 3m-th harmonics are missing, where m is a positive integer, because of the three-fold symmetry of the driving laser field, and ii) (3m + 1)-th and (3m + 2)-th harmonics are CP with the same polarization as ω and 2ω, respectively [9,11,12]. The conversion efficiency is comparable to the linearly polarized HH generation [9]. In the case of noncollinear geometry [10,13], the HHs generated by two noncolinear beams with the same color are spatially dispersed. The propagating direction of each HH is determined by the conservation of the spin angular momentum of photons.
The application of CP HHs sometimes requires focusing the single-order harmonic on a target. However, in collinear geometry, all harmonics spatially overlap. Thus, it is necessary to spatially separate the harmonics. Although the harmonic orders are spatially dispersed in noncollinear geometry [10], it is not tractable to focus a specific harmonic order on targets. The usage of a grating is more convenient to both separate and focus the beam, as has already been demonstrated in the observation of nanoscale magnetic imaging [16].
Here, the monochromatization and focusing of a CP harmonic generated in the collinear scheme was implemented by a time-delay compensated monochromator (TDCM) [17–19], consisting of a pair of toroidal gratings and a slit. The TDCM preserves the pulse duration of the selected harmonic [17–19] and focuses the harmonic pulses on target [18]. The TDCM is extensively used for time-resolved photoelectron spectroscopy using a linearly polarized harmonic [20–22]. To assess the applicability of the TDCM to isolate a single-order CP harmonic, the ellipticity of the selected harmonic was evaluated, because the grazing incidence to the toroidal gratings in the TDCM distorts the circular polarization to elliptical owing to the anisotropy of the complex coefficient of the diffraction on the grating. To obtain a CP HH, elliptically polarized harmonic pulses were generated by manipulating the polarization of the driving laser field and were corrected by the diffraction by the gratings. The first practical isolation and characterization of a CP single-order harmonic is demonstrated.
2. Experiment
The experimental setup is shown in Fig. 1. The driving laser field was synthesized by the inline optical system, called MAZEL-TOV, consisting of a BBO crystal, a calcite plate, and an achromatic quarter waveplate (AQW) [11]. The 900-µJ, 35-fs linearly polarized ω light delivered at 1 kHz by a Ti:sapphire laser system was partially converted to 300-µJ 2ω light with perpendicular polarization to ω by a BBO crystal. After adjusting the group delay between 2ω and ω using a calcite plate, the polarizations of these colinearly propagating beams were converted into counter-rotating circular polarizations by an AQW (Kogakugiken corp.). The circular polarizations of HHs were switched by rotating the AQW by 90 degree. The ellipticity of ω and 2ω were 0.99 and 0.98, respectively, measured using a linear polarizer and a quarter waveplate. In this work, the rotating direction of the circular polarization is defined as viewed by an observer facing the oncoming light. The counterclockwise and clockwise rotations of the light polarization are called left-handed (LH) and right-handed (RH) polarization, respectively. Because MAZEL-TOV is composed of static optical elements, the relative phase between ω and 2ω was fixed. The two CP beams were focused in a Kr gas jet by a concave mirror with a 50-cm focal length. The inset in Fig. 1 shows the photoelectron spectrum of Kr atoms irradiated by HHs. Each labeled harmonic order has two peaks because of the spin-orbit splitting of the cation. The generation of the 18th harmonic was suppressed, and its intensity was 18% and 0.7% of the 19th and 17th harmonics, respectively, reinforcing the three-fold symmetry of the synthesized driving laser field. Therefore, the generated HHs were expected to be highly CP. The TDCM consists of a pair of Pt-coated toroidal gratings (HORIBA JOBIN YVON, 54000910) and the slit [18,19]. The first grating disperses the harmonics spatially, and the slit selects a single-order harmonic. The second grating compensates for the pulse front tilt introduced by the diffraction to compress the pulse duration. The reflection angle of the grating is 142°. The harmonic order was monitored by a photoelectron spectrometer and the single order selection was always confirmed. The photon flux of the 17th harmonic with circularly polarization was ∼106 photons/pulse, comparable to that of linearly polarized light. The selected harmonic was detected by an electron multiplier (R2362, Hamamatsu Photonics) after the linear polarized described in the next section. The transmitted intensity I(ϕ) as a function of rotation angle of the polarizer ϕ was measured with an accumulation time of 3 sec. every 10 degree between 0 and 180 degree for circular polarization and every 5 degree for linear polarization with an assumption that I(ϕ) = I(ϕ−180).
Fig. 1. a)Experimental setup. AQW is an achromatic quarter waveplate, and EMT is an electron multiplier. TDCM is a time-delay compensated monochromator. The inset shows the photoelectron spectrum of Kr atoms irradiated by the labeled high harmonics. b) Schematics of a linear polarizer consisting of three Au mirrors and a grating with the grooves in the vertical direction.
3. Characterization of polarization
To characterize the polarization state of HHs, a linear polarizer for EUV light was constructed by three Au mirrors schematically shown in Fig. 1b [23], which has been used in EUV spectroscopy [24]. Intuitively, s-polarized light goes through the polarizer more because of the anisotropy in the reflectance of the Au mirror between s and p polarizations as listed in Table 1. These were calculated using the values in [25] and the Au mirrors with no coating were used to ensure the optical response of Au. In the constructed polarizer, the incident angles to the first and the third mirror were set as 70°, and that to the second mirror was set as 50° [23].
Table 1. Reflectance and reflectance phase of Au [25]
The Stokes vector of the completely polarized light beam $\overrightarrow S = ({{S_0},{S_1},{S_2},{S_3}} )$ is associated with I(ϕ) as follows: When the phase difference between the x and y components of a polarized electric field of light is δ, of which sign determines the handedness of a circular polarization,
To take account of the unpolarized components and the diffraction by the gratings quantitatively, the transmittance of the optical system is evaluated by operating the Mueller matrixes, characterizing the optical components, on the Stokes vector [26]. The first element of the Stokes vector S0 is proportional to I(ϕ), from which the Stokes vector and the optical parameters of the toroidal gratings are evaluated in this work. Using the complex reflection coefficients of an optical component ${r_s}\exp ({i{\delta_s}} )$ and ${r_p}\exp ({i{\delta_p}} )$ for s and p polarization, respectively, the Mueller matrix M for reflection is expressed as
4. Polarization after the time-delay compensated monochoromator
Firstly, to examine whether the reflection polarizer works correctly, I(ϕ) of linearly polarized 17th harmonic (47 nm) with TE and TM polarizations were measured, as shown in Fig. 2a. Here, the direction of 0° is parallel to the groove of the toroidal grating and TE polarization. The TM polarization is perpendicular to the TE polarization. Transmitted intensity approaches to maximum in the same direction of the electric field, while the intensity of the perpendicular direction to the electric field was 0.033 of the maximum as expected from the extinction ratio of the polarizer calculated using the optical constants tabulated in Table 1. Hence, quantitatively, the three sets of Au mirrors work as a linear polarizer.
Fig. 2. (a) Transmitted intensities of TE (
For the linear TE and TM polarizations of ${\vec{S}_{_{TM}^{TE}}} = ({1, \mp 1,0,0} )$, the first element of ${\vec{S}^{\prime}_{_{TM}^{TE}}}$ after the TDCM and the polarizer is proportional to α ± βcos(2ϕ) accordingly, where α = 1.69 and β = 1.58 for the 17th harmonic obtained using ψ and Δ of Au. The difference between α and β is due to the finite reflectivity of the Au mirror of the orthogonal component in the polarizer. The solid lines in Fig. 2a indicate the fitting results for these equations. Although only the proportional coefficient was a fitting parameter, the angle dependence was reproduced. Therefore, the reflectance and the phase in Table 1 appropriately describes the responses of the Au mirrors installed in the reflection polarizer.
When the polarizations of the HHs were switched to circular polarizations, the angle dependences of the 17th harmonic selected by the TDCM were changed to those of Fig. 2c. The angle dependence shows that the polarizations after the TDCM are no longer circular polarization. In contrast with linear polarization, however, the LH CP light (
To understand the angle dependence of the transmittance of the RH and LH CP light including the unpolarized component with ${\overrightarrow S _{_{LH}^{RH}}} = \textrm{A}({1,\,\,0,\,\,0,\,\, \pm 1} )+ \textrm{B}({1,\,\,0,\,\,0,\,\,0} )$, respectively, the first element of the Stokes vector ${\overrightarrow S ^\prime }_{_{LH}^{RH}} = {\bf R}({ - \phi } )\; {{\bf M}_{70}}{{\bf M}_{50}}{{\bf M}_{70}}{\bf R}(\phi ){{\bf M}_G}{{\bf M}_G}{\overrightarrow S _{_{LH}^{RH}}}$ is calculated. Here, A and B are proportional to the intensities of the polarized and nonpolarized components, respectively. The transmitted intensities of the RH and LH CP harmonics ${I_{_{LH}^{RH}}}(\phi )$, i.e. the first element of ${\overrightarrow S ^\prime }_{_{LH}^{RH}}$, are given as
where and respectively. For the 16th harmonic, α = 1.56 and β = 1.41. Because R depends on ΔG, the tilt direction of the principle axis of the transmittance depends on the circular polarization.To evaluate the optical constants ψG and ΔG, P, Q, and R are determined by fitting Eq. (5) to the experimental results. The fitting results are shown by the solid lines in Figs. 2b and 2c. ψG is uniquely determined by Eqs. (6) and (7), while the other parameters, A, B, and ΔG, cannot be determined uniquely. However, Eqs. (7) and (8) limit the range of A as follows: Eq. (7) gives the maximum of A as $\textrm{Q/}({\textrm{2}\beta \cos (2{\psi_G})} )$, where a HH is completely polarized, i.e. B = 0. Equation (8) also gives the lower limit of A as $\textrm{R/}({\beta {{\sin }^2}(2{\psi_G})} )$ to satisfy $\textrm{R/}({\textrm{A}\beta {{\sin }^2}(2{\psi_G})} )\le 1$. Consequently, the range of A is given by
Table 2. Parameters for right (RH)- and left-handed (LH) circularly polarized harmonics after TDCM
The CP HHs were reported to be partially depolarized, because of the dynamical symmetry breaking by medium ionization and the temporal evolution of the driving laser during the HH generation [28]. The DOP of the 17th harmonic was reported to be approximately 0.6 [28]. CP HHs generated in noncollinear scheme have a DOP of about 0.85 [13]. The depolarized components would be attributable to the ionization of the interacting gas, introducing decoherence in the process of HH generation. The DOP on target in the present work is 0.81 in the worst case, which is higher than that in [28]. On the gratings, only the spatially coherentcomponent with the same polarization can be diffracted. Therefore, the gratings work as filters passing through the polarized component. Higher DOP is one advantage of this scheme.
The obtained ψG is close to those of Pt, ψ = 36.6° for the 16th and ψ = 36.0°for the 17th harmonic, respectively, at the incident angle of 71° [25]. The phase shift of Pt, Δ = 319° for 16th and Δ = 321° for 17 harmonics, are also within the range of ΔG. Although the harmonics are not reflected but diffracted on the surface of the toroidal grating, the diffraction efficiency depends on the coated substance, Pt. Therefore, it is reasonable that ψG and ΔG have similar values to those of Pt. The ratio of the diffraction efficiency rTM2/rTE2 of the toroidal grating is related with ψG by $\tan {\psi _G} = {r_{TM}}/{r_{TE}}$, and it is 0.66 when the average value of ψG = 39.0° is employed for the 17th harmonic. This value is consistent with the experimentally measured value 0.70 ± 0.05 at 47 nm for linearly polarized light. The experimentally determined range of ɛ shows that the circular polarization of the selected single-order harmonics was deteriorated by the TDCM, owing to the anisotropy and the phase shift by diffraction.
5. Compensation of ellipticity for circluar polarization
One approach to obtain the CP harmonic at focus in this scheme is to generate elliptically polarized HHs and to correct the ellipticity by the anisotropic diffraction and the phase shift of the toroidal gratings. For example, the elliptical polarization along the TM direction is preferred, because the diffraction efficiency of TE mode is higher than that of TM mode. To generate elliptically polarized HHs, the polarization of ω with higher pulse energy than 2ω was set to parallel to TM mode and the ellipticity was introduced to the driving laser field by rotating the AQW from the optimum angle for the quarter wavelength. When the angle was rotated by 20° from the optimum angle, the polarizations of the driving laser field were changed to be elliptical. Figure 3a shows the angle dependence of the RH ω and LH 2ω intensities measured using a linear polarizer. The ellipticities of ω and 2ω were 0.48 and 0.52, respectively.
Fig. 3. (a) Transmitted intensities of elliptically polarized fundamental light ω (
These two laser fields were synthesized and generated the RH 17th harmonic, of which angle dependence of the intensity is shown in Fig. 3b. Because the optical parameters of the toroidal grating listed in Table 2 are not uniquely determined, $I(\phi )$ of $\overrightarrow S = ({{S_0},{S_1},{S_2},{S_3}} )$ are evaluated for two extreme cases with ΔG = 329° and with ΔG = 315°. The corresponding $I(\phi )$ are
) before the TDCM to the green sphere (
) after the TDCM on the Poincare sphere in Fig. 4.Fig. 4. Polarization states on the Poincare sphere. The red (
6. Summary
In this work, the polarizations of the monochromatized 16th and 17th harmonics of a Ti:sapphire laser by the TDCM were characterized for the development of ultrashort CP EUV light source. It was found that the circular polarization was distorted by the diffraction on the toroidal gratings. However, the diffraction on the grating increases DOP. The compensation of the ellipticity by manipulating the driving laser field was demonstrated for the first time. Here, we assumed DOP = 0.9 in reference to the case driven by CP driving lasers. The single-order CP HH pulses selected by the TDCM will be a versatile light source for the investigation of magnetism and chirality.
Funding
Core Research for Evolutional Science and Technology (JPMJCR15N1); MEXT Q-LEAP (JPMXS0118068681); Japan Society for the Promotion of Science (19H01814).
Disclosures
The authors declare no conflicts of interest.
References
1. B. Vodungbo, A. B. Sardinha, J. Gautier, G. Lambert, C. Valentin, M. Lozano, G. Iaquaniello, F. Delmotte, S. Sebban, J. Lüning, and P. Zeitoun, “Polarization control of high order harmonics in the EUV photon energy range,” Opt. Express 19(5), 4346 (2011). [CrossRef]
2. A. Mcpherson, G. Gibson, H. Iara, H. Johann, T. S. Luk, I. A. Mcintyre, K. Boyer, and C. K. Rodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4(4), 595 (1987). [CrossRef]
3. M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. B: At., Mol. Opt. Phys. 21(3), L31–L35 (1988). [CrossRef]
4. M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001). [CrossRef]
5. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004). [CrossRef]
6. Y. Nabekawa, T. Shimizu, T. Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric Autocorrelation of an Attosecond Pulse Train in the Single-Cycle Regime,” Phys. Rev. Lett. 97(15), 153904 (2006). [CrossRef]
7. K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, “Tailoring a 67 attosecond pulse through advantageous phase-mismatch,” Opt. Lett. 37(18), 3891 (2012). [CrossRef]
8. T. Gaumnitz, A. Jain, Y. Pertot, M. Huppert, I. Jordan, F. Ardana-Lamas, and H. J. Wörner, “Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared driver,” Opt. Express 25(22), 27506 (2017). [CrossRef]
9. A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen, “Spin angular momentum and tunable polarization in high-harmonic generation,” Nat. Photonics 8(7), 543–549 (2014). [CrossRef]
10. D. D. Hickstein, F. J. Dollar, P. Grychtol, J. L. Ellis, R. Knut, C. Hernández-García, D. Zusin, C. Gentry, J. M. Shaw, T. Fan, K. M. Dorney, A. Becker, A. Jaroń-Becker, H. C. Kapteyn, M. M. Murnane, and C. G. Durfee, “Non-collinear generation of angularly isolated circularly polarized high harmonics,” Nat. Photonics 9(11), 743–750 (2015). [CrossRef]
11. O. Kfir, E. Bordo, G. I. Haham, O. Lahav, A. Fleischer, and O. Cohen, “In-line production of a bi-circular field for generation of helically polarized high-order harmonics,” Appl. Phys. Lett. 108(21), 211106 (2016). [CrossRef]
12. O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright phase-matched circularlypolarized extreme ultraviolet high harmonics,” Nat. Photonics 9(2), 99–105 (2015). [CrossRef]
13. P.-C. Huang, C. Hernández-García, J.-T. Huang, P.-Y. Huang, C.-H. Lu, L. Rego, D. D. Hickstein, J. L. Ellis, A. Jaron-Becker, A. Becker, S.-D. Yang, C. G. Durfee, L. Plaja, H. C. Kapteyn, M. M. Murnane, A. H. Kung, and M.-C. Chen, “Polarization control of isolated high-harmonic pulses,” Nat. Photonics 12(6), 349–354 (2018). [CrossRef]
14. D. Azoury, O. Kneller, M. Krüger, B. D. Bruner, O. Cohen, Y. Mairesse, and N. Dudovich, “Interferometric attosecond lock-in measurement of extreme-ultraviolet circular dichroism,” Nat. Photonics 13(3), 198–204 (2019). [CrossRef]
15. P. B. Corkum, “Plasma perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993). [CrossRef]
16. O. Kfir, S. Zayko, C. Nolte, M. Sivis, M. Möller, B. Hebler, S. S. P. K. Arekapudi, D. Steil, S. Schäfer, M. Albrecht, O. Cohen, S. Mathias, and C. Ropers, “Nanoscale magnetic imaging using circularly polarized high-harmonic radiation,” Sci. Adv. 3(12), eaao4641 (2017). [CrossRef]
17. L. Poletto, P. Villoresi, E. Benedetti, F. Ferrari, S. Stagira, G. Sansone, and M. Nisoli, “Intense femtosecond extreme ultraviolet pulses by using a time-delay-compensated monochromator,” Opt. Lett. 32(19), 2897 (2007). [CrossRef]
18. M. Ito, Y. Kataoka, T. Okamoto, M. Yamashita, and T. Sekikawa, “Spatiotemporal characterization of single-order high harmonic pulses from time-compensated toroidal-grating monochromator,” Opt. Express 18(6), 6071 (2010). [CrossRef]
19. H. Igarashi, A. Makida, M. Ito, and T. Sekikawa, “Pulse compression of phase-matched high harmonic pulses from a time-delay compensated monochromator,” Opt. Express 20(4), 3725 (2012). [CrossRef]
20. A. Makida, H. Igarashi, T. Fujiwara, T. Sekikawa, Y. Harabuchi, and T. Taketsugu, “Ultrafast Relaxation Dynamics in trans-1,3-Butadiene Studied by Time-Resolved Photoelectron Spectroscopy with High Harmonic Pulses,” J. Phys. Chem. Lett. 5(10), 1760–1765 (2014). [CrossRef]
21. R. Iikubo, T. Fujiwara, T. Sekikawa, Y. Harabuchi, S. Satoh, T. Taketsugu, and Y. Kayanuma, “Time-Resolved Photoelectron Spectroscopy of Dissociating 1,2-Butadiene Molecules by High Harmonic Pulses,” J. Phys. Chem. Lett. 6(13), 2463–2468 (2015). [CrossRef]
22. R. Iikubo, T. Sekikawa, Y. Harabuchi, and T. Taketsugu, “Bond Selective Probe by Time-Resolved Photoelectron Spectroscopy: Ring-Opening Dynamics of 1,3-Cyclohexadiene,” Faraday Discuss. 194, 147–160 (2016). [CrossRef]
23. T. Koide, T. Shidara, M. Yuri, N. Kandaka, K. Yamaguchi, and H. Fukutani, “Elliptical-polarization analyses of synchrotron radiation in the 5–80-eV region with a reflection polarimeter,” Nucl. Instrum. Methods Phys. Res., Sect. A 308(3), 635–644 (1991). [CrossRef]
24. W. R. Hunter, “Polarization,” in Vacuum Ultraviolet Spectroscopy I, J. A. Samson and D. L. Ederer, eds. (Academic Press, San Diego, 1998).
25. W. S. M. Werner, K. Glantschnig, and C. Ambrosch-Draxl, “Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals,” J. Phys. Chem. Ref. Data 38(4), 1013–1092 (2009). [CrossRef]
26. R. M. A. Azzam, “Stokes-vector and Mueller-matrix polarimety,” J. Opt. Soc. Am. A 33(7), 1396 (2016). [CrossRef]
27. D. Maystre, “Gratings: Theory and Numeric Applications,” E. Popov, ed. (Institut Fresnel, Université d’Aix-Marseille, CNRS, 2014).
28. L. Barreau, K. Veyrinas, V. Gruson, S. J. Weber, T. Auguste, J.-F. Hergott, F. Lepetit, B. Carré, J.-C. Houver, D. Dowek, and P. Salières, “Evidence of depolarization and ellipticity of high harmonics driven by ultrashort bichromatic circularly polarized fields,” Nat. Commun. 9(1), 4727 (2018). [CrossRef]
) and TM (
) polarizations of the 17th harmonic as a function of the rotating angle of the polarizer 
) and right-handed (
) CP 16th and 17 harmonics as a function of 
) and the second harmonic 2ω (
) as a function of the rotating angle of the polarizer. (b) Transmitted intensities of RH elliptically polarized 17th harmonic as a function of the rotating angle of the linear polarizer. The solid lines are the fitting results of Eqs. (
) and green (
)spheres show the Stokes vectors of the 17th harmonic, generated elliptically polarized laser field, before and after the TDCM, respectively.