Measurement of complex refractive index with tunable extreme ultraviolet high harmonic source

Daisuke Hirano; Daisuke Hirano; Yuki Nagakubo; Junko Omachi; Junko Omachi; Junko Omachi; Kosuke Yoshioka; Kosuke Yoshioka; Makoto Kuwata-Gonokami

doi:10.1364/OE.392272

1. Introduction

With many applications in the extreme ultraviolet (EUV) spectral range, there is a lot of interest in gaining understanding of material properties at photon energies ranging from 20 to 120 eV. This is vital for improving the performance of multilayer mirrors and optical masks needed, for example, in EUV lithography [1–3]. The problem may be resolved in part by combining measurements of the EUV absorption spectra with a calculation of the real part of the refractive index using the Kramers-Kronig relations [4], however, such an approach is not always reliable when the photon energy exceeds 50 eV [5,6]. This difficulty can be avoided by using the double slit interference technique, which can provide information on both the imaginary and real part of the refractive index [7]. The accuracy of such measurements is limited by the incoherence in conventional synchrotron and laser-produced plasma (LPP) EUV sources [8,9]. Improving transversal coherence requires cutting out a small portion of the beam which reduces the number of photons available for measurement significantly suppressing the signal to noise ratio. Moreover, performing measurements of the complex refractive index in a wide spectrum range requires multiple adjustments of the setup [7].

Recent advances in higher harmonic generation (HHG) techniques offer an attractive alternative to the synchrotron and LPP EUV sources enabling well-established spectroscopy techniques for material characterization to be used [10–13]. Using HHG techniques it is possible to create a broadband coherent EUV radiation source that is characterized by a discretized spectrum consisting of the odd harmonics of the fundamental driving laser frequency, and with a near-uniform spectral intensity [14,15]. The dispersion of the real and imaginary parts of the refractive index can then be measured in a broad spectral range. Note that the inevitable gaps in the HHG spectrum can be reduced by tuning the wavelength of the fundamental beam.

In this paper, we describe an interferometric system that can measure the real and imaginary parts of the complex refractive index of a material in the EUV range. By using the HHG from a fundamental beam of an optical parametric amplifier, we can demonstrate quasi-continuous tuning of coherent EUV radiation with photon energy in the range of 63 to 79 eV. The proposed approach can measure the optical phase to an accuracy of 10 mrad; this value is one order of magnitude better than that of existing HHG-based systems [10,11]. The EUV interferometer that we developed can measure the complex refractive index in a broad spectral range and can be used for materials having pronounced dispersion features.

2. Method

The proposed method is based on a double slit interference technique that has already been used successfully to measure the real part of the refractive index with synchrotron radiation [7]. This technique uses two double slits.

The first double slit (reference) was used to create a reference interference pattern to let us characterize the setup as shown in Fig. 1(a). The signal on the screen is stronger where the blue and red wavefronts overlap in-phase and weaker where they overlap out-of-phase, creating an interference pattern. The period of the interference pattern depends on the optical wavelength and the slit spacing.

Fig. 1. (a) Interference pattern created by the reference double slit. (b) Interference pattern created by the evaluation double slit, in which one of the openings (denoted in yellow) is covered by an aluminum sample. (c) The experimental setup based on the double slit interferometer. Inset shows the reference and evaluation double slits irradiated by the EUV beam. The openings were made in a molybdenum plate, which was movable along the Y₀-axis.

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In the second double slit (evaluation), one slit is covered by the material to be characterized, as shown in Fig. 1(b). Since the optical phase passing through the sample is delayed, the interference pattern changes. The real and imaginary parts of the refractive index of the material can be obtained by comparing the interference patterns obtained from the two (reference and evaluation) double slits.

The measurement setup is shown in Fig. 1(c). The fundamental beam, tunable in the wavelength range from 640 to 670 nm, was obtained by using the second harmonics of an optical parametric amplifier (TOPAS-Prime with NirUVis, Light Conversion Ltd.), which was pumped by an amplified Ti:Sapphire laser (Legend Elite-DUO, Coherent, Inc.) at a 5 kHz repetition rate (see Appendix A). The pulse duration of the fundamental beam was measured to be around 25 fs. This beam was focused into a neon gas jet to produce high-order harmonics having photon energies in the vicinity of the aluminum L-edge. The focal spot size of the pump-pulse was about 10 µm. Phase matching conditions were optimized by adjusting the gas pressure.

The two pairs of rectangular slits were fabricated by focused ion beam (FIB) milling from a 5 µm thick molybdenum plate. In both pairs, the slits had 20 × 40 µm openings separated by 10 µm. The distance between the two pairs was adjusted so that the EUV beam would only irradiate one double slit at a time. The molybdenum plate was mounted on a translation stage to allow us to select which double slit was irradiated.

We studied the complex refractive index of an amorphous aluminum sample (LUXEL Co.) with a total thickness of 156 ± 5 nm (thickness and tolerance specified by the vendor). Ellipsometry measurements revealed that the aluminum film was covered by an oxide layer approximately 10-nm thick on each side. In order to suppress the effect of the oxide on the phase of the transmitted wave, we removed about 7.5 nm of the oxide layer from each side using argon sputtering. After sputtering, the sample was kept in an oxygen-free environment (at an oxygen partial pressure of below 100 Pa). The total thickness of the film after sputtering was 141 ± 5 nm of which the remaining oxide layer thickness (confirmed by XPS after the measurement [16]) was 6.5 nm. The oxide layer thickness is a saturation thickness that is determined by the purity of the neon gas for HHG and the partial pressure of oxygen in our sample transfer process.

The coherent EUV radiation generated in the neon jet passed through the double-slit, and entered the entrance slit of a spectrometer (Vacuum and Optical Instruments) and was diffracted by a toroidal grating (HORIBA JOBIN YVON 541 00 200). The toroidal grating reflected the interference patterns for all harmonics generated in the neon jet onto the surface of a two-dimensional charge-coupled device (CCD) camera (Andor DO940P BN) with a resolution of 2048 × 512 pixels. To analyze the interference image of a specific harmonic, we summed signals over 15 pixels along the Y₂-axis (shown in the figure). The energy resolution of the spectrometer was 330 meV at the photon energy from 63 to 78 eV.

For each harmonic generated in the neon jet, we measured the intensity distribution in the interference pattern in the reference and evaluation double slits. In order to increase the signal to noise ratio, we integrated the EUV signal for 200 seconds, which corresponded to 10⁶ pulses of the fundamental beam. The readout rate of the CCD camera was set at 50 kHz. A mechanical shutter blocked light during each measurement readout. Fluctuation of the optical path was minimized by using an active feedback control (see Appendix A).

In the experiment, we performed measurements for 4 harmonics from 35^th to 41^st of 13 fundamental wavelengths, i.e. we analyzed 52 interference patterns created by EUV radiation having photon energy from 63 to 78 eV. Such a densely populated spectrum enables a quasi-continuous change of the EUV phonon energy. Figures 2(a) and 2(b) show the intensity distribution in the interference pattern of the 39th harmonic of the fundamental beam at the wavelength of 649.8 nm for the reference and evaluation double slits, respectively. The evaluation double-slit is located 5.5 µm higher than the reference double-slit, which we took into account in our analysis.

Fig. 2. Double slit interference image of the 39th harmonic of the fundamental beam at the wavelength of 649.8 nm for the reference (a) and evaluation (b) double slit. The horizontal axis is the X₂ coordinate of the CCD camera, shown in Fig. 1(c). Open circles show the experimental data, while the blue solid lines show the results of fitting with Eq. (1) at $\xi = $ 90 µm, $F = $ 300 mm, ${P_\sigma } = $ 11.2 µm, and $R = $ 0.31 m. The fitting of the interference pattern of the evaluation slit in (b) returns the foil transmittance of $T = $ 0.1568 and phase shift of $\theta = $ 0.56 rad.

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3. Discussion

Fourier transform is conventionally used to recover the phase shift from the interference pattern [17]. In the EUV range however, such an analysis may lead to misinterpreting results because the phase shift in the evaluation double slit may originate not only from the presence of the sample material, but also from the finite curvature of the high harmonic beam wavefront, fluctuations of the higher harmonics beam position, and other characteristics of the measurement setup.

In order to visualize these contributions, the interference pattern from the reference double slit is described in terms of the Fresnel diffraction theory [18]. In the paraxial approximation, the distribution of the intensity of the diffracted wave at wavelength $\lambda $ along the X₂-axis of the CCD camera can be presented by the following equation:

(1)$$\begin{aligned}I_\lambda ^{\textrm{ref}}({{x_2}} )&= A\mathop {\int\!} \limits_{ - \infty }^{\infty} dx^{\prime}\exp \left[ { - \frac{{x{^{\prime2}}}}{{2P_\sigma^2(\lambda )}}} \right]\\ &\quad\times {{{\left|{\mathop {\int\!\!\!\int }\nolimits_{ - \infty }^\infty d{x_0}d{x_1}{g_\lambda }({{x_0} + x^{\prime}} ){f^{\textrm{ref}}}({{x_0}} )\exp \left[ {i\pi \frac{{{{({{x_0} - {x_1}} )}^2}}}{{{z_{01}}\lambda }}} \right]\exp [{i{W_{\lambda }}({{x_1}} )} ]\exp \left[ {i\pi \frac{{{{({{x_1} - {x_2}} )}^2}}}{{{z_{12}}\lambda }}} \right]} \right|}^2},} \end{aligned}$$

where A is a constant. The integration is performed over the X₀- and X₁-axes as shown in Fig. 1(c) on the double slit plane and grating, respectively. Additionally,

(2)$$\begin{array}{c} {{g_\lambda }({{x_0}} )= \; \exp\left[ { - i\pi \frac{{{x_0}^2}}{{R(\lambda )\lambda }}} \right]} \end{array}$$

describes the wavefront of the incident EUV beam centered at ${x_0}$ = 0 and having a curvature radius R in the paraxial approximation [19,20]. In the HHG process, the beam curvature may vary with harmonic number, i.e. R is believed to be wavelength dependent [19]. In Eq. (1), we assumed that the beam-pointing fluctuations of the HHG beam position from pulse to pulse around ${x_0}$ = 0 have a Gaussian distribution with standard deviation ${P_\sigma }$. The beam pointing is also discussed in the Appendix. In Eq. (1), ${f^{\textrm{ref}}}({{x_0}} ){\; }$ is the aperture function of the double slit, i.e. ${f^{\textrm{ref}}}({{x_0}} )$ = 1 if ${x_0}$ corresponds to the openings in the slits, and ${f^{\textrm{ref}}}({{x_0}} )$ = 0 if ${x_0}$ corresponds to the molybdenum plate. ${z_{01}}$ = 0.72 m is the distance between the molybdenum plate and the toroidal grating.

(3)$$\begin{array}{c} {{W_{\lambda }}({{x_1}} )= \frac{{2\pi \xi (\lambda ){x_1}}}{{{z_{12}}\lambda }} - \frac{{\pi {x_1}^2}}{{F(\lambda )\lambda }}} \end{array}$$

describes the phase added by the toroidal grating, where ${x_1}$ represents the position on the grating, and ${z_{12}}$ = 0.3 m is the distance between the grating surface and the CCD camera. The first term in the right-hand side of Eq. (3) describes the wavefront tilt produced by the toroidal grating, while the second term represents the wavefront curvature added by the toroidal grating. Note that both the tilt parameter $\xi $ and F are wavelength dependent, i.e. they should be defined for each harmonic.

The blue solid line in Fig. 2(a) shows the results of the fitting of the interference pattern for the reference double-slit using Eq. (1) for the 39th harmonic of the fundamental beam at the wavelength of 649.8 nm at $\xi = $ 90 µm, $F = $ 300 mm, ${P_\sigma } = $ 11.2 µm, and $R = $ 0.31 m. The curve-fitting result is closely aligned to the interference pattern over two orders of magnitude of signal strength, and as discussed in the Appendix, the ${{\chi }^2}$-test shows quantitatively that the fitting results well aligned. Tables 1 and 2 in the Appendix show the setup parameters obtained by fitting the reference double-slit interference pattern for all 52 wavelengths.

In order to determine the complex refractive index of the aluminum sample, we analyzed the interference pattern obtained with the evaluation double slit. The intensity distribution in the diffracted interference pattern is described by the same Eq. (1), where now the aperture function of the reference double slit ${f^{\textrm{ref}}}({{x_0}} )$ is replaced with the aperture function of the evaluation slit ${f^{\textrm{eva}}}({{x_0}} )$. If ${x_0}$ corresponds to the opening covered with the aluminum sample as shown in the inset to Fig. 1(c), ${f^{\textrm{eva}}}({{x_0}} )= {T^{1/2}}\textrm{exp}({i\theta } )$, where T is the foil transmittance and $\theta $ is the phase accrued by the transmitted wave. ${f^{\textrm{eva}}}({{x_0}} )= 1$ if ${x_0}$ corresponds to an empty opening, and ${f^{\textrm{eva}}}({{x_0}} )= 0$ if ${x_0}$ corresponds to the molybdenum plate. The other parameters describing the interference pattern in Eq. (1) remain the same.

The blue solid line in Fig. 2(b) shows the results of the fitting of the experimental data obtained for the evaluation double slit for the 39th harmonic of the fundamental beam at the wavelength of 649.8 nm.

Figure 3 shows the photon energy dependence of the phase shift and transmittance in the photon energy range 63 to 79 eV. The uncertainties (see Appendix for details) are shown in Fig. 3 by the error bars. The clearly observable peak in the phase shift spectrum and the sharp fall of the transmittance at a photon energy of about 72.8 eV correspond to the L-edge of the aluminum. Since in our experimental conditions the energy resolution (330 meV) was comparable with the spin-orbit splitting of the L-edge (440 meV) [21], this feature is not observed in Fig. 3.

Fig. 3. Dependence of the phase difference $\theta $ (a) and transmittance T (b) on the photon energy obtained by fitting Eq. (1) for the evaluation slit using setup parameters listed in Tables 1 and 2 (see Appendix). The color of the experimental points corresponds to the fundamental wavelength, which is presented by the color map at the top.

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To obtain the real and imaginary parts of the complex refractive index of aluminum ${N_{\textrm{Al}}} = 1 - {\sigma _{\textrm{Al}}} + i{\beta _{\textrm{Al}}}$, the presence of the Al₂O₃ (alumina) layer with the thickness of ${d_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}$= 6.5 nm needs to be accounted for because in the EUV range, the complex refractive index of alumina ${N_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}} = 1 - {\sigma _{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}} + i{\beta _{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}$ is much higher than the refractive index of aluminum [22]. Specifically, by using the measured phase shift $\theta $ and transmittance T the complex refractive index of the aluminum can be obtained from the following equations:

(4)$$\begin{array}{c} {{\sigma _{\textrm{Al}}} = \frac{{\frac{{\theta \lambda }}{{2\pi }} - {\sigma _{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}{d_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}}}{{d - {d_{\textrm{A}{\textrm{l}_\textrm{2}}{\textrm{O}_\textrm{3}}}}}},} \end{array}$$

(5)$$\begin{array}{c} {{\beta _{\textrm{Al}}} ={-} \frac{{\frac{\lambda }{{4\pi }}\ln T + {\beta _{\textrm{A}{\textrm{l}_2}{\textrm{O}_3}}}{d_{\textrm{A}{\textrm{l}_2}{\textrm{O}_3}}}}}{{d - {d_{\textrm{A}{\textrm{l}_2}{\textrm{O}_3}}}}},} \end{array}$$

where ${\sigma _{\textrm{A}{\textrm{l}_2}{\textrm{O}_3}}}$ and ${\beta _{\textrm{A}{\textrm{l}_2}{\textrm{O}_3}}}$ are values found in the literature [22]. Uncertainty in the refractive index was calculated taking into account the contributions of $\theta $ and T and the sample thickness d. Typical errors in the real part of the refractive index, taking account of the errors of phase (10 mrad), and sample thickness (5 nm) by using Eq. (4), were estimated at less than 0.0002 (0.02%).

Figures 4(a) and 4(b) show that in the vicinity of the L-edge, the spectra of the real and imaginary parts of the aluminum complex refractive index are a good match to the spectra obtained via reflection and photoelectron spectroscopy by Birken et al. [23]; however, they differ from those measured by synchrotron radiation double slit interferometer via Chang et al. [7]. Such an inconsistency may originate from the different crystallinity of the aluminum sample used by Chang et al. [7]. It is worth noting that at the photon energy below the L-edge, our results correlate with results from absorption spectroscopy by Gullikson et al. [24]. Comparison with these previous studies shows that our instrument can correctly evaluate the refractive index of the sample. We note that there is a systematic discrepancy between these experimental results and the well-known CXRO database ([4,25], not shown). For example, $- {\sigma _{\textrm{Al}}}$ at 75 eV from the database is 44% larger than our value.

Fig. 4. Spectra of the real (a) and imaginary (b) parts of the complex refractive index of aluminum measured in this double slit HHG interferometer (black dots), synchrotron radiation double slit interferometer by Chang et al. [7] (gray dots), reflection and photoelectron spectroscopy by Birken et al. [23] (green squares), and absorption spectroscopy by Gullikson et al. [24] (blue line). The vertical bars show the uncertainty range.

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4. Conclusion

We have shown that the HHG-based table-top coherent EUV source, which can be quasi-continuously tuned in a wide photon energy range, can be used to measure the complex refractive index of samples as part of a practical interferometric method. In the experiment, we measured the real and imaginary part of the complex refractive index of aluminum in the range of 63 to 78 eV to an accuracy of 0.02%, which is good enough to meet the design requirements for EUV optical components. The proposed approach was shown to be a reliable, practical, and scalable procedure for determining material parameters that are of crucial importance for designing lithographic systems employing EUV and soft-X-ray optics.

Appendix A: A detailed schematic of the experimental setup

Wavelength-tunable fundamental pulses were obtained by second-harmonic generation of the signal beam from the optical parametric amplifier (TOPAS-Prime with NirUVis, Light Conversion Ltd.), which was pumped by a regenerative amplified Ti:Sapphire laser system (Legend Elite-DUO, Coherent, Inc.). The fundamental beam was stabilized by using two home-made beam stabilizers based on the position sensitive detector (PSD, S2044 Hamamatsu Photonics K.K.). The beam stabilizer consisted of a piezoelectric actuator mounted on a mirror holder (PZT mirror) controlled by a feedback circuit reacting from a PSD signal. Since the distance from the Brewster window 1 to the PSD 1 was the same as the distance from the Brewster window 1 to the PZT mirror 2, it was possible to stabilize the beam position in the PZT mirror 2 using the beam stabilizer 1. The focused beam position inside the vacuum chamber was stabilized by stabilizer 2. The chirp produced by the two Brewster windows and the entrance window of the vacuum chamber was pre-compensated by a negative chirp mirror pair. The magnifying optical system before the vacuum chamber enlarged the beam diameter and compensated for the beam aberration. The light was focused on a neon gas jet in the vacuum chamber. The power density at the focal point was of the order of 10¹⁴ W/cm². A key point to the setup was the beam stabilizing mechanism, highlighted in green and yellow in Fig. 5.

Fig. 5. Experimental setup.

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Appendix B: Effect of the beam pointing

In the experiment, the drift of the focal point of the fundamental beam resulting from a change in the environment, such as room temperature, was measured to be 4 µm / min at maximum. This drift can cause a phase shift of about 10 mrad during a single 200 second measurement cycle. In order to avoid this systematic error, the position of the fundamental beam was stabilized using PZT mirror holders 1 and 2 (see Fig. 5). This allowed us to suppress the focal point drift down to within 0.1 µm / min and the corresponding phase uncertainty down to 0.08 mrad. Note that stabilization of the beam position also compensated for fluctuations of the optical path that accompanied changes in the fundamental wavelength. The PSD-based stabilization system suppressed a slow drift of the EUV beam center, however fluctuations of the focal point for adjacent pulses that arrived at intervals of 200 µs remained. In Eq. (1), these fluctuations were provided for by assuming that they had a normal Gaussian distribution with a standard deviation ${P_\sigma }$ around the beam center position.

Table 1. Setup parameters obtained from the fitting of the interference patterns of the reference slit for 15.83-16.95 nm using Eq. (1). The 68% confidence intervals for each parameter obtained from the χ²-test is shown in the brackets.

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Table 2. Setup parameters obtained from the fitting of the interference patterns of the reference slit for 17.02-19.57 nm using Eq. (1). The 68% confidence intervals for each parameter obtained from the χ²-test is shown in the brackets.

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Appendix C: Fitting parameter errors

Tables 1 and 2 show the calculated 68% confidence intervals for all fitting parameters by considering statistical and systematic uncertainty. In order to quantitatively check the fitness of the function we performed the ${\chi ^2}$-test of the 52 interference patterns. $\chi _r^2$ was defined by ${\chi ^2}$ normalized with degrees of freedom, and varied from 1.6 to 6.4. This indicated that the experimental data was well represented by the fitting function, however the residuals showed a systematic trend. The systematic residuals were of a similar order of magnitude as the statistical uncertainties making it difficult to further improve this fitting model. If it is assumed that the systematic residuals were normally distributed, and with the standard deviation taken as the root mean square of the systematic residuals, the 68% confidence interval ${\Delta }{\alpha _{\textrm{syst}}}$ for each parameter $\alpha $ can be calculated. The total error ${\Delta }{\alpha _{\textrm{tota}}}$ including the statistical error ${\Delta }{\alpha _{\textrm{stat}}}$ is then described as

(6)$$\begin{array}{c} {\Delta {\alpha _{\textrm{tota}}} = \sqrt {{\Delta }\alpha _{\textrm{stat}}^2 + \Delta \alpha _{\textrm{syst}}^2} .} \end{array}$$

Appendix D: Effect of the slit shape

Although FIB processing errors result in submicron fluctuations of the slit shape, we found that changing the width of the openings by less than 0.5 µm did not change the fitting results for $\theta $ and T. In order to remove high-frequency components in the simulated interference pattern we modelled rectangular openings with the error function having a width of 1 µm.

Funding

Ministry of Education, Culture, Sports, Science and Technology (Center of Innovation Program, CIAiS, NanoQuine, Nanotechnology Platform" (project No. 12024046), Photon Frontier Network Program, Quantum Leap Flagship Program (JPMXS0118067246)); New Energy and Industrial Technology Development Organization.

Acknowledgments

We thank Y. Svirko for the fruitful discussions and critical reading of our manuscript. We also thank J. Yumoto, Y. Morita, and K. Konishi for their support in the experiments and helpful discussions, and H. Sakurai for editing the manuscript. This work was conducted in Research Hub for Advanced Nano Characterization, The University of Tokyo, supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

Disclosures

The authors declare no conflicts of interest.

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Wavelength (nm)	$ξ$ (µm)	$F$ (mm)	$R$ (mm)	$P_{σ}$ (µm)
15.83	84.4(0.2)	299.9(0.8)	285(17)	9.9(1.1)
15.89	85.4(0.1)	300.0(0.5)	297(14)	10.4(0.8)
15.94	86.0(0.1)	300.5(0.5)	323(14)	12.1(0.8)
16.00	87.2(0.1)	301.0(0.5)	300(14)	10.6(0.9)
16.06	87.8(0.1)	300.6(0.6)	291(14)	10.9(0.9)
16.12	88.4(0.1)	301.3(0.6)	324(15)	12.5(0.9)
16.18	89.0(0.1)	300.3(0.5)	309(14)	11.2(0.9)
16.20	89.4(0.1)	299.8(0.5)	315(15)	12.0(0.9)
16.23	90.0(0.2)	300.5(0.6)	328(15)	13.3(0.9)
16.28	90.3(0.1)	300.5(0.6)	308(14)	11.6(0.9)
16.32	91.4(0.1)	299.0(0.5)	301(14)	11.2(0.9)
16.40	92.2(0.2)	299.8(0.5)	299(14)	12.1(0.9)
16.47	92.5(0.2)	300.0(0.6)	280(14)	10.6(0.9)
16.53	92.6(0.1)	299.0(0.5)	297(14)	11.2(0.8)
16.61	93.2(0.1)	298.9(0.5)	296(14)	10.6(0.9)
16.64	88.9(0.2)	299.6(0.6)	318(15)	11.1(1.0)
16.69	94.1(0.2)	300.8(0.6)	299(14)	11.3(0.9)
16.71	89.5(0.1)	300.3(0.5)	312(14)	11.9(0.8)
16.75	90.5(0.1)	300.0(0.5)	306(14)	11.3(0.8)
16.82	92.2(0.1)	299.7(0.5)	305(14)	11.9(0.9)
16.89	91.4(0.2)	300.9(0.6)	303(15)	11.6(0.9)
16.95	91.4(0.2)	300.3(0.5)	299(15)	11.5(0.9)

Wavelength (nm)	$ξ$ (µm)	$F$ (mm)	$R$ (mm)	$P_{σ}$ (µm)
17.02	93.1(0.1)	299.6(0.5)	306(14)	11.5(0.8)
17.04	93.3(0.1)	299.5(0.5)	325(13)	12.9(0.8)
17.07	93.4(0.1)	300.3(0.5)	323(13)	12.4(0.8)
17.12	94.2(0.1)	300.1(0.5)	333(13)	13.1(0.8)
17.15	95.0(0.1)	301.0(0.5)	315(13)	12.1(0.8)
17.23	95.8(0.1)	300.9(0.5)	327(13)	12.5(0.8)
17.31	96.3(0.1)	300.5(0.5)	333(13)	12.7(0.8)
17.38	96.8(0.1)	300.8(0.5)	324(13)	12.0(0.8)
17.47	97.5(0.1)	300.6(0.5)	333(13)	12.7(0.8)
17.53	92.7(0.1)	301.2(0.5)	330(13)	12.5(0.8)
17.55	97.8(0.1)	301.2(0.5)	329(13)	12.5(0.8)
17.61	93.5(0.1)	300.9(0.5)	318(13)	12.1(0.8)
17.66	94.6(0.1)	301.0(0.5)	321(13)	12.2(0.8)
17.74	95.4(0.1)	301.1(0.5)	325(13)	12.0(0.8)
17.81	96.2(0.1)	301.3(0.5)	333(13)	12.4(0.8)
17.87	96.9(0.1)	301.2(0.5)	319(13)	11.8(0.8)
17.93	97.9(0.1)	300.7(0.5)	328(13)	12.1(0.8)
17.96	98.1(0.1)	300.4(0.5)	324(13)	12.1(0.8)
18.00	98.6(0.1)	301.2(0.5)	344(13)	13.2(0.8)
18.05	99.2(0.1)	300.2(0.5)	315(13)	11.2(0.8)
18.08	99.8(0.1)	300.8(0.5)	329(13)	12.6(0.8)
18.16	100.6(0.1)	300.1(0.5)	341(13)	13.1(0.8)
18.24	101.1(0.1)	300.5(0.5)	331(13)	12.5(0.8)
18.33	101.5(0.1)	300.7(0.5)	344(13)	13.1(0.8)
18.42	102.2(0.1)	300.4(0.5)	331(13)	12.2(0.8)
18.51	102.5(0.1)	300.0(0.5)	332(13)	11.6(0.8)
18.54	97.8(0.1)	300.1(0.5)	337(14)	12.7(0.8)
18.63	99.0(0.1)	300.2(0.5)	315(13)	11.6(0.8)
18.68	99.8(0.1)	299.9(0.5)	334(13)	12.2(0.8)
18.76	100.8(0.1)	300.4(0.5)	336(14)	12.6(0.8)
18.83	101.3(0.1)	300.3(0.5)	330(13)	12.0(0.8)
18.90	102.0(0.1)	300.3(0.5)	335(14)	12.3(0.8)
18.95	103.1(0.1)	299.7(0.5)	325(13)	11.3(0.8)
18.98	103.3(0.1)	299.8(0.5)	334(14)	12.3(0.8)
19.02	104.0(0.1)	299.6(0.5)	330(14)	11.6(0.8)
19.07	104.4(0.1)	299.2(0.5)	332(14)	11.7(0.8)
19.11	105.1(0.1)	298.9(0.5)	332(14)	11.7(0.8)
19.20	106.1(0.1)	299.3(0.5)	337(13)	12.2(0.8)
19.28	106.5(0.1)	299.0(0.5)	319(13)	11.1(0.8)
19.37	107.0(0.1)	299.1(0.5)	325(13)	11.3(0.8)
19.47	107.5(0.1)	299.1(0.5)	331(13)	11.9(0.8)
19.57	107.9(0.1)	299.0(0.5)	326(13)	11.4(0.8)

Wavelength (nm)	$ξ$ (µm)	$F$ (mm)	$R$ (mm)	$P_{σ}$ (µm)
15.83	84.4(0.2)	299.9(0.8)	285(17)	9.9(1.1)
15.89	85.4(0.1)	300.0(0.5)	297(14)	10.4(0.8)
15.94	86.0(0.1)	300.5(0.5)	323(14)	12.1(0.8)
16.00	87.2(0.1)	301.0(0.5)	300(14)	10.6(0.9)
16.06	87.8(0.1)	300.6(0.6)	291(14)	10.9(0.9)
16.12	88.4(0.1)	301.3(0.6)	324(15)	12.5(0.9)
16.18	89.0(0.1)	300.3(0.5)	309(14)	11.2(0.9)
16.20	89.4(0.1)	299.8(0.5)	315(15)	12.0(0.9)
16.23	90.0(0.2)	300.5(0.6)	328(15)	13.3(0.9)
16.28	90.3(0.1)	300.5(0.6)	308(14)	11.6(0.9)
16.32	91.4(0.1)	299.0(0.5)	301(14)	11.2(0.9)
16.40	92.2(0.2)	299.8(0.5)	299(14)	12.1(0.9)
16.47	92.5(0.2)	300.0(0.6)	280(14)	10.6(0.9)
16.53	92.6(0.1)	299.0(0.5)	297(14)	11.2(0.8)
16.61	93.2(0.1)	298.9(0.5)	296(14)	10.6(0.9)
16.64	88.9(0.2)	299.6(0.6)	318(15)	11.1(1.0)
16.69	94.1(0.2)	300.8(0.6)	299(14)	11.3(0.9)
16.71	89.5(0.1)	300.3(0.5)	312(14)	11.9(0.8)
16.75	90.5(0.1)	300.0(0.5)	306(14)	11.3(0.8)
16.82	92.2(0.1)	299.7(0.5)	305(14)	11.9(0.9)
16.89	91.4(0.2)	300.9(0.6)	303(15)	11.6(0.9)
16.95	91.4(0.2)	300.3(0.5)	299(15)	11.5(0.9)

Wavelength (nm)	$ξ$ (µm)	$F$ (mm)	$R$ (mm)	$P_{σ}$ (µm)
17.02	93.1(0.1)	299.6(0.5)	306(14)	11.5(0.8)
17.04	93.3(0.1)	299.5(0.5)	325(13)	12.9(0.8)
17.07	93.4(0.1)	300.3(0.5)	323(13)	12.4(0.8)
17.12	94.2(0.1)	300.1(0.5)	333(13)	13.1(0.8)
17.15	95.0(0.1)	301.0(0.5)	315(13)	12.1(0.8)
17.23	95.8(0.1)	300.9(0.5)	327(13)	12.5(0.8)
17.31	96.3(0.1)	300.5(0.5)	333(13)	12.7(0.8)
17.38	96.8(0.1)	300.8(0.5)	324(13)	12.0(0.8)
17.47	97.5(0.1)	300.6(0.5)	333(13)	12.7(0.8)
17.53	92.7(0.1)	301.2(0.5)	330(13)	12.5(0.8)
17.55	97.8(0.1)	301.2(0.5)	329(13)	12.5(0.8)
17.61	93.5(0.1)	300.9(0.5)	318(13)	12.1(0.8)
17.66	94.6(0.1)	301.0(0.5)	321(13)	12.2(0.8)
17.74	95.4(0.1)	301.1(0.5)	325(13)	12.0(0.8)
17.81	96.2(0.1)	301.3(0.5)	333(13)	12.4(0.8)
17.87	96.9(0.1)	301.2(0.5)	319(13)	11.8(0.8)
17.93	97.9(0.1)	300.7(0.5)	328(13)	12.1(0.8)
17.96	98.1(0.1)	300.4(0.5)	324(13)	12.1(0.8)
18.00	98.6(0.1)	301.2(0.5)	344(13)	13.2(0.8)
18.05	99.2(0.1)	300.2(0.5)	315(13)	11.2(0.8)
18.08	99.8(0.1)	300.8(0.5)	329(13)	12.6(0.8)
18.16	100.6(0.1)	300.1(0.5)	341(13)	13.1(0.8)
18.24	101.1(0.1)	300.5(0.5)	331(13)	12.5(0.8)
18.33	101.5(0.1)	300.7(0.5)	344(13)	13.1(0.8)
18.42	102.2(0.1)	300.4(0.5)	331(13)	12.2(0.8)
18.51	102.5(0.1)	300.0(0.5)	332(13)	11.6(0.8)
18.54	97.8(0.1)	300.1(0.5)	337(14)	12.7(0.8)
18.63	99.0(0.1)	300.2(0.5)	315(13)	11.6(0.8)
18.68	99.8(0.1)	299.9(0.5)	334(13)	12.2(0.8)
18.76	100.8(0.1)	300.4(0.5)	336(14)	12.6(0.8)
18.83	101.3(0.1)	300.3(0.5)	330(13)	12.0(0.8)
18.90	102.0(0.1)	300.3(0.5)	335(14)	12.3(0.8)
18.95	103.1(0.1)	299.7(0.5)	325(13)	11.3(0.8)
18.98	103.3(0.1)	299.8(0.5)	334(14)	12.3(0.8)
19.02	104.0(0.1)	299.6(0.5)	330(14)	11.6(0.8)
19.07	104.4(0.1)	299.2(0.5)	332(14)	11.7(0.8)
19.11	105.1(0.1)	298.9(0.5)	332(14)	11.7(0.8)
19.20	106.1(0.1)	299.3(0.5)	337(13)	12.2(0.8)
19.28	106.5(0.1)	299.0(0.5)	319(13)	11.1(0.8)
19.37	107.0(0.1)	299.1(0.5)	325(13)	11.3(0.8)
19.47	107.5(0.1)	299.1(0.5)	331(13)	11.9(0.8)
19.57	107.9(0.1)	299.0(0.5)	326(13)	11.4(0.8)

Measurement of complex refractive index with tunable extreme ultraviolet high harmonic source

Abstract

1. Introduction

2. Method

3. Discussion

4. Conclusion

Appendix A: A detailed schematic of the experimental setup

Appendix B: Effect of the beam pointing

Appendix C: Fitting parameter errors

Appendix D: Effect of the slit shape

Funding

Acknowledgments

Disclosures

References

Cited By

Figures (5)

Tables (2)

Equations (6)

Optics Express