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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26363–26375
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Fluence scan: an unexplored property of a laser beam

Jaromír Chalupský, Tomáš Burian, Věra Hájková, Libor Juha, Tomáš Polcar, Jérôme Gaudin, Mitsuru Nagasono, Ryszard Sobierajski, Makina Yabashi, and Jacek Krzywinski  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26363-26375 (2013)
http://dx.doi.org/10.1364/OE.21.026363


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Abstract

We present an extended theoretical background of so-called fluence scan (f-scan or F-scan) method, which is frequently being used for offline characterization of focused short-wavelength (EUV, soft X-ray, and hard X-ray) laser beams [J. Chalupský et al., Opt. Express 18, 27836 (2010)]. The method exploits ablative imprints in various solids to visualize iso-fluence beam contours at different fluence and/or clip levels. An f-scan curve (clip level as a function of the corresponding iso-fluence contour area) can be generated for a general non-Gaussian beam. As shown in this paper, fluence scan encompasses important information about energy distribution within the beam profile, which may play an essential role in laser-matter interaction research employing intense non-ideal beams. Here we for the first time discuss fundamental properties of the f-scan function and its inverse counterpart (if-scan). Furthermore, we extensively elucidate how it is related to the effective beam area, energy distribution, and to the so called Liu’s dependence [J. M. Liu, Opt. Lett. 7, 196 (1982)]. A new method of the effective area evaluation based on weighted inverse f-scan fit is introduced and applied to real data obtained at the SCSS (SPring-8 Compact SASE Source) facility.

© 2013 Optical Society of America

1. Introduction

Rigorous spot-size and fluence profile characterization of focused short-wavelength (EUV, soft and hard X-ray) laser beams belongs to important prerequisites for experiments employing such sources. Contrary to conventional UV/vis/NIR lasers, which are nowadays capable of producing almost perfect Gaussian beams [1

1. A. E. Siegman, Lasers (University Science Books, Mill Valley, California 1986).

], the homogeneity of short-wavelength laser beams still requires some improvements. Due to fundamental (largely single-pass) mechanisms of X-ray lasing (e.g. ASE – Amplified Spontaneous Emission or SASE – Self-amplified Spontaneous Emission) and absence of resonator cavity, the short-wavelength laser beams often exhibit non-uniformities in their intensity profiles and wave-front. Furthermore, a specific behavior of short-wavelength and highly coherent radiation at “imperfect” reflective or refractive optical surfaces may introduce additional distortions to the laser beam. Therefore, X-ray laser beams need to be treated as non-Gaussian [2

2. A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), pp. 184–199, paper MQ1. http://www.opticsinfobase.org/abstract.cfm?uri=DLAI-1998-MQ1

] rather than Gaussian.

An existence of a sharp and invariable ablation threshold is the most important prerequisite for all methods utilizing ablation imprints. Since applications of PMMA targets are spectrally restricted to EUV and soft X-ray radiation below the carbon K-edge, a novel fluence scan method [10

10. J. Chalupský, J. Krzywinski, L. Juha, V. Hájková, J. Cihelka, T. Burian, L. Vysín, J. Gaudin, A. Gleeson, M. Jurek, A. R. Khorsand, D. Klinger, H. Wabnitz, R. Sobierajski, M. Störmer, K. Tiedtke, and S. Toleikis, “Spot size characterization of focused non-Gaussian X-ray laser beams,” Opt. Express 18(26), 27836–27845 (2010). [CrossRef] [PubMed]

] was developed. It employs the fact that the ablation threshold contour imprinted on a flat target surface visualizes an iso-fluence contour of the beam at fixed threshold fluence Fth, i.e. beam cross-section at clip level f = Fth/F0 of maximum. By varying the laser pulse energy Epulse (and thus the peak fluence), we record iso-fluence contours at different threshold-to-peak fluence ratios f (different fractional levels of maximum) and scan the beam in terms of fluence (from here the designation “fluence scan” follows). Values of the threshold-to-peak fluence ratio f always fall into a left-open and right-closed interval ranging from zero to unity and have a meaning of the so called normalized fluence. For the purposes of normalization, the threshold pulse energy Eth must be known (see [10

10. J. Chalupský, J. Krzywinski, L. Juha, V. Hájková, J. Cihelka, T. Burian, L. Vysín, J. Gaudin, A. Gleeson, M. Jurek, A. R. Khorsand, D. Klinger, H. Wabnitz, R. Sobierajski, M. Störmer, K. Tiedtke, and S. Toleikis, “Spot size characterization of focused non-Gaussian X-ray laser beams,” Opt. Express 18(26), 27836–27845 (2010). [CrossRef] [PubMed]

] for more details) since f = Eth/Epulse. By plotting the normalized fluence f as a function of the corresponding ablation contour area S, we obtain normalized fluence scan (f-scan) curve f(S), which has several important properties thoroughly discussed in this paper. Contrary to the former method of the beam profile reconstruction exploiting ablative imprints in PMMA, the fluence scan method greatly facilitates issues connected with in-focus X-ray laser beam characterization. Time consuming AFM measurements are not needed as a standard optical microscopy can be used for ablation (threshold) contours inspection. Furthermore, ablation contours occur at relatively low and fixed threshold fluence which efficiently prevents thermal and hydrodynamic processes from a harmful influence on results. This essentially extends accessible dynamic range. Finally, spectral range of utilization can be flexibly varied through a proper choice of the target material.

It should be noted that the first ablation imprints method was reported by Liu [13

13. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]

] in 1982. In this study a silicon wafer was used for focused Gaussian beam characterization in visible and ultraviolet spectral domain. It was shown that the slope of the so called Liu’s plot (designation for the relation between ablation contour area and natural pulse energy logarithm) represents the beam spot area at 1/e of maximum. Nevertheless, Liu’s approach was primarily developed for Gaussian beams as their Liu’s plots are always linear, whereas non-Gaussian Liu’s plots are generally nonlinear. In this work we focus on fundamental properties of a general non-Gaussian fluence scan, its relation to the respective Liu’s plot, and energy distribution within the beam profile. Furthermore, a new method of weighted inverse f-scan fitting is developed and applied to real data obtained at the SCSS (SPring-8 Compact SASE Source) facility [14

14. T. Shintake, H. Tanaka, T. Hara, T. Tanaka, K. Togawa, M. Yabashi, Y. Otake, Y. Asano, T. Bizen, T. Fukui, S. Goto, A. Higashiya, T. Hirono, N. Hosoda, T. Inagaki, S. Inoue, M. Ishii, Y. Kim, H. Kimura, M. Kitamura, T. Kobayashi, H. Maesaka, T. Masuda, S. Matsui, T. Matsushita, X. Marechal, M. Nagasono, H. Ohashi, T. Ohata, T. Ohshima, K. Onoe, K. Shirasawa, T. Takagi, S. Takahashi, M. Takeuchi, K. Tamasaku, R. Tanaka, Y. Tanaka, T. Tanikawa, T. Togashi, S. Wu, A. Yamashita, K. Yanagida, C. Zhang, H. Kitamura, and T. Ishikawa, “A compact free-electron laser for generating coherent radiation in the extreme ultraviolet region,” Nat. Photonics 2(9), 555–559 (2008). [CrossRef]

]. The effective area of the focused SCSS beam at wavelength of 60 nm is evaluated in this paper.

2. Theory

Let us first define the spatial fluence (time-integrated intensity) distribution of a general non-Gaussian beam propagating along the z-axis in Cartesian coordinates as F(x,y,z) = F0(z)f(x,y,z). Here F0(z) is the peak fluence and f(x,y,z) is the normalized fluence profile. As we do not study phenomena connected with beam propagation, we can focus on the transverse beam profile f(x,y) at a given z-position; therefore, we do not use the z-coordinate in the following equations. By definition, the normalized fluence profile f(x,y) satisfies a condition 0 ≤f(x,y) ≤ 1 for all points in the transverse xy-plane. By integrating the fluence profile F(x,y) and normalized fluence profile f(x,y) over the entire transverse plane, we obtain pulse energy and the effective beam area [10

10. J. Chalupský, J. Krzywinski, L. Juha, V. Hájková, J. Cihelka, T. Burian, L. Vysín, J. Gaudin, A. Gleeson, M. Jurek, A. R. Khorsand, D. Klinger, H. Wabnitz, R. Sobierajski, M. Störmer, K. Tiedtke, and S. Toleikis, “Spot size characterization of focused non-Gaussian X-ray laser beams,” Opt. Express 18(26), 27836–27845 (2010). [CrossRef] [PubMed]

,15

15. ISO 11254–1:2000, “Laser and laser-related equipment - Determination of laser-induced damage threshold of optical surfaces - Part 1: 1-on-1 test

], respectively. Hence we can write a relation:
Epulse=R2F(x,y)dxdy=F0R2f(x,y)dxdy=F0Aeff,
(1)
which is applicable to a general beam, whether it be Gaussian or non-Gaussian.

For the purposes of illustration, normalized fluence profiles of an ideal Gaussian beam and exemplary simple non-Gaussian beam are depicted in Fig. 1
Fig. 1 (a) Normalized fluence profile of an ideal Gaussian beam defined as f(r) = exp(−|r|2/ρ2), where ρ = 7.02 μm is the radius at 1/e of maximum and r = (x,y) is the transverse coordinate vector. (b) Normalized fluence profile of a simple non-Gaussian beam defined as f(r) = f1exp(−|r|2/ρ12) + f2exp(−|r|2/ρ22), where f1 = 0.7, ρ1 = 3.99 μm, f2 = 0.3, and ρ2 = 11.28 μm.
. Effective areas of these two beam profiles are identical (Aeff = 155 μm2), albeit full widths at half maxima (FWHM) and overall beam shapes may significantly differ. This is a consequence of the non-Gaussian nature of the beam in Fig. 1(b), which has been modeled as an incoherent sum of a narrow Gaussian-like central peak and broad surrounding Gaussian-like background.

In the following we use these two representative model beam profiles as illustrative examples. Firstly, we define the normalized and non-normalized fluence scan (f-scan and F-scan) and the corresponding inverse counterparts (if-scan and iF-scan). Secondly, we consider statistical properties of the fluence scan, which will immediately lead us to a description of the effective area and energy distribution within the beam profile. Next, we make a note on the connection between the fluence scan and the Liu’s plot. Eventually, we introduce a new method of the so called weighted inverse f-scan fitting, mathematically prove its correctness, and apply this method to real data.

2.1 Fluence and inverse fluence scan

In Fig. 2
Fig. 2 Normalized fluence scan (f-scan) and corresponding cumulative f-scan of the ideal Gaussian beam (black solid curve and black dashed curve) and simple non-Gaussian beam (red solid curve and red dashed curve).
normalized fluence scans of the two model beam profiles are depicted. Normalized fluence scan f(S) is generally a monotonically decreasing function of S (within the definition domain 0 ≤ S < ∞) with a global maximum f(0) = 1. Consequently, this implies an existence of the so called inverse normalized fluence scan S(f), i.e. if-scan, which is defined in an interval 0 < f ≤ 1 (the iso-fluence contour area diverges as f tends to zero). Up to now we have been concerned with a normalized fluence scan. Analogously, a non-normalized fluence scan (F-scan or just fluence scan) can be defined for single pulses with known pulse energy Epulse through a relation F(S) = F0 f(S), where F0 = Epulse/Aeff is the peak fluence. Except for the normalization factor F0, the non-normalized fluence scan has the same properties as f-scan; therefore, inverse (non-normalized) fluence scan S(F), i.e. iF-scan, can be defined in an interval 0 < FF0. The most important property of the above introduced functions is that the area below their curves corresponds to the effective area, in case of normalized scans (f-scan and if-scan), and pulse energy, in case of non-normalized scans (F-scan and iF-scan). Hence we can write:

Aeff=0f(S)dS=01S(f)df,
(3a)
Epulse=F0Aeff=0F(S)dS=0F0S(F)dF.
(3b)

2.2 Effective area and energy distribution within the beam profile

Such non-Gaussian inhomogeneities need to be considered in various laser-matter experiments attempting to study nonlinear intensity-dependent phenomena with non-ideal beams. Enumerating the cumulative effective area (energy) density (analogous to cumulative distribution function) as a function of normalized fluence f (fluence F) we figure out (see dashed curves in Fig. 3) that a Gaussian profile contains 50% of the effective area (pulse energy) in the “low-intensity” interval 0 < f ≤ 1/2 (0 < FF0/2), whereas 75% of the effective area (pulse energy) is accommodated in the same interval in case of our model simple non-Gaussian profile. Such an imbalance may greatly distort results of various (e.g. spectroscopic) experiments if incorrect, typically Gaussian, assumptions of the beam profile are a priori accepted. Unlike Gaussian beam, the non-Gaussian disproportionality may lead to a prevailing contribution of low-intensity-induced, e.g. fluorescence, signal (within the interval 0 < f ≤ 1/2) over the complementary high-intensity-induced signal acquired during the experiment. Precise spectroscopic measurements have demonstrated that considerably better agreement between numerical simulations and measurements can be achieved if real beam profiles are taken into account [16

16. S. M. Vinko, O. Ciricosta, B. I. Cho, K. Engelhorn, H. K. Chung, C. R. D. Brown, T. Burian, J. Chalupský, R. W. Falcone, C. Graves, V. Hájková, A. Higginbotham, L. Juha, J. Krzywinski, H. J. Lee, M. Messerschmidt, C. D. Murphy, Y. Ping, A. Scherz, W. Schlotter, S. Toleikis, J. J. Turner, L. Vysin, T. Wang, B. Wu, U. Zastrau, D. Zhu, R. W. Lee, P. A. Heimann, B. Nagler, and J. S. Wark, “Creation and diagnosis of a solid-density plasma with an X-ray free-electron laser,” Nature 482(7383), 59–62 (2012). [CrossRef] [PubMed]

]. In this particular experiment X-ray emission from warm and dense aluminum plasma created by focused LCLS (Linac Coherent Light Source) beam was studied and compared to numerical simulations. Real energy density distributions, measured by means of ablative imprints in lead tungstate (PbWO4), were used as input values for the simulation code.

Dashed curves in Fig. 2 represent cumulative f-scans (or cumulative effective area densities) as functions of iso-fluence contour area. Cumulative f-scan (F-scan) can be considered as a generalization of the so called “power in the bucket” function formerly addressed by Siegman [2

2. A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), pp. 184–199, paper MQ1. http://www.opticsinfobase.org/abstract.cfm?uri=DLAI-1998-MQ1

] as it quantifies a fractional amount of the effective area (energy) being contained within a closed iso-fluence contour. Evidently, cumulative f-scan (F-scan) converges to the effective beam area (pulse energy) as the iso-fluence contour area tends to infinity. The same applies to cumulative effective area (energy) density in Fig. 3 as the normalized fluence tends to unity (fluence tends to the peak fluence F0).

2.3 Relation between the fluence scan and Liu’s plot

By plotting the ablation contour area S as a function of natural pulse energy logarithm ln(Epulse), we obtain the so called Liu’s plot [13

13. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]

]. Ablation threshold energy Eth can be obtained through an appropriate, in most cases linear, extrapolation of S(ln(Epulse)) to zero ablation contour area (no ablative damage), i.e. S = 0 μm2. Without loss of generality we can express the Liu’s dependence as a function of the peak-to-threshold fluence ratio p = F0/Fth = Epulse/Eth, i.e. as S(ln(p)). Using a substitution u = ln(p), we can express the slope of the Liu’s plot by means of the first derivative as A(u) = duS(u). Provided that the ablation contour corresponds to the iso-fluence beam contour at normalized fluence level f = 1/p = exp(−u), the slope A(u) stands for the beam spot area at 1/e of maximum. This statement usually (but not exclusively) holds true for Gaussian beams as the slope is independent of pulse energy, i.e. A(u) = πρ2 = Aeff. Non-Gaussian Liu’s plots are generally nonlinear, as shown for example in Fig. 4
Fig. 4 Liu’s plots and corresponding first derivatives derived from the ideal Gaussian beam (black solid curve and black dashed curve) and simple non-Gaussian beam (red solid curve and red dashed curve).
, and so the corresponding derivatives are not constant, i.e. assigned a single value attributable to the beam spot area. However, with regard to the second integral in Eq. (3a), we can write:
Aeff=01S(f)df=0S(u)exp(u)du=p.p.0dSduexp(u)du=0A(u)exp(u)du,
(5)
whence it follows that the effective area can be considered as a mean value of ablation (iso-fluence) contour S(u) or first derivative of the Liu’s dependence A(u) in the exponential distribution ~exp(−u). Here the absolute term emerging from the per partes (p.p.) integration is zero.

Liu’s plots and respective derivatives derived for the Gaussian and simple non-Gaussian model beams are depicted in Fig. 4. Noticeably, the non-Gaussian Liu’s plot derivative varies in an interval approximately bounded by effective areas of the two constitutive Gaussian modes (A1 < A(u) < A2), whereas the Gaussian Liu’s plot derivative is constant and equal to the effective beam area (A(u) = AG = Aeff).

2.4 Weighted inverse f-scan fit

Ideally, if the normalized fluence scan is known in its continuous form, the effective area can be evaluated by means of Eq. (3a). However, real f-scan measurements are usually represented by a discrete, very often noisy and incomplete, sequence {fi, Si}i = 1..N of N data points. Each data point corresponds to a single ablative imprint created by an individual pulse of variable energy. Albeit not measured, the data point {1, 0} can be artificially but legally added to the data set as the fluence scan is normalized. Discretizing the integral relation (3a), the effective area can be calculated by means of numerical integration, e.g. by the trapezoidal rule of integration [10

10. J. Chalupský, J. Krzywinski, L. Juha, V. Hájková, J. Cihelka, T. Burian, L. Vysín, J. Gaudin, A. Gleeson, M. Jurek, A. R. Khorsand, D. Klinger, H. Wabnitz, R. Sobierajski, M. Störmer, K. Tiedtke, and S. Toleikis, “Spot size characterization of focused non-Gaussian X-ray laser beams,” Opt. Express 18(26), 27836–27845 (2010). [CrossRef] [PubMed]

].

It would be worthy to determine the effective area and the measurement error as a fitting parameter. Though not generally, the model function (2b) can be used in some particular cases. Usually, but not exclusively, the model function (2a) is to be applied to Gaussian beams; however, it can be proven that the corresponding inverse f-scan SG(f) = −AGln(f) can be fitted to a general (non-Gaussian) inverse f-scan S(f) through the least squares method employing a suitably chosen weight w(f) = −1/ln(f). First, we express the weighted sum of squares χw2(AG) in a continuous form as:
χw2(AG)=01w(f)[S(f)SG(f)]2df=011ln(f)[S(f)+AGln(f)]2df.
(6a)
The weighted sum of squares can be minimized through differentiation with respect to the fitting parameter AG. The first derivative must equal zero in a local extreme; hence, interchanging the order of the integral and derivative and using Eq. (3a), we can write:
dχw2dAG=001S(f)df=Aeff=AG01ln(f)df=AG.
(6b)
The second derivative of χw2(AG) with respect to AG is positive which indicates that minimum has been found. An equivalence between the fitting parameter AG and effective area Aeff is hereby proven, provided that the fitting is done in terms of the weighted least squares method.

In order to apply the method of weighted inverse f-scan fitting to a discrete sequence of measured data points, the integral expression (6a) must be properly discretized and weight factors must be suitably defined. Let the sequence {fi, Si}i = 1..N be sorted in an ascending order with respect to fi in an interval 0 < fi ≤ 1; values falling outside this interval must be excluded from the data set. The first data point {f1, S1} corresponds to an ablative imprint obtained at the highest pulse energy, whereas the last one {fN, SN} = {1, 0} represents the artificially added “zero ablation contour” at the threshold pulse energy. By means of the rectangle rule of integration, the weighted sum of squares in Eq. (6a) is to be expressed as:
χw2(AG)=i=1Nwi[Si+AGln(fi)]2,
(7a)
where the corresponding weight factors are of the following form:
wi=|f1/ln(f1);for:i=1(fifi1)/ln(fi);for:1<i<N0;for:i=N
(7b)
Without loss of generality the last weight factor wN can equal to zero as it generally holds true that [SNSG(fN)]2 = 0. More accurate expressions can be obtained if trapezoidal or higher-order integration rules are used. The fitting parameter AG, which has been proven to be equal to the effective area, is then to be determined by minimizing the weighted sum of squares in Eq. (7a). If applied to our model beams in Fig. 1, the method results in Aeff = (155 ± 0) μm2 and Aeff = (154.3 ± 1.5) μm2 for the ideal Gaussian and simple non-Gaussian beam, respectively.

3. Results and discussion

The method of weighted inverse f-scan fit has been applied to experimental data obtained at the SCSS (SPring-8 Compact SASE Source, RIKEN/Japan) facility [14

14. T. Shintake, H. Tanaka, T. Hara, T. Tanaka, K. Togawa, M. Yabashi, Y. Otake, Y. Asano, T. Bizen, T. Fukui, S. Goto, A. Higashiya, T. Hirono, N. Hosoda, T. Inagaki, S. Inoue, M. Ishii, Y. Kim, H. Kimura, M. Kitamura, T. Kobayashi, H. Maesaka, T. Masuda, S. Matsui, T. Matsushita, X. Marechal, M. Nagasono, H. Ohashi, T. Ohata, T. Ohshima, K. Onoe, K. Shirasawa, T. Takagi, S. Takahashi, M. Takeuchi, K. Tamasaku, R. Tanaka, Y. Tanaka, T. Tanikawa, T. Togashi, S. Wu, A. Yamashita, K. Yanagida, C. Zhang, H. Kitamura, and T. Ishikawa, “A compact free-electron laser for generating coherent radiation in the extreme ultraviolet region,” Nat. Photonics 2(9), 555–559 (2008). [CrossRef]

], which has been recently operated as a test facility for the new SACLA (SPring-8 Angstrom Compact free-electron LAser, RIKEN/Japan) laser [17

17. T. Ishikawa, H. Aoyagi, T. Asaka, Y. Asano, N. Azumi, T. Bizen, H. Ego, K. Fukami, T. Fukui, Y. Furukawa, S. Goto, H. Hanaki, T. Hara, T. Hasegawa, T. Hatsui, A. Higashiya, T. Hirono, N. Hosoda, M. Ishii, T. Inagaki, Y. Inubushi, T. Itoga, Y. Joti, M. Kago, T. Kameshima, H. Kimura, Y. Kirihara, A. Kiyomichi, T. Kobayashi, C. Kondo, T. Kudo, H. Maesaka, X. M. Marechal, T. Masuda, S. Matsubara, T. Matsumoto, T. Matsushita, S. Matsui, M. Nagasono, N. Nariyama, H. Ohashi, T. Ohata, T. Ohshima, S. Ono, Y. Otake, C. Saji, T. Sakurai, T. Sato, K. Sawada, T. Seike, K. Shirasawa, T. Sugimoto, S. Suzuki, S. Takahashi, H. Takebe, K. Takeshita, K. Tamasaku, H. Tanaka, R. Tanaka, T. Tanaka, T. Togashi, K. Togawa, A. Tokuhisa, H. Tomizawa, K. Tono, S. Wu, M. Yabashi, M. Yamaga, A. Yamashita, K. Yanagida, C. Zhang, T. Shintake, H. Kitamura, and N. Kumagai, “A compact X-ray free-electron laser emitting in the sub-ångström region,” Nat. Photonics 6(8), 540–544 (2012). [CrossRef]

]. SCSS was successfully put into operation in 2006 when self-amplified spontaneous emission (SASE) at wavelength of 49 nm, i.e. in the extreme ultraviolet (EUV) spectral domain, was observed [18

18. T. Shintake and SCSS Team, “Status of Japanese XFEL Project and SCSS test accelerator,” Proc. FEL 2006, BESSY, Berlin, Germany, 33–36 (2006).

]. The major purpose of the SCSS facility was to develop and test novel technologies for its hard X-ray successor SACLA, which started operation in 2011 and currently runs in user mode. Newly developed components, namely in-vacuum short-period undulator with variable gap, high-gradient C-band accelerator cavities, and low-emittance thermionic electron gun [17

17. T. Ishikawa, H. Aoyagi, T. Asaka, Y. Asano, N. Azumi, T. Bizen, H. Ego, K. Fukami, T. Fukui, Y. Furukawa, S. Goto, H. Hanaki, T. Hara, T. Hasegawa, T. Hatsui, A. Higashiya, T. Hirono, N. Hosoda, M. Ishii, T. Inagaki, Y. Inubushi, T. Itoga, Y. Joti, M. Kago, T. Kameshima, H. Kimura, Y. Kirihara, A. Kiyomichi, T. Kobayashi, C. Kondo, T. Kudo, H. Maesaka, X. M. Marechal, T. Masuda, S. Matsubara, T. Matsumoto, T. Matsushita, S. Matsui, M. Nagasono, N. Nariyama, H. Ohashi, T. Ohata, T. Ohshima, S. Ono, Y. Otake, C. Saji, T. Sakurai, T. Sato, K. Sawada, T. Seike, K. Shirasawa, T. Sugimoto, S. Suzuki, S. Takahashi, H. Takebe, K. Takeshita, K. Tamasaku, H. Tanaka, R. Tanaka, T. Tanaka, T. Togashi, K. Togawa, A. Tokuhisa, H. Tomizawa, K. Tono, S. Wu, M. Yabashi, M. Yamaga, A. Yamashita, K. Yanagida, C. Zhang, T. Shintake, H. Kitamura, and N. Kumagai, “A compact X-ray free-electron laser emitting in the sub-ångström region,” Nat. Photonics 6(8), 540–544 (2012). [CrossRef]

,18

18. T. Shintake and SCSS Team, “Status of Japanese XFEL Project and SCSS test accelerator,” Proc. FEL 2006, BESSY, Berlin, Germany, 33–36 (2006).

], made it possible to construct a compact X-ray free-electron laser, which routinely crosses the frontiers of the hard X-ray spectral domain. Nevertheless, both the SCSS and SACLA still belong to the family of linac-based free-electron lasers, sharing very similar conceptual design. In the following paragraphs we briefly describe fundamental principles of the SCSS facility [14

14. T. Shintake, H. Tanaka, T. Hara, T. Tanaka, K. Togawa, M. Yabashi, Y. Otake, Y. Asano, T. Bizen, T. Fukui, S. Goto, A. Higashiya, T. Hirono, N. Hosoda, T. Inagaki, S. Inoue, M. Ishii, Y. Kim, H. Kimura, M. Kitamura, T. Kobayashi, H. Maesaka, T. Masuda, S. Matsui, T. Matsushita, X. Marechal, M. Nagasono, H. Ohashi, T. Ohata, T. Ohshima, K. Onoe, K. Shirasawa, T. Takagi, S. Takahashi, M. Takeuchi, K. Tamasaku, R. Tanaka, Y. Tanaka, T. Tanikawa, T. Togashi, S. Wu, A. Yamashita, K. Yanagida, C. Zhang, H. Kitamura, and T. Ishikawa, “A compact free-electron laser for generating coherent radiation in the extreme ultraviolet region,” Nat. Photonics 2(9), 555–559 (2008). [CrossRef]

,18

18. T. Shintake and SCSS Team, “Status of Japanese XFEL Project and SCSS test accelerator,” Proc. FEL 2006, BESSY, Berlin, Germany, 33–36 (2006).

] and performance of its focusing optics [19

19. H. Ohashi, Y. Senba, M. Nagasono, M. Yabashi, K. Tono, T. Togashi, T. Kudo, H. Kishimoto, T. Miura, H. Kimura, and T. Ishikawa, “Performance of focusing mirror device in EUV beamline of SPring-8 Compact SASE Source (SCSS),” Nucl. Instrum. Methods Phys. Res. A 649(1), 163–165 (2011). [CrossRef]

].

The laser chain starts with an injector section which employs a CeB6 thermionic cathode as a source of electrons, being pre-accelerated by pulsed high-voltage. This leads to formation of individual electron bunches being further compressed in the longitudinal direction and accelerated up to 45 MeV with use of S-band accelerator modules. Pre-accelerated electron bunches are further propagated to a C-band linear accelerator (linac) section where 5712-MHz (C-band) radio-frequency electromagnetic field is synchronously applied. The effective electrical field can be as high as 35 MV/m; hence the electrons are forced to accelerate up to 250 MeV during one passage and at a relatively short distance. Linear accelerator also accommodates bunch compressors (magnetic chicanes) which compress the passing electron bunches in the longitudinal direction and thus raise the peak current. This is an important prerequisite for the subsequent SASE (self-amplified spontaneous emission) process occurring in undulators, placed just behind the linac section. The SCSS facility employs two in-vacuum short-period undulators with the undulator period of 15 mm. Static but alternating magnetic undulator field forces the electrons to oscillate in the transverse direction and to radiate spontaneously. Simultaneously, the generated electromagnetic field exerts additional transverse forces on the electron bunch causing significant modifications of the charge distribution. The electron bunch splits into micro-bunches which within a single micro-bunch radiate coherently. As the electron bunch propagates through the undulator, the radiated intensity exponentially increases until saturation is reached.

After leaving the undulator, the electron bunch is dumped in an absorber and the optical pulse further travels through an optical beamline towards photon diagnostics and focusing optics. Pulse energy can be flexibly varied with use of a gas-filled attenuator while being continuously monitored with a calibrated ion chamber [19

19. H. Ohashi, Y. Senba, M. Nagasono, M. Yabashi, K. Tono, T. Togashi, T. Kudo, H. Kishimoto, T. Miura, H. Kimura, and T. Ishikawa, “Performance of focusing mirror device in EUV beamline of SPring-8 Compact SASE Source (SCSS),” Nucl. Instrum. Methods Phys. Res. A 649(1), 163–165 (2011). [CrossRef]

]. For the purposes of additional attenuation, thin metallic foils can be utilized. The focusing element is located approx. 24 m downstream the undulator and consists of two separate focusing mirrors coated with a thin layer of silicon carbide (SiC). Both mirrors are operated in grazing incidence geometry in order to maximize the reflectivity. In Table 1

Table 1. Focusing mirrors at the SCSS facility1

table-icon
View This Table
specifications of both focusing mirrors are listed (see ref [19

19. H. Ohashi, Y. Senba, M. Nagasono, M. Yabashi, K. Tono, T. Togashi, T. Kudo, H. Kishimoto, T. Miura, H. Kimura, and T. Ishikawa, “Performance of focusing mirror device in EUV beamline of SPring-8 Compact SASE Source (SCSS),” Nucl. Instrum. Methods Phys. Res. A 649(1), 163–165 (2011). [CrossRef]

]. for more details).

Due to high incidence angles, grazing incidence optics is usually very sensitive to adjustment as even a small misalignment can imply aberrations, especially astigmatism and coma. Occurrence of aberrations usually leads to increased focal spot size and reduced peak fluence; however, focusing performance can be significantly improved by adjusting the mirrors appropriately. SCSS focusing optics was iteratively optimized in order to suppress aberrations to a minimum. Furthermore, the optimized focus size was measured with use of 10-μm scanning pinhole at wavelength of 60 nm. Horizontal and vertical full widths at half maximum (FWHM) were determined to be 26 μm and 22 μm, respectively [19

19. H. Ohashi, Y. Senba, M. Nagasono, M. Yabashi, K. Tono, T. Togashi, T. Kudo, H. Kishimoto, T. Miura, H. Kimura, and T. Ishikawa, “Performance of focusing mirror device in EUV beamline of SPring-8 Compact SASE Source (SCSS),” Nucl. Instrum. Methods Phys. Res. A 649(1), 163–165 (2011). [CrossRef]

].

During the experiment the SCSS was tuned at 60 nm within a bandwidth of 1%, average pulse energy was ~10 μJ, and pulse duration was ~100 fs. The source is able to work at maximum repetition rate of 60 Hz. The primary aim of the experiment was to investigate response of various solid-state targets to weakly penetrating EUV radiation, which mostly deposits in the near-surface layer. Initially, a 500-nm thin layer of poly(methyl methacrylate) spin-coated on a silicon wafer (Silson, UK) was used to characterize the incident focused beam by means of ablative imprints method. Among all the other tested materials, a Cu/Nb multilayer, consisting of 25 copper-niobium bilayers magnetron-sputtered on a silicon wafer (each individual layer is 30 nm thick; manufactured by T. Polcar, Czech Technical University in Prague), was irradiated under the same beam conditions. This allows not only to study the target response under well-defined beam conditions, but also to test the ablative imprints methods with use of two distinctly different materials.

The experiment was carried out in a movable vacuum chamber allowing longitudinal translation in range of several tens of centimeters across the focal region. Samples were mounted on a motorized triaxial stage enabling independent and micro-precise target movements in both the transverse and longitudinal direction. Samples were irradiated in the tight focus by individual laser shots (single-shot mode) and under normal incidence conditions.

Ablative imprints in both the PMMA and Cu/Nb multilayer are displayed in Fig. 5
Fig. 5 Ablative imprints in PMMA (a) and Cu/Nb multilayer (b) in dependence on increasing pulse energy. The images were obtained by means of Nomarski (DIC – differential interference contrast) microscopy and are in scale.
as an ascending sequence sorted with respect to increasing pulse energy. Evidently, at comparable pulse energies the ablative imprints in PMMA appear larger than imprints in Cu/Nb multilayer. This is a consequence of a significant difference in ablation threshold fluences. Ablation threshold fluence for PMMA was found to be as low as (6 ± 1) mJ/cm2, whereas ablation threshold fluence for Cu/Nb multilayer is (116 ± 7) mJ/cm2 at wavelength of 60 nm. Presuming a Gaussian laser pulse with FWHM of 100 fs, the ablation threshold can be quantified in terms of intensity as (56 ± 9) GW/cm2 and (1.09 ± 0.07) TW/cm2 for PMMA and Cu/Nb multilayer, respectively. Contrary to Cu/Nb multilayer, PMMA imprints are capable to visualize much larger iso-fluence contours, although equivalent laser pulses, carrying the same amount of energy, were used to damage the targets. Nonetheless, iso-fluence contours corresponding to equal normalized fluence levels are almost identical for both materials. Potential discrepancies are usually caused by shot-to-shot fluctuations of the beam and its profile (e.g. caused by positional and pointing jitter) originating in the source itself and being even more pronounced by vibrations of optical components. If apertures are placed into a jittering beam, the Airy diffraction pattern (see the PMMA imprint in Fig. 5(a) at 13.6 μJ) may undergo noticeable shot-to-shot changes.

It turns out that Cu/Nb multilayer performs very well at this particular wavelength and thus can be used for beam profile characterization. This can be supported by the corresponding inverse f-scan curve plotted in Fig. 6
Fig. 6 Inverse f-scans obtained from PMMA (black circles) and Cu/Nb (red circles) ablation imprints. The logarithmic curves (black and red solid curve) were fitted to experimental data by means of the weighted least squares method in order to measure the effective area of the beam.
which is almost identical to the if-scan obtained from PMMA ablation imprints. The effective areas Aeff, PMMA = (345 ± 18) μm2 and Aeff, Cu/Nb = (365 ± 22) μm2, measured by means of the weighted if-scan fitting, are in a very good agreement, albeit Cu/Nb data are evidently incomplete (low fluence data are missing). This is due to the fact that the weight factors in Eq. (7b) decline as the normalized fluence approaches zero; hence the beam tail is only lightly weighted and its contribution to the weighted sum of squares is reduced. On the contrary, the top part of the beam is heavily weighted since the weight factors increase as the normalized fluence tends to unity. Nevertheless, the best results can be obtained, provided that the domain of the if-scan function (0 < f ≤ 1) is uniformly covered with measured data points.

Once the (inverse) normalized fluence scan curve is known, the beam cross-section area at a half of maximum (a two-dimensional analogue of FWHM), i.e. the iso-fluence contour area S(1/2), can be evaluated and compared to the spot size measurements done with use of the scanning pinhole. From the horizontal and vertical full widths at half maximum reported in [19

19. H. Ohashi, Y. Senba, M. Nagasono, M. Yabashi, K. Tono, T. Togashi, T. Kudo, H. Kishimoto, T. Miura, H. Kimura, and T. Ishikawa, “Performance of focusing mirror device in EUV beamline of SPring-8 Compact SASE Source (SCSS),” Nucl. Instrum. Methods Phys. Res. A 649(1), 163–165 (2011). [CrossRef]

], we obtain the area of the corresponding elliptical contour SFWHM ≈449 μm2, whereas the f-scan measurements, done for the same wavelength, result in S(1/2) ≈235 μm2. The results seem to be markedly different; however, the discrepancy does not mean that one of the measurements was incorrect. The explanation resides in the non-Gaussian nature of the beam, largely caused by diffraction effects in this particular case. Ablative imprints in Fig. 5 clearly evidence an asymmetric beam shape which cannot be modeled with use of elliptical contours. Therefore, the value of SFWHM overestimates the real beam cross-section area at f = 1/2, albeit the horizontal and vertical full widths at half maximum could have been measured correctly (here we have to assume a negligible influence of the pointing and positional jitter on the scanning pinhole measurements). In case of a general non-Gaussian beam, FWHM provides only a partial and rather a qualitative measure of the real spot size. Rigorous spot size characterization would require FWHM measurements in all possible directions. Therefore, considering the value of SFWHM as an upper estimate, the area S(1/2) fulfills our expectations of the beam cross-section area at f = 1/2. The same applies to the measured effective area.

In order to derive the effective area (energy) density from a discontinuous f-scan (F-scan) measurement, an appropriate beam model must be chosen and fitted to f-scan (F-scan) data. Starting with the double-exponential model (2b), we immediately come to a conclusion that the measured f-scan tends rather to a single exponential dependence in this particular case, albeit the transverse beam profile is evidently non-Gaussian (see Fig. 5). By fitting the exponential model (2a) to all (Cu/Nb and PMMA) data merged together, we obtain the effective area Aeff = (339.0 ± 6.9) μm2. The effective area and energy density is then to be calculated according to Eqs. (2a), (4a), and (4b), whence it follows that the effective area as well as energy is almost uniformly distributed within the entire fluence interval 0 < f ≤ 1 and 0 < FF0, respectively. It is a surprising finding that even a strongly distorted non-Gaussian beam profile can (in some particular cases) have similar properties as an ideal Gaussian beam.

4. Conclusions

Acknowledgments

This work was partially funded by FP7 project RADINTERFACES (NMP3-SL-2011-263273). The Czech co-authors appreciate funding by grants LG13029, CZ.1.07/2.3.00/30.0057, 13-28721S, P108/11/1312, P205/11/0571, P208/10/2302, and M100101221. J.Ch. thanks to Academy of Sciences of the Czech Republic for postdoctoral financial support. T.B. thanks to Grant Agency of the Charles University in Prague (GAUK - 1374213). Authors are grateful to Professor Tetsuya Ishikawa and the SCSS team for providing the beamtime and making this work possible.

References and links

1.

A. E. Siegman, Lasers (University Science Books, Mill Valley, California 1986).

2.

A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), pp. 184–199, paper MQ1. http://www.opticsinfobase.org/abstract.cfm?uri=DLAI-1998-MQ1

3.

M. Kirm, A. Andrejczuk, J. Krzywinski, and R. Sobierajski, “Influence of excitation density on luminescence decay in Y3Al5O12:Ce and BaF2 crystals excited by free electron laser radiation in VUV,” Phys. Status Solidi C 2(1), 649–652 (2005). [CrossRef]

4.

Y. Dong, G. Zhou, J. Xu, G. Zhao, F. Su, L. Su, G. Zhang, D. Zhang, H. Li, and J. Si, “Luminescence studies of Ce:YAG using vacuum ultraviolet synchrotron radiation,” Mater. Res. Bull. 41(10), 1959–1963 (2006). [CrossRef]

5.

M. Nikl, “Wide band gap scintillation materials: Progress in the technology and material understanding,” Phys. Status Solidi A 178(2), 595–620 (2000). [CrossRef]

6.

J. Hartmann, “Bemerkungen über den Bau und die Justirung von Spektrographen,” Z. Instrum. 20, 47–58 (1900).

7.

S. Le Pape, Ph. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. François, “Electromagnetic-field distribution measurements in the soft X-ray range: Full characterization of a soft X-ray laser beam,” Phys. Rev. Lett. 88(18), 183901 (2002). [CrossRef] [PubMed]

8.

B. Flöter, P. Juranić, S. Kapitzki, B. Keitel, K. Mann, E. Plönjes, B. Schäfer, and K. Tiedtke, “EUV Hartmann sensor for wavefront measurements at the Free-electron LASer in Hamburg,” New J. Phys. 12(8), 083015 (2010). [CrossRef]

9.

http://www.andor.com

10.

J. Chalupský, J. Krzywinski, L. Juha, V. Hájková, J. Cihelka, T. Burian, L. Vysín, J. Gaudin, A. Gleeson, M. Jurek, A. R. Khorsand, D. Klinger, H. Wabnitz, R. Sobierajski, M. Störmer, K. Tiedtke, and S. Toleikis, “Spot size characterization of focused non-Gaussian X-ray laser beams,” Opt. Express 18(26), 27836–27845 (2010). [CrossRef] [PubMed]

11.

J. Chalupský, L. Juha, J. Kuba, J. Cihelka, V. Hájková, S. Koptyaev, J. Krása, A. Velyhan, M. Bergh, C. Caleman, J. Hajdu, R. M. Bionta, H. Chapman, S. P. Hau-Riege, R. A. London, M. Jurek, J. Krzywinski, R. Nietubyc, J. B. Pelka, R. Sobierajski, J. Meyer-Ter-Vehn, A. Tronnier, K. Sokolowski-Tinten, N. Stojanovic, K. Tiedtke, S. Toleikis, T. Tschentscher, H. Wabnitz, and U. Zastrau, “Characteristics of focused soft X-ray free-electron laser beam determined by ablation of organic molecular solids,” Opt. Express 15(10), 6036–6043 (2007). [CrossRef] [PubMed]

12.

J. Chalupsky, P. Bohacek, V. Hajkova, S. P. Hau-Riege, P. A. Heimann, L. Juha, J. Krzywinski, M. Messerschmidt, S. P. Moeller, B. Nagler, M. Rowen, W. F. Schlotter, M. L. Swiggers, and J. J. Turner, “Comparing different approaches to characterization of focused X-ray laser beams,” Nucl. Instrum. Methods Phys. Res. A 631(1), 130–133 (2011). [CrossRef]

13.

J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]

14.

T. Shintake, H. Tanaka, T. Hara, T. Tanaka, K. Togawa, M. Yabashi, Y. Otake, Y. Asano, T. Bizen, T. Fukui, S. Goto, A. Higashiya, T. Hirono, N. Hosoda, T. Inagaki, S. Inoue, M. Ishii, Y. Kim, H. Kimura, M. Kitamura, T. Kobayashi, H. Maesaka, T. Masuda, S. Matsui, T. Matsushita, X. Marechal, M. Nagasono, H. Ohashi, T. Ohata, T. Ohshima, K. Onoe, K. Shirasawa, T. Takagi, S. Takahashi, M. Takeuchi, K. Tamasaku, R. Tanaka, Y. Tanaka, T. Tanikawa, T. Togashi, S. Wu, A. Yamashita, K. Yanagida, C. Zhang, H. Kitamura, and T. Ishikawa, “A compact free-electron laser for generating coherent radiation in the extreme ultraviolet region,” Nat. Photonics 2(9), 555–559 (2008). [CrossRef]

15.

ISO 11254–1:2000, “Laser and laser-related equipment - Determination of laser-induced damage threshold of optical surfaces - Part 1: 1-on-1 test

16.

S. M. Vinko, O. Ciricosta, B. I. Cho, K. Engelhorn, H. K. Chung, C. R. D. Brown, T. Burian, J. Chalupský, R. W. Falcone, C. Graves, V. Hájková, A. Higginbotham, L. Juha, J. Krzywinski, H. J. Lee, M. Messerschmidt, C. D. Murphy, Y. Ping, A. Scherz, W. Schlotter, S. Toleikis, J. J. Turner, L. Vysin, T. Wang, B. Wu, U. Zastrau, D. Zhu, R. W. Lee, P. A. Heimann, B. Nagler, and J. S. Wark, “Creation and diagnosis of a solid-density plasma with an X-ray free-electron laser,” Nature 482(7383), 59–62 (2012). [CrossRef] [PubMed]

17.

T. Ishikawa, H. Aoyagi, T. Asaka, Y. Asano, N. Azumi, T. Bizen, H. Ego, K. Fukami, T. Fukui, Y. Furukawa, S. Goto, H. Hanaki, T. Hara, T. Hasegawa, T. Hatsui, A. Higashiya, T. Hirono, N. Hosoda, M. Ishii, T. Inagaki, Y. Inubushi, T. Itoga, Y. Joti, M. Kago, T. Kameshima, H. Kimura, Y. Kirihara, A. Kiyomichi, T. Kobayashi, C. Kondo, T. Kudo, H. Maesaka, X. M. Marechal, T. Masuda, S. Matsubara, T. Matsumoto, T. Matsushita, S. Matsui, M. Nagasono, N. Nariyama, H. Ohashi, T. Ohata, T. Ohshima, S. Ono, Y. Otake, C. Saji, T. Sakurai, T. Sato, K. Sawada, T. Seike, K. Shirasawa, T. Sugimoto, S. Suzuki, S. Takahashi, H. Takebe, K. Takeshita, K. Tamasaku, H. Tanaka, R. Tanaka, T. Tanaka, T. Togashi, K. Togawa, A. Tokuhisa, H. Tomizawa, K. Tono, S. Wu, M. Yabashi, M. Yamaga, A. Yamashita, K. Yanagida, C. Zhang, T. Shintake, H. Kitamura, and N. Kumagai, “A compact X-ray free-electron laser emitting in the sub-ångström region,” Nat. Photonics 6(8), 540–544 (2012). [CrossRef]

18.

T. Shintake and SCSS Team, “Status of Japanese XFEL Project and SCSS test accelerator,” Proc. FEL 2006, BESSY, Berlin, Germany, 33–36 (2006).

19.

H. Ohashi, Y. Senba, M. Nagasono, M. Yabashi, K. Tono, T. Togashi, T. Kudo, H. Kishimoto, T. Miura, H. Kimura, and T. Ishikawa, “Performance of focusing mirror device in EUV beamline of SPring-8 Compact SASE Source (SCSS),” Nucl. Instrum. Methods Phys. Res. A 649(1), 163–165 (2011). [CrossRef]

OCIS Codes
(140.2600) Lasers and laser optics : Free-electron lasers (FELs)
(140.7240) Lasers and laser optics : UV, EUV, and X-ray lasers
(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)
(140.3295) Lasers and laser optics : Laser beam characterization

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 22, 2013
Revised Manuscript: September 12, 2013
Manuscript Accepted: October 8, 2013
Published: October 25, 2013

Citation
Jaromír Chalupský, Tomáš Burian, Věra Hájková, Libor Juha, Tomáš Polcar, Jérôme Gaudin, Mitsuru Nagasono, Ryszard Sobierajski, Makina Yabashi, and Jacek Krzywinski, "Fluence scan: an unexplored property of a laser beam," Opt. Express 21, 26363-26375 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26363


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References

  1. A. E. Siegman, Lasers (University Science Books, Mill Valley, California 1986).
  2. A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), pp. 184–199, paper MQ1. http://www.opticsinfobase.org/abstract.cfm?uri=DLAI-1998-MQ1
  3. M. Kirm, A. Andrejczuk, J. Krzywinski, and R. Sobierajski, “Influence of excitation density on luminescence decay in Y3Al5O12:Ce and BaF2 crystals excited by free electron laser radiation in VUV,” Phys. Status Solidi C2(1), 649–652 (2005). [CrossRef]
  4. Y. Dong, G. Zhou, J. Xu, G. Zhao, F. Su, L. Su, G. Zhang, D. Zhang, H. Li, and J. Si, “Luminescence studies of Ce:YAG using vacuum ultraviolet synchrotron radiation,” Mater. Res. Bull.41(10), 1959–1963 (2006). [CrossRef]
  5. M. Nikl, “Wide band gap scintillation materials: Progress in the technology and material understanding,” Phys. Status Solidi A178(2), 595–620 (2000). [CrossRef]
  6. J. Hartmann, “Bemerkungen über den Bau und die Justirung von Spektrographen,” Z. Instrum.20, 47–58 (1900).
  7. S. Le Pape, Ph. Zeitoun, M. Idir, P. Dhez, J. J. Rocca, and M. François, “Electromagnetic-field distribution measurements in the soft X-ray range: Full characterization of a soft X-ray laser beam,” Phys. Rev. Lett.88(18), 183901 (2002). [CrossRef] [PubMed]
  8. B. Flöter, P. Juranić, S. Kapitzki, B. Keitel, K. Mann, E. Plönjes, B. Schäfer, and K. Tiedtke, “EUV Hartmann sensor for wavefront measurements at the Free-electron LASer in Hamburg,” New J. Phys.12(8), 083015 (2010). [CrossRef]
  9. http://www.andor.com
  10. J. Chalupský, J. Krzywinski, L. Juha, V. Hájková, J. Cihelka, T. Burian, L. Vysín, J. Gaudin, A. Gleeson, M. Jurek, A. R. Khorsand, D. Klinger, H. Wabnitz, R. Sobierajski, M. Störmer, K. Tiedtke, and S. Toleikis, “Spot size characterization of focused non-Gaussian X-ray laser beams,” Opt. Express18(26), 27836–27845 (2010). [CrossRef] [PubMed]
  11. J. Chalupský, L. Juha, J. Kuba, J. Cihelka, V. Hájková, S. Koptyaev, J. Krása, A. Velyhan, M. Bergh, C. Caleman, J. Hajdu, R. M. Bionta, H. Chapman, S. P. Hau-Riege, R. A. London, M. Jurek, J. Krzywinski, R. Nietubyc, J. B. Pelka, R. Sobierajski, J. Meyer-Ter-Vehn, A. Tronnier, K. Sokolowski-Tinten, N. Stojanovic, K. Tiedtke, S. Toleikis, T. Tschentscher, H. Wabnitz, and U. Zastrau, “Characteristics of focused soft X-ray free-electron laser beam determined by ablation of organic molecular solids,” Opt. Express15(10), 6036–6043 (2007). [CrossRef] [PubMed]
  12. J. Chalupsky, P. Bohacek, V. Hajkova, S. P. Hau-Riege, P. A. Heimann, L. Juha, J. Krzywinski, M. Messerschmidt, S. P. Moeller, B. Nagler, M. Rowen, W. F. Schlotter, M. L. Swiggers, and J. J. Turner, “Comparing different approaches to characterization of focused X-ray laser beams,” Nucl. Instrum. Methods Phys. Res. A631(1), 130–133 (2011). [CrossRef]
  13. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett.7(5), 196–198 (1982). [CrossRef] [PubMed]
  14. T. Shintake, H. Tanaka, T. Hara, T. Tanaka, K. Togawa, M. Yabashi, Y. Otake, Y. Asano, T. Bizen, T. Fukui, S. Goto, A. Higashiya, T. Hirono, N. Hosoda, T. Inagaki, S. Inoue, M. Ishii, Y. Kim, H. Kimura, M. Kitamura, T. Kobayashi, H. Maesaka, T. Masuda, S. Matsui, T. Matsushita, X. Marechal, M. Nagasono, H. Ohashi, T. Ohata, T. Ohshima, K. Onoe, K. Shirasawa, T. Takagi, S. Takahashi, M. Takeuchi, K. Tamasaku, R. Tanaka, Y. Tanaka, T. Tanikawa, T. Togashi, S. Wu, A. Yamashita, K. Yanagida, C. Zhang, H. Kitamura, and T. Ishikawa, “A compact free-electron laser for generating coherent radiation in the extreme ultraviolet region,” Nat. Photonics2(9), 555–559 (2008). [CrossRef]
  15. ISO 11254–1:2000, “Laser and laser-related equipment - Determination of laser-induced damage threshold of optical surfaces - Part 1: 1-on-1 test
  16. S. M. Vinko, O. Ciricosta, B. I. Cho, K. Engelhorn, H. K. Chung, C. R. D. Brown, T. Burian, J. Chalupský, R. W. Falcone, C. Graves, V. Hájková, A. Higginbotham, L. Juha, J. Krzywinski, H. J. Lee, M. Messerschmidt, C. D. Murphy, Y. Ping, A. Scherz, W. Schlotter, S. Toleikis, J. J. Turner, L. Vysin, T. Wang, B. Wu, U. Zastrau, D. Zhu, R. W. Lee, P. A. Heimann, B. Nagler, and J. S. Wark, “Creation and diagnosis of a solid-density plasma with an X-ray free-electron laser,” Nature482(7383), 59–62 (2012). [CrossRef] [PubMed]
  17. T. Ishikawa, H. Aoyagi, T. Asaka, Y. Asano, N. Azumi, T. Bizen, H. Ego, K. Fukami, T. Fukui, Y. Furukawa, S. Goto, H. Hanaki, T. Hara, T. Hasegawa, T. Hatsui, A. Higashiya, T. Hirono, N. Hosoda, M. Ishii, T. Inagaki, Y. Inubushi, T. Itoga, Y. Joti, M. Kago, T. Kameshima, H. Kimura, Y. Kirihara, A. Kiyomichi, T. Kobayashi, C. Kondo, T. Kudo, H. Maesaka, X. M. Marechal, T. Masuda, S. Matsubara, T. Matsumoto, T. Matsushita, S. Matsui, M. Nagasono, N. Nariyama, H. Ohashi, T. Ohata, T. Ohshima, S. Ono, Y. Otake, C. Saji, T. Sakurai, T. Sato, K. Sawada, T. Seike, K. Shirasawa, T. Sugimoto, S. Suzuki, S. Takahashi, H. Takebe, K. Takeshita, K. Tamasaku, H. Tanaka, R. Tanaka, T. Tanaka, T. Togashi, K. Togawa, A. Tokuhisa, H. Tomizawa, K. Tono, S. Wu, M. Yabashi, M. Yamaga, A. Yamashita, K. Yanagida, C. Zhang, T. Shintake, H. Kitamura, and N. Kumagai, “A compact X-ray free-electron laser emitting in the sub-ångström region,” Nat. Photonics6(8), 540–544 (2012). [CrossRef]
  18. T. Shintake and SCSS Team, “Status of Japanese XFEL Project and SCSS test accelerator,” Proc. FEL 2006, BESSY, Berlin, Germany, 33–36 (2006).
  19. H. Ohashi, Y. Senba, M. Nagasono, M. Yabashi, K. Tono, T. Togashi, T. Kudo, H. Kishimoto, T. Miura, H. Kimura, and T. Ishikawa, “Performance of focusing mirror device in EUV beamline of SPring-8 Compact SASE Source (SCSS),” Nucl. Instrum. Methods Phys. Res. A649(1), 163–165 (2011). [CrossRef]

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