Since their discovery in the 1980s,1,2 laser harmonicsof high order have posed a challenge to researchersbecause of their unique characteristics and the oppor-tunities that they provide: short duration and dis-crete plateaulike spectra up to a water window,3–5
small divergence,6 spatial and temporal coherence,7and high brightness.6 Interest in these high-orderharmonics then naturally is focused on a twofold ob-jective: to understand the way in which they work,from earlier studies of picosecond interactions up torecent investigations in which few-optical-cycle pulseswere used, and to exploit their properties as a radia-tion source.
Our aims in the present research are in line withthe purposes stated above. We have to study high-order harmonic �HH� generation in different interac-tion configurations by changing the target medium torange from atoms to Van der Waals clusters and by
The authors are with the Laboratory for Ultraviolet and X-RayOptical Research, Department of Information Engineering, Uni-versity of Padova, via Gradenigo 6�B, 35131 Padova, Italy. L.Poletto’s e-mail address is [email protected].
varying the laser’s intensity and wave front. Forthis purpose we need a spectrometer with goodthroughput, absolutely calibrated to provide preciseestimates of conversion efficiency in absolute units,with a resolution ���� in the range 500–1000, toinvestigate spectral variations by changing interac-tion parameters. Moreover, the utilization of HHsin several experiments has already demonstratedtheir efficacy in nonlinear processes and in pump–probe experiments. We then need either to mono-chromatize the extreme-ultraviolet �EUV� radiationto select a single harmonic order and simultaneouslyaccept a pulse’s time stretching8 or to provide accessfor a sample to an intermediate HHs image in whichthe sample can be exposed to HHs radiation and to aportion of the laser pulse in a pump–probe scheme.
It is then evident that an instrument with a relaymirror is needed to produce an image of the HHssource, as is a dispersion system coupled with eithera bidimensional detector or with an exit slit, to beused both for spectral analysis and to monochroma-tize the radiation. We present in what follows theoptical design and performance of such instrument,which can be operated in the 5–75-nm spectral range.
The laser source is a Ti:sapphire laser operating ata high repetition rate with chirped-pulse amplifica-tion based on a nine-pass confocal amplifier stage anda prism compressor. The system generates laser
pulses of 30 fs to 1 mJ centered at 795 nm at a 1-kHzrepetition rate. The pulse duration can be reducedto 5 fs to 0.25 mJ by the hollow-fiber compressiontechnique.9 The laser beam enters the laser–gas in-teraction chamber through a 0.3-mm-thick sapphirewindow and is focused onto the gas jet by a sphericalmirror of 25-cm focal distance mounted inside thechamber, which gives an �30-�m diffraction-limitedspot size. The gas is injected into the interactionchamber by an electromagnetic valve that can be op-erated up to 50 Hz with an opening time of the orderof 300–400 �s, producing a jet diameter at the nozzleof 0.4 mm. Alternatively, the gas is injected into theinteraction chamber through a 1.5 mm � 0.2 mmelliptical nozzle, with the major axis oriented alongthe direction of propagation of the beam, to increasethe interaction length and the EUV emission.
The EUV HH radiation is focused onto the entranceslit of the spectrometer by a grazing-incidence toroidalmirror. The spectrum is then acquired by a grazing-incidence flat-field stigmatic spectrometer with a toroi-dal mirror and a variable-line-spaced �VLS� flatgrating illuminated in converging light.10,11 The mir-ror of the spectrometer is used in the Rowland config-uration to produce a stigmatic image of the entranceslit on the spectral focal plane, and the VLS grating ismounted close to the mirror to intercept the convergingbeam. The mirror provides focusing in the plane per-pendicular to the spectral dispersion plane. The spec-tral aberrations are then minimized by appropriatedistribution of the line spacing along the grating sur-face. The resultant spectrum is stigmatic and almostflat, even in a wide spectral region. The spectrometerspans the 5–75-nm region with a 600 groove�mm grat-ing. The detector is a microchannel plate �MCP� in-tensifier with a phosphor screen optically coupled to alow-noise fast-readout CCD camera, which is moved bya linear drive to acquire different portions of the spec-trum.
The main advantage of using a design with a VLSflat grating compared with other designs with spher-ical gratings12,13 is the possibility of converting theinstrument into a monochromator with a constantsubtended angle by substituting a fixed exit slit forthe detector block without changing either the mirroror the grating. Spectral scanning is achieved by ro-tation of the grating about an axis that passesthrough the center and is parallel to the grooves ofthe grating. As the rotating surface is flat, varia-tions of the length of the exit arm for best spectralfocusing are minimized, so the image is focused onthe exit slit, even for a wide spectral scanning. Withthe 600-groove�mm grating with a subtended angleof 165°, a monochromator for the 5–50-nm spectralregion is fabricated. This flexibility is not guaran-teed by conventional flat-field spectrometer designswith spherical gratings: When the spherical gratingis rotated for spectral scanning, large variations ofthe exit arm for the best spectral focusing are ex-pected, so it is not possible to have a constant-outputarm in a wide spectral region.
2. Variable-Line-Spaced Flat Gratings for StigmaticImage Focusing
The optical configuration of the grazing-incidencespectrometer–monochromator adopts a VLS flat grat-ing placed to intercept a converging beam coming froma focusing toroidal mirror.10 The groove space varia-tion of a VLS grating is defined by a polynomial equa-tion in which the variable y spans the surface of thegrating along the direction perpendicular to thegrooves with origin O at the center of the grating itself:
d� y� � d0 � d1 y � d2 y2 � d3 y3, (1)
where d�y� is the local groove density, d0 is the cen-tral groove density, and d1–d3 are the parameters forgroove space variation.
A schematic layout of the spectrometer is shown inFig. 1. Point A is the source point on the entranceslit plane. In absence of a grating, the mirror givesa stigmatic image of point A at point B�. The zero-order image is focused on point B, which is symmetricto point B� with respect to a plane parallel to thegrating surface and passing through the grating’scenter. The zero-order image is almost stigmatic, asthe residual aberrations of the toroidal mirror in theRowland configuration are negligible.
The spectrum is focused approximately along a cir-cle centered on grating center O and having radius pequal to the distance O–B.14 The sagittal focusing ofthe toroidal mirror minimizes the spatial aberra-tions, i.e., the aberrations in a plane perpendicular tothe spectral dispersion plane. The spectral aberra-tions are instead minimized by appropriate distribu-tion of the line spacing along the grating surface.
The main optical aberrations that have to be min-imized to produce a high-resolution spectrum arespectral and spatial defocusing, respectively, in theplane of dispersion and in a plane perpendicular to it.The focal curves for zero defocusing are
where and are, respectively, the incidence anddiffraction angles, � is the wavelength, m is the dif-fracted order, and qspect and qspat are the exit armscalculated from point O to have zero spectral or spa-tial defocusing, respectively. Diffraction angles atdifferent wavelengths are calculated by the gratingequation
sin � sin � m�d0, (4)
where and are taken with positive signs.It is clear from Eq. �3� that the spatial focal curve is
a circle centered on the grating with radius p. Rul-ing parameter d1 is then determined to minimize thedistance between the spectral and spatial focal curveswithin the spectral range to be acquired. There isone perfectly stigmatic point at wavelength �0, wherethe two curves intersect �qspect � qspat � p�. Oncestigmatic wavelength �0 has been selected, parame-ter d1 is chosen by the equation
d1 �cos2 � cos2 0
m�0 p, (5)
where 0 is the diffraction angle at the stigmaticwavelength. Therefore it can be shown that param-eters d2 and d3 can be chosen to minimize coma andspherical aberration.12
We can also apply this optical layout to the designof a monochromator by substituting a fixed exit slitfor the detector without changing either the mirror orthe grating. Spectral scanning is achieved by rota-tion of the grating about an axis passing through itscenter. The two configurations are shown schemat-ically in Fig. 2.
For a monochromator the grating equation is ex-pressed as
�K2
� a sin� m�d0
2 cos�K�2�� , (6)
where k is the constant subtended angle �K � � �.The exit arms that give the best spatial and spectralfocusing are evaluated by use of Eqs. �2� and �3�.Because the rotating grating is flat, the variations ofthe length of the exit arm required for the best spec-tral focusing are minimized, so the image is focusedon the exit slit, even for wide spectral scanning.
3. Spectrometer–Monochromator Design
The optical layout described above was applied to thedesign of an EUV spectrometer–monochromator foranalysis and utilization of the HHs in the 5–75-nmspectral region by use of a 600-groove�mm VLS flatlaminar grating provided by Jobin-Yvon �France�.The layout of the system is shown in Fig. 3. Theoptical parameters are listed in Table 1. The systemis designed for an f�100 maximum angular accep-tance in the plane of spectral dispersion �i.e., 10mrad�, which is higher than the measured divergenceof the HH emission ��5 mrad at FWHM�.13
A toroidal mirror in the Rowland configuration fo-cuses radiation on the entrance plane of a spectrom-eter. The spectrometer is operated without anentrance slit because of the limited size of the emit-ting source. In fact, the pump laser’s spot size is�30 �m, and the HH signal comes from a pointsmaller than the pump beam’s size. A primary ad-vantage of operating without an entrance slit is thatsuch a slit could reduce the flux by an unknownamount, making it impossible to measure with goodaccuracy the conversion efficiency of the HH genera-tion process.
Stigmatic wavelength �0 and consequently the rul-ing parameters have been chosen to minimize thedistance at the lowest wavelengths between the spec-tral and spatial focal curves, which are shown in Fig.4 for the primary spectral region of operation �5–35nm�. The detector is placed on the best linear fit ofthe spectral focal curve to maximize the spectral res-olution. Note that the maximum distance betweenthe spatial and spectral focal curves is �2 mm, cor-responding to spatial defocusing of 20 �m with 10-mrad aperture if the detector plane is placed on thespectral focal curve.
The detector is a single-stage MCP open intensifierwith a magnesium fluoride photocathode. The MCP
Fig. 2. Optical layout of �a� the spectrometer and �b� the mono-chromator.
has a 40-mm outside diameter and a 10-�m pore sizeon a 12-�m pitch. Photons impinging on the photo-cathode are converted into electrons that are thenamplified into the channels. The electron cloud atthe exit of the MCP is accelerated onto a phosphorscreen, which is optically coupled by an objective toan interline-transfer CCD camera with low readoutnoise �10 e rms� and fast frame rate �maximum 10frames�s�. The CCD format is 1280 � 1024 pixelswith 6.7 �m � 6.7 �m pixel size. When the 40-mmphosphor screen diameter is projected on the CCD’s
1280-pixel long side, corresponding to an objectivedemagnification of �4.7, the resolution of the detec-tion system is 31 �m�pixel. As the sensitive area ofthe detector covers only a portion of the spectralrange, it is necessary to move the intensifier along thefocal curve to scan the whole 5–75 nm spectrum. Todo so, we mount the detector on a linear drive andconnect it to the spectrometer by a bellows such thatthe detector plane can be moved to match the actualfocal curve. The dispersion curve is shown in Fig. 5.Various portions of the spectrum can be focused onthe detector by a simple rotation of the grating also,but this involves a loss of resolution and is not feasi-ble for the whole 5–75-nm spectral range. The ab-errations on the detector plane as obtained by aray-tracing procedure are shown in Fig. 6 for theprimary spectral region of operation. The FWHMaberrations are always less than the spectral resolv-ing element, so the resolution is limited by the detec-tor pixel size and not by the optical performance.
To change from a spectrometer to a monochroma-tor we substitute a fixed exit slit for the whole detec-tor block, and the rotation of the grating gives thespectral scanning. We do this by mounting the grat-ing upon a rotating motor with which it can be ro-tated about an axis that is parallel to the grooves and
Fig. 4. Focal curves in the 3–35-nm region. The origin is placedat the center of the grating, the X axis is parallel to the gratingsurface along the direction perpendicular to the grooves, and the Yaxis is perpendicular to X and parallel to the grooves.
Fig. 5. Dispersion curve of the spectrometer �600-groove�mmgrating, 31-�m pixel size�.
Fig. 6. FWHM spectral and spatial aberrations of the spectrom-eter in the 5–35-nm region on the detector plane. The detector isplaced on a straight line that matches at the best the spectral focalcurve.
Table 1. Optical Parameters of the Spectrometer–Monochromator
Toroidal mirror for refocusingEntrance arm 309 mmExit arm 309 mmIncidence angle 87.3°Tangential radius 6500 mmSagittal radius 14.7 mmSize 60 mm � 20 mmCoating Platinum
passes through the grating’s center. This configura-tion is at a constant subtended angle, that is, � �K, which has been chosen to be 165° for the 5–50-nmregion. The extreme incidence and diffraction an-gles are, respectively, � 83.16° and � 81.84° at 5nm and � 89.10° and � 75.90° at 50 nm. At longwavelengths, when the grating is operated at ex-treme grazing incidence the actual acceptance of themonochromator is less than 10 mrad because of thelimited size of the grating: The effective acceptanceis 7 mrad � f�140� at 40 nm and 3 mrad � f�350� at 50nm. The grating-to-exit-slit distance was chosen tobe 428 mm to minimize spectral aberrations in thefull range. The variations of the spectral exit arm asgiven by Eq. �2� are shown in Fig. 7: The shift of thebest spectral focal point is less than 3 mm. TheFWHM resolution, calculated as the ratio betweenwavelength and the FWHM of the spectral range atthe exit slit �����FWHM�, is shown in Fig. 8 for a50-�m slit.
4. Instrument Performance
The spectrometer was assembled, aligned, and testedat the Laboratory for Ultraviolet and X-Ray OpticalResearch �Padua�. As a source, the EUV radiationemitted by a laser-produced plasma generated by aNd:YAG laser �8 ns and 150 mJ� was used. An im-
age of the spectrum of a Be target is shown in Fig. 9.The image is almost perfectly stigmatic, showing op-tical performance similar to that predicted by theray-tracing procedure.
The absolute response of the system was measuredin the 5–75-nm spectral region by use of two diffrac-tometers �a grazing-incidence diffractometer for the5–30-nm region and a normal-incidence one for the30–75-nm region� and a calibrated photodiode as anabsolute reference.15,16 The grating efficiency isshown in Fig. 10: It is defined as the ratio betweenthe flux measured at the first diffraction order andthe global monochromatic flux arriving on the grat-ing. The maximum efficiency is �13% in the region
Fig. 7. Exit arm for the best spectral focus of the monochromatorin the 5–50-nm spectral region. The subtended angle is 165°, andthe scanning is performed by grating rotation.
Fig. 8. Resolution of the monochromator with a 50-�m exit slit.It has been calculated as the ratio between the wavelength and theFWHM of the spectral range at the slit.
Fig. 9. Spectrum of a laser-produced plasma with a Be target:�a� full CCD image in the 5–25-nm region; �b� zoom of the 7–11-nmspectral region �rectangular region outlined in �a�; �c� three-dimensional plot across the spectrum in the region shown in �b�.The horizontal axis of the CCD images is the wavelength scaleincreasing toward the right-hand side of the image. A 35-�mpinhole was placed on the entrance slit plane to limit the size of thesource.
near 10 nm, in agreement with the theoretical pre-dictions made by the manufacturer. The efficiencyof the detection system �intensifier, objective, andCCD camera� with 950 V applied across the MCP isshown in Fig. 11�a�. The gain ranges from 3 to 0.75DU�photon, where DU is the digital unit read fromthe CCD analog-to-digital converter. The detectorgain changes with the voltage applied across theMCP, following the curve shown in Fig. 11�b�. Theglobal response of the spectrometer is finally shownin Fig. 12: It ranges from 0.01 to 0.25 DU per source
photon. Defining the minimum detectable signal asthe photon flux necessary to give a signal comparableto the rms noise of the CCD camera, that is, �3.5 DUrms, the minimum detectable signal is �15 photonsemitted from the source at 6.7 nm, �160 photons at25 nm, and �350 photons at 75 nm. It is then pos-sible to give the absolute EUV flux of the HH emis-sion and to measure the efficiency of the generationprocess.
A HH spectrum obtained with Ne gas in the inter-action chamber and with sub-10-fs laser pulses isshown in Fig. 13 for the 6–31-nm region. The spec-trum was acquired in 3 s with the valve operating at10 Hz and a gas backing pressure of 6 � 105 Pa; thevoltage applied across the MCP was 750 V. Theharmonics are clearly distinguishable down to thecutoff at �10 nm �79th harmonic�.
Fig. 10. Absolute first-order efficiency of the VLS plane grating at87°: Here the efficiency is defined as the ratio between the fluxmeasured at the first diffraction order and the global flux arrivingon the grating.
Fig. 11. �a� Efficiency of the detection system �intensifier, objec-tive, and CCD camera� with 950 V applied across the MCP. �b�Gain as a function of the voltage across the MCP normalized to thegain measured at 950 V. The response is given in digital units ofthe CCD camera per source photon.
Fig. 12. Global response of the spectrometer �two mirrors, grat-ing, and detector� with 950 V applied to the MCP.
Fig. 13. Image on the CCD of a high-order harmonic spectrumwith Ne and sub-10 laser pulses: �a� image in the 7–31-nm region�the vertical size of the image is 150 pixels�; �b� plot across thespectrum.
The optical design and performance of aspectrometer–monochromator for EUV and soft-x-ray HH emission have been described. The designcomprises a stigmatic focusing toroidal mirror and avariable-line-spaced plane grating illuminated by theconverging light coming from the mirror. The mir-ror provides focusing in the plane perpendicular tothe spectral dispersion plane. Spectral aberrationsare minimized by choice of appropriate distribution ofthe line spacing on the VLS grating. The resultantfocal surface is almost flat and perpendicular to thedirection of the exit beam, so the detector is mountedat normal incidence. The spectrum is acquired by aMCP intensifier that can be moved by means of alinear drive to scan various portions of the spectrum.
The same configuration is applied to the design ofa constant-deviation-angle monochromator by substi-tution of an exit slit for the detector block: Thewavelength is scanned by rotation of the plane VLSgrating. Because the grating is flat, the length ofthe exit arm for optimum spectral focusing changesslightly with rotation, so the exit beam is almost fo-cused on the fixed exit slit plane.
A spectrometer configuration has been achieved.Almost perfectly stigmatic images were obtained dur-ing the alignment phase, showing optical performanceclose to that predicted by the ray-tracing simulations.Furthermore, we have absolutely calibrated the spec-trometer to enable us to measure the absolute photonflux and the conversion efficiency of HH generation.The instrument has been installed in the Departmentof Physics, Politecnico, Milan, Italy.
The experiments on HH production were per-formed in the framework of two projects for advancedresearch of the National Institute for the Physics ofMatter �Italy�, led by S. De Silvestri and G. Tondello.
The authors thank P. Surpi and P. Zambolin forhelp in the mechanical design and alignment of theinstrument and M. Pascolini for the help with dataprocessing.
References1. R. L. Carman, C. K. Rhodes, and R. F. Benjamin, “Observation
of harmonics in the visible and ultraviolet created in the CO2-laser-produced plasmas,” Phys. Rev. A 24, 2649–2663 �1981�.
2. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A.McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphotonproduction of vacuum-ultraviolet radiation in the rare gases,”J. Opt. Soc. Am. B 4, 595–601 �1987�.
3. A. L’Huilier and Ph. Balcou, “High-order harmonic generationin rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett. 70,774–777 �1993�.
4. T. Brabec and F. Krausz, “Intense few-cycle laser fields: fron-tiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 �2000�.
5. A. Rundquist, “Phase-matched generation of coherent softx-rays,” Science 280, 1412–1415 �1998�.
6. M. Nisoli, E. Priori, G. Sansone, S. Stagira, G. Cerullo, S. DeSilvestri, C. Altucci, R. Bruzzese, C. de Lisio, P. Villoresi, L.Poletto, M. Pascolini, and G. Tondello, “High-brightnesshigh-order harmonic generation by truncated Bessel beamsin the sub-10-fs regime,” Phys. Rev. Lett. 88, 033902 �2002�.
7. M. Bellini, C. Lynga, A. Tozzi, M. B. Gaarde, T. W. Hansch, A.L’Huillier, and C. G. Wahlstrom, “Temporal coherence of ul-trashort high-order harmonic pulses,” Phys. Rev. Lett. 81,297–300 �1998�.
8. P. Villoresi, “Compensation of optical path lengths in extreme-ultraviolet and soft-x-ray monochromators for ultrafast puls-es,” Appl. Opt. 38, 6040–6049 �1999�.
9. M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of highenergy 10 fs pulses by a new pulse compression technique,”Appl. Phys. Lett. 68, 2793–2795 �1996�.
10. M. Hettrick and S. Bowyer, “Variable line-space gratings:new designs for use in grazing incidence spectrometers,” Appl.Opt. 22, 3921–3932 �1983�.
11. M. Hettrick, “High resolution gratings for the soft x-ray,” Nucl.Instrum. Methods A 266, 404–413 �1988�.
12. L. Poletto, G. Naletto, and G. Tondello, “Grazing-incidenceflat-field spectrometer for high-order harmonic diagnostics,”Opt. Eng. 40, 178–185 �2001�.
13. L. Poletto, G. Tondello, and P. Villoresi, “High-order laserharmonics detection in the EUV and soft x-ray spectral re-gions,” Rev. Sci. Instrum. 72, 2868–2874 �2001�.
14. M. Hettrick, “Aberrations of varied line-space grazing inci-dence gratings in converging light beams,” Appl. Opt. 23,3221–3235 �1984�.
15. G. Bonanno, G. Naletto, and G. Tondello, “A test facility tocalibrate EUV detectors,” in Proceedings of a European SpaceAgency Symposium on Photon Detectors for Space Instrumen-tation,” H. Habing, ed. ESA Spec. Publ. 356, �European SpaceAgency, Munich, Germany, 1992�, pp. 233–236.
16. L. Poletto, A. Boscolo, and G. Tondello, “Optical performanceand characterization of an EUV and soft X-ray test facility,”in Ultraviolet and X-Ray Detection, Spectroscopy, and Pola-rimetry III, S. Fineschi, ed., Proc. SPIE 3764, 94–102 �1999�.
