Since their discovery,1,2 high-order harmonics (HHs)generated by the interaction between ultrashort laserpulses and gas jets are considered to be very relevantand effective sources of coherent extreme-ultraviolet(EUV) and soft x-ray radiation of tabletop size, veryshort time duration, and high peak brilliance. Thespectrum of a HH is generally described as a sequenceof peaks corresponding to the odd harmonics of thefundamental laser wavelength and having an inten-sity distribution characterized by a vast plateau whoseextension is related to pulse intensity.3 The combina-tion of the use of advanced phase-matching mecha-nisms and interaction geometries as well as veryadvanced and intense ultrafast lasers has made it pos-sible to extend the harmonic spectrum up to the waterwindow region �2.3–4.4 nm�, while still using a table-top laser source.4,5 Moreover, radiation generatedwith the scheme of the HHs generated by laser pulsesof a few optical cycles has recently become a toolfor the investigation of matter with attosecond re-solution �1 as � 10�18 s� (Refs. 6–8), for ultrafastpump–probe experiments or for maximizing the in-
stantaneous power in ionization and excitation inter-actions. In this paper HHs generated by a Ti:sapphirelaser at 800 nm will be considered.
Let us consider the experimental problem of theextraction of a single harmonic (or a group of har-monics) within a broad HH spectrum to obtain anultrafast EUV pulse at a suitable wavelength, andlater to be scanned in a given range. The monochro-mator used for this purpose is also used to preservethe pulse temporal duration of the EUV pulse asshort as in the generation process. This is crucial inorder to have both high temporal resolution and highpeak power.
It is therefore clear that the study and design ofsuch a compensated monochromator has to extendthe usual domain of the geometrical optics and EUVdiffraction grating mountings to include the analysisof the EUV pulse transformation in both the spec-trum and the spectral phase. The monochromator canbe modeled as a filter with a complex frequency re-sponse K���, which includes both the nonuniformspectral transmission and the distortion in the spec-tral phase.9 Since the EUV pulse at the generationmay be produced to be close to its transform limit, anymodification of its complex spectrum results in a se-vere time broadening as described by its Fouriertransform. For a Gaussian profile with no modulationof either phase or frequency, the product of the spec-tral width at half-height ��1�2 times the duration athalf-height ��1�2 has a lower limit expressed by therelation
��1�2��1�2 � 4 ln 2 � 2.77. (1)
The authors are with the Laboratory for UV and X-Ray OpticalResearch, Department of Information Engineering, National Re-search Council, National Institute for the Physics of Matter,Padova, Italy. L. Poletto’s e-mail address is [email protected].
Received 19 April 2006; revised 28 June 2006; accepted 6 July2006; posted 10 July 2006 (Doc. ID 70100).
Two conditions have to be verified by the monochro-mator to maintain the time duration expressed byEq. (1): (i) the bandpass ��m transmitted by the mono-chromator has to be greater than ��1�2 and (ii) thecomplex transfer function K��� has to be almost con-stant in the vicinity of the harmonics. Since harmonicpeaks are well separated, the first condition is verifiedif the monochromator selects the whole spectral bandof a single harmonic (or a group of them) so no modi-fications in the Fourier spectrum are induced. Thesecond condition is almost always verified if the mono-chromator is realized by reflecting optics: The varia-tions of reflectivity of the coating within the linewidthof a single harmonic that scale approximately as theinverse of the harmonic order are usually negligible, soK��� can be considered almost constant, althoughlower than unity.
The simplest way to obtain the spectral selection ofHHs with very modest time broadening is the use ofa multilayer mirror in normal incidence, which doesnot alter the pulse time duration up to fractions of afemtosecond and is moreover very efficient. In fact,the functions of selecting a single harmonic peak andfocusing it can be demanded of a single concave op-tics, maximizing the flux. The choice of the type ofmultilayer can be made among many materials (i.e.,the spacer and the absorber) to optimize the responsein a given spectral region.10 Monochromators withone11 or two12 multilayer mirrors have been proposedand realized. The main drawback of the use of mul-tilayer optics is the necessity of many different mir-rors to have the tunability on a broad spectral regionas the whole harmonic spectrum.
The spectral selection of HHs can also be accom-plished by an ordinary diffraction grating. In thiscase, the major mechanism that alters the time du-ration of the pulse is the difference in the lengths ofthe optical paths of the rays diffracted by differentgrating grooves. In fact, a single grating inevitablygives a time broadening of the ultrafast pulse becauseof the diffraction: The total difference in the opticalpaths of the rays diffracted by N grooves illuminatedby radiation at wavelength � is Nm�, where m is thediffracted order. This effect is negligible for picosec-ond or longer pulses, but is dramatic in the femtosec-ond time scale. Let us consider a 300 groove�mmgrating illuminated by radiation at 40 nm over alength of 20 mm. The total number of grooves in-volved in the diffraction is 6000, corresponding toa maximum delay in the first diffracted order of240 �m, i.e., 800 fs. In the case of a femtosecondpulse, this dramatically reduces both the time reso-lution capability and the peak intensity at the exit ofthe monochromator.
Nevertheless, it is possible to design grating mono-chromators that do not alter the temporal duration ofan ultrafast pulse by using at least two gratings in asubtractive configuration to compensate for the disper-sion.13 In such a configuration, the second grating com-pensates for the time and spectral spread introducedby the first one. Here we define such a configuration asa time-delay compensated monochromator.
From the point of view of the ray paths, there aretwo conditions with which the design must comply:(1) the differences in the path lengths of rays with thesame wavelength but with different entrance direc-tions within the beam aperture that are caused by thefirst grating must be compensated by the second grat-ing; and (2) two rays at different wavelengths withinthe spectrum of the pulse to be selected have to befocused on the same point; i.e., the global spectraldispersion has to be zero. Both these conditions aresatisfied by a scheme with two equal concave gratingsmounted with opposite diffraction orders13; the inci-dence angle on the second grating is equal to thediffraction angle of the first grating. The spectralselection is performed by a slit placed in an interme-diate position between the gratings, where the radi-ation is focused by the first grating. This design hasproved to be very effective in time compensation of afew femtoseconds or even lower for wavelengthslonger than �40 nm (i.e., a harmonic order lowerthan H21), where the normal-incidence reflectivityof conventional coatings is high so that a normal-incidence configuration can be adopted.14 Its mainadvantages are the simplicity, due to the use of onlytwo optical elements, the tunability in a broad spec-tral band, and the possibility of being operated also inspectral regions where multilayers are not available(e.g., for wavelengths higher than 60 nm). Unfortu-nately, the main drawback of using two normal-incidence gratings is the low efficiency in the EUV.By choosing a suitable EUV coating (e.g., gold orplatinum), the efficiency of a single grating can beestimated in the 0.1–0.2 range, so the monochroma-tor efficiency results are 0.01–0.04.
For wavelengths below �35 nm (i.e., a harmonicorder higher than H23), grazing-incidence configura-tions have to be adopted because of the low reflec-tivity of conventional coatings in normal incidence.The compensation in this case is harder, due to theintrinsic difficulties arising from grazing-incidencemountings, which are very sensitive to aberrationsand misalignments. A configuration with two toroidalgratings has been presented and discussed in Ref. 13.The time compensation is again very effective, butonce the grating radii and the subtended angle arechosen, the compensation is optimum only in a nar-row spectral region. Also in this case, the global effi-ciency of the monochromator is expected to be ratherpoor. The efficiency is obviously the major factor dis-criminating among different time-delay compensatedmonochromators: an instrument with low output fluxcould not be useful for scientific experiments. Let usconsider as an example the experiment of HH gener-ation realized by the authors in collaboration with thegroup at Politecnico, Milan, Italy. The flux emitted atH23 was measured at �2 � 106 photons�harmonic�shot using a laser pulse of 25 fs and a few hundredmicrojoules.15,16 The corresponding intensity in thecase of a 50 �m diameter spot and 5 fs duration is�108 W�cm2. The harmonics are therefore suffi-ciently bright to be a useful probe for pump–probe
experiments, if a high-efficiency time-delay compen-sated monochromator is provided.
We present the design of a time-delay compensatedgrating monochromator with high efficiency and tun-able in a broad spectral band. It uses two gratings inthe off-plane mount, in which the direction of theincident light belongs to a plane parallel to the direc-tion of the grooves. It is well known that the efficiencyof such a configuration is much higher than that ofthe classical diffraction mount and very close to thereflectivity of the coating.17–20 It will be shown thata grazing-incidence time-delay compensated mono-chromator with two gratings used in the off-planemount can be operated in a very large spectral regionin the EUV with effective time compensation andhigher efficiency than that of the classical diffractionmount. The principle of the off-plane mount is brieflypresented in Section 2. The design of the time-compensated monochromators is discussed in Section3. Finally, a comparison with the classical mount ispresented in Section 4.
2. Off-Plane Mount
The off-plane mount, also called the conical diffrac-tion mount, differs from the classical one in that theincident and diffracted wave vectors are almost par-allel to the grooves.21 The geometry is shown in Fig.1. The direction of the incoming rays is described bytwo parameters, the altitude and the azimuth. Thealtitude � is the angle between the direction of theincoming rays and the direction of the grooves. Itdefines the half-angle of the cone into which the lightis diffracted: all the rays leave the grating at thesame altitude angle at which they approach. The az-imuth � of the incoming rays is defined to be zero ifthey lie in the plane perpendicular to the gratingsurface and parallel to the rulings, so � is the azi-muth of the zero-order light. Let � define the azimuthof the diffracted light at wavelength � and order m.The grating equation is written as
sin �sin � sin �� � m� , (2)
where � is the groove density.The blaze condition of maximum efficiency is de-
scribed as in classical diffraction: The light has toleave the grating in such a way that it performs aspecular reflection on the groove surface, that is, � � � 2�, where � is the blaze angle of the grating.In addition, shadowing effects from adjacent groovesmust be avoided, that is, � �. It follows that thehighest efficiency of a blaze grating in the off-planemount is achieved when � � � �, that is, when eachgroove of the grating is seen by the incident ray as aportion of a plane mirror. The grating equation in theblaze condition becomes 2 sin sin � � m� , indicat-ing that both incident and diffracted rays at the blazewavelength lie in a plane that is parallel to the di-rection of the grooves and also perpendicular to theirsurface. It has been theoretically shown and experi-mentally measured that the efficiency in the off-planemount is close to the reflectivity of the coating, as a
result much higher efficiencies than those in the clas-sical diffraction mount can be obtained in theEUV.22–24
3. Time-Delay Compensated Monochromator in theOff-Plane Mount
Two configurations are presented here using theoff-plane mount, either with plane or concave grat-ings.
A. Scheme with Plane Gratings
The off-plane mount has been extensively studied inthe case of a plane grating illuminated in parallellight.25 In the case of a source at a finite distance, thisrequires the use of two additional grazing-incidencemirrors for the collimation and focusing of the light.Consequently, the design of a time-delay compen-sated monochromator requires six optical elements,as schematically shown in Fig. 2.
The monochromator is divided into two equal sec-tions, each with two toroidal mirrors and a planegrating. The first section gives a spectrally dispersedimage of the source of the HHs on the intermediateplane, where a slit carries out the spectral selection ofthe harmonics. Only a selected portion of the spec-trum, i.e., a single harmonic or a set of few harmonics,propagates through the slit toward the second sectionthat compensates for both the temporal spread andthe spectral dispersion and gives a spectrally selectedstigmatic image on its focal plane.
The first mirror of each section acts as the colli-mator, the second mirror as the condenser. The fourmirrors are operated at equal grazing angle andunity magnification to minimize the aberrations,i.e., the input arm of each of the two collimators isequal to the output arm of each of the two condens-ers. With reference to Fig. 2, the term “input arm”refers to the two collimators and indicates the dis-tance between the source of the HHs and the vertexof mirror 1 and the distance between the slit andthe vertex of mirror 3. The term “output arm” refers
to the two condensers and indicates the distancebetween the vertex of mirror 2 and the slit andthe distance between the vertex of mirror 4 andthe output focal point. The tangential and sagittalradii, indicated, respectively, as R and , are thesame for all four mirrors and are chosen by
R �2pM
sin �, � � 2pM sin �, (3)
where is the grazing angle of the four mirrors andpM is the input arm of the collimators or the outputarm of the condensers.
Wavelength scanning is performed by rotatingthe gratings around an axis tangent to their vertexand parallel to the grooves. In such a way, thealtitude angle � is kept constant while the azimuth� is varied with the wavelength to be selected in thecondition � �, following the grating equation2 sin sin � m� . The maximum efficiency condi-tion, that is, � � � �, is exactly fulfilled only at thewavelength �B � 2 sin sin ��m depending on theblaze angle of the grating profile. At different wave-lengths, the efficiency decreases because the gratingis operated off-blaze, although remaining higher thanthat of classical diffraction schemes.26
The spectral dispersion at the slit plane is
�l��
�m pM
cos �� m pM. (4)
To select the single harmonic Hn (n odd), i.e., to havethe adjacent harmonics completely filtered out, theslit aperture is
�SHn � m pM
��H�n�2��H�n�2�
2 , (5)
where ��H�n�2��H�n�2� indicates the difference in wave-length between the two harmonics H�n � 2� andH�n � 2�, that is expressed by
��H�n�2��H�n�2� � �0� 1n � 2 �
1n � 2�� �0
4
n2, (6)
where �0 is the laser fundamental wavelength, thatis, 800 nm for the Ti:sapphire laser.
The corresponding slit width results in
�SHn �2
n2 m pM�0. (7)
As an example, a monochromator for the 17–61 nmregion (H45-H13) is designed. Its characteristics arelisted in Table 1. The mirrors are operated with250 mm arms at a 3° grazing angle to have highreflectivity in the whole spectral region of operation(e.g., the gold reflectivity at 3° is approximately 0.87in the 17–61 nm region). Two 300 groove�mm planegratings at 5° altitude angle are used. The acceptedangular aperture is 10 mrad, which is higher thanthe harmonic divergence.27 The simulations of theoptical performance were performed by a ray-tracingprogram written and modified in our laboratory to cal-culate the length of the various ray trajectories.
The optical performance and the analysis of thecompensation of the optical paths are reported inTable 2 for some of the harmonics. The spread of thepath lengths in a single harmonic, i.e., the differencein length between the longest ray and the shortestone, are shown both at the slit plane and at the out-put plane. The differences in the path lengths arealmost completely canceled by the compensated con-figuration. The residual time spread at a fixed wave-length is less than 1 fs.
Fig. 2. Time-delay compensated monochromator for HHs withtwo plane gratings in the off-plane mount.
Table 1. Characteristics of the Time-Delay CompensatedMonochromator
Mirrors Toroidal
Input�output arms 250 mmIncidence angle 87°Tangential radius 9550 mmSagittal radius 26.2 mmSize 50 mm � 5 mm
Gratings Plane
Groove density 300 grooves�mmAltitude angle 5°Size 30 mm � 5 mmWavelength region 17–61 nm (H45–H13)Total monochromator length 1.3 m
Gratings Toroidal
Groove density 300 grooves�mmTangential radius 2840 mmSagittal radius 21.7 mmSize 30 mm � 5 mmAltitude angle 5°Input�output arms 250 mmWavelength region 17–61 nm (H45-H13)Total monochromator length 1 m
The second condition for time compensation thathas to be verified is that rays at different wavelengthswithin the spectrum of the pulse to be selected arefocused on the same point and with equal opticalpaths. The FWHM spectral width of the nth har-monic, assumed to be Fourier-transform limited, isderived by Eq. (1) as
��1�2,Hn �1
n2
�02
��1�2
2.772�c , (8)
where c is the speed of light in vacuum.The spreads of the path lengths of rays at different
wavelengths within the spectrum of the selected har-monic are reported in Table 3 for pulses of 25 and 5 fs.The rays are focused on the same point because of thenegative dispersion of the second grating (i.e., thetotal spectral dispersion of the monochromator iszero) with a residual maximum time spread of ap-proximately 1 fs.
B. Scheme with Concave Gratings
Concave gratings are often used in EUV spectros-copy in the classical mount to minimize the numberof optical elements and maximize the instrumentthroughput. The simplest of such monochromatorsconsists of a single optical element, namely, the grat-ing, which provides both the spectral dispersion andthe spatial reimaging of the source.14
A schematic of the time-delay compensated mono-chromator with concave gratings in the off-planemount is shown in Fig. 3. The two gratings aremounted in time-delay compensated configurationand subtractive dispersion.28 Each grating providesboth the spectral dispersion and the focusing. In this
way, a polychromatic point source formed by the con-tributions of discrete wavelengths is imaged on thegrating focal plane in several monochromatic pointscorresponding to the different wavelengths: They arespatially distinct because of the spectral dispersionand focused because of the focusing properties of theoptics. Since the gratings work in grazing incidence,the focusing has to be performed by a surface withtwo different radii in the tangential and sagittalplane, such as a toroidal one. As in the case of usingplane gratings, wavelength scanning is performed byrotating the gratings around an axis tangent to theirvertex and parallel to the grooves.
The configuration presented here has two toroidalgratings. Each grating is operated in Rowland con-figuration, i.e., with equal entrance and exit arms, tohave minimum aberrations on its focal plane. Thetangential and sagittal grating radii, indicated, re-spectively, as R and , are calculated to minimize thedefocusing within the spectral range to be acquired.The explicit formulas for R and can be derived fromthe expressions of the tangential and sagittal defo-cusing terms in the light path function,29,30 also tak-ing into account the geometry of the off-plane mountshown in Fig. 4. The curves for zero tangential andsagittal defocusing are expressed, respectively, by
sin 2�
r�
sin 2��
r��
sin � � sin ��
R
� �z
r�2�1 � 2 sin 2�
r�
sin �
2R �� �z�
r��2�1 � 2 sin 2��
r��
sin ��
2R �� 0, (9)
Table 2. Optical Performance and Analysis of the Compensation of Optical Path Lengths for the Time-Delay Compensated Monochromatora
aThe source divergence is 10 mrad. ABOUT indicates the FWHM aberrations of the image at the output plane. �SHn is the slit width toselect the harmonic Hn. �SLIT is the optical path spread at the slit plane. �OUT is the optical path spread at the output plane.
Table 3. Analysis of the Compensation of Optical Path Lengths Within the Spectrum of the Harmonics to be Selecteda
where the symbols �, ��, r, r�, z, z� are defined inFig. 4.
In the following, the grating will be supposed to beoperated in the condition � � and with equal en-trance and exit arms p � q. This gives r � r� � r,z � z� � z, and � � �� � �. Equations (9) and (10)are then expressed as
R �p
sin
cos 2
cos
�
�1 � tan 2 cos 2��1 � tan 2 �32 tan 2 sin 2�
1 � tan 2 � tan 2 � 2 tan 2 sin 2,
(11)
� � p sin cos 1 � tan 2 � �3�2�tan 2 sin 2
1 � tan 2 � �5�2�tan 2 sin 2.
(12)
The altitude angle is small because of the grazingincidence on the gratings � � 10°�. Equations (11)and (12) are then finally reduced to
R �p
sin cos 2 cos , (13)
� � p sin cos . (14)
Once a reference wavelength �R within the spectralregion of operation has been selected, the referenceazimuth angle R is calculated from Eq. (2) as
R � sin �1� m�
2 sin �, (15)
and the radii are chosen from Eqs. (13) and (14)with � R. They are slightly smaller than the radiiof a toroidal mirror used in the same conditions as thegrating, i.e., with the same arms and altitude angle. Toselect a single harmonic, the spectral dispersion of theslit plane and the slit width is calculated from Eqs.(4)–(7) where p is replaced by pM.
The monochromator for the 17–61 nm region isalso designed with toroidal gratings. Its characteris-tics are summarized in Table 1. Two 300 groove�mmtoroidal gratings are used with a 250 mm arm and 5°altitude angle. It is intended that the rulings shouldbe so spaced on the concave surface as to be equi-distant on the chord of the circular arc. Also fortoroidal gratings, the maximum efficiency conditionis exactly fulfilled only at the blaze wavelength�B � 2 sin sin ��m depending on the blaze angle ofthe grating profile. The optical performance and theanalysis of the time compensation are reported inTable 2. The use of toroidal surfaces is very effectivein the correction of the aberrations, which are wellconfined below 15 �m in the output plane. The resid-ual time spread at a fixed wavelength is again lessthan 1 fs. The spreads of the path lengths of rays atdifferent wavelengths within the spectrum of the se-lected harmonic are in the 1–2 fs range, as shown inTable 3.
4. Comparison with the Classical Mount
The design with plane gratings presented in Sub-section 3.A can also be applied to the classicalmount. With reference to Fig. 2, the groove direc-tion and the slit have to be rotated by 90°, i.e., the
Fig. 4. Geometry of the off-plane mount for a toroidal grating. S,source point; O, the grating vertex; I, image point; p, grating en-trance arm (i.e., the distance between the source point and thegrating vertex); q, grating exit arm (i.e., the distance between thegrating vertex and the image point).
Fig. 3. Time-delay compensated monochromator for HHs withtwo toroidal gratings in the off-plane mount.
grooves are perpendicular to the direction of prop-agation of the light and also the direction of spectraldispersion is perpendicular to the off-plane case.The gratings are operated at a constant deviationangle, and wavelength scanning is performed by arotation around an axis parallel to the groove, tan-gent to the grating surface and passing through thegrating center. The diffraction efficiency has beenmeasured to be much lower than that in the off-plane case,26 giving a decrease on the output flux ofapproximately 1 order of magnitude when consid-ering the use of two gratings.
Also the design with two toroidal gratings of Sub-section 3.B can be applied to the classical mount.13 Ithas been shown that the compensation of the opticalpaths is of the order of 1–2 �m. Again, the gratingsare operated at constant deviation angle, and thescanning in wavelength is performed by the rotationof the gratings around an axis tangent to their vertexand parallel to the grooves. The time-delay compen-sated monochromator is expected to have no movingparts except the grating rotation, i.e., constant en-trance and exit arms and fixed intermediate slit,since the source of the HHs is not movable, and theoutput focal point should be fixed for the experi-ments. Then each of the two sections of the instru-ment has to be designed as a simple monochromatorwith fixed arms. Unfortunately, it is well known thatthe main difficulty of a design with a grazing-incidence toroidal grating in a classical mount is tohave a stigmatic image at a constant arm in a widespectral region, unless adopting gratings with non-uniform groove spacing or designs with two or moreoptics,14 increasing then the complexity of the time-delay compensated instrument.
In contrast, the off-plane mount with a toroidalgrating gives a stigmatic image at a fixed distancealso in a wide spectral region. This means that, giventhe entrance arm p and the grating radii R and , theoutput arm to have the best spectral and spatial fo-cusing must be almost constant with the grating ro-tation, so the image is always focused on the fixedintermediate slit plane and the monochromator hasno moving parts.
The length of the output arm qspet��� that mini-mizes the spectral defocusing at the wavelength �,which is the main aberration in the dispersion plane,is derived from Eqs. (9) and (11) in the approximationof grazing-incidence geometry as
qspet��� � � 2R sin
cos 2 cos �1p��1
� pcos R
2 cos � cos R. (16)
The length of the output arm qspat��� that minimizesthe spatial defocusing at wavelength �, that is, themain aberration in the plane perpendicular to thedispersion plane, is similarly derived from Eqs. (10)and (12) as
qspat��� � �2�
cos sin �1p��1
� pcos R
2 cos � cos R.
(17)
It is clear from Eqs. (16) and (17) that a grazing-incidence toroidal grating in the off-plane mount isthen perfectly stigmatic independently from the grat-ing rotation, i.e., qspet��� � qspat��� � q���. We foundhere that the system is stigmatic; that is, the image ofa point source is a point, at least for small � when thecontribution of higher-order aberrations can be ne-glected. This is a fundamental difference with thedesign of toroidal gratings in classical diffractionwhere the stigmaticity is guaranteed only at a singlewavelength.
At the reference wavelength �R the time-delay com-pensated monochromator operates in Rowland condi-tion, that is, q��R� � p. If no moving parts arerequired, the image of the HH source has to be spec-trally dispersed and focused on the fixed intermedi-ate slit plane for each wavelength, i.e., the variationsof the position of the grating focal point with thewavelength have to be minimized. The relative vari-ations of q��� are expressed by
�q���p �
q��� � pp � 2
cos R � cos
2 cos � cos R. (18)
The reference wavelength �R, hence the reference an-gle R, has to be selected to minimize the relativevariations given by Eq. (18) within the whole spectralrange to be acquired. As an example, the graphs ofthe relative variations of the output arm for � rangingin the 2°–10° interval, and different R are shown inFig. 5. In such a case, the choice R � 7° reduces thevariations of the nominal arm to less than 1.5%.
In the case of the monochromator previously de-signed, the absolute variations of the nominal output
Fig. 5. Relative variations of the nominal output arm for a toroi-dal grating in the off-plane mount. The azimuth angle � ranges inthe 2°–10° interval. Three curves with different R are shown.
arms are lower than 1 mm on the whole spectralregion of operation, corresponding to a defocusing onthe (fixed) intermediate slit and on the (fixed) outputfocal plane of lower than 10 �m.
5. Conclusions
The design of a time-delay compensated gratingmonochromator with high efficiency and tunable ina very broad spectral band has been presented, suit-able for the spectral selection of ultrashort pulses inthe extreme-ultraviolet region. It uses two gratingsin the off-plane mount, which is known to givemuch higher efficiency than the classical diffractionmount. The spread of the optical path lengthscaused by the first grating is compensated for by asecond grating in negative dispersion, so the ultra-short temporal duration of the pulse is preserved.Both configurations with plane or concave gratingshave been discussed and compared with similarconfigurations with gratings in the classical mount.In particular, it has been shown that the use of twotoroidal gratings in the off-plane mount gives atime-delay compensated grazing-incidence mono-chromator with the minimum number of optics andno moving components even in a broad spectralregion. The simulations of the performance of amonochromator for the 16–61 nm region show thatthe time compensation could be as good as a fewhundred attoseconds for both configurations. In par-ticular, the toroidal grating design is more elegant,compact, and simpler to be aligned, although sometechnological effort is required by the manufacturersof such concave optics to guarantee a diffraction effi-ciency as high as the plane substrates.
In the case of high-order harmonic generation inthe extreme-ultraviolet region by ultrashort laserpulses, a monochromator with two gratings used inthe off-plane mount can be operated in a very largespectral region, with effective time compensation andhigh efficiency.
The authors acknowledge the contribution of PaoloZambolin to the mechanical design of the differentconfigurations and thank Giuseppe Tondello formany useful discussions. This work has been par-tially supported within the framework of the Self-Amplified Pulsed Source for Coherent Radiation(SPARC) Special Integrative Research Fund (FISR)project funded by the Italian Ministry for Universityand Scientific Research.
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