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We discuss requirements on relativistic-irradiance (I0 > 1018 W/cm2) high-power (multi-terawatt) ultrashort (femtosecond) lasers for efficient generation of high-order harmonics in gas jet targets in a new regime discovered recently (Pirozhkov et al., 2012). Here, we present the results of several experimental campaigns performed with different irradiances, analyse the obtained results and derive the required laser parameters. In particular, we found that the root mean square (RMS) wavefront error should be smaller than ~100 nm (~λ/8). Further, the angular dispersion should be kept considerably smaller than the diffraction divergence, i.e., μrad level for 100–300-mm beam diameters. The corresponding angular chirp should not exceed 10−2 μrad/nm for a 40-nm bandwidth. We show the status of the J-KAREN-P laser (Kiriyama et al., 2015; Pirozhkov et al., 2017) and report on the progress towards satisfying these requirements.

We experimentally demonstrate a new regime of high-order harmonic generation by relativistic-irradiance lasers in gas jet targets. Bright harmonics with both odd and even orders, generated by linearly as well as circularly polarized pulses, are emitted in the forward direction, while the base harmonic frequency is downshifted. A 9 TW laser generates harmonics up to 360 eV, within the 'water window' spectral region. With a 120 TW laser producing 40 uJ/sr per harmonic at 120 eV, we demonstrate the photon number scalability. The observed harmonics cannot be explained by previously suggested scenarios. A novel high-order harmonics generation mechanism [T. Zh. Esirkepov et al., AIP Proceedings, this volume], which explains our experimental findings, is based on the phenomena inherent in the relativistic laser - underdense plasma interactions (self-focusing, cavity evacuation, and bow wave generation), mathematical catastrophe theory which explains formation of electron density singularities (cusps), and collective radiation due to nonlinear oscillations of a compact charge.

We present experimental results, theory, and simulations demonstrating two novel sources of coherent X-ray radiation generated in the relativistic laser (>10 18 W/cm 2 ) interaction with easily accessible, repetitive, and debris-free gas jet targets. The first source is based on a relativistic mirror reflecting a counter-propagating laser pulse. A strongly nonlinear breaking wake wave driven by an intense laser pulse can act as a semi-transparent relativistic flying mirror. Such a mirror directly converts counter-propagating laser light into a high-frequency (XUV or X-ray) ultrashort pulse due to the double Doppler effect. In the experimental demonstration with the 9 TW J-KAREN laser, the flying mirror generated in a He gas jet partially reflected a 1 TW pulse, providing up to ~10 10 photons, 60 nJ (~10 12 photons/sr) in the XUV range (12.8-22 nm). The second source is demonstrated with the laser power ranging from 9 to 170 TW in experiments with the J-KAREN and Astra Gemini lasers. The odd and even order harmonics generated by linearly as well as circularly polarized pulses are emitted forward out of the gas jet. The 120 TW laser pulses produce harmonics with ~3×10 13 photons/sr (~600 μJ/sr) in the 120±5 eV spectral range. The observed harmonics cannot be explained by previously known mechanisms (atomic harmonics, betatron radiation, nonlinear Thomson scattering, etc.). We introduce a novel mechanism of harmonic generation based on the relativistic laser-plasma phenomena (self-focusing, cavity evacuation, bow wave generation), mathematical catastrophe theory which explains the formation of structurally stable electron density singularities, spikes, and collective radiation of a compact charge driven by a relativistic laser.

Soft X-ray spherical normal-incidence mirrors (D = 60 mm, r = 2000 mm) with metal-carbon multilayer coatings, which provide a narrow-band reflection in the spectral range λ ~ 4.5 nm, have been synthesized using the pulsed laser deposition technique. The peak reflectivity of the multilayers reaches 13%, and the wavelength-to-bandwidth ratio λ/Δλ ~ 80. The spectral characteristics of the mirrors and their aperture uniformity have been evaluated using a broadband laser-plasma XUV radiation source. Discussed briefly are the applications to the investigation of complex spectra of broad-band sources (the Sun, laser-produced plasma, etc.) employing telescopes for X-ray astronomy and stigmatic high-resolution laboratory spectrometers.

We report the implementation of a novel diffraction spectroscopic instrument comprising two focusing multilayer mirrors at near-normal incidence and a conventional blazed plane grating at grazing incidence. The nearly perfect stigmatism and the theoretical resolving power above 6 × 104 are due to the separation of the focusing and dispersing functions. For higher throughput, two multilayer mirrors with nearly identical resonance reflection curves around λ0 135 A have been synthesized employing a magnetron ion-sputtering source. The instrument performance has been assessed using a laser-plasma radiation source. The spectral resolution in excess of 4 × 103 and the applicability to space-resolved spectroscopy and plasma diagnosis have been demonstrated.

A strongly nonlinear wake wave driven by an intense laser pulse can act as a partially reflecting relativistic mirror (the flying mirror) [S. V. Bulanov, et al., Bulletin of the Lebedev Physics Institute, No. 6, 9 (1991); S. V. Bulanov, et al., Phys. Rev. Lett. 91, 085001 (2003)]. Upon reflection from such mirror, a counter‐propagating optical‐frequency laser pulse is directly converted into high‐frequency radiation, with a frequency multiplication factor ∼4γ2 (the double Doppler effect). We present the results of recent experiment in which the photon number in the reflected radiation was at least several thousand times larger than in our proof‐of‐principle experiment [M. Kando, et al., Phys. Rev. Lett. 99, 135001 (2007); A. S. Pirozhkov, et al., Phys. Plasmas 14, 123106 (2007)]. The flying mirror holds promise of generating intense coherent ultrashort XUV and x‐ray pulses that inherit their temporal shape and polarization from the original optical‐frequency (laser) pulses. Furthermore, the reflected radi...

Theoretically demonstrated that aperiodic multilayer mirrors can compress negatively and positively chirped XUV pulses. In particular, temporal profiles of reflected trains of positively chirped high-order harmonics of a laser radiation were calculated.

Aperiodic multilayer structures (MSs) show promise as broadband soft X-ray mirrors for stigmatic diffraction spectroscopic instruments. We have derived aperiodic MSs optimized for maximum uniform normal-incidence reflectivity throughout a prescribed wavelength range, e.g., 130 - 190 a (R=24 %), 125 - 250 a (16 %), etc. Each of these aperiodic MSs exhibits an unparalleled integral reflectivity which substantially exceeds that of any periodic multilayer mirror pertaining to the corresponding wavelength range. Several Mo/Si aperiodic MSs were synthesized by magnetron sputtering on concave substrates to exhibit a relatively uniform reflectivity of (15 - 11)% in the 125 - 250 a range, close to the theoretical predictions. These multilayers served as the focusing elements of high-transmission stigmatic transmission grating spectrograph with a plate scale of 20 or 4 a/mm. The spectrograph was employed to investigate the laser plasma - gas jet interaction and characterize the Xe gas-jet laser-plasma XUV radiation source simultaneously with spatial and spectral resolution in the wavelength range above 124 a. We have theoretically explored into the reflection of extremely short X-ray pulses by MSs. Special-design aperiodic MSs were shown to possess the unrivaled capacity to reflect few-cycle X-ray pulses ranging into the attoseconds. Aperiodic MSs have been calculated that are capable of reflecting pulses which comprise only three wave periods of an X-ray electromagnetic wave.

A spectroscopic investigation was made of a debris-free soft X-ray radiation source driven by the pulses of a solid-state laser (0.4 J, 6 ns, 1.08 microns) focused in a pulsed xenon jet. Source images at a wavelength of 180 a were obtained using a concave soft X-ray multilayer mirror. To obtain space-resolved source emission spectra above 125 a, advantage was taken of a stigmatic high-transmission broadband diffraction spectrograph. The spectrograph comprised a large-aperture transmission diffraction grating (1000 or 5000 lines/mm) and a novel aperiodic focusing normal-incidence multilayer mirror possessing a uniform reflectivity in the 125 -250 a range. The yield of soft X-ray radiation was determined with the aid of a fast absolute-calibrated X-ray AXUV-5 photodiode. The photoabsorption in the peripheral gas-jet regions was found to play a significant role in the soft X-ray yield. Numerical model simulations were performed to elucidate the plasma dynamics. The soft X-ray spectrograph was also employed to study the interaction of the pulsed gas jet with the incident stream of the plasma produced by laser irradiation of a ~1-cm distant solid target. The soft X-ray spectra arising from the interaction were attributed to the charge exchange of multiply charged plasma ions with gas jet atoms.

A new approach is proposed for the design of wide band-pass multilayer optical elements for the hard x-ray spectral region. The method, based on the combination of analytical and numerical methods, solves the inverse problem consisting of inferring the composition profile of a depth-graded multilayer coating. First, assuming the multilayer d-spacing profile to be a monotone function of the depth and the d- spacing gradient to be large enough, we derived the differential equation that describes the change of period necessary to guarantee a given spectral reflectivity profile. Then, a computer code using an algorithm of steepest descent was used to refine numerically the multilayer period profile, each layer thickness being treated as an independent variable. When using the solution to the differential equation as a starting point of the direct problem, a many-fold decrease of computer time could be obtained. At each step, the spectral dependence of reflectivity was accurately computed using a standard matrix method. Simulations of the particular case of constant reflectivity and maximum integrated reflectivity over a wide spectral range are presented. The best choice of material pairs for comprising a depth-graded multilayer structure is discussed from the viewpoint of maximum achievable reflectivity and least number of bi-layers. Features of depth-graded multilayer mirrors, which are distinctive from conventional periodic mirrors, are examined.

We report the experimental results on production of multilayer soft x-ray and EUV mirrors and their application in x-ray spectroscopy and fluorescence analysis, as well as for development of EUV lithographic and x-ray microscopic devices and soft x-ray point sources. The problem of the production and the investigation of short-period x-ray multilayers and multilayer (gamma) -filters is discussed.

Spectral characteristics of plane multilayer amplitude molybdenum-silicon diffraction gratings (1000 and 2000 lines/mm, d-spacing of 115 angstrom), fabricated by electron- beam lithography, were determined using a laser-produced plasma XUV radiation source. The gratings were studied at near-normal incidence and at an angle of incidence of 36 degrees in stigmatic and quasi-stigmatic spectrograph systems with moderate dispersion. The task of focusing radiation was imposed on either a grazing-incidence toroidal mirror or a normal-incidence Mo-Si multilayer mirror with a d-spacing of 115 angstrom. The spectral profile of resonance reflection by the gratings was determined in the first and second Bragg orders of the multilayer structure for different angles of incidence. Line spectra of multiply charged F, Na, Mg, and Cl ions were recorded in the 160 - 230 angstrom range by means of these multilayer gratings, and the resolving power of the gratings was determined.

Along with ultrahigh-resolution narrow-band spectrometers, a demand exists for medium- and high-resolution stigmatic instruments of a survey type, covering a spectral range of more than a hundred angstroms. Here, we describe several stigmatic spectroscopic configurations intended for characterizing various soft x-ray radiation sources (laser- produced plasmas, XUV lasers, etc.) and optical components [multilayer mirrors (MMs), absorption filters, etc.] in a broad spectral range. The combination of a grazing-incidence toroidal mirror and a large-area transmission diffraction grating (TG) made up a broadband spectrograph with a medium dispersion, with a plate scale of 4-to-20 angstrom/mm, which has proven to be inherently suited for characterizing plane MMs and the laser-plasma source itself. Two versions of W- coated toroidal mirrors were used, which operated at grazing angles of 7.6 degrees and 4 degrees and had respective practical short-wave cutoffs at about 40 and 15 angstrom. Line spectra of low-Z targets and quasicontinuous spectra of a tungsten target were obtained with a resolution of about 800. The configuration of a TG spectrograph was used to characterize CoC MMs with a d-spacing of 38 angstroms fabricated on Si(111) substrates by e-beam deposition and Kr+ ion beam polishing of metal layers. The absolute reflectivities near 75 angstrom were measured at 10%. The combination of a large-area TG and a concave MM with a strong lateral gradient of the d-spacing made up a stigmatic spectrograph for the 110 - 300 angstrom range. When the gradient was parallel to the TG lines, the TG was placed in the converging beam. When the gradient was orthogonal to the grating lines, the TG dispersed, unlike the configurations used previously, the diverging beam incident on the focusing MM. Removing the entrance slit transforms the spectrograph into a spectroheliograph. The latter configuration is well suited for producing 2-D solar images in the radiation of spectral lines and far-field images of single- and many- frequency x-ray lasers.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Using soft x-ray multilayer mirrors (MMs) and a laser-plasma broadband radiation source, we have implemented a pulsed 0.5-Hz-repetition-rate source of polarized quasimonochromatic radiation in the XUV. The x-ray optical setup comprises a focusing MM at near-normal incidence, a plane polarizing MM at 41 degrees off axis, and a plane multilayer analyzer which can be rotated by 90 degrees with respect to the polarizer. A stigmatic broadband spectrometer comprising a grazing incidence toroidal mirror and a large-aperture (5 cm2) transmission grating (TG) has proved to be useful in spectroscopic characterization of plane multilayer mirrors and the laser-plasma source. The second (reference) x-ray optical channel comprises a focusing MM and serves to monitor the energy of individual pulses. The focusing MMs image the laser-plasma source onto the sodium-salicylate-covered surfaces of flexible 0.7-cm-long light guides 13 mm in diameter coupled through light-guide disks to photomultipliers outside the vacuum tank. The visible and VUV radiation outside the resonance reflection peak is rejected by free-standing Al filters placed before the detectors. The dimension of the x-ray source was measured at 100 microns (width at base) using a CCD array covered with sodium salicylate. The polarizance of the plane MM was measured at 98.2% while the peak theoretical value for this Mo-Si multilayer structure (2d equals 240 angstrom, N equals 25, lambdao equals 171.4 angstrom, 41 degrees off axis) is 98.75%. The polarized source yields of the order of 5 (DOT) 108 photons per pulse in the resonance reflection band of the MMs.

We have implemented a variety of stigmatic high-throughput high-resolution spectroscopic configurations in the XUV using focusing multilayer mirrors (MMs), transmission gratings (TGs), and conventional plane reflection gratings. A Type-I 1-m-long spectrograph, which comprises a couple of identical MMs with reflection peaks centered at 180 angstrom and a 1800 line/mm blazed grating operating in the second outside spectral order, has a residual astigmatism of 16 microns, a plate scale of 0.35 Angstrom/mm, a bandwidth of approximately 15 angstrom (FWHM), and a resolution of 24,000 (demonstrated). The solid angle of acceptance is a square which measures 0.03 rad multiplied by 0.015 rad. A density-dependent Stark shift of the 2p 4 3s levels of Mg IV was observed in a laser plasma. A Type-II highly versatile spectrometer, which comprises one focusing MM and a TG used to disperse a converging beam, offers a high throughput and a moderate dispersion, with a plate scale typically in the range 5 - 50 angstrom/mm. With respect to these applications, a number of Mo-Si MMs were synthesized on fused silica substrates (r equals 2000 mm, D equals 60 mm). In combination with a point-like laser-plasma broadband radiation source, the Type-II configuration is by itself inherently suited for spectroscopic characterization of imaging MMs. Our capacity to evaluate the spectral response of MMs has improved dramatically after invoking a 5-cm 2 -aperture TG with a density of about 1000 lines/mm initially intended for x-ray astronomy. Stigmatic line spectra in a range of 165 - 185 angstrom were obtained in the Type-II configuration, and a resolution of 500 was demonstrated.

A variety of normal‐incidence multilayer mirrors (MMs) intended for studies of astrophysical and laboratory soft‐x‐ray radiation sources have been synthesized on concave (r=1.6−2.0 m) fused silica substrates. The MMs range in resonance wavelength λ0 from 4.5 to 31 nm. Their imaging capability has been evaluated from small‐source imaging tests employing to a laser‐plasma broadband XUV radiation source and a high‐resolution XUV photographic film. The photographs testify to a subarcsecond angular resolution. For 17.5‐nm MMs, a resolution of at least ≊0.32 arcseconds has been demonstrated, which is only 2.4λ0/D for the MMs involved.

For XUV-imaging of the Sun with sub-arc second resolution it is proposed to use the Herschel telescope with aspherical (toroidal) multilayer mirror working at out-of-axis angle 1.5 - 2 degree(s). In that case aberrations (mainly astigmatism) are sufficiently reduced so high resolution better than 1' may be obtained. In comparison with the Ritchey-Chretien two- mirror telescope which is regarded as perspective to reach closely the diffraction limited resolution, the Herschel telescope is more simple, less critical to adjustment and has higher throughput. Toroidal mirrors with diameter D equals 30 mm, focal length F equals 800 mm and ratio of sagittal and meridional radii of curvature Rm/Rs equals 1.001 have been made on super polished fused quartz substrates (roughness better than 7 A). After shape correction mirrors were covered by Mo-Si coating for 175 A wavelength band. The mirrors were used in high resolution channel of the TEREK-C telescope designed for the CORONAS space solar observatory which was launched on March 2, 1994. An example of the solar image obtained by this telescope is presented.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A number of high-performance normal-incidence multilayer mirrors (MMs) have been fabricated on concave (r equals 1.6 - 2.0 m) fused silica substrates using laser deposition and a magnetron ion sputtering source. The resonance wavelengths (lambda) 0 equals 2nd of the MMs synthesized are proximate to 45, 130, 175, 190, and 304 angstroms. The MMs have been subjected to scrutiny by a spectroscopic technique employing a laser-plasma broadband XUV radiation source. The spectral shapes of the resonance reflection curves, the (lambda) 0 values, and the aperture uniformity (topography) of the mirrors have been determined spectroscopically. Normal-incidence reflection maxima, which correspond to higher-order reflection (k(lambda) equals 2n(lambda )d, k > 1), have been observed for all of the Mo-Si MMs with (lambda) >= 175 angstroms.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A novel diffraction spectroscopic instrument comprising two focusing multilayer mirrors (MMs) at near-normal incidence and a conventional blazed plane grating at grazing incidence has been implemented. A nearly perfect stigmatism and a theoretical resolving power above 6 X 104 are due to the separation of the focusing and dispersing functions. For higher throughput, MMs with nearly identical resonance reflection curves around (lambda) 0 approximately equals 135 angstroms have been synthesized employing a magnetron ion sputtering source. The instrument performance has been assessed using a laser-plasma XUV radiation source. The spectral resolution in excess of 4 X 103 and the applicability to space-resolved spectroscopy and plasma diagnosis have been demonstrated.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A new observation method of providing a precise collision of two full-power counter-propagating laser pulses is proposed and demonstrated. The method is a combination of top-view imaging, side-view shadowgram, extra-ultraviolet (XUV) spectrograph, and returning pulse monitoring. This allows us to align two counter-propagating laser pulses at their colliding point in a real situation (full power laser operation in plasma). The achieved spatial resolution of the monitor in the plasma is 1.35 µm with the precision level of alignment better than 15 µm even when there is plasma present.

Proton acceleration experiments involving a 5μm thick Ti foil target irradiation are carried out with the femtosecond Ti:sapphire laser JLITE-X. The plasma emission at 13.5nm is recorded employing concave multilayer mirrors, which image the front- and rear-side plasmas onto the sensitive surfaces of a fast x-ray photodiode and a backside-illuminated charge coupled device. Online time-of-flight fast-particle measurements are performed simultaneously with the extreme ultraviolet (XUV) measurements. A strong correlation is observed between the energetic proton signal and the spatiotemporal behavior of the XUV plasma emission. In particular, the longer duration of the prepulse-produced XUV plasma emission indicates a lowering of the maximum proton energy. This allows using the XUV emission for the diagnostics of the high-intensity laser–solid-target interaction.

We describe several spectroscopic techniques for space-resolved diagnostics of inhomogeneous plasmas from the line and continuous XUV spectra of multiply charged ions, involving measurements of temperature, density, ion composition, ablation velocity, etc. To this end, we have developed a family of stigmatic high-throughput spectroscopic instruments ranging in resolution from 500 to over 20000. The new instruments harness separation of the focusing and dispersion functions: the XUV radiation is dispersed by plane grazing-incidence gratings or transmission diffraction gratings while the focusing is transferred to concave normal-incidence multilayer mirrors or grazing-incidence toroidal mirrors. We have obtained medium-to-high resolution spectra of laser-produced plasmas to infer the plasma parameters (density profiles, expansion velocity, etc). The operating range of a spectrograph which incorporates periodic multilayer mirrors is confined to the resonance reflection band of the mirrors. To meet the demand for broadband stigmatic instruments, a panoramic (110 - 300 angstrom) medium-resolution spectrograph was made employing a Mo/Si multilayer mirror with a lateral gradient of the period structure (0.9 Angstrom/mm) and a transmission diffraction grating (5000 lines/mm). An alternative way to obtain panoramic stigmatic spectra involves the development of broadband aperiodic multilayer mirrors. We have developed a numerical technique based on the fast calculation of derivatives, which allows us to determine aperiodic structures with prescribed reflectance spectra and augmented integral reflectivity. This technique has proved to be efficient both in the soft and hard X-ray ranges.