Optimum design of a grazing-incidence flat-field spectrograph with a spherical varied-line-space grating

A grazing-incidence spectrograph is designed by use of the flat-field image-focusing property of a spherical varied-line-space grating. Optimum grating parameters for mechanical ruling are selected by application of genetic algorithms. Two gratings, one for 2-5-nm and the other for 5-20-nm spectral regions, are designed, and their fabrication tolerances are analyzed.     

Fabrication and evaluation of a wideband multilayer laminar-type holographic grating for use with a soft-x-ray flat-field spectrograph in the region of 1.7 keV

A multilayer laminar-type holographic grating having an average groove density of 2400 lines/mm is designed and fabricated for use with a soft-x-ray flat-field spectrograph covering the 0.70-0.75 nm region. A varied-line-spaced groove pattern is generated by the use of an aspheric wavefront recording system, and laminar-type grooves are formed by a reactive ion-etching method. Mo/SiO2 multilayers optimized for the emission lines of Hf-M, Si-K, and W-M are deposited on one of the three designated areas on the grating surface in tandem. The measured first-order diffraction efficiencies at the respective centers of the areas are 18%-20%. The flat-field spectrograph equipped with the grating indicates a spectral linewidth of 8-14 eV for the emission spectra generated from electron-impact x-ray sources.     

Efficiency and polarization performance of a multilayer-coated laminar grating in the 6.5-6.9-nm wavelength region

We applied a Mo/B4C multilayer coating to a laminar holographic grating with 2400 grooves/mm and a 1-m radius of curvature. By use of synchrotron soft x rays the multilayer-coated grating was evaluated to have diffraction efficiencies of 3.1% and 0.017% for s- and p-polarized radiation, respectively, at a 6.7-nm wavelength at a 45.35 degrees grazing angle of incidence in the +1 (inside) grating order. Thus the polarizance was estimated to be 98.9% at least. The zero-order peak was suppressed by the destructive interference caused by the groove profile.     

Optical constants of gold in the soft-x-ray region from reflection and transmission measurements

The optical constants of gold deposited on 300-nm-thick freestanding polyimide films have been measured in the energy range of 40-1350 eV. The optical constants of the polyimide films were known from a previous investigation. By performing both transmission measurements with Kramers-Kronig analysis and multiangle reflection measurements with analysis by fitting to a Fresnel multilayer model including roughness, one could carry out a detailed error analysis. In the energy range above 500 eV systematic deviations between the results obtained by both methods were found. For gold films the discrepancies can be attributed to deviations from Beckmann-type behavior at small grazing-incidence angles.     

Mo/Si multilayer-coated ruled blazed gratings for the soft-x-ray region

Two Mo/Si multilayer-coated blazed gratings have been fabricated for operation at soft-x-ray wavelengths above the Si L edge, λ ≥ 12.4 nm, at (near) normal incidence. The sawtooth profile of the grating structure was mechanically ruled into a 200-nm Au film that was deposited onto a plane glass substrate. To smooth the rough Au surface and to prevent interdiffusion of the Au film with the upper Mo/Si multilayer, a carbon film was evaporated onto the Au grating surface of one of the gratings before the deposition of the multilayer coating. We matched the multilayer grating, working on blaze in the third diffraction order, in which an absolute diffraction efficiency of 3.4% at a wavelength of 14 nm was measured, whereas only 1.1% was achieved for a similar grating (without a carbon interlayer). These efficiencies are higher than those obtained for other ruled blazed gratings reported in the literature. As a result of the multilayer and grating periodicity, the wavelength of diffraction can be tuned bya rotation of the grating, which is important for application in a soft-x-ray monochromator.     

Quasi-Talbot effect of a grating in the deep Fresnel diffraction region

Based on the theory of scalar diffraction, the diffraction of gratings in the deep Fresnel diffraction region is developed, and the general formula of the diffraction intensity of the one-dimensional grating is presented by using the Hankel function. Through numerical calculations, some interesting diffraction phenomena are found. In the deep Fresnel diffraction region, the dominant effects, with increasing propagation distance from the grating, are, in order, the geometrical effect, the quasi-geometrical effect, and the interference and diffraction effects. Furthermore, the diffraction intensities vary periodically in the diffraction effect region with increasing propagation distance. Quasi-Talbot imaging of the grating exists in the interference and diffraction regions, and the intensity distributions most similar to the structure of the grating are not at the exact Talbot distances. These phenomena in the deep Fresnel diffraction region are distinct from those in the Fresnel diffraction region. The formation origin of quasi-Talbot imaging of the grating is also discussed, and the numerical calculations powerfully verify the theoretical results.     

Effect of tin diffusion on the optical behavior of float glass in the soft-x-ray region

The optical responses of two sides of float glass in the soft-x-ray region were studied at the Indus-1 synchrotron facility. To the best of our knowledge these are the first experimentally obtained optical data for both sides of float glass in the soft-x-ray region. Optical constants delta and beta were determined by use of angle-dependent reflectance techniques in the wavelength range 80-200 A. On the side of the glass that was tin indiffused, a significant difference in delta value from that of the non-tin-side surface was observed. The measured data were compared with Henke's tabulated value of SiO2. The surface roughness of float glass was separately determined by hard-x-ray reflectivity to minimize the number of fitting variables. The effect of a contamination layer on the determination of optical constants was avoided by an appropriate sample-cleaning method.     

Design of a high-throughput grazing-incidence flat-field spectrometer

The optical design of a high-throughput grazing-incidence flat-field spectrometer is presented. The spectral focal curve is almost a straight line because of the flat-field focusing properties of spherical variable-line-spaced gratings. The angular acceptance in the direction perpendicular to the plane of dispersion is maximized by means of a focusing spherical mirror mounted with its tangential plane coincident with the sagittal plane of the grating. Analytical calculations for the determination of the optimum mirror parameters are presented. A spectrometer for high-throughput experiments in the 800-60-eV region is designed with an extreme-ultraviolet-enhanced CCD detector: when the available flux is compared with that of a spectrometer with the same kinds of grating and detector but without a focusing mirror, the increase is as much as a factor 3.     

Analysis of multimode effects in the free-propagation region of a silicon-on-insulator-based arrayed-waveguide grating demultiplexer

Multimode effects in the free-propagation regions (FPRs) of an arrayed-waveguide grating (AWG) demultiplexer based on silicon-on-insulator are considered. Some undesired multimode effects, such as the increase of the insertion loss and the cross talk, are studied by use of a method of three-dimensional guided-mode propagation analysis. It is found that the multimode effects for the edge channels are more serious than those for the central channel. For an AWG demultiplexer with a small channel number, the multimode effects can be minimized by choosing appropriate FPR parameters such as the length and the thickness of the FPR. The coupling coefficient between the FPR and an arrayed waveguide is sensitive to the thickness of the FPR.     

Electromagnetic forces in the vacuum region of laser-driven layered grating structures

Symmetric multilayer grating structures that have an embedded vacuum channel and that are powered by external laser beams are analyzed for their ability to manipulate charged particle beams. It is shown that acceleration, deflection and focusing forces can all be generated in a controlled fashion from the same grating architecture and by adjustment of phase of the incoming laser beams     

Color separation of high-density dielectric rectangular grating in the Fresnel diffraction region

A high-density dielectric rectangular grating is designed for color separation in a Fresnel diffraction field. The Fresnel field distribution is analyzed and the optimization conditions for color separation are given. The process of the modes propagating and energy exchanging with the diffraction orders are expressed by modal method. The color separation for different polarizations can be realized. The energy efficiency is 96.3% at the 633 nm wavelength and 86.9% at the 488 mm wavelength for both TE polarizations, while the energy efficiency is theoretically 96.3% at the 633 nm wavelength for TE polarization and 90.6% at the 488 nm wavelength for TM polarization. The field distributions are scanned by the near-field scanning optical microscopy, and the efficiency is 71.2% for the 633 nm wavelength and 67.3% for the 488 nm wavelength for both TE polarizations experimentally.     

Time-delay compensated monochromator in the off-plane mount for extreme-ultraviolet ultrashort pulses

The design of ultrafast monochromators using grazing-incidence gratings in the off-plane mount for the spectral selection of extreme-ultraviolet femtosecond pulses in a broad spectral region is presented. Their application in the selection of high-order laser harmonics is analyzed in detail. The main advantage of the off-plane mount is a much higher efficiency than that of the classical mount. It is shown that two-grating configurations preserve the length of the optical paths of different diffracted rays, maintaining the extremely short time duration of the pulse. Configurations with plane or toroidal gratings are discussed. As a test case, the design of a monochromator for the 17-61 nm region with a time compensation better than 1 fs is presented.     

Coma correction and extension of the focusing geometry of a soft-x-ray monochromator

I show analytically and numerically how to use a varied line-space grating to reduce coma aberration in a soft-x-ray synchrotron radiation monochromator: a plane grating in combination with one or more spherical mirrors arranged in front of the grating and rotated around a fixed axis outside the mirror surface. It seems that the variation extent of groove spacing is too small to be manufactured; thus, a holographic grating of equivalent imaging properties is proposed. Based on the analysis of a focusing equation, I found that, if the plane grating is replaced by a spherical one, the monochromator can also be made free of defocus.     

Efficiency calibration of the first multilayer-coated holographic ion-etched flight grating for a sounding rocket high-resolution spectrometer

We have fabricated the four flight gratings for a sounding rocket high-resolution spectrometer using a holographic ion-etching technique. The gratings are spherical (4000-mm radius of curvature), large (160 mm x 90 mm), and have a laminar groove profile of high density (3600 grooves/mm). They have been coated with a high-reflectance multilayer of Mo/Si. Using an atomic force microscope, we examined the surface characteristics of the first grating before and after multilayer coating. The average roughness is approximately 3 A rms after coating. Using synchrotron radiation, we completed an efficiency calibration map over the wavelength range 225-245 A. At an angle of incidence of 5 degrees and a wavelength of 234 A, the average efficiency in the first inside order is 10.4 +/- 0.5%, and the derived groove efficiency is 34.8 +/- 1.6%. These values exceed all previously published results for a high-density grating.     

Thin-film interference effects on the efficiency of a normal-incidence grating in the 100-350-A wavelength region

Thin-film interference effects were observed in the normal-incidence efficiency of a 2400-groove/mm replica grating. The efficiency was measured in the 100-350-A wavelength range and had an oscillatory behavior that resulted from the presence of a thin SiO(2) coating. The thicknesses of the SiO(2) and the underlying oxidized aluminum layers were inferred from computer modeling of the zero-order efficiency. The efficiencies in the diffracted orders were calculated with the modified integral approach and accounting for the multilayer coating and the groove profile derived from atomic force microscopy. The calculated and measured efficiencies were in good agreement.