Search Results (3)

Free electron laser (FEL) is capable of producing ultra-short X-ray pulses. The estimation of X-ray pulse propagation is the key process of X-ray FEL beamline design. By using the Kostenbauder matrix approach, the evolution of an ultra-short pulse in a beamline system can be calculated. Therefore, it is of significant importance to investigate the Kostenbauder matrices of different kinds of X-ray optics. In this work, we derive a unified 6 × 6 optical matrix to describe various kinds of X-ray optical elements, including varied-line-spacing (VLS) toroidal grating, VLS spherical grating, VLS cylindrical grating, VLS plane grating, toroidal grating, spherical grating, cylindrical grating, plane grating, toroidal mirror, spherical mirror, cylindrical mirror, and plane mirror. These optics are usually adopted in soft X-ray regime. We apply this method to describe the transverse focusing, pulse front tilt, and pulse stretching after an X-ray pulse going through a VLS plane grating monochromator (VLS-PGM). We also use this approach to simulate a grating compressor which can be used to compress chirped soft X-ray pulse. This work is helpful in the design and optimization of X-ray beamline systems. Full article

Variable-period scanning beam interference lithography (VP-SBIL) can be used to fabricate varied-line-spacing (VLS) plane gratings. The exposure phase modulation method to pattern a VLS grating with a desired groove density must be carefully devised. In this paper, a mathematical model of the total exposure dose for VLS plane grating fabrication is established. With model-based numerical calculations, the phase modulation effects of the parameters, including the fringe locked phase, fringe density, and step size, are analyzed. The parameter combinations for the phase modulation are compared and chosen, and the optimal coordinate for phase compensation is selected. The calculation results show that the theoretical errors of the groove density coefficients can be controlled within 1e-8. The mathematical model can represent the deposited exposure dose for patterning VLS gratings during the lithography process, and the chosen parameters and proposed phase modulation method are appropriate for patterning VLS gratings with VP-SBIL. Full article

Concerted rotations of a self-focused varied line-space diffraction grating about its groove axis and surface normal define a new geometric class of monochromator. Defocusing is canceled, while the scanned wavelength is reinforced at fixed conjugate distances and horizontal deviation angle. This enables high spectral resolution over a wide band, and is of particular advantage at grazing reflection angles. A new, rigorous light-path formulation employs non-paraxial reference points to isolate the lateral ray aberrations, with those of power-sum ≤ 3 explicitly expanded for a plane grating. Each of these 14 Fermat equations agrees precisely with the value extracted from numerical raytrace simulations. An example soft X-ray design (6° deviation angle and 2 × 4 mrad aperture) attains a resolving power > 25,000 over a three octave scan range. The proposed rotation scheme is not limited to plane surfaces or monochromators, providing a new degree of freedom in optical design. Grating rotation about its third (meridional) axis may be employed to cancel vertical deflection of the diffracted beam while maintaining the above aberration correction. This enables a simpler (pure rotary) motion for the exit slit and a fixed beam direction both horizontally and vertically. Full article