Design and theoretical studies of a novel transmission self-focusing grating

Combining the dispersion properties of traditional transmission grating and the focusing properties of Fresnel zone plate, we propose a novel transmission self-focusing grating used in soft X-ray region. According to Fresnel diffraction theory, the gratings diffraction properties are derived theoretically, proving that there is a focal plane perpendicular to the grating plane and light waves with different wavelengths focus on different positions of the focal plane. At the focal plane, the photon energy varies linearly with the focal position, which means its able to achieve linear measurement of photon energy. The broadening pattern of focal spot at and perpendicular to the focal plane are obtained by analytic derivation. According to Kirchhoff diffraction formula, a detailed numerical simulation of diffraction patterns is performed by setting practical parameters, and the corresponding measured spectral range and spectral resolution are discussed in detail.