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Single-order diffraction gratings with quasi-random structures are effective optical elements in suppressing harmonics contamination. However, background intensity fluctuations introduced by quasi-random structures may affect the measurement of the spectra and the fluctuations lack quantitative description. A unified theoretical method is provided to describe quasi-random diffraction structures with arbitrary distribution functions and an arbitrary number of microstructures. The effect of the number of microstructures and distribution functions on the level of background fluctuations is evaluated. This work provides important guidance for the design and optimization of single-order diffraction gratings, which are attractive for spectral analysis and monochromator applications in synchrotron beam lines.

Dielectric laser accelerator (DLA) is a promising technology for achieving high gradient acceleration in a compact design. Its advantages include ease of cascading and energy gain per unit distance that can exceed that of conventional accelerators by two orders of magnitude. This paper establishes rules for efficient particle acceleration using dielectric structures based on basic equations, proposes a design principle for DLA structures with clear physical images, and verifies the accuracy of the corresponding energy gain formula. DLA structures with different specifications, materials, and geometric shapes are constructed, and the achievable acceleration gradient is calculated. Our results demonstrate that effective acceleration can be achieved when the electric field sensed by particles in the acceleration cavity has zero frequency, which provides a powerful method for designing such devices. Furthermore, we demonstrate that the simplified formula for calculating energy gain presented in this paper can accurately determine the energy gain of particles during the design of dielectric accelerator acceleration structures.

Dielectric laser accelerators (DLAs) are considered promising candidates for on-chip particle accelerators that can achieve high acceleration gradients. This study explores various combinations of dielectric materials and accelerated structures based on the inverse Cherenkov effect. The designs utilize conventional processing methods and laser parameters currently in use. We optimize the structural model to enhance the gradient of acceleration and the electron energy gain. To achieve higher acceleration gradients and energy gains, the selection of materials and structures should be based on the initial electron energy. Furthermore, we observe that the variation of the acceleration gradient of the material is different at different initial electron energies. These findings suggest that on-chip accelerators are feasible with the help of these structures and materials.