Large-aperture gratings have significant applications in inertial confinement fusion, immersion lithography manufacturing and astronomical observation. Currently, it is challenging and expensive to manufacture sizable monolithic gratings. Therefore, tiled multiple small-aperture gratings are preferred. In this study, the impact of seam phase discontinuity on the modulation of the laser beam field was explored based on the measurement results of the Shenguang-II laser large-aperture multi-exposure-tiled grating. An innovative method for accurately calculating the phase jump of multi-exposure-tiled grating seams was proposed. An intensive electromagnetic field analysis was performed by applying rigorous coupled-wave analysis to a reasonably constructed micrometer-level periodic grating seam structure, and the phase jump appearing in millimeter-scale seams of large-aperture tiled gratings was obtained accurately.

In this paper, we study global-in-time, weighted Strichartz estimates for the Dirac equation on warped product spaces in dimension $n\geq 3$ . In particular, we prove estimates for the dynamics restricted to eigenspaces of the Dirac operator on the compact spin manifolds defining the ambient manifold under some explicit sufficient condition on the metric and estimates with loss of angular derivatives for general initial data in the setting of spherically symmetric and asymptotically flat manifolds.

The processing method applied to the side surface is different from the method applied to the light pass surface in neodymium phosphate glass (Nd:glass), and thus subsurface defects remain after processing. The subsurface defects in the side surface influence the gain uniformity of Nd:glass, which is a key factor to evaluate the performance of amplifiers. The scattering characteristics of side subsurface defects were simulated by finite difference time domain (FDTD) Solutions software. The scattering powers of the glass fabricated by a computer numerical control (CNC) machine without cladding were tested at different incident angles. The trend of the curve was similar to the simulated result, while the smallest point was different with the complex true morphology. The simulation showed that the equivalent residual reflectivity of the cladding glass can be more than 0.1% when the number of defects in a single gridding is greater than 50.

The physical meaning and essence of Fresnel numbers are discussed, and two definitions of these numbers for off-axis optical systems are proposed. The universal Fresnel number is found to be $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}N=(a^{2}/\lambda z ) \ast C_{1} +C_{2} $. The Rayleigh–Sommerfeld nonparaxial diffraction formula states that a simple analytical formula for the nonparaxial intensity distribution after a circular aperture can be obtained. Theoretical derivations and numerical calculations reveal that the first correction factor $C_{1} $ is equal to $\cos \theta $ and the second factor $C_{2} $ is a function of the incident wavefront and the shape of the diffractive aperture. Finally, some diffraction phenomena in off-axis optical systems are explained by the off-axis Fresnel number.

Considering the time delay in different hohlraum wall positions caused by oblique incidence, the spatio-temporal optical field distribution characteristics of a hohlraum wall, especially during the rising edge of a flat-topped pulse, is simulated by a fast Fourier transform method together with chromatography. Results demonstrate that beam propagation along the hohlraum wall is a push-broom process with complex dynamic spatial–temporal evolution. In the first few picoseconds, the optical intensity of the front position increases rapidly, while that of the rear position is relatively weak. The ratio $R$ of the optical intensity during the rising edge is smaller than that of the steady state. $R$ gradually increases and finally tends to the value of the steady state with time. Calculation also shows that, with shorter total width of the rising edge, $R$ of the optical field decreases and the difference compared to the steady state becomes larger. The evolution is more severe with smaller angle of inclination.

We report an alternative interruption scheme to effectively improve the abruptness of GaN/AlGaN superlattices by minimizing the asymmetric feature of different types of heterointerfaces. It is found by x-ray diffraction that the interface abruptness is degraded and the GaN thickness is reduced with the interruption time increasing. Detailed investigation with scanning transmission electron microscopy demonstrates that the Al diffusion and the interface etching effect at the GaN/AlGaN interface are the critical reasons leading to the interfacial asymmetry. An alternative interface–interruption scheme is then proposed to enhance the abruptness of the superlattice interfaces, and consequently, the emission efficiency can also be significantly enhanced.