The process of transition from an octagonal quasicrystal to a crystal with P-Mn-type structure in Cr-Ni-Si alloy was investigated theoretically and experimentally.Using the linear phason strain field theory, the computer simulation of the diffraction patterns described the process of transition.

The smile effect, which happens when various light-emitting units convert vertical offsets into angular offsets following fast-axis alignment, is an unavoidable part of the packaging process for diode laser arrays and has a detrimental influence on the feedback locking of external cavity diode lasers. The external cavity spectral beam combining system without output coupler, which employs the 0th order diffracted light with low grating energy to enable feedback locking of the light-emitting unit, is particularly severely impacted by the grin effect. The external cavity spectral beam combining system without output coupler uses three different types of corrective structures to simulate and explain the grin effect in various ways. The results show that while also ensuring adequate feedback and better combined beam quality, the double - separated fast-axis collimator can significantly correct the smile effect-induced beam shift. However, some light-emitting units' output beams cannot be corrected for the S-shaped smile effect with complex position offset changes. The fast-axis telescope system can effectively offset the inadequate feedback brought on by the various types of grin effect, but it is unable to enhance the beam quality of the combined beam spot, which degrades as the degree of smile effect increases. The combination of double-separated fast-axis collimator and fast-axis telescope system can complement each other to ensure sufficient feedback for different forms of smile effect to achieve stable wavelength locking and better beam quality of the combined spot.