This paper investigates perturbation to the Noether symmetry of discrete holonomic nonconservative dynamical systems on a uniform lattice. Firstly, we give the Noether theorem of system. Secondly, both criterion of perturbation to the Noether symmetry and the Noether adiabatic invariants of system are obtained. Finally, an example is given to illustrate these results.
The output far-field intensity distributions of off-axial cylindrical hybrid resonator with different mirror misalignments are simulated by coordinate transformation fast Fourier-transform algorithm. The simulations showed that the mirror misalignments influence is different in anticlockwise and clockwise tilt direction. According to the calculation results, the output beam quality of off-axial unstable resonator is analyzed, from the aspects of M^2 value and power in the bucket curves. Furthermore, the analysis brings out an interesting contradiction that the beam quality changing evaluated by M^2 value is different from that by power in the bucket curves when the mirror misalignments occurred in anticlockwise direction. It demonstrated that the beam quality evaluation of off-axial unstable resonator should not be one-sided.