Deformation of volume Bragg gratings affecting M²-factor of Gaussian beams

Considering the changes of the background refractive index and the period of the volume Bragg grating (VBG) induced by surface thermal distortion, which further lead to the change of the dielectric constant of the VBG, the propagation properties of Gaussian laser beams propagating in the VBG have been studied. The scalar wave equation for Gaussian beam propagation in the VBG with deformation has been solved numerically and iteratively by finite-different and sparse matrix methods. The changes of the power reflection coefficient, beam waist width, far-field divergence angle and M2-factor of laser beams through the VBG with deformation have been analyzed quantitatively. The result shows that the power reflection coefficient decreases obviously with the increasing of the grating deformation,