Model of passive $Q$ switching taking account of the anisotropy of nonlinear absorption in a crystal switch with phototropic centres

A model is proposed of passive $Q$ switching in a laser by a crystal switch with phototropic centres. Expressions for the output energy and duration of a giant pulse are derived taking account of the geometric factor representing the distribution of the orientations of these centres relative to the crystal lattice of the passive switch. The calculated results are in agreement with those obtained in an experimental investigation of passive $Q$ switching in a neodymium laser with a switch in the form of a doped LiF:$F_2^-$ or Cr$^{4+}$:YAG crystal.