Polarization states of a single-mode (microchip) Nd3+:YAG laser. I. Theory

We present a microscopic mathematical model for the polarization states of a single-frequency Nd³⁺:YAG laser. It is a plane wave, mean field, vector model carried to all orders in the laser field. The crystal is assumed to be optically pumped longitudinally with a laser of specified polarization. For D₂ site symmetry and an odd number of electrons, we establish the phase relationships between the components of the electric dipole matrix elements between the Kramers states. These relationships are central in determining the site-specific coupling between both, the pump and laser fields to the Nd ³⁺ ions. The laser cavity is assumed to be linear and quasi-isotropic. The residual optical anisotropies are included using a round-trip Jones matrix formalism