Comprehensive Four-Level Laser Model With Power Conservation Part I: Laser Kinetics and Application to ${\rm Nd}{:}{\rm YVO}_{4}$

This paper is the first of a two-part manuscript whose overall objective is to present a unified mathematical kinetics model of four-level laser systems solidly anchored to known physics, optics, and materials considerations, but ultimately viewed from an engineering systems perspective, and with power conservation obeyed throughout. This paper provides the basis for Part II, which couples this kinetics model with a treatment of solid-state laser amplifiers and oscillators, leading to the presentation of a new laser engineering systems model.