Finite element transmission matrix method for calculation of multi-element optical resonator modes

A finite element transmission matrix model is founded for the eigenmode of multi-element optical resonator. A novel conception of mode calculation relative error(MCRE) and its mathematical expression are introduced. The conception can well reflect the effect of finite element amount on the mode calculation precision of resonators with different Fresnel number, because it is mainly independent of Fresnel number. Another new conception of finite element fineness (FEF) is proposed to characterize the division precision of finite elements. FEF is defined as the ratio of the finite element amount of cavity mirror to Fresnel number, where Fresnel number is used as the relative requirement of the division number. The relationship between MCRE and FEF is analyzed, and an empirical expression betwe