多元件谐振腔模式的有限元传输矩阵分析方法
Finite element transmission matrix method for calculation of multi-element optical resonator modes
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摘要: 建立了多元件谐振腔本征模的有限元传输矩阵模型。提出了模式计算相对误差概念及相应表达式，该表达式在数值上不受菲涅耳数的影响，能够很好反映有限单元划分方案对不同菲涅耳数的谐振腔的模式计算精度的影响。提出了有限单元划分精细度的概念和相应表达式，用以表征有限单元划分的精细程度。该表达式以菲涅耳数作为有限元传输矩阵法对腔镜单元格数划分的相对要求，用镜面实际划分的单元格数与菲涅耳数的比值来表征有限单元划分的精细程度。分析了不同谐振腔参数变化时模式计算相对误差与有限单元划分精细度的关系,建立了3种不同函数形式的经验表达式，并通过比较拟合残差选择了拟合效果较好的表达式。Abstract: 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
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