利用多光束干涉原理的等效腔模型对四分之一波长多层介质镜进行了研究。证明在反射镜中心频率ω0附近,形为ρ(ω)exp[iψ(ω)]的反射系数中的ρ(ω) 等于ρ(ω0),ψ(ω)与频率成正比。求得了在介质具有微弱吸收情况下,吸收引起的四分之一波长镜反射下降和反射时延的表达式,研究了反射率下降以及反射时延与膜层数目的奇偶性的关系。在此基础上还引入了一个具有一定普适性的权重因子,通过这个权重因子可以定量描述镜子中各层对多层介质镜反射率下降、反射时延等重要特性的影响。

By using equivalent-cavity model, quarter-wave multilayer dielectric mirrors are studied. For the reflection coefficient with the form as ρ(ω)exp[iψ(ω)], it is proved that around the central frequency ω0 of the mirror, ρ(ω) is equal to ρ(ω0) and ψ(ω) is proportional to the frequency ω. And the expressions for the reflectivity reductions and reflection delays of the weakly absorptive quarter-wave multilayer dielectric mirrors are derived. Studies are made on the dependence of the reflectivity reductions and reflection delays on the parity of the layer number. Based upon these studies, A set of weighting factors is extracted, which can be used to quantify the contributions of any individual layer to such important mirror characteristics as reflection reduction, reflection delay, etc.