稳定谐振腔中横模特性的准几何近似的适用性研究(Ⅰ)——G1=G2=0.5

本文比较了用准几何近似与用矩阵理论(严格衍射理论),两种方法计算所得的光学谐振腔TEM_pl模的损耗和相移,并研究了它们相互间的关系。得出结论:(1)两种方法所计得的相移之差与衍射损耗的关系近似于指数关系;(2)当衍射损耗大于20％时,有可能导致准几何近似中模简并关系的明显破坏,从而可能引起共振频率的分裂;(3)两种方法所得出的横模损耗间有斜率约为0.36的线性关系。以上结论,在菲涅耳数N大于2时,基本上与N,l,p值无关。上述讨论是对G₁=G_{2关键词：}

A STUDY OF APPLICABILITY OF QUASI-GEOMETRIC APPROXIMATION ON CHARACTERISTICS OF TRANSVERSE MODES IN STABLE RESONATORS (Ⅰ)——G1=G2=0.5

The diffraction losses and phase-shifts of TEM_pl modes in optical resonators are calculated by quasi-geometric approximation and by the matrix theory (a strict diffraction theory), and the values obtained from the two methods are compared and studied. We come to the following conclusions: (I) The relation of the diffraction losses with the phaseshifts differences between the values obtained from the two methods are close to exponential. (II) When the diffraction losses≥20%, the frequency degeneracy of TEM_pl modes may be destroyed in a marked manner, and this would lead to the split of resonant frequency. (III) The exact diffraction loss values calculated from the strict method are nearly linear with the loss values calculated from the approximation method, its slope is b = 0.3559. When the Fresnel number of resonator ?> 2, all the conclusions are independent of mode numbers l, p, and Fresnel number ?. The above mentioned conclusions are obtained only for characteristics of transverse modes, whose losses≤99%, in axial-symmetric stable resonators G₂ = G₂= 0.5.
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