根据光波导短程透镜母线曲率半径与光传输损耗的关系, 利用数值计算的方法, 通过计算不同母线参数条件下, 四种解析解设计的短程透镜母线曲率半径, 研究比较了短程透镜卷边对其损耗的影响, 得出了短程透镜损耗与其有效区半径关系的曲线图, 发现透镜凹面半径一定时, 有效区半径越小, 即卷边越大时, 光传输损耗越小; 短程透镜的解析改进解和最优解设计的透镜卷边存在曲率奇点。并由此得出了四种解析解设计的短程透镜有效区半径选取原则及其满足低损耗条件的取值范围。

The effects of rim zone on optical propagation loss of four analytical designs of geodesic lenses are studied by calculating curvature radiuses of their meridional curves for different parameters according to relations between meridional curvature radius of waveguide geodesic lense and optical propagation loss. The relation curves between optical propagation loss and effective aperture radius are obtained. For a fixed radius of lens aperture, the smaller effective aperture radius is (namely larger rim zone), the smaller optical propagation loss is. Curvature singular points are found on the joint of rim zone and true lens of the geodesic lenses described by improved analytical designs and optimal designs. The selection rule of effective aperture radius of the above geodesic lenses and range with low loss are given.