锥形梯度折射率纤维透镜的成像特性

The Image Property of Tapered Gradient-index Fiber Lens

锥形纤维透镜是一种新颖光学元件。本文从锥形聚焦纤维的光线轨迹方程出发,推导锥形纤维透镜的物像关系式,并求得等效焦距和主平面的位置。文中给出几幅锥形聚焦纤维透镜的成像相片。

The subject of gradient-index optical is subdivided into two majorapplications. The first is gradient-index elements used for communications. The se-cond major application is for imaging purposes. Gradient-index fiber is a new com-ponent of gradient-index optics. The surfaces of constant refractive index for cy-lindrical gradient-index fiber will be cylinders concentric with the axis, after be-ing pulled into a tapered form, the surfaces of constant refractive index will becones concentric with the axis and having a common apex. Tapered gradient-indexfiber lens is a novel optical plane lens. In this paper, starting from the paraxialmeridional ray path equation, object-image relationships are found and used to de-termine the equivalent focal length and the principal planes of tapered gradient-indexfiber lens. The position of principal planes and focal point for the entry and exitof the tapered gradient-index fiber lens could have been obtained directiy by invo-king the symmetry condition and replacing r_1 or r_2. These equations reduce to theknown formulas when k=0, r_1=r_2 (that is, for a cylindrical gradient-index fiberlens). The image of tapered gradient-index fiber lens (r_1=0.54mm, r_2=0.27mm,z_0=3mm; r_1=0.54mm, r_2=0.38mm, z_0=2.5mm) is shown by photographs.