一种新的阶跃折射率光纤本征函数表达形式

为了阐明阶跃折射率光纤的模式特性,根据电磁波辐射的能量守恒定律和经过狄拉克函数奇异性修正的亥姆霍兹方程,通过数学推导和证明得出:柱面径向行波场的本征函数是经过狄拉克函数修正的整数阶汉克尔函数,阶跃折射率光纤模式场的本征函数是零、一阶贝塞尔函数经过狄拉克函数修正的零、一阶诺埃曼函数和虚参量汉克尔函数.该结论揭示了光纤芯层和包层模式场分别是径向驻波场和倏逝波场的本质,并基此推导出新的光纤模式特征方程,模式存在条件,模式数目和符合光纤实际的基模归一化截止频率的理论值.

A Sort of Novel Expression for the Eigenfunctions of Step Index Fiber

For the sake of clarifying the mode characteristic of step index fiber, the conservation energy law of electromagnetic radiation and the Helmholtz equation singularity modified by Dirac function are engaged, the novel conclusions, such as, no other than the integer order Hankel functions modified by Dirac function are the characterization functions of cylindrical radial travelling wave field, no but the zero and first order Bessel functions, the zero and first order neumann functions and the imaginary parameter Hankel functions modified by Dirac functions are the eigenfunctions of mode field in the step index fiber, are educed by the methods of mathematical derivation and confirmation. Hereby, the inbeing of the mode fields in fiber core and cladding are standing wave fields and evanescent wave fields is revealed, the virgin eigenvalue equations of the fiber are deduced, the new existent conditions of fiber modes are presented, the original formulas of the fiber mode numbers are recommended, the uptodate theoretical value of cut off normalized frequency of the fundamental modes, which gives a good fit to fiber, is concluded in this paper.