|
This paper studies self-focusing optical fiber by wave motion optical method. The equation of electromagnetic energy flaw line of TE_0 mode is derived. The essence of phenomenon of self-focusing is represented. 本文采用波动光学的方法研究自聚焦光纤,导出了TE。模的电磁能流线方程,阐明了自聚焦现象的实质。 This paper treats the axisymmetric field distribution in a SELFOC fiber,and discusses the errors in Ref.[1].We point out that the axi- symmetric transverse components E of an axisymmetric mode can not be Cartesian components Ex or Ey,and can only be Cylindrical comp- onents Er or E_0.Hence,the governing equation of E shouldbe 1/r d/(dr)(r(dE)/(dr))+[ω~2*/c~2K-1/r~2-β~2]E=0 where term -E/r~2 can not be discarded for the beam launched centrally along the axis.The solution to the zeroth-order is found and expressed... This paper treats the axisymmetric field distribution in a SELFOC fiber,and discusses the errors in Ref.[1].We point out that the axi- symmetric transverse components E of an axisymmetric mode can not be Cartesian components Ex or Ey,and can only be Cylindrical comp- onents Er or E_0.Hence,the governing equation of E shouldbe 1/r d/(dr)(r(dE)/(dr))+[ω~2*/c~2K-1/r~2-β~2]E=0 where term -E/r~2 can not be discarded for the beam launched centrally along the axis.The solution to the zeroth-order is found and expressed by generalized Laguerre polynomials.The solution to the first-order approximation is found by the perturbation method. 本文研究了自聚焦光纤中的轴对称场分布问题,讨论了 Gambling 和 Ma-tsumura 文章中的错误。我们指出,轴对称电场横向分量 E 不可能是笛卡儿坐标分量 E_x 或 E_y,E 只可能是柱坐标分量 E_r 或 E_(?)。因此,E 的方程应该是1/r d/(dr)(r (dE)/(dr))+[w~2/c~2K-1/r~2)-β~2]E=0对于沿轴线中心射入的光束,上式中的-E/r~2项不应略去。本文求出了方程的零级解,它用广义拉盖尔多项式表示。本文并采用微扰法求出了方程的一级近似解。 This paper deals with the propagation characteristics and mode conversion of axisymmetric modes in an imperfect SELFOC fiber with longitudinal gradually varying dielectric constant K=∈/∈_o=K_o-K_2(z)r~2. This problem has been considered by Sodha and others but we point out that the solution obtained by them is incorrect since a term -ψ/r~2 was missed out from the wave equation they used. After supplying the missing term, we find the analytic solution which is expressed in terms of generalized Laguerre polynomials.... This paper deals with the propagation characteristics and mode conversion of axisymmetric modes in an imperfect SELFOC fiber with longitudinal gradually varying dielectric constant K=∈/∈_o=K_o-K_2(z)r~2. This problem has been considered by Sodha and others but we point out that the solution obtained by them is incorrect since a term -ψ/r~2 was missed out from the wave equation they used. After supplying the missing term, we find the analytic solution which is expressed in terms of generalized Laguerre polynomials. 本文讨论了介电系数K是轴向z的缓变函数K=K_0-K_2(z)r~2这类不完善的自聚焦光纤中的轴对称模的传播特性及模式变换问题.我们指出Sodha等人所采用的极坐标标量波动方程遗漏了一项-ψ/r~2,因而结果是错误的.在补充了-ψ/r~2这项后,我们求出了用广义拉盖尔多项式表示的解析解.
|