Hi, I am trying to find the wave equation solutions in a fiber optics. The wave equation is already expressed in Cylindrical coordinates. Mathematica doesn't have any problem with finding the solutions in the core of the fiber optics, which is clearly a sum of Bessel function. But when a step index profile is introduced, then the DSolve[] function seems not to be able to calculate the fields in the cladding.The method, I used is attached. I appreciate is if somebody can suggest a method in Mathematica, that works.

   n[[Rho]] = Piecewise[{{n2, [Rho] >= a}, {n1, [Rho] < a}}];
    Assuming[n2 < n1, 
     DSolve[k0^2 (n[[Rho]])^2 + (
        Derivative[1][F][[Rho]]/[Rho] + (F^[Prime][Prime])[[Rho]])/
        F[[Rho]] + (Z^[Prime][Prime])[z]/
        Z[z] + ([Phi]1^[Prime][Prime])[[Phi]]/([Rho]^2 
    [Phi]1[[Phi]]) == 0, F[[Rho]], [Rho]]]

Thanks in advance!