Recovery of graded index profile by cubic spline function
  We present in this paper a method to recover the refractive index profile of graded waveguide from the effective indices by cubic spline interpolation function. It is proved by numerical analysis of several typical index distributions that the refractive index profile can be reconstructed closely to its exact profile with the presented interpolation model. This method can reliably retrieve index profile of both more-mode (more than 4 guiding mode) and fewer-mode (2-4) waveguides. 
Weijun Liao, Xianfeng Chen, Yuping Chen, Yuxing Xia and Yingli Chen