Debye series expansion of shaped beam scattering by GI-POF

We derive Debye series expansion (DSE) for infinitely long multilayered cylinders normally incident by shaped beam. Typically the interaction between multilayered cylinders and Gaussian beam is derived in detail, and localized approximation is introduced to calculate the beam shaped coefficients. Finally DSE is employed to the study of rainbow scattering by graded-index polymer optical fiber (GI-POF).