Relation between Debye series and generalized Lorentz–Mie theory of laser beam scattering by multilayer cylinder

With the recursive relations of Bessel function and applying inductive approach, the consistency between the scattering coefficient formula of Debye series and that of the generalized Lorentz–Mie theory (GLMT) in the scattering of a multilayer cylinder illuminated by a laser beam is proved in detail. As an application example, rainbow phenomenon in the scattering of a two-layer cylinder is discussed by the Debye series components. It can be concluded that the radius and the refractive index of a two-layer cylinder have an effect on the twin-primary rainbow, and the high-order Debye series components which are associated with the high-order rainbows are more complex than those of a homogeneous cylinder.