On evanescent waves and blowing-ups of the finite series technique in spherical wave expansion of shaped beams

In generalized Lorenz-Mie theory, the beam shape coefficients of Gauss-like beams obtained with finite series method blow up when the wave order is high. The blowing-ups caused by the loss of significant digits may be suppressed by increasing numerical precisions. Once the elimination of such blowing-ups is carried out, blowingup phenomena still occur whose origin is still not clear to us. The work presented here attempts to provide an explanation on this issue. Based on the angular spectrum representation of the beam field, it is found that the blowing-up originates from the contribution of evanescent waves.