Asymptotic analysis of the T -matrix method for calculating the optical characteristics of dielectric particles

We address the problem of constructing a stable T-matrix formulation for electromagnetic scattering by smooth dielectric particles, with particular emphasis on axisymmetric geometries. The proposed approach is based on an asymptotic analysis of the matrix elements using the saddle-point method, which helps identify the dominant contributions at high multipole orders. A key feature of the work is the LOT scheme, which combines Tikhonov regularization with a parity-based decomposition of the basis functions. This strategy improves the numerical stability of the resulting linear systems and reduces the effective dimensionality of the problem. Benchmark tests show quantitatively reasonable agreement with the reference Mie theory: the relative errors are typically of order 5–10% over the tested benchmark range, with the best cases below 1% and a minimum error as low as 0.3%.