With the derivation of the hacek (ˇ) coefficients the analogy can now be extended to the case of outgoing spherical waves reflected and transmitted by concave spherical surfaces.
2000, Michael I. Mishchenko, Joachim W. Hovenier, and Larry. D. Travis [eds.], Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, part III: “Compounded, Heterogenous, and Irregular Particles”, chapter 8: Kirk A. Fuller and Daniel W. Mackowski, ‘Electromagnetic Scattering by Compounded Spherical Particles’, § iii: « Scattering and Absorption of Light by Homogenous and Concentrically Stratified Spheres », subsection E: ‹ Concentrically Stratified Spheres ›, page 237
For incoming spherical waves, the LM coefficients of order n for the scattered and internal partial fields are the spherical wave analogs to the Fresnel coefficients for reflection and refraction of a plane wave at a planar boundary. With the derivation of the “ˇ” (háček) coefficients (Nussenzveig, 1992, Chapter 9; Fuller, 1993a, b; Mackowski and Jones, 1995), the analogy can now be extended to the case of outgoing spherical waves reflected and transmitted by concave spherical surfaces.