Zero slopes of the scattering function and scattering matrix for strict forward and backward scattering by mirror symmetric collections of randomly oriented particles

- An extended scattering matrix is introduced for certain collections of particles.
- Symmetry is used to uncover its angular dependence.
- The results are used to study the scattering matrix.
- Derivatives of this matrix tend to zero if the scattering angle tends to zero or π.
- Several practical examples and applications are presented.

Single scattering of light by a finite mirror symmetric collection of independently scattering randomly oriented particles is considered as observed in the far-field. It is shown that the slopes of the scattering function and all other elements of the scattering matrix are functions of the scattering angle that tend to zero when the direction of the scattered light tends to the strict forward or backward direction. This result is obtained by introducing an extended scattering matrix, based on symmetry arguments. The theory is illustrated and clarified by practical examples of scattering functions and scattering matrices. Various applications are also considered.