Sh-matrices method applied to light scattering by finite circular cylinders

We present a rigorous analytical solution describing light scattering by a finite circular cylinder of arbitrary dimensions. This solution uses a modification of the extended boundary condition method (EBCM) that is based on the introduction of the so-called Sh-matrices. The Sh-matrices depend only on the shape of particles and do not depend on the particle size or optical constants. The Sh-matrices can be used to find the transition-matrix (T-matrix), that contains all the scattering information from the particle system. The solution is confirmed by corresponding discrete-dipole approximation (DDA) and traditional EBCM calculations.