Formation of required distributions on the basis of decomposition by vortex eigen functions of a bounded non-paraxial propagation operator

The solution of the problem of overcoming the diffraction limit based on the representation of an optical signal in the form of a superposition of communication modes matched with the vortex eigenfunctions of a bounded (in the object and spectral regions) nonparaxial propagation operator in free space is considered. Nonparaxial propagation of laser beams is described using an expansion in terms of conic waves based on the $m$-th order Fourier-Hankel transform. The eigenfunctions of such an operator, which have near-unity eigenvalues, determine the number of degrees of freedom and characteristics of an optical signal transmitted without distortion over a given distance. Based on the considered approach, a parametric method was developed for solving the inverse diffraction problem, including overcoming the diffraction limit.