Axially Symmetric Hermite-Gaussian Beams for the Space-Earth Quantum Cryptography Channel

The work provides a description of Hermite Gaussian beams with an axially symmetric polarization structure. It is shown that the axial polarization symmetry makes such beams insensitive to the rotations relative to the optical axis. That property makes such beams preferred for the quantum space communication and cryptography systems. The possible creation and detection of such beams within the framework of a polarization coding protocol is discussed.