Bekshayev O. Transformations of light beams in paraxial optical systems

With employment of energetic and mechanical characteristics and the Wigner function, a generalized description of the beam transformations is created. The accomplished picture of the optics of astigmatic lens-like systems is developed. Problems of a beam propagation through plane dispersion elements and through lens-like systems with light scattering are solved analytically. A beam characterization by means of space-angle intensity moments is improved. On this base, a general representation of the beam orbital angular momentum is obtained and the "vortex" and "asymmetry" forms of transverse energy circulation are quantitatively characterized. The full study of two-mirror lens-like resonators with arbitrary astigmatism is given. The improved theory for dispersion resonators of tunable lasers refines the mechanism of a laser tuning and reveals new possibilities for the control of their generation spectrum.