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Light beams with phase singularities: some aspects of analysis and synthesis

Structurally stable laser beams with phase singularities that are rotating under propagation (so called spiral beams) have been investigated in various aspects. Some integral invariants of general laser beams and an optical analog of the Steiner theorem in mechanics are presented. Similarity and distinction of spiral beams for different rotation behavior are shown. A usage of spiral beams shaped like a predetermined planar curve applying for construction of phase focusing element is discussed.