Generation of optical vortices by the periodic motion of a monochromatic source and its radiation spectrum

We present an analytical investigation of the influence of the periodic motion of a light source (a monochromatic Gaussian beam) on its frequency spectrum. The radiation of a source that travels along an elliptical path (or vibrates along straight line) possesses a discrete spectrum with frequency components shifted by nΩ with respect to the optical frequency, where n is an integer and Ω is the frequency of the periodic motion of the source. We show that the nth-order harmonic spectrum component contains n anisotropic optical vortices arranged symmetrically along the direction of the big axis of the ellipse. In the case of linear vibration of the source edge dislocations appear instead of vortices. During wave propagation in free space the vortices come closer to each other and finally join into one central n-charged optical vortex in the far field.