Diffractive optical elements with a trigonometric phase dependence on radius are considered. They allow the formation of multiple local light segments on the optical axis. The dependence of the focal distribution on the optical element parameters is studied analytically and numerically. It is shown that by varying the parameters, both the positions and relative magnitudes of the foci can be independently changed. A detailed comparison of a sinusoidal lens with a parabolic one is performed. Binarization of a sinusoidal lens leads to non-obvious effects: this process does not create new foci, but significantly changes the energy distribution between the foci. In particular, the intensity can increase at positions where the focal magnitude was very small before binarization. Moreover, the trigonometric elements have very interesting chromatic dispersion features: changing the wavelength leads to significant variations in the ratio of the focal energies, which is not typical of parabolic lenses. The obtained results are promising for the field of multiplexing optical information transmission channels, increasing the depth of focus, laser material processing and optical trapping.
Ustinov et al. (Fri,) studied this question.