A general method for designing multifocal diffractive lenses used in the present work was described in Refs. 5 and 17. For the sake of consistency, we briefly repeat the basic equations. Let us consider an incident beam with the complex amplitude given by Display Formula
(1)where is the radial coordinate in the lens plane. In this case, the phase function of the multifocal lens takes the form Display Formula
(2)where is the lens aperture radius and the functions , are the phase functions of lenses with some focal lengths and and in the paraxial case are given by Display Formula
(3)where is the wavenumber. The function in Eq. (2) performs a nonlinear transformation of the phase function . In the case when the incident beam has a plane wavefront (i.e., ), the multifocal lens can be represented as a superposition of a conventional lens and a zone plate with the phase functions and , respectively. The nonlinear function in Eq. (2) generates additional diffraction orders.18 The energy distribution between the orders is determined by the particular form of this function. Thus, the complex amplitude of the beam transmitted through the multifocal lens can be represented as the following superposition of spherical beams:5,17Display Formula
(4)where Display Formula
(5)are the beam foci and Display Formula
(6)are the Fourier coefficients of the function .