We discuss a method for solving the diffractive problem on the optical elements with the symmetrical distribution of the permittivity. The method under discussion is the generalization of the rigorous coupled wave analysis (RCWA) for structures with the radial symmetry. As the basis for the decomposition of the solution the conic waves are choosen. This conic waves are the solution of the Maxwell’s equations in the medium with the constant permittivity.

A method of designing a refracting surface to generate a line-shaped image is presented. A relationship for the surface is derived as an envelop e of family of cartesian ovals. The refracting surface that generates the imaginary picture of the line-segment is presented as an approximate solution of the problem of generating the rectangular directivity diagram.

A method of designing a refracting surface to generate a directivity diagram represented as a-vector function of one argument is presented. A design of a refracting surface that generates a line-segment directivity diagram with specified intensity distribution is reduced to solving of a first-order differential equation solved for the derivative. We design a refracting surface to generate a-wide angle size line-segment directivity diagram.

A method of designing a refracting surface to generate a directivity diagram represented as a vector function of one argument is presented. A general relationship for the refracting surface is derived as an envelope of a parametric family of rotational ellipsoids or hyperboloids (depend on of the refractive indexes of the mediums, divided b y the refracting surface). Each ellipsoid or hyperboloid in the family transforms a spherical illuminating beam from the point source into a beam with plane wavefront of desired direction. The incident and refracted rays lie on the circular cone. We design a refracting surfaces to generate a line-segment directivity diagram.

The calculation of the eikonal from the condition of focusing into a line with designed energy distribution reduces to a first-order differential equation solved for the derivative. We design a DOE and non-diffractive refractive optical elements to produce a line-segment focus and a circular-arc focus. The simulation shows that the optical elements produce high-quality focal lines.

We discuss an asymptotic method for computing the intensity of the light field produced by a diffractive optical element (DOE) to focus into an arbitrary line using the curvilinear coordinates. The structure of the light field produced by the DOE intended to focus into a linesegment is studied. A comparison is drawn between the results of the asymptotic and numerical methods of computation.