Diffraction by a conical axicon considering multiple internal reflections

In this paper we consider diffraction of a laser beam by a narrow axicon when the cone angle is much less than a limit (at which total internal reflection occurs). In this case, the correct description of the propagation of light through the axicon calls for the consideration of multiple internal reflections. The diffraction is considered using two models: through a geometric optics approach and via solving the Helmholtz equation by a finite element method. Based on the geometrical model, analytical expressions are found for the angles defining the boundaries of the real and imaginary foci. Simulations conducted using the finite element method have confirmed the theoretical results.