Properties of an Axial Optical Vortex Generated with the Use of a Gaussian Beam and Two Ramps

The behavior of an axial optical vortex (OV), which is generated with the use of a Gaussian beam and two ramps implemented by a phase-only spatial light modulator (SLM), is studied as a function of the parameters of two ramps. The analytic solution of a wave equation is obtained in the Fresnel approximation for the diffraction of a Gaussian beam on the two-ramp structure. Nonlinear dependences of the ellipticity gamma of the intensity distribution in the OV core, as well as the angle (phi between the x-axis and the major ellipse axis of the vortex core, on the ramp phase gradient K, are analyzed. The values of given parameters obtained in optical and numerical experiments are in good agreement. It is shown that, as the gradients of the phases of two ramps vary in the limits of 3pi rad/cm, the ellipticity and the slope angle of the major axis ellipse are changed, respectively, by 0.3 and 56 degrees. This gives possibility to efficiently control the parameters of OVs.