Vector Vortices in Linear Optical Media

The present work investigates the linear regime of propagation of modulated vector optical fields in isotropic dispersive media by focusing on the formation of complex vector vortex structures with amplitude-type singularities. A mathematical algorithm designed to derive novel exact analytical solutions for the linear vector amplitude equation is presented, enabling the systematic development and classification of diffraction-free vector solutions. Various types of solutions for the two orthogonal components of the vector amplitude function are obtained, resulting in non-trivial spatial amplitude structures in their cross sections. The proposed approach allows for precise analytical governance of the spatial and polarization properties of the obtained vortices via the vortex parameter n. The presented model offers a comprehensive framework for generating different types of vector vortex structures by choosing the values of the parameters n and m, depending on the initial phase of the components. The derived solutions extend the capabilities of conventional phase modulation techniques. It is demonstrated that by changing the vortex parameter n, the structural complexity of both the amplitude distributions and polarization patterns increases. A number of numerical simulations, based on the obtained analytical solutions, are performed. They validate the model and clearly illustrate the characteristic vectorial features via detailed vector diagrams.