Paraxial propagation of Gaussian beam through curved tapered graded-index waveguides

On the basis of the unitary transformation technology widely used in quantum mechanics, we obtain the analytical propagation kernel of a light field through curved taper GRaded-INdex (GRIN) waveguides. The results show that, compared with the results in straight tapered GRIN waveguides, the curve of tapered GRIN waveguides can result in two new effects during the light beam propagation: one is a phase shift including a global one and a local one, which result in a change in the propagation direction of the light beam through such a curved taper GRIN waveguide. The other is to transform an on-axis light beam into an off-axis light one. In addition, the deviation of the Gaussian beam distribution center from the center of the curved taper GRIN waveguide is calculated, and the deflection generated by the curve of taper GRIN waveguide is also analyzed.