Shortcuts to Adiabaticity for Optical Beam Propagation in Nonlinear Gradient Refractive-Index Media

In recent years, the concept of "shortcuts to adiabaticity" has been originally proposed to speed up sufficiently slow adiabatic process in various quantum systems without final excitation. Based on the analogy between classical optics and quantum mechanics, we present a study on fast non-adiabatic compression of optical beam propagation in nonlinear gradient refractive-index media by using shortcuts to adiabaticity. We first apply the variational approximation method in nonlinear optics to derive the auxiliary equation for connecting the beam width with the refractive index of the medium. Then, the gradient refractive index is inversely designed through the perfect compression of beam width with the appropriate boundary conditions. Finally, the comparison with conventional adiabatic compression is made, showing the advantage of our shortcuts.