Abstract
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.
Highlights
In recent decades, beam propagation in the paraxial approximation has been extensively investigated for many years in the applications of integrated optics waveguide and optical communications [1,2,3]
Other interesting cases have been studied in optical waveguides with nonlinearity [11] and PT-symmetry [12], where the adiabatic criteria could be influenced or improved
The length of most optical devices designed from adiabatic passages should be long enough to fulfill adiabatic criteria, which does not meet the requirement of miniature in integrated optics
Summary
Beam propagation in the paraxial approximation has been extensively investigated for many years in the applications of integrated optics waveguide and optical communications [1,2,3]. The trap frequency is inversely designed from the Ermakov equation derived from the dynamical invariant, such that the fast expansion of harmonic trap is achieved without final excitation or heating Afterwards, such theoretical proposals have been experimentally verified for the frictionless cooling of cold atoms and Bose-Einstein condensates in magnetic traps [22,23]. There exists freedom left in the method of inverse engineering by only fixing the boundary condition, the optimal control theory can be supplemented with perturbation theory to maximize the stability of shortcuts-to-adiabaticity protocols with respect to noise and systematic errors [32,33,34] In this context, the compatible coupled optical waveguides have been designed from STA, and the better tolerances with respect to input wavelength and spacing errors are achieved as well [35,36,37,38,39].
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