Short and robust directional couplers designed by shortcuts to adiabaticity.

We propose short and robust directional couplers designed by shortcuts to adiabaticity, based on Lewis-Riesenfeld invariant theory. The design of directional couplers is discussed by combining invariant-based inverse engineering and perturbation theory. The error sensitivity of the coupler is minimized by optimizing the evolution of dynamical invariant with respect to coupling coefficient/input wavelength variations. The proposed robust coupler devices are verified with beam propagation simulations.