In this paper, we propose the use of the invariant based shortcuts to adiabaticity for the analysis of directional couplers. By describing the dynamical evolution of the system using the eigenstates of the invariant through new parameterizations, the system stability against errors in coupling coefficient and propagation constants mismatch is connected with the new parameters, which can be linked back to system parameters through inverse engineering. The merits and limitations of the conventional tapered directional coupler designs with various window functions are obtained through the analysis. We then propose an optimal design of compact directional couplers that is stable against errors in input wavelength and coupling coefficient simultaneously. The designed directional coupler has better tolerance, as compared to the conventional resonant couplers with smooth shape functions of Hamming and Blackman. These results are verified by beam propagation simulations.
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