K-series approximation of vectorial optical fields for designing diffractive optical elements with subwavelength feature sizes

Diffractive optical elements (DOEs) are widely applied as compact solutions for desired light manipulations via wavefront shaping. Recent advanced chip applications further require their feature sizes to move down to the subwavelength, which inevitably brings forth vectorial effects of optical fields and makes the typical scalar-based theory invalid. However, simulating and optimizing its vectorial fields, which are associated with the billions of pixel parameters in the optical element, are difficult to do, because of the issues on numerical stability and the highly-demanding computational cost. To address this problem, this research proposes an applicable algorithm by means of wave-vector (k) series approximation of vectorial optical fields. Together with the semi-analytical rigorous coupled wave analysis (RCWA), an adequate selection scheme on k-series enables computationally efficient yet still predictive calculations for DOEs. The performance evaluations for exemplary designs by the finite difference time domain (FDTD) method show that the predicted intensity profiles by the proposed algorithm agree with the target by a fractional error. Together with optimizing the degrees of freedom (i.e. DOE depth h) as compensation for errors from the cut of k-series, the algorithm demonstrates its outperformance by one or two orders of magnitude in accuracy versus the scalar-based model, and demands only a reasonable computational resource under a specific selection of k-series.