1. Results

Diffractive Interface Theory (DIT), an approach capable of drastic speedup in calculations of electromagnetic response of optically thin complex diffractive structures, known as metasurfaces, was originally reported in Ref [1]. It was shown that while the DIT is adequate in calculating the optical response of substantially thin composites, the accuracy of DIT is reduced when the thickness of the metasurface is increased beyond roughly 1/20-th of the free space wavelength. Surprisingly, the accuracy of the DIT has appeared to deteriorate for resonant metasurface-based resonators such as polarization converter reported in [2]. This deterioration was attributed to DIT’s inability to accurately describe the phase of the transmitted light.

However, during our subsequent research focused on improvements to DIT (see, e.g. Ref [3]), we have identified a typo in the numerical implementation of the original formalism. The typo affected calculations of reflection when light incident from under the metasurface, the part of the formalism used to analyze optical response of multilayer metasurface-containing systems. As result, the typo affected only Fig. 5 of the original work.

All equations presented in original manuscript, as well as Figs. 1-4, and Fig. 6 in Ref [1] are correct. Optical response of the metasurface-based polarization converter, suggested in Ref [2], calculated with properly implemented DIT formalism is shown in Fig. 1 of this erratum. It is clearly seen that DIT adequately describes the response of this resonant structure, rendering discussions about the relationship between validity of DIT for strongly resonant structures, presented at the end of Sec. 4.2 of Ref [1], unnecessary. An updated implementation of DIT has been posted online [5].

 

Fig. 1 Optical properties of nano-antenna-based polarization converter; (a) cross-section of the structure and of the nano-antenna plane. The nano- antennae layer and gold ground layer are both 200nm thick ($h_g$); periodicity ${\text{Λ}}_x={\text{Λ}}_y=68\mu m$, antenna wire length $L=82\mu m$, antenna width $w=10\mu m$, dielectic layer height $h_d=33\mu m,$ and angles $\theta ={45}^o$, and $\alpha ={25}^o$. (b-d) Co-polarized (blue) and Cross-polarized (green) 0th order reflection calculated with DIT (solid lines) and Rigorous Coupled Wave Analysis (RCWA [4]) (dashed lines) with (b) highly lossy spacer layer [${ϵ}_d=3(1+2i)$)], (c) medium loss spacer layer [${ϵ}_d=3(1+0.5i)$], and (d) low loss spacer layer [${ϵ}_d=3(1+0.05i)$].

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