Publisher Correction: Topological optical differentiator

Correction to: Nature Communications 10.1038/s41467-021-20972-4, published online 29 January 2021.

The original PDF version of this Article contained errors in Equations 3, which incorrectly read:

$${\mathbf{e}}_{\mathbf{o}\mathbf{u}\mathbf{t}}\mathbf{R}\left(k_x=0,k_y=0\right){\mathbf{e}}_{\mathbf{i}\mathbf{n}}=0$$ 3

The correct form of Eq. (3) is:

$${\mathbf{e}}_{\mathbf{o}\mathbf{u}\mathbf{t}}^{†}\mathbf{R}\left(k_x=0,k_y=0\right){\mathbf{e}}_{\mathbf{i}\mathbf{n}}=0$$ 3

The PDF version also contained an error in the inline equation at the end of the first paragraph of the first Results’ subsection, which incorrectly read:

$$r\left(k_x,k_y\right)={\mathbf{e}}_{\mathbf{o}\mathbf{u}\mathbf{t}}\mathbf{R}\left(k_x,k_y\right){\mathbf{e}}_{\mathbf{i}\mathbf{n}}$$

instead of

$$r\left(k_x,k_y\right)={\mathbf{e}}_{\mathbf{o}\mathbf{u}\mathbf{t}}^{†}\mathbf{R}\left(k_x,k_y\right){\mathbf{e}}_{\mathbf{i}\mathbf{n}}$$

Both in the PDF and html versions of the article, at the end of the first paragraph of the first Results’ subsection, in Equation 2 and in the inline equations after the sentence “The entire reflection process is then described by…”, the tilde notations should be exactly above the symbols “S”

Both in the PDF and html versions of the article, at the end of the first paragraph of the first Results’ subsection, the inline equation in the sentence starting with “which shows that the zero of…” should read:

$$r\left(k_x,k_y\right)$$

rather than

$$rt\left(k_x,k_y\right)$$

Both the pdf and the html have been updated to include these corrections.