Correction to: Nature Communications https://doi.org/10.1038/s41467-018-05579-6, published online: 28 August 2018.

The original version of this Article contained in Eq. (6). The last term of this equation incorrectly read “\(E_x^{n - 1}\left( {n_x,n_j} \right)\)”, instead of “\(E_x^{n + 1}(n_x,n_j)\)”.

The correct form of Eq. (6) is:

$$E_x^{n + 1}(n_x,n_j + 1) = \frac{{1 - j\omega \chi _{ee}^{ux}dt/4ds}}{{1 + j\omega \chi _{ee}^{ux}dt/4ds}}E_x^n\left( {n_x,n_j + 1} \right)\\ + \frac{{dt}}{{\varepsilon _0ds(1 + j\omega \chi _{ee}^{ux}dt/4ds)}}\left( {H_z^{n + 1/2}\left( {n_x,n_j + 1} \right) - H_z^{n + 1/2}\left( {n_x,n_j} \right)} \right)\\ - \frac{{j\omega \chi _{ee}^{ux}dt/4ds}}{{1 + j\omega \chi _{ee}^{ux}dt/4ds}}\left( {E_x^n\left( {n_x,n_j} \right) + E_x^{n + 1}\left( {n_x,n_j} \right)} \right).$$

This has been corrected in both the PDF and HTML versions of the Article.

The original version of the Supplementary Information associated with this Article contained an error in Supplementary Eq. (6). The last term of this equation incorrectly read “\(E_y^{n - 1}(n_i,n_y)\)”, instead of “\(E_y^{n + 1}(n_i,n_y)\)”.

The HTML has now been updated to include a corrected version of the Supplementary Information.

The corrected equations do not affect the simulations results and conclusions presented in the Article.