Correction to: Nature Photonics https://doi.org/10.1038/s41566-022-01044-5, published online 23 June 2022.

In the version of this article initially published, in the fourth paragraph of main text, there was a typographical error in the sentence now reading “Although the poling period is designed for phase-matched SHG, the poling defect locally changes the phase relationship between the first-harmonic (FH) and the second-harmonic (SH) waves by Δϕ = ϕ2ω − 2ϕω = π” where a delta originally appeared at the end of the equation. The error has been corrected in the HTML and PDF versions of the article.