Dividing sets as nodal sets of an eigenfunction of the Laplacian

We show that for any convex surface S in a contact 3-manifold, there exists a metric on S and a neighbourhood contact isotopic to $S \times I$ with contact structure given as $\ker(ud - \star du)$ where u is an eigenfunction of the Laplacian on S, and $\star$ is the Hodge star from the metric on $S$. This answers a question posed by Komendarczyk.