Recovering two coefficients in an elliptic equation via phaseless information

For fixed \begin{document} $y \in \mathbb{R}^3$ \end{document} , we consider the equation \begin{document} $L u+k^2u = - δ(x-y), \>x \in \mathbb{R}^3$ \end{document} , where \begin{document} $L=\text{div}(n(x)^{-2}\nabla)+q(x)$ \end{document} , \begin{document} $k >0$ \end{document} is a frequency, \begin{document} $n(x)$ \end{document} is a refraction index and \begin{document} $q(x)$ \end{document} is a potential. Assuming that the refraction index \begin{document} $n(x)$ \end{document} is different from \begin{document} $1$ \end{document} only inside a bounded compact domain \begin{document} $Ω$ \end{document} with a smooth boundary \begin{document} $S$ \end{document} and the potential \begin{document} $q(x)$ \end{document} vanishes outside of the same domain, we study an inverse problem of finding both coefficients inside \begin{document} $Ω$ \end{document} from some given information on solutions of the elliptic equation. Namely, it is supposed that the point source located at point \begin{document} $y \in S$ \end{document} is a variable parameter of the problem. Then for the solution \begin{document} $u(x,y,k)$ \end{document} of the above equation satisfying the radiation condition, we assume to be given the following phaseless information \begin{document} $f(x,y,k)=|u(x,y,k)|^2$ \end{document} for all \begin{document} $x,y \in S$ \end{document} and for all \begin{document} $k≥ k_0>0$ \end{document} , where \begin{document} $k_0$ \end{document} is some constant. We prove that this phaseless information uniquely determines both coefficients \begin{document} $n(x)$ \end{document} and \begin{document} $q(x)$ \end{document} inside \begin{document} $Ω$ \end{document} .