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We consider solutions of the defocusing nonlinear Schr\"odinger equation inthe quarter plane whose Dirichlet boundary data approach a single exponential$\alpha e^{i\omega t}$ as $t \to \infty$. In order to determine the long timeasymptotics of the solution, it is necessary to first characterize theasymptotic behavior of the Neumann value in terms of the given data. Assumingthat the initial data decay as $x \to \infty$, we derive necessary conditionsfor the Neumann value to asymptote towards a single exponential of the form$ce^{i\omega t}$. Since our approach yields expressions which relate $\alpha$,$\omega$, and $c$, the result can be viewed as a characterization of the large$t$ behavior of the Dirichlet to Neumann map for single exponential profiles.

Admissible boundary values for the defocusing nonlinear Schr\"odinger equation with asymptotically time-periodic data