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In this paper, we study the meromorphic continuation of the resolvent for theSchr\"{o}dinger operator in a three-dimensional planar waveguide. We prove theexistence of a resonance-free region and an upper bound for the resolvent. Asan application, the direct source problem is shown to have a unique solutionunder some appropriate assumptions. Moreover, an increasing stability isachieved for the inverse source problem of the Schr\"{o}dinger operator in thewaveguide by using limited aperture Dirichlet data only at multiplefrequencies. The stability estimate consists of the Lipschitz type datadiscrepancy and the high frequency tail of the source function, where thelatter decreases as the upper bound of the frequency increases.

Direct and inverse problems for the Schr\"{o}dinger operator in a three-dimensional planar waveguide