  Quantum networks using photonic channels require control of the interactions
between the photons, carrying the information, and the elements comprising the
nodes. In this work we theoretically analyse the spectral properties of an
optical photon emitted by a solid-state quantum memory, which acts as a
converter of a photon absorbed in another frequency range. We determine
explicitly the expression connecting the stored and retrieved excitation taking
into account possible mode and phase mismatch of the experimental setup. The
expression we obtain describes the output field as a function of the input
field for a transducer working over a wide range of frequencies, from
optical-to-optical to microwave-to-optical. We apply this result to analyse the
photon spectrum and the retrieval probability as a function of the optical
depth for microwave-to-optical transduction. In the absence of losses, the
efficiency of the solid-state quantum transducer is intrinsically determined by
the capability of designing the retrieval process as the time-reversal of the
storage dynamics.
