  We explore theoretically the feasibility of using frequency conversion by
sum- or difference-frequency generation, enabled by three- wave-mixing, for
selectively multiplexing orthogonal input waveforms that overlap in time and
frequency. Such a process would enable a drop device for use in a transparent
optical network using temporally orthogonal waveforms to encode different
channels. We model the process using coupled-mode equations appropriate for
wave mixing in a uniform second- order nonlinear optical medium pumped by a
strong laser pulse. We find Green functions describing the process, and employ
Schmidt (singular- value) decompositions thereof to quantify its viability in
functioning as a coherent waveform discriminator. We define a selectivity
figure of merit in terms of the Schmidt coefficients, and use it to compare and
contrast various parameter regimes via extensive numerical computations. We
identify the most favorable regime (at least in the case of no pump chirp) and
derive the complete analytical solution for the same. We bound the maximum
achievable selectivity in this parameter space. We show that including a
frequency chirp in the pump does not improve selectivity in this optimal
regime. We also find an operating regime in which high-efficiency frequency
conversion without temporal-shape selectivity can be achieved while preserving
the shapes of a wide class of input pulses. The results are applicable to both
classical and quantum frequency conversion.
