  We describe how a coherent optical drive that is near-resonant with the upper
rungs of a three-level ladder system, in conjunction with a short pulse
excitation, can be used to provide a frequency-tunable source of on-demand
single photons. Using an intuitive master equation model, we identify two
distinct regimes of device operation: (i) for a resonant drive, the source
operates using the Autler-Townes effect, and (ii) for an off-resonant drive,
the source exploits the ac Stark effect. The former regime allows for a large
frequency tuning range but coherence suffers from timing jitter effects, while
the latter allows for high indistinguishability and efficiency, but with a
restricted tuning bandwidth due to high required drive strengths and detunings.
We show how both these negative effects can be mitigated by using an optical
cavity to increase the collection rate of the desired photons. We apply our
general theory to semiconductor quantum dots, which have proven to be excellent
single-photon sources, and find that scattering of acoustic phonons leads to
excitation-induced dephasing and increased population of the higher energy
level which limits the bandwidth of frequency tuning achievable while retaining
high indistinguishability. Despite this, for realistic cavity and quantum dot
parameters, indistinguishabilities of over $90\%$ are achievable for energy
shifts of up to hundreds of $\mu$eV, and near-unity indistinguishabilities for
energy shifts up to tens of $\mu$eV. Additionally, we clarify the
often-overlooked differences between an idealized Hong-Ou-Mandel two-photon
interference experiment and its usual implementation with an unbalanced
Mach-Zehnder interferometer, pointing out the subtle differences in the
single-photon visibility associated with these different setups.
