  We describe a time lens to expand the dynamic range of photon Doppler
velocimetry (PDV) systems. The principle and preliminary design of a time-lens
PDV (TL-PDV) are explained and shown to be feasible through simulations. In a
PDV system, an interferometer is used for measuring frequency shifts due to the
Doppler effect from the target motion. However, the sampling rate of the
electronics could limit the velocity range of a PDV system. A four-wave-mixing
(FWM) time lens applies a quadratic temporal phase to an optical signal within
a nonlinear FWM medium (such as an integrated photonic waveguide or highly
nonlinear optical fiber). By spectrally isolating the mixing product, termed
the idler, and with appropriate lengths of dispersion prior and after to this
FWM time lens, a temporally magnified version of the input signal is generated.
Therefore, the frequency shifts of PDV can be "slowed down" with the
magnification factor $M$ of the time lens. $M=1$ corresponds to a regular PDV
without a TL. $M=10$ has been shown to be feasible for a TL-PDV. Use of this
effect for PDV can expand the velocity measurement range and allow the use of
lower bandwidth electronics. TL-PDV will open up new avenues for various
dynamic materials experiments.
