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.
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