Time Lens Photon Doppler Velocimetry (TL-PDV) for Extreme Measurements

Photon Doppler velocimetry (PDV) is widely used for measuring velocities in shock physics, including laser-driven micro-flyers, dynamic compression, and explosive detonation testing, due to robust telecom-grade components and long record lengths. Conventional PDV operates by mixing Doppler-shifted light reflected from a moving target with a reference laser to generate a beat frequency that is proportional to velocity (about 1.3 GHz per 1 km/s at 1550 nm). However, digitizer bandwidth limitations constrain conventional PDV to roughly a 10 km/s velocity range, which is inadequate for extreme experiments such as those in inertial confinement fusion (ICF) where velocities can exceed 100 km/s and even approach hundreds of km/s. VISAR is often used for extreme velocities but is intensity-based, more alignment-sensitive, has limited multiplexing compatibility, and typically provides shorter record lengths. The need for accurate, high-dynamic-range velocity diagnostics in ICF and related extreme environments motivates new methods that extend PDV capability without impractical electrical bandwidth requirements. TL-PDV seeks to meet this need by temporally magnifying the PDV beat signal in the optical domain so that lower-bandwidth electronics can record very high velocities.

Several PDV variants have been developed to expand velocity dynamic range, including approaches using frequency shifting, multiple local oscillators at different wavelengths, and leapfrog PDV. Time-stretched PDV (TS-PDV) introduced time-to-wavelength mapping and dispersion to slow down high-frequency PDV signals, bringing PDV into the ICF regime. However, TS-PDV requires chirped probe illumination, has limited record length, non-uniform wavelength-dependent amplification, complex synchronization, and is bandwidth-inefficient in the optical domain, limiting magnification, maximum measurable velocity, and wavelength multiplexing. Time lens systems, based on temporal imaging and often realized via four-wave mixing (FWM), provide higher bandwidth efficiency, particularly for large time-bandwidth product signals, enabling larger temporal magnification and dynamic range. Prior foundational work on temporal imaging (space-time duality, temporal magnifiers, and time lenses) establishes the theoretical and technological basis for TL-PDV. TL-PDV was recently proposed conceptually as an alternative to TS-PDV to overcome the bandwidth and record-length challenges while preserving PDV’s operational simplicity and multiplexing benefits.

TL-PDV architecture uses a temporal imaging system implemented with a four-wave mixing (FWM) time lens. A chirped pump pulse interacts with a continuous-wave (CW) signal (PDV return mixed with local oscillator) in a highly nonlinear fiber (HNLF), generating an idler that inherits the signal’s amplitude and phase and the pump’s linear chirp, effecting temporal magnification. The temporal imaging equation relates dispersions: 1/Ds + 1/Di = 2/Dp, where Ds, Di, and Dp are the dispersions in the signal, idler, and pump arms, respectively. Experimental setup (Fig. 2) consists of three arms: pump, signal, and idler. The pump originates from a 100 MHz mode-locked laser (Menlo Systems C-Fiber), spectrally filtered and dispersed (e.g., 201 ps/nm and further dispersion), then amplified (EDFAs). The PDV return plus local oscillator forms the signal arm; it is combined with the pump via a WDM and launched into HNLF to generate the idler. The idler is filtered, dispersed (e.g., −853 ps/nm), amplified, and passed through a programmable filter (Finisar Waveshaper 1000A) to suppress pump leakage before detection. Detection uses an InGaAs photodiode (EOT ET-3500F) and a 12.5 GHz oscilloscope (Tektronix DPO71254C). The pump repetition rate is 200 MHz, with a pump temporal window of approximately 500 ps that is magnified to about 4 ns in the idler, yielding a temporal magnification M ≈ 7.6 (design computed from frequency-domain parameters B2L and idler center wavelength; λ0/f ≈ 1.0997×10−7 × (B2L/1.4419×10−2) = 7.6). Calibration and sensitivity: Temporal magnification is calibrated by heterodyning two CW lasers to emulate large Doppler shifts. One laser is fixed at 1541.47 nm; the other is tuned from 1540.70 to 1541.43 nm at low power (−15 dBm) to emulate weak return signals. For each pump pulse, the idler time trace is Fourier-transformed; the beat frequency is extracted from the FFT peak, and averaged over 199 pulses to determine the magnification. The measured magnification agrees with the design; a ±2σ band (σ = standard deviation over pulses) gives a 95% confidence interval. Power sensitivity is characterized by fixing the local oscillator at 1541.47 nm, the input laser at 1541.00 nm, and varying input power from −3 to −21 dBm in 3 dB steps. FFT peak extraction over 199 pulses provides standard deviation and corresponding fractional velocity uncertainty versus input power. LDMF experiment: To validate under realistic conditions, TL-PDV is inserted into a PDV system measuring laser-driven micro-flyer (LDMF) velocities. A single-mode fiber (SMF) is imaged onto the flyer surface with a 4f system (f1 = 2.54 cm, f2 = 20 cm). The sample is housed in vacuum, with front/back cameras for alignment and a high-speed camera for side-on imaging. The flyer stack comprises a borosilicate glass substrate, epoxy, and an aluminum disc; a Nd:YAG laser pulse ablates the epoxy, generating hot gases that propel the Al disc. TL-PDV recordings are analyzed with short-time FFTs (5 ns windows), extracting beat frequency per window; velocities are derived using the known 1.3 GHz/(km/s) scaling at 1550 nm, accounting for the temporal magnification factor. Flyer preparation and launch (Methods): Flyers are 1.5 mm diameter, 100 µm thick Al discs fabricated in 7×7 arrays on a glass–epoxy–metal stack (glass: 50×50×0.625 mm borosilicate; epoxy: Henkel Loctite Ablestik 24; Al sheets from AluFoil). Glass and Al are cleaned (acetone, IPA), epoxied under compression for >24 h, and the Al layer is laser-cut (Clark-MXR femtosecond laser) into 7×7 flyers with 6 mm spacing. Launch uses a 1064 nm Nd:YAG (up to 2.5 J, 10 Hz, 10 ns; temporally stretched to 21 ns; M2 ~15), expanded to ~25 mm, shaped to a top-hat profile (diffractive optic) and focused (250 mm lens) to ~1.85 mm diameter through the glass onto the epoxy. Laser fluence is controlled by a HWP and polarizing beamsplitter. TL-PDV measures normal surface velocity; a Shimadzu high-speed camera (10,000,000 fps) provides side-view imagery. Time multiplexing (signal arm): To eliminate observation gaps inherent in periodic magnification, the authors demonstrate temporal multiplexing (up to 8×) by carving a 1 µs segment of the PDV signal and using cascaded 50:50 couplers, polarization controllers, and tunable delays to create replicas. By offsetting pump alignment by the 500 ps pump window across replicas, full coverage of a 1 µs window with temporal magnification up to 8× is enabled. Generally, log2(M) multiplexing stages are required for continuous coverage at magnification M.

• First experimental demonstration of time lens PDV (TL-PDV) with temporal magnification M = 7.6 using a four-wave-mixing time lens in fiber, enabling measurement of extreme velocities with lower-bandwidth electronics. • Validated over a 74 km/s velocity dynamic range with high accuracy; the system uses 12.5 GHz electrical bandwidth and achieves the stated range with less than ~100 m/s velocity uncertainty (from Discussion). • Calibration with two CW lasers across 1540.70–1541.43 nm shows excellent agreement between designed and measured temporal magnification; statistics from 199 pulses yield ±2σ (95% CI) bands around the mean frequency estimates. • Input power sensitivity down to −21 dBm with fractional velocity uncertainty better than 3×10−3 (based on 199-pulse statistics). • Laser-driven micro-flyer validation: Terminal flyer velocities 600–800 m/s were measured. Conventional PDV produced beat frequency shifts of ~0.7–1.0 GHz, while TL-PDV (M = 7.6) yielded ~0.10–0.13 GHz shifts. Despite FFT windowing limits (5 ns), peak localization gave reliable frequency estimates, and TL-PDV velocities showed excellent agreement with conventional PDV for two different launch energies. • Demonstration of signal-arm time multiplexing up to 8×, enabling continuous sampling over a 1 µs PDV record with temporal magnification, indicating a scalable path to closing observation gaps for high-repetition pump sampling. • TL-PDV maintains PDV advantages: operational simplicity, compatibility with multiplexing, robustness to reflectivity changes, long record lengths, and compatibility with low-noise EDFAs at 1550 nm.

The study addresses the central challenge of measuring extreme velocities (>50–100 km/s) without requiring prohibitively large electronic bandwidths. By temporally magnifying the PDV beat signal with a fiber-based FWM time lens, TL-PDV effectively compresses the required electrical bandwidth while retaining the phase and amplitude information needed for accurate velocity extraction. The achieved 74 km/s dynamic range with M = 7.6 and 12.5 GHz electronics demonstrates that TL-PDV can bridge the gap to ICF-relevant velocities while using commercially available components. Calibration and sensitivity experiments confirm accurate magnification and robust performance down to low return signal powers. Validation on laser-driven micro-flyers shows strong agreement with conventional PDV, supporting the technique’s accuracy in real experiments. Importantly, TL-PDV’s free-running operation and bandwidth efficiency distinguish it from TS-PDV, enabling longer record times and better suitability for multiplexed measurements. The proposed temporal multiplexing strategy further addresses the remaining observation-window gaps, offering a scalable route to continuous coverage over microsecond time windows and larger magnification factors, which is directly relevant for facilities such as the Z-machine and the National Ignition Facility. Overall, TL-PDV significantly enhances PDV’s velocity dynamic range while preserving its operational strengths, positioning it as a powerful diagnostic for extreme-conditions research, including ICF optimization and equation-of-state studies.

This work experimentally demonstrates TL-PDV for the first time, achieving a temporal magnification of 7.6 and validating accurate measurements across a 74 km/s velocity dynamic range using 12.5 GHz electronics. Power sensitivity down to −21 dBm with sub-0.3% fractional velocity uncertainty and excellent agreement with conventional PDV in laser-driven micro-flyer experiments underscore the method’s accuracy and robustness. TL-PDV preserves PDV’s operational simplicity, multiplexing compatibility, and long record lengths while enabling access to extreme velocities previously beyond conventional PDV’s reach. The proposed temporal multiplexing enables continuous measurement windows at high magnification, addressing observation gaps and paving the way for deployment in high-energy-density environments such as ICF. Future work can focus on scaling magnification and multiplexing for even higher velocities and continuous coverage, integration with multi-point PDV arrays, and application to real ICF shots to inform fuel optimization and EOS characterization.

• The TL-PDV and conventional PDV measurements for the LDMF validation were not recorded on the same launch event, so exact trace matching is not expected. • The current periodic magnification introduces observation gaps between pump windows; continuous coverage requires additional time-multiplexing stages (demonstrated up to 8×) and precise delay alignment. • Sensitivity at very low return powers depends on system configuration (e.g., coupler ratio); improvements (e.g., 99:1) are suggested for single-channel operation. • Although the system is designed for extreme velocities, experimental validation was performed on laser-driven flyers with velocities near 1 km/s, i.e., at the low end of the system’s dynamic range; direct validation at >10–100 km/s in ICF-like conditions remains for future work.