Objective 
Achieving ultra-precise temporal resolution in ionizing radiation detection is essential, particularly in positron emission tomography, where precise timing enhances signal-to-noise ratios and may enable reconstruction-less imaging. A promising approach involves utilizing ultrafast modulation of the complex refractive index, where sending probe pulses to the detection crystals will result in changes in picoseconds (ps), and thus a sub - 10 ps coincidence time resolution can be realized. Towards this goal, here, we aim to first measure the ps changes in probe pulses using an ionizing radiation source with high time resolution.
Approach 
We used relativistic, ultrafast electrons to induce complex refractive index and use probe pulses in the near-infrared (800 nm) and terahertz (THz, 300 µm) regimes to test the hypothesized wavelength-squared increase in absorption coefficient in the Drude free-carrier absorption model. We measured BGO, ZnSe, BaF2, ZnS, PBG, and PWO with 1 mm thickness to control the deposited energy of the 3 MeV electrons, simulating ionization energy of the 511 keV photons. 
Main results 
Both with the 800 nm and THz probe pulses, transmission decreased across most samples, indicating the free carrier absorption, with an induced signal change of 11% in BaF2, but without the predicted Drude modulation increase. To understand this discrepancy, we simulated ionization tracks and examined the geometry of the free carrier distribution, attributing the mismatch in THz modulations to the sub-wavelength diameter of trajectories, despite the lengths reaching 500 µm to 1 mm. Additionally, thin samples truncated the final segments of the ionization tracks, and the measured initial segments have larger inter-inelastic collision distances due to lower stopping power (dE/dx) for high-energy electrons, exacerbating diffraction-limited resolution. 
Significance
Our work offers insights into ultrafast radiation detection using complex refractive index modulation and highlights critical considerations in sample preparation, probe wavelength, and probe-charge carrier coupling scenarios.
Keywords: Coincidence Time Resolution; Modulation in Complex Refractive Index; Radiation Detection; Time-of-flight Positron Emission Tomography.
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