A two-color laser pulse whose focus changes speed could give researchers a way to control the shape of terahertz radiation, according to a modeling study. The preprint combines an analytical model with numerical simulations to examine whether the velocity of the moving focus can be used to prescribe the wavefront—the shape of the advancing radiation.
In the modeled system, the changing focus creates an ionization front in argon. The researchers compared flying-focus trajectories that decelerated uniformly with trajectories that moved at a constant velocity, then examined the resulting near-field terahertz geometry and radial fluence, a measure of how the radiation’s energy was distributed across the beam.
A moving focus changes the shape of the emitted field
The central design idea is to work backward from a desired, cylindrically symmetric wavefront. The analytical construction maps that target surface to the time-dependent velocity required of the ionization front. For a parabolic wavefront, the relation calls for a constant deceleration from an initially superluminal velocity—one faster than the relevant terahertz phase velocity—toward the terahertz phase velocity.
The simulations followed two-color terahertz generation while resolving the frequencies in the pulse. They included the effects of neutral-gas dispersion, third-order bound-electron nonlinearity, free-electron current density and energy depletion caused by ionization. The modeled cases were laser and plasma configurations, rather than a participant study.
Each trajectory was assigned an initial relative phase chosen to maximize modeled terahertz energy. In the decelerating cases, constant-velocity intervals were included before and after the acceleration, allowing the calculations to compare prescribed trajectory shapes.
Parabolic in one test, ring-shaped in another
At an initial ionization-front velocity of 1.004 c, with the final velocity set to c, the decelerating simulation produced the intended parabolic near-field terahertz wavefront. Its fluence was spread more uniformly across the radius instead of being concentrated mainly in a narrow ring.
The constant-velocity comparison behaved differently. At 1.004 c, it produced a conical wavefront and a narrow ring-shaped fluence profile, while the decelerating trajectory gave the more distributed profile. The comparison shows how changing the focus trajectory can alter both wavefront geometry and energy distribution in the modeled field.
The analytical relation also links the starting velocity to the focusing geometry through the f-number, a standard measure of how strongly an optical system focuses. In the simulations, the f-number fell as the initial velocity rose, followed the analytical trend through 1.005 c, and then reached a plateau.
The advantage was not simply more energy
Changing the trajectory affected the energy response as well. Decelerating trajectories produced terahertz energy that was relatively insensitive to the initial velocity, whereas the constant-velocity cases showed a velocity-dependent peak near 1.002 c and lower energy away from that maximum.
The calculations also tied the strength of generation to the phase at the ionization front. Terahertz generation was highest when the relative phase between the fundamental and its second harmonic reached π/2 at that front.
The modeled benefit had a boundary. In the highest-velocity decelerating case, starting at 1.005 c, terahertz generation was suppressed early in the focal range, where the velocity was high. The reported mechanism was nonuniform generation along the trajectory, which can limit how closely the emitted field follows the designed wavefront.
A computational design proposal, not a demonstrated device
The authors present the ionization-front trajectory as a design variable for shaping terahertz radiation. They extend the analytical framework beyond the parabolic and conical examples to arbitrary cylindrically symmetric wavefronts, while noting that useful shaping depends on keeping terahertz generation sufficiently uniform along the focal path.
That broader claim remains a proposal in this study: arbitrary-wavefront performance was not numerically demonstrated in the supplied analysis. The work reports analytical calculations and numerical UPPE simulations of a modeled two-color laser–argon system, with no experimental production or measurement of the shaped wavefronts.
The calculations also do not show that the shaped fields improve collection efficiency, focusing efficiency or performance in a particular application. The study’s evidence is limited to the modeled near-field wavefronts, fluence profiles and related simulation outputs.
The model has further built-in limits. Its analytical construction applies to terahertz generation driven by superluminal ionization fronts, with the front moving at least as fast as the terahertz phase velocity. The numerical implementation uses cylindrical symmetry, a singly ionizable gas and a fixed electron–neutral collision frequency.
No uncertainty intervals, replicate scheme or inferential statistical analysis was reported. The analysis also notes that changes in longitudinal intensity and spot size, together with evolving neutral and plasma phase, can make terahertz generation nonuniform along the focal trajectory.
What comes next
The next test is experimental: whether the predicted parabolic and other wavefronts can be produced and measured when optical imperfections are present. The supplied analysis also leaves open how phase, intensity, spot size and optical design might be optimized to preserve uniform generation at higher velocities.
Further work would need to determine whether the shaped wavefronts improve collected or focused terahertz performance in specific applications, and how well the design holds across different gases and operating parameters. Those questions are outside the evidence reported here.
The manuscript is an arXiv preprint, version one, identified as arXiv:2608.20142v1 and dated 20 Aug 2026. Funding was acknowledged from the DOE/NNSA University of Rochester National Inertial Confinement Fusion Program, the U.S. Department of Energy Office of Science and the Air Force Office of Scientific Research.
Paper data and sources
Original title: Wavefront shaping of terahertz radiation using two-color flying-focus pulses with time-dependent focal velocities
Authors: A. L. Elliott, H. Markland, K. G. Miller et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text