Full 3D + 1 modeling of tilted-pulse-front setups for single-cycle terahertz generation

The tilted-pulse-front setup utilizing a diffraction grating is one of the most successful methods to generate single-to few-cycle terahertz pulses. However, the generated terahertz pulses have a large spatial inhomogeneity, due to the noncollinear phase-matching condition and the asymmetry of the prism-shaped nonlinear crystal geometry, especially when pushing for high optical-to-terahertz conversion efficiency. A 3D + 1 (x, y, z, t) numerical model is necessary in order to fully investigate the terahertz generation problem in the tilted-pulse-front scheme. We compare in detail the differences among 1D + 1, 2D + 1, and 3D + 1 models. The simulations show that the size of the optical beam in the pulse-front-tilt plane sensitively affects the spatiotemporal properties of the terahertz electric field. The terahertz electric field is found to have a strong spatial dependence such that a few-cycle pulse is generated only near the apex of the prism. Even though the part of the beam farther from the apex can contain a large fraction of the energy, the terahertz waveform shows less few-cycle character. This strong spatial dependence must be accounted for when using the terahertz pulses for strong-field physics and carrier-envelope-phase sensitive experiments such as terahertz acceleration, coherent control of antiferromagnetic spin waves, and terahertz high-harmonic generation.