Physics of the conical broadband terahertz emission from two-color laser-induced plasma filaments

We propose a comprehensive physical model explaining the conical character of broadband terahertz generation from femtosecond two-color laser-induced air plasma filaments. We show, that, in contrast to other models, emission is always conical, resulting from phase matching of the radiation produced inside the filament combined with a partial back reflection of the generated terahertz field from the filament itself due to the frequency-dependent critical plasma density. The obtained conical angle varies from 2${}^{\circ }$ to 10${}^{\circ }$, depending on the plasma density distribution and filament length. Unlike previously proposed models, our model shows good agreement with our experiments as well as a wide range of experimental findings from the literature.

Figure 1

Schematic representation of two-color filament THz generation model.

Figure 2

Minimum peak plasma density for comical emission (a), simulation results for far-field THz profiles of 10 mm (b) and 20 mm (c) long filaments with maximum plasma density of $7\times {10}^{16}{\text{cm}}^{-3}$ and $7\times {10}^{17}{\text{cm}}^{-3}$ respectively calculated with and without phase change inside the filament, (d) conical emission angle for filaments with different maximum plasma density, (e) total terahertz yield for filaments with different maximum plasma density (scaled and shifted for readability), (f) far-field THz profiles of filaments with maximum plasma density of $1\times {10}^{17}{\text{cm}}^{-3}$ and different lengths, (g) far-field THz profiles of 9-mm-long filaments with various maximum plasma densities, scaled to fit the plot, multipliers shown with arrows.

Figure 3

Experimental setup for two-color plasma terahertz generation and far-field THz beam profiling; inset: measured conical profile of the THz emission from two-color plasma filament. PM: parabolic mirror, HDPE: high density polyethilene filter, BBO: $\beta$ barium borate type-I crystal. Inset shows measured THz profile.

Figure 4

Terahertz generation in symmetric (a), (c), (e) and asymmetric (b),(d), (f) plasma density distribution filaments: (a), (b) — photo of filaments, (c),(d) — conical angle of generated THz, blue points represent experimental results, lines show simulation results, (e),(f) — far field THz intensity profiles produced by filaments shown in (a) and (b) respectively. Dots represent experimental results and lines show simulation results. The inset in (c) shows the maximum plasma density dependency vs. length used in the model for this specific figure.

Figure 5

(a),(b) Far-field THz patterns through germanium filter, experimental (triangles) and theoretical (crosses) points taken from [5] and compared with our model (dashed line), for two cases of (a) 10-mm filament produced by 1.3-mJ pulse, (b) 40-mm filament produced by 5-mJ pulse; (c),(d) far-field THz patterns: experimental points (triangles) taken from [15] and compared with our model (dashed line), for two cases of (c) filament produced through 100-mm lens, (d) filament produced through 200-mm lens, pulse energy in both cases 0.71 mJ; (e) far-field THz pattern from [16] repeated and explained with our model (dashed line); (f) simulated THz spectra for various collection angles, experimental data taken from [17], followed by dashed lines calculated with our model; (g)–(j) THz patterns from [18] (triangles), with their theory (crosses) and reproduced with our model (dashed line).