Azimuthally polarized terahertz radiation generation using radially polarized laser pulse in magnetized plasma

An analytical formulation of a radially polarized laser pulse propagating in a homogeneous, magnetized plasma is presented using Lorentz force, continuity and Maxwells equations. Perturbation technique and quasi-static approximation (QSA) have been used to study the generated fields in nonlinear regime. The generated slow, oscillating, transverse electric and magnetic fields having equal amplitude, constitute a radiation field having frequency in the terahertz (THz) range. Particle-in-cell (PIC) simulation code FBPIC is used to validate analytical findings. Simulation studies also show that the generated THz radiation field propagates beyond the plasma boundary, indicating coherent electromagnetic radiation emission. Furthermore, the field amplitude scales nonlinearly with plasma density and increases linearly with external magnetic field strength, highlighting the role of these parameters in controlling radiation amplitude.

💡 Research Summary

The paper presents a comprehensive theoretical and numerical study of terahertz (THz) radiation generation when a radially polarized laser pulse propagates through a homogeneous plasma that is immersed in a static axial magnetic field. Starting from the Lorentz force, continuity equation, and Maxwell’s equations, the authors develop a perturbative analytical model. The laser field is described by a Gaussian envelope with radial polarization, and the external magnetic field is taken as a uniform B₀ aligned with the propagation direction (z‑axis). By expanding the electron density and velocity in powers of the laser strength parameter a₀, the first‑order solution yields quiver velocities: a radial component driven directly by the laser electric field and an azimuthal component proportional to the cyclotron frequency ω_c = eB₀/m. The first‑order density perturbation scales as a₀².

In the second‑order (slow) dynamics, the nonlinear ponderomotive term couples the first‑order quantities to generate a transverse electric field E_θ (azimuthal) and a radial magnetic field B_r. The authors transform to a co‑moving frame (ξ = z – vt, τ = t) and apply the quasi‑static approximation (∂/∂τ ≈ 0) to simplify Maxwell’s equations. The resulting coupled equations show that E_θ and B_r have identical amplitudes, are in phase, and oscillate at the plasma frequency ω_p = √(n₀e²/ε₀m). Consequently, if ω_p lies in the THz band (≈1–10 THz), the pair of fields constitutes a coherent THz radiation source. The analytical expressions reveal that the field amplitude scales nonlinearly with plasma density (approximately ∝ n₀ or √n₀ depending on the regime) and linearly with the external magnetic field strength (∝ B₀), reflecting the role of the magnetic field in enhancing the azimuthal electron motion.

To validate the theory, the authors perform fully electromagnetic quasi‑3D Fourier‑Bessel particle‑in‑cell (FBPIC) simulations. The simulation domain spans z = –10 µm to 120 µm and r = 0 to 20 µm with high spatial resolution (≥10 cells per laser wavelength). The laser parameters are a₀ = 0.3, λ = 0.8 µm, waist w₀ = 15 µm, and duration τ = 40 fs. The plasma density is n₀ = 3.8 × 10²³ m⁻³ with a 20 µm density ramp, and a uniform magnetic field B₀ = 71 T is applied. The simulation resolves the laser‑plasma interaction, including energy depletion and pulse evolution.

Results show that the azimuthal electric field E_θ and radial magnetic field B_r develop the predicted radial profiles: both start from zero on axis, increase to a maximum at a few micrometres radius, and then decay. The simulated peak E_θ reaches ≈0.9 × 10⁵ V/m at r ≈ 7 µm, whereas the analytical model predicts ≈8 × 10⁵ V/m; the discrepancy is attributed to the quasi‑static and first‑order approximations, as well as to laser depletion not captured analytically. Both fields persist beyond the plasma‑vacuum interface (z > 250 µm), confirming that a genuine electromagnetic wave propagates into vacuum. Spectral analysis of the fields yields a dominant spatial wavelength of ≈55 µm, corresponding to a frequency of ≈5.4 THz, consistent with the plasma frequency. Parameter scans confirm the predicted scaling: increasing n₀ enhances the field amplitude nonlinearly, while increasing B₀ leads to a linear increase.

The study concludes that the combination of a radially polarized laser and an axial magnetic field provides an efficient mechanism for generating azimuthally polarized THz radiation. The mechanism relies on the magnetic field‑induced azimuthal electron motion, which together with the radial laser drive creates a coherent E_θ–B_r pair. The work highlights the controllability of the THz output via plasma density and magnetic field strength, offering a pathway toward tunable, high‑brightness THz sources. Future directions suggested include exploring non‑uniform magnetic fields, multi‑color laser schemes, higher‑intensity regimes where higher‑order nonlinearities become important, and experimental realization of the proposed configuration.