Polarized coherent microwave supercontinua with a terawatt laser driver

Ultrafast laser-plasma interactions driven by ultrashort terawatt laser pulses are shown to give rise to a bright multioctave microwave radiation, whose polarization and spatial mode structure provides a sensitive probe for laser-driven plasma electrodynamics, helping detect the symmetries of plasma currents and signatures of multiple ionization. Polarization mode structure of this radiation is dominated, as polarization-resolved measurements show, by a radially polarized mode, indicating the significance of ponderomotively driven plasma currents as sources of microwave emission. Angle-resolved analysis of microwave supercontinua reveals regimes in which the microwave emission is drastically enhanced, via coherence buildup, manifested in a well-resolved Cherenkov-emission cone.

Figure 1

Nonlinear dynamics of a terawatt laser pulse with a central wavelength ${\lambda }_0=0.8\mu \mathrm{m}$, a pulse width ${\tau }_0=35\mathrm{fs}$, and an input beam diameter $d_0=7\mathrm{cm}$ focused, with a focal length $f=2.5\mathrm{m}$, into a gas cell filled with argon at a variable gas pressure $p$: (a)–(e) $\mathit{rz}$ maps of the field intensity integrated over the pulse ${\int }_{-\infty }^{\infty }{I}_{\mathrm{L}}\left(r,z,\eta \right)d\eta$ (a), (c), (e) and the electron density in the wake of the laser pulse (b), (d), (f) maximum field intensity ${max}_{r,\eta }{I}_L\left(r,z,\eta \right)$, (g) maximum electron density ${max}_{r,\eta }\rho \left(r,z,\eta \right)$, and (h) beam-radius trajectory $r_{\mathrm{L}}\left(z\right)$. The pulse energies and gas pressures are as specified in the panels.

Figure 2

Experimental setup: SM, spherical mirror; KDP, crystal for second-harmonic generation, WCA, waveguide-to-coaxial adapter. Also shown are the radially polarized mode of THz/μWv radiation (green arrows), detection angle $\beta$, the angle $\theta$ between the $x$ axis and direction to the WCA in the $\mathit{xy}$ plane (the OA line), the angle $\phi$ between the coaxial cable of the WCA (shown red) and the OA line.

Figure 3

(a) Temporal trace of microwave radiation detected with WCA2 in an experiment with a single-color driver with ${\lambda }_0\approx 0.8\mu \mathrm{m}, {\tau }_0\approx 35\mathrm{fs}$, and $E_0\approx 60\mathrm{mJ}$ focused into a gas cell filled with air at $p\approx 0.5\mathrm{mbar}$. (b) Pressure scans of the microwave output of laser plasmas driven in air by laser pulses with ${\lambda }_0\approx 0.8\mu \mathrm{m}, {\tau }_0\approx 35\mathrm{fs}$, and $E_0\approx 10\mathrm{mJ}$ (blue filled circles) and 60 mJ (pink open circles). (c), (d) Pressure scans of the microwave output of laser plasmas driven by a single-color (c) and two-color (d) laser field with ${\lambda }_0\approx 0.8\mu \mathrm{m}, {\tau }_0\approx 35\mathrm{fs}$, and $E_0\approx 60\mathrm{mJ}$ in (c) ${\mathrm{N}}_2$ (open green triangles), air (open pink circles), and argon (filled wine triangles) and (d) atmospheric air. Measurements are performed using WCAs with detection ranges of (c) 4 to 18 GHz and (d) 2 to 12 GHz (blue line) and 12 to 32 GHz (pink line).

Figure 4

(a) The microwave output $\mathrm{\Phi }$ of laser plasmas driven by a two-color laser field in air at $p\approx 0.5\mathrm{mbar}$ vs the pulse energy $E_0$ of the laser driver with ${\lambda }_0\approx 0.8\mu \mathrm{m}, {\tau }_0\approx 35\mathrm{fs}$, and the peak power $P_0$ as shown in the upper axis. Measurements are within the WCA detection range of 2 to 12 GHz (blue) and 12 to 32 GHz (pink). (b) The microwave output measured as a function of $\beta$ with WCA1 (blue) and WCA2 (red) at $D\approx 40\mathrm{cm}$ for ${\lambda }_0\approx 0.8\mu \mathrm{m}, {\tau }_0\approx 35\mathrm{fs}, E_0\approx 60\mathrm{mJ}$, and $p\approx 3\mathrm{mbar}$: (circles) experimental results and (dashed line) their best fit with the Cherenkov phase-matching function $\mathcal{I}\left(\beta \right)$. (c), (d) Polarization-resolved microwave output as a function of the angle $\theta$ measured in a single-color (c) and two-color (d) experiment with ${\lambda }_0\approx 0.8\mu \mathrm{m}, {\tau }_0\approx 35\mathrm{fs}, E_0\approx 60\mathrm{mJ}, E_{\mathrm{SH}}\approx 2.5\mathrm{mJ}$, and $p\approx 1\mathrm{mbar}$ (c) and 50 mbar (d) with WCA2 at $D\approx 40\mathrm{cm}$ and $\phi \approx 0^{\circ }$ (filled blue circles) and $\phi \approx {90}^{\circ }$ (open pink circles). The solid line is the best $\xi cos\left(\theta -\alpha \right)$ fit, with (c) $\xi =0$ and (d) $\xi =1, \alpha ={70}^{\circ }$ (blue line) and $\xi =0.5, \alpha ={160}^{\circ }$ (pink line).

Figure 5

(a) A map of the electron density $\rho \left(r,z\right)=\rho (r,z,\eta >{\tau }_0)$ found by solving the field evolution Eq. (1) jointly with Eq. (2) for a laser pulse with ${\lambda }_0=0.8\mu \mathrm{m}, {\tau }_0=35\mathrm{fs}, d_0=7\mathrm{cm}, P_0=1.5\mathrm{TW}$, and $f=2.5\mathrm{m}$ in a gas cell filled with argon at $p=0.1\mathrm{bar}$. Also shown are the contour lines, dividing the map into eight areas, with the electron density below ${10}^{11}\mathrm{c}{\mathrm{m}}^{-3}$ (1) and ranging from ${10}^{11}$ to ${10}^{12}\mathrm{c}{\mathrm{m}}^{-3}$ (2), ${10}^{12}$ to ${10}^{13}\mathrm{c}{\mathrm{m}}^{-3}$ (3), ${10}^{13}$ to ${10}^{14}\mathrm{c}{\mathrm{m}}^{-3}$ (4), ${10}^{14}$ to ${10}^{15}\mathrm{c}{\mathrm{m}}^{-3}$ (5), ${10}^{15}$ to ${10}^{16}\mathrm{c}{\mathrm{m}}^{-3}$ (6), ${10}^{16}$ to ${10}^{17}\mathrm{c}{\mathrm{m}}^{-3}$ (7), and ${10}^{17}$ to ${10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$ (8). (b) Radiation spectra calculated by integrating over the volume $V_q$ of the $q\mathrm{th}$ plasma region, with $q=1$ (curve 1), 2 (2), 3 (3), 4 (5), 5 (5), 6 (6), 7 (7), and 8 (8). (c) Plasma attenuation length $l_{\mathrm{p}}$ as a function of radiation frequency for a plasma with an electron density of ${10}^{11}\mathrm{c}{\mathrm{m}}^{-3}$ and the electron collision rate ${\nu }_e=0.3\mathrm{THz}$. (d) Radiation spectra calculated by integrating over the total volume of plasma regions 1–8 (dashed pink line) and the volume $V_1$ of the subsurface plasma region with $q=1$ (solid black line).