Terahertz radiation as a probe of the dynamics of coherently injected photocurrents in quantum well and graphene systems

We calculate the terahertz radiation that would be emitted from rotating current densities coherently injected by two-color optical pulses in GaAs and graphene samples in a magnetic field. This is done for realistic experimental geometries and parameters, with scattering and relaxation processes taken into account phenomenologically. Results are presented in the time domain for the expected terahertz signal observed at a detector. We include predictions for bilayer graphene as well as monolayer graphene, and compare with results expected in the absence of a magnetic field.

Figure 1

(a) Illustration of rotation of electron (e) and hole (h) current densities in a uniform optical field. (b) Illustration of electron and hole densities about points in the sample, injected by a pulse finite in space and time; the charges rotate about the points as shown.

Figure 2

Experimental geometries for (a) GaAs and (b) graphene and bilayer graphene.

Figure 3

Schematic of energy levels of bilayer graphene.

Figure 4

Injected current density (in A/m) vs relative polarization angle for GLT [(a) and (e)], 2BT [(b) and (f)], 3BT [(c) and (g)], and SOT [(d) and (h)]. Top row shows $x$ components, bottom row shows $y$ components. The angle is measured from the $2{\omega }_0$-pulse polarization direction (here assumed to be the $+x$ direction) to the ${\omega }_0$-pulse polarization direction. The experimental parameters are identical to those given in Sec. 5 for the bilayer, but with the pulse frequencies doubled and infinite scattering time.

Figure 5

Lissajous figures for GaAs with collinear incident pulses. For $\tau =5$ ps, we plot the (a) electron contribution, (b) hole contribution, and (c) total contribution; (d) shows the total contribution for $\tau =200$ fs. The time $T$, measured at the sample, runs from $-200$ fs to 1.5 ps, where $T=0$ corresponds to the peak incident intensity at the sample. See text for pulse parameters.

Figure 6

Lissajous figures for GaAs for total (electron + hole) field for (a) cross-linear polarization $\tau =5$ ps; (b) cross-linear polarization and $\tau =200$ fs; (c) co-circular polarization and $\tau =5$ ps; (d) co-circular polarization and $\tau =200$ fs. The time $T$, measured at the sample, runs from $-200$ fs to 1.5 ps, where $T=0$ corresponds to the peak incident intensity at the sample. See text for pulse parameters.

Figure 7

Total field vs time for monolayer graphene for (a) collinear polarization, $\tau =5$ ps; (b) collinear polarization, $\tau =50$ fs; (c) co-circular polarization, $\tau =5$ ps; (d) co-circular polarization, $\tau =50$ fs. Solid line represents the $p$ component and dashed line represents the $s$ component. The time $T$ is measured at the sample, where $T=0$ corresponds to the peak incident intensity at the sample. See text for pulse parameters.

Figure 8

Total field vs time for bilayer graphene for (a) collinear polarization, $\tau =5$ ps; (b) collinear polarization, $\tau =50$ fs; (c) co-circular polarization, $\tau =5$ ps; (d) co-circular polarization, $\tau =50$ fs. Solid line represents the $p$ component and dashed line represents the $s$ component. The time $T$ is measured at the sample, where $T=0$ corresponds to the peak incident intensity at the sample. See text for pulse parameters.