Ellipticity control of terahertz high-harmonic generation in a Dirac semimetal

We report on terahertz high-harmonic generation in a Dirac semimetal as a function of the driving-pulse ellipticity and on a theoretical study of the field-driven intraband kinetics of massless Dirac fermions. Very efficient control of the third-harmonic yield and polarization state is achieved in electron-doped ${\mathrm{Cd}}_3{\mathrm{As}}_2$ thin films at room temperature. The observed tunability is understood as resulting from terahertz-field-driven intraband kinetics of the Dirac fermions. Our study paves the way for exploiting the nonlinear optical properties of Dirac matter for applications in signal processing and optical communications.

Figure 1

(a) An idealized driving pulse with linear polarization, a central frequency of $f=0.69$ THz, and full width at half maximum (FWHM) of 0.11 THz. (b) Intensity of driving pulse for various ellipticities ${\varepsilon }_f$. Intensity of emitted third-order harmonic radiation ($3f$), for (c) parallel $I_{\parallel }$ and (d) perpendicular $I_{\perp }$ components, as a function of the ellipticity for various relaxation times $\tau =2$, 6, 10, and 20 fs. The intensity is normalized to the maximum value of $I_{\parallel }$. Intensity of emitted fifth-order harmonic radiation ($5f$) vs ellipticity for (e) parallel and (f) perpendicular components.

Figure 2

Electric-field components (a) $E_{\parallel }$ and (b) $E_{\perp }$ of emitted terahertz radiation from ${\mathrm{Cd}}_3{\mathrm{As}}_2$ at room temperature. The data are normalized to the maximum value of $E_{\parallel }$ at ${\varepsilon }_f=0$. (c) Intensity $I_{3f}$ of terahertz THG from ${\mathrm{Cd}}_3{\mathrm{As}}_2$ as a function of ellipticity at room temperature. The dashed lines are guides to the eyes. (d) Ellipticity ${\varepsilon }_{3f}$ of observed THG vs driving-pulse ellipticity ${\varepsilon }_f$. The dashed line depicts ${\varepsilon }_{3f}={\varepsilon }_f$. (e) Intensity and (f) ellipticity of theoretically obtained THG vs driving-pulse ellipticity ${\varepsilon }_f$ for $\tau =10$ fs.

Figure 3

Projection of the electron distribution function on the ($p_{\perp },p_{\parallel }$) momentum plane at selected time delays 3.52, 3.87, 4.25, 4.51, and 4.95 ps [corresponding to the dashed lines in (d) and (e) and in Figs. 1 and 1] for a relaxation time $\tau =10$ fs and various ellipticities (a) ${\varepsilon }_f=0$, (b) 0.36, and (c) 0.90. The momenta are given in units of the Fermi momentum $E_F/v_F$. The time derivative of the current density (d) $d{j}_{\parallel }/dt$ and (e) $d{j}_{\perp }/dt$ as a function of time delay, which is normalized to the maximum value of $d{j}_{\parallel }/dt$.