Second-Harmonic Generation Induced by Electric Currents in GaAs

We demonstrate a new, nonlinear optical effect of electric currents. First, a steady current is generated by applying a voltage on a doped GaAs crystal. We demonstrate that this current induces second-harmonic generation of a probe laser pulse. Second, we optically inject a transient current in an undoped GaAs crystal by using a pair of ultrafast laser pulses and demonstrate that it induces the same second-harmonic generation. In both cases, the induced second-order nonlinear susceptibility is proportional to the current density. This effect can be used for nondestructive, noninvasive, and ultrafast imaging of currents. These advantages are illustrated by the real-time observations of a coherent plasma oscillation and spatial resolution of current distribution in a device. This new effect also provides a mechanism for electrical control of the optical response of materials.

Figure 1

SHG induced by an electrically generated steady current. (a) The SH signal as a function of current density. The inset shows schematically the device geometry. (b) Image of the SH signal measured by scanning the probe laser spot across the device. (c) The same as (b), but close to the bottom edge of the electrodes.

Figure 2

(a) Diagrammatic representation of the sequence of events in coherent current injection. 1: Single photon band-to-band transition caused by the SH photon; 2 and 3: two-photon transition caused by two fundamental photons with transition matrix elements incorporating the electron momentum; 4: interference of the two above processes results in the difference of electron-hole pair generation at $+k$ and $-k$ causing current injection. (b) Diagrammatic representation of the sequence of events in current-induced SHG. 1: A dc current is the result of an asymmetric distribution of carriers in $k$ space; 2 and 3: virtual two-photon transition caused by two fundamental photons with transition matrix elements incorporating the electron momentum and detuning from resonance by $\Delta E_k$; 4: polarization at two-photon frequency causes emission of a SH photon.

Figure 3

SHG induced by an optically generated transient current. (a) The measured $\Delta P$ as a function of the probe delay and $\Delta \varphi$, when the probe spot overlaps with the current-injecting spots (defined as $x=0$). The peak carrier density is $7.2\times {10}^{17}/{\mathrm{cm}}^3$. (b) Two cross sections of (a) with fixed probe delays of $-0.02$ and 0.15 ps, respectively, as indicated by the vertical lines in (a). (c) $\Delta P$ as a function of time for several carrier densities of 7.2 (squares), 6.0 (circles), 4.8 (up triangles), 3.6 (down triangles), 2.4 (diamonds), and $1.2\times {10}^{17}/{\mathrm{cm}}^3$ (hexagons), respectively, measured with $\Delta \varphi =\pi /2$. (d) The period (left axis) and the frequency (right axis) of the oscillations. The solid line indicates the $\sqrt{N_{2\mathrm{D}}}$ dependence of the frequency.