Terahertz Bloch Oscillator with a Modulated Bias

Electrons performing Bloch oscillations in an energy band of a dc-biased superlattice in the presence of weak dissipation can potentially generate THz fields at room temperature. The realization of such a Bloch oscillator is a long-standing problem due to the instability of a homogeneous electric field in conditions of negative differential conductivity. We establish the theoretical feasibility of stable THz gain in a long superlattice device in which the bias is quasistatically modulated by microwave fields. The modulation waveforms must have at least two harmonics in their spectra.

Figure 1

(a),(b) Two waveforms of the bias modulation $E_{\mathrm{mod}}(t)$ which result in the same dynamical conductivity of a SL [Eq. (1)]. (c) Gain profiles calculated using Eq. (1) for $E_0=4E_{\mathrm{cr}}$ and $T_0/T≕0$, 0.05, 0.1, 0.2. (d) Sketch of the Bloch oscillator with a modulated bias.

Figure 2

(a) Esaki-Tsu characteristic (thin blue line) [Eq. (4)] and the characteristic of a SL modified by the bichromatic field [Eq. (6)] (thick black line) for $E_1=2.1E_{\mathrm{cr}}$, $E_2=1.7E_{\mathrm{cr}}$, $n=3$, $\varphi =0$. (b) Dynamical conductivity [Eq. (5)] as a function of $\omega$ (thick black line) for the same bichromatic modulation and $E_{\mathrm{dc}}=4E_{\mathrm{cr}}$. The thin blue curve shows the usual Bloch gain profile [Eq. (2)].

Figure 3

Regions of a spatially homogeneous electric field (red) in the ${\sigma }_b\mathrm{\text{−}}{\omega }_{\mathrm{pl}}^2$ plane in the case of (a) asymmetric and (b) symmetric pulse voltages with $\Omega \tau =0.05$ and $T_0/T=0.1$. The SL has the length $500d$.