Theory of Parametric Amplification in Superlattices

We consider a high-frequency response of electrons in a single miniband of superlattice subject to dc and ac electric fields. We show that Bragg reflections in miniband result in a parametric resonance which is detectable using ac probe field. We establish theoretical feasibility of phase-sensitive THz amplification at the resonance. The parametric amplification does not require operation in conditions of negative differential conductance. This prevents a formation of destructive domains of high electric field inside the superlattice.

Figure 1

Two schemes of the parametric amplification in superlattice without corruption from generated harmonics. In the presence of ac pump (red online) of the frequency $\omega$, parametric gain for a weak signal (green online) of the frequency ${\omega }_1$ arises either at ${\omega }_1≕\omega /2,3\omega /2,\dots$ in biased SL ($E_{\mathrm{dc}}\ne 0$) or at ${\omega }_1≕2\omega ,4\omega ,\dots$ in unbiased SL ($E_{\mathrm{dc}}=0$).

Figure 2

Amplification at even harmonics in unbiased superlattice for $\varphi ={\varphi }_{\mathrm{opt}}$. Regions above the marked curves correspond to gain at ${\omega }_1≕2\omega$, $4\omega$, $6\omega$. Dark (red online) areas correspond to electric instability.

Figure 3

Magnitude of negative absorption at even harmonics (marked curves) as a function of the pump frequency $\omega$ for the fixed pump amplitude $E_0=5.1$ and $\varphi ={\varphi }_{\mathrm{opt}}$. Dark (red online) segments indicate intervals of NDC.

Figure 4

Amplification with a low threshold at ${\omega }_1=\omega /2$ in biased superlattice for $E_{\mathrm{dc}}=1$ and $\varphi ={\varphi }_{\mathrm{opt}}$. Marked region between curves corresponds to gain, while dark (red online) area corresponds to electric instability. Inset: magnitude of negative absorption as function of the pump amplitude $E_0$ for $\omega \tau =0.25$.