Coherent Control of Harmonic Generation in Superlattices: Single-Mode Response

We study the harmonic generation spectrum in a semiconductor superlattice (a quantum-dot array) at slow relaxation. The effect of a single-mode response in an alternating rectangular (meander) electric field is demonstrated: For certain values of field parameters, the extremely wide discrete output spectrum with slowly decaying tails (multiharmonic generation) shrinks to one single harmonic (single-harmonic generation). Similarly, the effect is manifested in the transient continuous spectrum by diminishing the divergencies (peaks) at all odd harmonics but one. Substantial control over the spectrum is demonstrated.

Figure 1

Discrete ac spectra $j_d$ (log plot, arbitrary units) vs harmonic order $\nu$: transition from a wide-spectrum ($\epsilon =7.5$, upper dots) [Eqs. (6, 7)] through $\epsilon =7.01$, 7.0001, 7.000001 to a single-mode response ($\epsilon =7$, single dot, same magnitude) [Eq. (9)]. Continuous curves serve as guidelines only.

Figure 2

Current oscillation $\upsilon (t)$ [Eq. (3)] (arbitrary units) as a function of $\omega t$ within a period $T$, a function of $\epsilon$. Transition from cuspless oscillation at $\epsilon =1$ (SMR, $\epsilon =\mathrm{odd}$) through intermediate values with cusps, $1<\epsilon \le 2$, to vanishing kinetic spectrum at $\epsilon =2$ (induced localization, $\epsilon =\mathrm{even}$).

Figure 3

Continuous harmonic spectra $j_c$ (arbitrary units), scaled by $\alpha T$, vs harmonic order $\Omega$: transition from resonances at $\Omega =\mathrm{odd}$ and smaller antiresonances at $\Omega =\mathrm{even}$ for $\epsilon =3.5$ (upper plot, $\epsilon \ne \mathrm{odd}$) to all small antiresonances with the only nonsmall SMR resonance for $\epsilon =3$ (lower plot, SMR, $\epsilon =\mathrm{odd}$). The dotted curves are for $\alpha \to 0$, solid curves $\alpha =0.1$.