Model of the Influence of an External Magnetic Field on the Gain of Terahertz Radiation from Semiconductor Superlattices

We theoretically analyze the influence of magnetic field on small-signal absorption and gain in a superlattice. We predict a very large and tunable THz gain due to nonlinear cyclotron oscillations in crossed electric and magnetic fields. In contrast to Bloch gain, here the superlattice is in an electrically stable state. We also find that THz Bloch gain can be significantly enhanced with a perpendicular magnetic field. If the magnetic field is tilted with respect to the superlattice axis, the usually unstable Bloch gain profile becomes stable in the vicinity of Stark-cyclotron resonances.

Figure 1

(a) Frequency of the nonlinear oscillations $\Omega$ [Eq. (8)] as a function of ${\omega }_B$ for ${\omega }_c\tau ≕2$, 4. The dashed lines separate the cyclotronlike and Bloch-like regimes of motion. (b) VI characteristics for ${\omega }_c\tau ≕0$, 2, 4. (c)–(f) Absorption and gain profiles for ${\omega }_c\tau =4$ and different values of electric field ${\omega }_B\tau ≕0$ (c), 6 (d), 7.5 (e) and 8.5 (f).

Figure 2

(a) Cyclotron gain profiles for ${\omega }_B\tau =3.6$, ${\omega }_c\tau =2$ and ${\omega }_B\tau =8.5$, ${\omega }_c\tau =5$. (b) Bloch gain profiles for ${\omega }_B\tau =8$ and different values of the magnetic field ${\omega }_c\tau ≕0$, 2.5, 3.5. The gain profiles were calculated using Eqs. (3, 4, 5).

Figure 3

(a) VI characteristic in tilted magnetic field, calculated using Eqs. (3, 4, 5), for ${\omega }_c\tau =2$ and ${\omega }_{c\perp }\tau =5$ (black line). The thin blue line shows the Esaki-Tsu VI characteristic [Eq. (7)]. (b) Gain profile for the same magnetic field and dc bias ${\omega }_B\tau =4.75$ (black line). The thin blue line indicates the usual Bloch gain at $\mathbf{B}=\mathbf{0}$ [Eqs. (6, 7)].