Amplification of acoustic phonons in superlattice

The amplification of acoustic phonons in a superlattice in the presence of an electric field $E =E_0 + E_1 cos(\omega t)$ has been investigated theoretically and numerically by computational methods. The calculation is done in the hypersound regime $(ql\gg 1)$ where the attenuation coefficient depends on the phonon wave vector $q =[-\frac{\pi}{q} \quad \frac{2pi}{q}]$ and the frequency $\omega_q = 10^{12} s^{-1}$ . An inversion is attained where amplification far exceeds absorption and the ratio $frac\mid\frac{\Gamma/\Gamma_0\mid_{min}}{\mid\Gamma/\Gamma_0\mid_{max}}\approx 3$ . A high frequency build up of acoustic energy from noise (phonon spectrum) is obtained by using specialized spectral techniques. This indicates an amplification of the phonons generated in the terahertz range leading to the possibility of obtaining a hypersound MASER.