Topological modes in non-hermitian phononic crystals optically induced in a quantum-well array

We study theoretically propagation of acoustic waves in an array of quantum wells, where a spatially modulated amplification and attenuation of sound is realized by optical excitation with a frequency close to the exciton resonance. The dispersion of sound waves near Bragg resonances corresponding to the modulation wave vector is calculated. The appearance of “imaginary” stop bands, where the imaginary parts of the Bloch mode frequencies are split, is described. The emergence of acoustic topological modes at the edge of the structure is demonstrated.