Abstract
This paper deals with the quantization of the acoustic modes in nanomechanical systems with coupled acoustic and electromagnetic modes in piezoelectric structures. Specifically, the well-known Bleustein-Gulyaev (BG) modes in the theory of surface acoustic wave devices, are second quantized so that the relationship between the acoustic modes and the electromagnetic modes can be examined in the limit where the acoustic mode is a single acoustic phonon. By considering a theory where the quantized acoustic phonons are explicitly related to the electromagnetic modes, this treatment allows a description of nanomechanical systems where acoustic and electromagnetic modes can be described in the nanoscale limit. This effort will examine quantitatively the electromagnetic-acoustic interaction caused by the piezoelectricity in the limit where the classical acoustic waves must be described in terms of phonons.
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