ABSTRACT
The optomechanical interaction is already nonlinear: it is quadratic in the field amplitudes and linear in the mechanical oscillator amplitudes. We saw this, for instance, in Sections 4.5.2 and 6.1, where the canonical (polaron) transformation was used to decouple the mechanical and optical degrees of freedom, thereby introducing a quartic nonlinearity in the field. In this chapter we will discuss alternative forms of nonlinearity in both the potential energy stored in the mechanical degree of freedom and in the coupling of the mechanical element to the cavity field.
