Photoacoustic effect in a periodically modulated structure

We discuss the photoacoustic effect in one-dimensional phononic structures with sinusoidal modulation of its acoustic properties. The periodic structure is considered to have a modulation in its density or compressibility of the form $1-2\gamma \cos (\frac{2\pi x}{a})$, where $\gamma$ is the modulation factor and $a$ is the periodic length of the phononic structures. The properties of the photoacoustic waves are determined by an inhomogeneous Mathieu equation. We give several different methods including Green's function solutions, series expansions, and variation of parameters solutions for determining closed from solutions to the inhomogeneous Mathieu equation to obtain the properties of the photoacoustic effect.