title: Mathieu function solutions for photoacoustic waves in sinusoidal one-dimensional structures.
abstract: The photoacoustic effect for a one-dimensional structure, the sound speed of which varies sinusoidally in space, is shown to be governed by an inhomogeneous Mathieu equation with the forcing term dependent on the spatial and temporal properties of the exciting optical radiation. New orthogonality relations, traveling wave Mathieu functions, and solutions to the inhomogeneous Mathieu equation are found, which are used to determine the character of photoacoustic waves in infinite and finite length phononic structures. Floquet solutions to the Mathieu equation give the positions of the band gaps, the damping of the acoustic waves within the band gaps, and the dispersion relation for photoacoustic waves. The solutions to the Mathieu equation give the photoacoustic response of the structure, show the space equivalent of subharmonic generation and acoustic confinement when waves are excited within band gaps.
authors.affiliation: Brown University, Department of Chemistry, Providence, RI 02912, USA.
authors.forename: Binbin
authors.initials: B
authors.lastname: Wu
authors.forename: Gerald J
authors.initials: GJ
authors.lastname: Diebold
mesh_terms: D003198:Computer Simulation; D008027:Light; D008962:Models, Theoretical; D012212:Rheology / Q000379:methods*; D012542:Scattering, Radiation; D013016:Sound