Piezoelectric resonator arrays for tunable acoustic waveguides and metamaterials J. Appl. Phys. 112, 064902 (2012) Focused high frequency needle transducer for ultrasonic imaging and trapping Appl. Phys. Lett. 101, 024105 (2012) A rigid, monolithic but still scannable cavity ring-down spectroscopy cell Rev. Sci. Instrum. 83, 043115 (2012) Acoustic resonator based on periodically poled transducers: Concept and analysisThe mechanical and electrical properties of transducers are modeled by finite-difference representations of the relevant physical equations, and the numerical problems are discussed. The theory is applied to ͑a͒ a ceramic transducer of dimensions 1 cmϫ1 cmϫ200 m, ͑b͒ a polymer P of the same dimensions, and ͑c͒ a 1-3 composite transducer consisting of transverse rods of ceramic embedded in a matrix of polymer. The results for the ceramic agree with the one-dimensional model, viz.:voltage of order 4-5 V and no resonance below 10 MHz. For the polymer, the resonant frequency of 3.9 MHz is close to the 4 MHz predicted by the one-dimensional theory. For the composite, introduction of the ceramic has an immediate effect on s 11 , s 12 and s 13 , whereas it has little effect on d 31 unless the density of the ceramic in the mix is 30% or higher.