Directivity of a Planar Hard-Dielectric Fabry-Pérot Optical Ultrasound Sensor

A planar hard-dielectric Fabry-Pérot (FP) optical ultrasound sensor was modelled analytically to study how different wave modes affect the directionality. The sensor was modelled as a multilayered structure using the global matrix method. Modal dispersion curves were extracted from the model to enable features of the directional response to be linked to specific wave phenomena. The analytical model showed good agreement with the measured directional response. The key features of the directional response are linked to wave effects such as the water-substrate and water-spacer compressional and shear critical angles. A region of high sensitivity immediately after the shear critical angle is associated with a leaky-Rayleigh wave which has a frequency-dependent phase speed. At higher frequencies, this region is diminished by a minimum which occurs when the mirrors have the same vertical displacement, resulting in a lack of sensitivity.