The Influence of Strain-Optic Coefficients on the Transduction Mechanism of Planar Glass Etalon Fabry-Pérot Ultrasound Sensors

The Fabry-Pérot (FP) ultrasound sensor can detect ultrasound over a broadband frequency range (tens of MHz) with small element sizes (tens of microns). The FP sensor is an optical interferometer where an incident acoustic wave modulates the optical path length via two mechanisms. The first is from a change in the optical-cavity thickness and the second is from a strain-induced change in refractive index. One way to investigate the transduction mechanisms is to examine the sensor's frequency-dependent directional response. Previously, the strain-optic effect was neglected when modeling the directional response, however, some experimental studies have shown it to be significant in some circumstances. In this paper, the contributions of the two mechanisms are investigated for a planar air-backed glass-etalon Fabry-Pérot sensor. The sensor was modeled as a multilayered elastic structure, and the strain and displacement fields were calculated using the partial wave method. For an optically isotropic, homogeneous and non-absorbing spacer material the strain-optic effect is only dependent on two coefficients, p
₁₁
and p
₁₂
. The modeled directivity was similar when including or excluding the strain-optic coefficients and had good agreement with directional response measurements made on an air-backed glass-etalon sensor. The directional response is dominated by the normal strain in the sensor except at the compressional critical angle where the transverse strain is larger than normal strain. Understanding how the strain-optic mechanism affects the directional response can help improve future sensor design. For example, exploiting materials with large strain-optic coefficients could increase the sensitivity of Fabry-Pérot sensors.