Analysis of Dielectric Waveguide Grating and Fabry-Perot Modes in Elastic Grating in Optical Detection of Ultrasound

In our previous work, we have demonstrated that dielectric elastic grating can support Fabry-Perot modes and provide embedded optical interferometry to measure ultrasonic pressure. The Fabry-Perot modes inside the grating provide an enhancement in sensitivity and figure of merit compared to thin film-based Fabry-Perot structures. Here, in this paper, we propose a theoretical framework to explain that the elastic grating also supports dielectric waveguide grating mode, in which optical grating parameters control the excitation of the two modes. The optical properties of the two modes, including coupling conditions and loss mechanisms, are discussed. The proposed grating has the grating period in micron scale, which is shorter than the wavelength of the incident ultrasound leading to an ultrasonic scattering. The gap regions in the grating allow the elastic grating thickness to be compressed by the incident ultrasound and coupled to a surface acoustic wave mode. The thickness compression can be measured using an embedded interferometer through one of the optical guided modes. The dielectric waveguide grating is a narrow bandpass optical filter enabling an ultrasensitive mode to sense changes in optical displacement. This enhancement in mechanical and optical properties gives rise to a broader detectable pressure range and figure of merit in ultrasonic detection; the detectable pressure range and figure of merit can be enhanced by 2.7 times and 23 times, respectively, compared to conventional Fabry-Perot structures.