Detection of Circular-Crested Lamb Waves Using Surface-Bonded Fiber-Optic Ultrasound Sensors: A Theoretical Perspective

A theoretical framework is established to study the interaction between circular-crested Lamb waves (CCLWs) and a fiber-optic ultrasound sensor (FOUS) bonded onto the surface of a plate structure. CCLW is a universal expression of guided Lamb waves, regardless of the source-sensor distance. In the theory developed here, strain transfer and transformation, birefringence of the fiber sensor, and modulation of refractive index by elasto-optic effects are incorporated. Explicit expression for calculating the ultrasound-induced wavelength shift of fiber Bragg gratings (FBGs) is derived. To showcase application of the established theory in a more general situation, a chirped FBG Fabry-Perot interferometer based FOUS is simulated, in combination with transfer matrix method. Results uncover quantitatively the interplay of the following factors governing the sensor response: 1) co-existence of both axial and lateral normal strains in the fiber, especially in the near field; 2) elasto-optic properties of the fiber material; 3) initial polarization state of the fiber sensor; 4) incident angle of the CCLWs; and 5) ratio between the equivalent ultrasonic wavelength and the effective sensor length. The calculated results uncover the underlying mechanisms responsible for several experimental observations reported but inadequately explained in the literature. The theoretical framework is also applicable to other non-FBG-based FOUSs that rely on phase modulation by ultrasounds.