Phase Gradient Control by Elastic Metasurface in Realizing Arbitrary Wavefront Manipulation


Student thesis: Doctoral Thesis

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Award date8 Aug 2023


Metasurfaces are man-made engineered planar structures that have drawn a significant amount of attention in recent years, owing to their impressive capabilities in shaping wavefronts, and their potential for multiple applications, such as structural health monitoring, energy harvesting, and enhanced sensing. As compared to the bulky three-dimensional metamaterial, metasurface with ultrathin thickness occupies less physical space and provides the possibility in minimizing the propagation loss of waves. Begin in the field of optics, the concept of metasurface is later extended to acoustics and elastic fields. Arbitrary wavefront manipulation is realized by a metasurface through introduction of abrupt phase shifts at interfaces based on the concept of generalized Snell’s Law. Unlike electromagnetic and acoustic metasurfaces that have similarity between their governing equations, applying the concept of metasurface in solids is rather complicated as more degrees of freedom needs to be considered because of the innate coupling between longitudinal (P-) and shear (S-) waves as well as the conversion of wave mode. Therefore, manipulation of elastic waves through a metasurface remains challenging.

Generally, metasurfaces can be classified into three categories: transmissive, reflective and absorptive metasurfaces. These metasurfaces generate phase discontinuities via either passive or adaptive approach to achieve desired phase profiles for different functionalities. A passive metasurface is not tunable after its fabrication and is therefore limited to execution of predetermined functions at single or specific frequencies. In contrast, an adaptive metasurface is reconfigurable after fabrication, enabling it to adapt to changing operating frequencies while allowing it to perform various functionalities. As phase shifts play an important role in controlling wavefronts at will, a new type of metasurface namely coding metasurface has emerged as a new technology in wavefront manipulation. The coding metasurface is comprised of 2N types of coding units whereby N refers to the bit number of metasurface, allowing a simpler phase distribution along the interfaces as compared to traditional metasurface. Based on the bit number of coding metasurface with phase gradient of 2π/2N, the coding metasurface can perform similar features as the traditional metasurface. Moreover, due to complexities in designing a metasurface, machine learning approach has been utilized in metasurface design to solve problems using big data.

In this study, the primary research presented aimed to investigate different approaches that enable phase shift control by elastic metasurface to actualize arbitrary wavefront manipulation, including but not limited to anomalous wave steering, wave focusing and nonparaxial wave propagation. This thesis is divided into seven chapters. CHAPTER 1 briefly discusses the overview, scope and objectives of the presented research. For CHAPTER 2, a comprehensive literature review on the design mechanism of metasurface, the development of traditional and coding metasurfaces, and application of adaptive controls and machine learning in metasurfaces is conducted. Then, CHAPTER 3 AND 4 evolves around an adaptive elastic metasurface composed of piezoelectric stacks connected with negative capacitive (NC) shunt serving as traditional and coding elastic metasurfaces, respectively, to manipulate elastic P-waves. By tuning the effective Young’s modulus through the NC shunts, the proposed adaptive elastic metasurface was able to attain desired phase profiles to perform switchable functionalities in broadband frequencies, ranging from 85 to 200 kHz.

Furthermore, CHAPTER 5 discusses a piezoelectric-based elastic metasurface with hybrid shunting circuits (NC – LC – NC shunts) that comprising only three unit cells in its functional unit to realize manipulation of flexural waves. The proposed piezoelectric-based metasurface enabled a more compact design and is capable of demonstrating multiple functionalities at different working frequencies. It was reported that the functional unit with the same structural configuration, but only single type of shunting circuit cannot achieve the same output as those of the proposed piezoelectric-based metasurface. Subsequently, CHAPTER 6 is directed towards high efficiency generation of S-waves by transmissive coding metasurface based on machine learning approach. Inspired by Lamb’s problem, an analytical model was developed to study the transmitted wavefield of elastic half-space under the excitation of a vertical loading. Due to mathematical complexities in attaining the corresponding wavefields, a machine learning approach was proposed to analyze the entire wavefield of the elastic half-space. It was discovered that exertion of multiple vertical loadings with opposite magnitudes can induce beam splitting of transmitted shear waves. Through utilization of binary coding units, wave mode conversion of P-waves to S-waves are realized in an elastic half-space.

Finally, CHAPTER 7 concludes the outcomes reported in the previous chapters and outlines the limitations and recommendations for the presented work.