Liquid Surface Wave Propagation Behavior In The Modulation Of The Periodic Structure

In the thesis, the propagation of liquid surface waves in periodic structures is studied experimentally and theoretically. The thesis is divided into five chapters.In the first chapter, the backgrounds of research on the liquid surface waves in the periodic structures are introduced, including the classification of water waves and the status of investigation, the relation between the liquid surface waves and photonic crystals (PCs), the characteristic and importance of our investigation.In the second chapter, the theoretical methods are presented. Several theoretical methods for the PCs are applied to the liquid surface waves in periodic structures. We use transfer matrix method (TMM) for the series of ID steps, multiple scattering method (MSM) for the 2D cylinder arrays, and plane wave method (PWM) for the system with periodically drilled bottom. Band structures, transmissions and patterns of field distribution can be calculated.In the third chapter, the experimental methods and the experimental setup are introduced. Difficulties in our experimental design and how we resolve them are presented. Quantitative measurement of the wave amplitude is emphasized here.In the fourth chapter, we studied all dimensional reflection in ID steps system. Band structure, transmissions and reflections are calculated which indicate the Brewster angle phenomenon. Similar to that in photonic crystals, all dimensional reflection is realized in ID system for liquid surface waves theoretically.In the fifth chapter, some physical phenomena of liquid surface waves in the 2D systems are studied experimentally and theoretically. Superlensing effect in the 2D cylinder arrays, complete gap, self-collimation and negative refraction in the 2D holes arrays system are presented. Band structure and CFC (constant frequency contours) analysis are carried out to understand these phenomena physically. The experiment results are first realized in liquid surface waves. It is also the most important work in the thesis.In the sixth chapter, the nonlinear phenomena in liquid surface waves are introduced. One nonlinear symmetric pattern phenomenon is observed fist time in our experiment. Compare with the Faraday wave patterns, we analyze this phenomenon and simulated the distribution pattern numerically. Furthermore, chaos in liquid surface waves is also introduced.