The relevance of the people you love most is trully revealed when they are apart. Life goes on, memories remain.To my brother, Toño.
La relevancia de las personas que más quieres se manifiesta realmente cuando no están. La vida sigue, los recuerdos permanecen.A mi hermano, Toño.
AknowledgementsIt has been a long time since, after being involved for the first time in research during the realization of my Master Thesis, Víctor Sánchez gave me the oportunity to work with him to investigate subharmonic generation in resonant cavities. Soon after, he proposed me to start my PhD in the context of wave propagation in sonic crystals. I remember quite well my doubts and lack of confidence to start a PhD on this topic at that time. However, it was easy for Víctor to convince me, as science is a truly passion for him and he transmits it to everyone in his sorroundings. I am really grateful to him for sharing this years working together and totally convinced that I made the right choice. I also appreciate my other PhD supervisor, Rubén Picó, for his outstanding contribution and attitude, always open to discussion and helpful.Fortunately, by the time I started my PhD studies, our research group experimented a quick growth and several researchers gradually started to work with us, enriching my work deeply. Vicent Romero worked in Gandía for two years, and still collaborate with us. He made a huge contribution to our research group and to this thesis. He helped me in many ways and situations, including numerical simulations, experimental techniques, and any doubt I might have. I also want to acknowledge Lluis García Raffi, who collaborated a lot with me too. He is always ready to share his knowledge in mathematics and physics with me and able to generate a huge amount of ideas and proposals. I also appreciate the contributions from other members of the group, such as Javier Redondo, and the people from ICREA in Terrasa. I appreciate the contributions from Kestutis Staliunas, whose astonishing knowledge of physics is always an inspiration to us, and Yu-Chieh Cheng, our collaborations working in periodic structures in optics and acoustics were of great interest for me and her extreme efficiency in every task she performs is amazing.Chapter 5 of this thesis, and other works that are not included here, were developed in the University of Colorado at Boulder, in the USA, were I spent almost one year. I would like to acknowledge Mahmoud Hussein, from Dpt. of Aerospace Engineering Sciences, for giving me the oportunity to integrate myself in his group to work in the development of numerical techniques for elastic band structure calculation, and also for pushing hard to start and mantain a collaboration with our group in Gandía. It was an amazing experience were all the members of the group made me feel at home. Osama R. Bilal, Michael Frazier, Romik Khajehtourian, Dimitri Krattiger, Clémence Basquet and Hossein Honarvar, thank you all.Además de las personas con las que he trabajado en tareas directamente relacionadas con mi tesis, mi...