Estabilidad e inestabilidad en la propagación no lineal de haces ópticos de Bessel con momento angular orbital

Abstract

Nevertheless, after an uncertain first year, nonlinear waves and their vortices finally caught me up. And also my doctoral advisor, Professor MiguelÁngel Porras. It's hard to express how thankful I am for his generosity in sharing with me both his time and his work the way he did. He didn't teach me all the Physics I know, but he definitely taught me how to persevere in discovering the Physics I don't know (which is a lot more!), and that's priceless. Thank you, MiguelÁngel. And as a bonus, I was also very lucky to have a senior Ph.D. candidate colleague that still to this day shows me the way to follow through when I don't know where the end of the tunnel is, Dr. Carlos Ruiz Jiménez. You helped me a lot more than you can imagine, believe me, both with our work and your words. During the last years I learned much from the two of you, and your patience and kindness were always there, during good and bad moments. I will never forget the endless rehearsal for my presentation at the XXXVI Bienal de Física in Santiago de Compostela in 2017, and the adrenaline rush when I finally got it right for the first time. And I truly have the feeling to have collaborated in bringing some new and useful knowledge around, which makes everything worthwhile.Also, I would like to thank the Grupo de Sistemas Complejos, in particular Professor Rosa María Benito, for kindly accepting me in the research group and offering me the opportunity to know first-hand what the world of scientific research is; and Professor Juan Carlos Losada, for always volunteering when help was needed, both for scientific and organizational matters. The research group is fairly large, and it would be out of place to name everybody here, but I'd like to say I'm grateful for the kindness I always received from all of you, and that I'm sorry for the CPU time Matlab R ruthlessly ate up at the servers with our endless numerical simulations. Some special words of gratitude must be dedicated to Marta Antón, who helped me a lot with the front cover during those idle moments at work. I guess my sense of aesthetics needed more inspiration than I expected in first place.And at last, but surely not least, I would like to thank my family for putting up with me during my long isolation periods necessary to do what I had to do these last years. In fact, I wanted to make a point with that by using quotations from people who are closest to me to introduce each chapter, instead of picking more glamorous ones from historically relevant characters. I would like this choice to be seen not as the result of indolence or arrogance, but as a way of thanking people that, although feeling distant from the "weird things" physicist are usually interested in, they should know that they are still part of it all, at least for me. I hope I will now have more spare time to make up for it correctly. Thank you Marisa, Xavier, Ana and Nico for your support. This particular acknowledgement may be short, but it is from the heart.