Pulse shaping and ultrashort laser pulse filamentation for applications in extreme nonlinear optics Antonio Lotti To cite this version: Antonio Lotti. Pulse shaping and ultrashort laser pulse filamentation for applications in extreme nonlinear optics. Optics [physics.optics]. Ecole Polytechnique X, 2012. English. pastel-00665670 HAL Id: pastel-00665670 https://pastel.archives-ouvertes.fr/pastel-00665670 Submitted on 2 Feb 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNIVERSITA` DEGLI STUDI DELL’INSUBRIA ECOLE´ POLYTECHNIQUE THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF PHILOSOPHIÆ DOCTOR IN PHYSICS Pulse shaping and ultrashort laser pulse filamentation for applications in extreme nonlinear optics. Antonio Lotti Date of defense: February 1, 2012 Examining committee: ∗ Advisor Daniele FACCIO Assistant Prof. at University of Insubria Advisor Arnaud COUAIRON Senior Researcher at CNRS Reviewer John DUDLEY Prof. at University of Franche-Comte´ Reviewer Danilo GIULIETTI Prof. at University of Pisa President Antonello DE MARTINO Senior Researcher at CNRS Paolo DI TRAPANI Associate Prof. at University of Insubria Alberto PAROLA Prof. at University of Insubria Luca TARTARA Assistant Prof. at University of Pavia ∗ current position: Reader in Physics at Heriot-Watt University, Edinburgh Abstract English abstract This thesis deals with numerical studies of the properties and applications of spatio-temporally coupled pulses, conical wavepackets and laser filaments, in strongly nonlinear processes, such as harmonic generation and pulse reshap- ing. We study the energy redistribution inside these wavepackets propagating in gases and condensed media, in the linear and nonlinear regime. The en- ergy flux constitutes a diagnostic for space-time couplings that we applied to actual experimental results. We analyze the spectral evolution of filaments in gases and derive the conditions for the generation of ultrashort pulses in the UV range. We study high harmonic generation in a gas from ultrashort conical wavepackets. In particular, we show how their propagation proper- ties influence the harmonic output. We also study the interference of different electron trajectories. Finally, we derive the shape of stationary Airy beams in the nonlinear regime. For each topic, we present experimental results that motivated our works or were motivated by our simulations. French abstract Cette these` traite de l’etude´ numerique´ des propriet´ es´ et des applications des impulsions spatio-temporellement couplees,´ paquets d’ondes coniques et fila- ments laser, dans les processus fortement non-lineaires,´ comme la gen´ eration´ d’harmoniques d’ordre elev´ e.´ Nous etudions´ la redistribution de l’energie´ au sein de ces paquets d’ondes en propagation lineaire´ et non-lineaire.´ Le flux d’energie´ constitue un diagnostic des couplages spatio-temporels que nous avons applique´ a` des resultats´ experimentaux´ reels.´ Nous analysons l’evolution´ spectrale des filaments dans un gaz et nous obtenons les condi- tions pour la gen´ eration´ d’impulsions de quelques cycles dans le spectre iv UV. Nous etudions´ la gen´ eration´ d’harmoniques d’ordre elev´ e´ par des ondes coniques ultra-courtes. En particulier, nous montrons comment leurs pro- priet´ es´ de propagation influencent le champ gen´ er´ e´ dans la region´ X-UV. Nous etudions´ aussi l’interference´ des differents´ chemins quantiques cor- respondant aux trajectoires electroniques.´ Enfin, nous obtenons la forme des faisceaux d’Airy stationnaires dans le regime´ non-lineaire.´ Pour chaque sujet, nous presentons´ des resultats´ experimentaux´ qui ont motive´ nos travaux ou ont et´ e´ motives´ par nos simulations. Italian abstract Questo lavoro di tesi tratta dello studio numerico delle proprieta` di impulsi con accoppiamento spazio-temporale, pacchetti d’onda conici e filamenti la- ser, e di loro applicazioni a processi fortemente non lineari, come generazio- ne di armoniche di ordine superiore o rimodulazione di impulsi. Studiamo la ridistribuzione dell’energia all’interno dei pacchetti d’onda in propagazione lineare e non lineare. Il flusso della densita` di energia costituisce una dia- gnostica per accoppiamenti spazio-temporali, che abbiamo applicato a reali risultati sperimentali. Analizziamo l’evoluzione spettrale di filamenti in gas e deriviamo le condizioni per la generazione di impulsi UV ultracorti. Studia- mo la generazione di armoniche di ordine superiore in gas da impulsi conici. In particolare, mostriamo come le loro proprieta` propagative influenzino il risultato. Studiamo inoltre l’interferenza tra diversi cammini elettronici. De- riviamo infine il profilo di fasci di Airy stazionari in regime non lineare. Per ogni argomento, presentiamo i risultati sperimentali che hanno motivato il nostro lavoro, o basati sulle nostre simulazioni. Acknowledgments In this dissertation I have reported most of the scientific results and work I dealt with during my Ph.D. studies. First of all, I want to thank my two co-tutors, Daniele Faccio from Univer- sity of Insubria and Arnaud Couairon from Ecole´ Polytechnique, who equally supported my work, suggested research lines, helped with the interpretation of the results and pushed towards the finalization of the works. From a per- sonal point of view, I want to thank them for their friendship and availability, and for all the good moments we spent together. In particular, I want to wish good luck to Daniele for his new position at Heriot-Watt University and to him and his family (Silvia and Cesare) for their new life in Scotland. I also want to thank the heads of the institutions and the leaders of the research groups in which I worked: at Ecole´ Polytechnique, Patrick Mora, head of the CPHT, and Stefan Huller,¨ head of the Laser Plasma Interaction group at CPHT. I wish to thank Prof. Paolo Di Trapani from University of Insubria for host- ing me in his group at the beginning of my Ph.D., and the group of general relativity, analogue gravity and theoretical physics of Dr. Sergio Cacciatori and Prof. Vittorio Gorini, with Prof. Ugo Moschella as group leader, for host- ing me in the last part of this thesis. In particular, I want to thank Prof. Di Trapani for his deep insights not only related to physics, but in general to the approach towards Science and Nature. The works presented in these pages was also performed thanks to a vari- ous network of collaborations. I want to thank, in no precise order: the UNIS group at the FORTH in Heraklion, Greece. In particular, • the group leader, Prof. Stelios Tzortzakis and his colleague Prof. Di- mitris Papazoglou; and the Ph.D. students Paris Panagiotopoulos and Daryoush Abdollahpour; vi the AUO group at the ICFO in Barcelona, Spain, in the persons of the • group leader, Prof. Dr. Jens Biegert, the Post-Doc Researchers Dane Austin, Philip Bates and the Ph.D. students Stephan Teichmann, Alexan- der Grun;¨ Prof. Mette B. Gaarde from Louisiana State University, Baton Rouge; • the Ultrafast Laser Optics group at Leibniz Universitat,¨ Hannover, Ger- • many. In particular, the group leaders, Prof. Dr. Milutin Kovacevˇ and Prof. Dr. Uwe Morgner, the Post-Doc Researcher Daniel Steingrube, the Ph.D. students Emilia Schulz and Tobias Vockerodt; Prof. Miroslav Kolesik and Prof. Jerome Moloney, from the College of • Optical Sciences at the University of Arizona, Tucson. I want to thank the two referees, Prof. Dudley and Prof. Giulietti, for having accepted to review my thesis work, and all the committee members, Prof. De Martino, Prof. Parola, Prof. Di Trapani, Dr. Tartara and the above mentioned referees, for having accepted to judge my work. I also want to thank the directors of the doctoral schools: Prof. Philip Ratcliffe at University of Insubria, Prof. Michel Rosso and Prof. Pierre Legrain at Ecole´ Polytech- nique, for giving me the opportunity to achieve this thesis in co-tutorship. I thank all the colleagues I worked with in Como, from a professional and more important, from a personal point of view for their friendship and support: Matteo Clerici and Lucia Caspani, to whom I wish good luck in Canada (hop- ing they will come back soon) and a happy married life. Eleonora Rubino and Fabio Bonaretti; in particular I must apologize to Eleo- nora, as the colleague sitting at the desk next to mine, for all the times I was quite maddening. Marta Pigazzini, wishing her good luck for her Ph.D. adventure. Francesco Dalla Piazza, as the host who accepted the friendly invasion of his office, and thus the second person who had to bear me. Ottavia Jedrkiewicz and Alessandro Averchi. All the other people meeting for lunch at the open-space on the 3rd floor of via Valleggio building: Chiara Cappellini, Fabio Risigo, Antonio Bulgheroni, Matteo Bina. Finally, my greatest thank goes to my parents and my family, for their support, love and encouragement. Contents List of Figures xi Introduction 1 1 Propagation equations and physical effects 5 1.1 Equation governing the nonlinear propagation of laser pulses 5 1.2 Unidirectional Propagation and Forward Maxwell Equation . 7 1.3 EnvelopeEquations...................... 9 1.4 Linearbehavior ........................ 11 1.5 Nonlinear terms . 12 1.5.1 Kerreffect ...................... 12 1.5.2 Nonlinear absorption . 15 1.5.3 Plasma effects . 16 1.5.4 Ramaneffect ..................... 17 1.5.5 Self-steepening . 18 1.5.6 Optical field ionization . 19 1.6 High harmonic generation . 22 1.6.1 The three-step model . 23 1.6.2 Quantum-mechanical model . 25 1.6.3 Phase matching . 30 1.6.4 Absorption . 33 2 Conical waves and filamentation regime 35 2.1 Propagation equation .