HYDRODYNAMIC and ELECTRODYNAMIC IMPLICATIONS of OPTICAL FEMTOSECOND FILAMENTATION Nihal Jhajj

ABSTRACT Title of Dissertation: HYDRODYNAMIC AND ELECTRODYNAMIC IMPLICATIONS OF OPTICAL FEMTOSECOND FILAMENTATION Nihal Jhajj, Doctor of Philosophy, 2017 Dissertation directed by: Professor Howard Milchberg Department of Physics The propagation of a high peak power femtosecond laser pulse through a dielectric medium results in filamentation, a strongly nonlinear regime characterized by a narrow, high intensity core surrounded by a lower intensity energy “reservoir” region. The structure can propagate over many core diameter-based Rayleigh ranges. When a pulse of sufficiently high power propagates through a medium, the medium response creates an intensity dependent lens, and the pulse begins to focus in a runaway process known as optical collapse. Collapse is invariably mitigated by an arrest mechanism, which becomes relevant as the pulse becomes increasingly intense. In air, collapse is arrested through plasma refraction when the pulse becomes intense enough to ionize the medium. Following arrest, the pulse begins to “filament” or self- guide. In gaseous media, energy deposited in the wake of filamentation eventually thermalizes prompting a neutral gas hydrodynamic response. The gas responds to a sudden localized pressure spike by launching a single cycle acoustic wave, leaving behind a heated, low density channel which gradually dissipates through thermal diffusion. This dissertation presents a fundamental advance in the theory of optical collapse arrest, which is how a pulse transitions from the optical collapse regime to the filamentation regime. We provide experimental evidence, supported by theory and numerical simulation that pulses undergoing collapse arrest in air generate spatiotemporal optical vortices (STOVs), a new and previously unobserved type of optical vortex with phase and energy circulation in a spatiotemporal plane. We argue that STOV generation is universal to filamentation, applicable to all collapsing beams, independent of the initial conditions of the pulse or the details of the collapse arrest mechanism. Once formed, STOVs are essential for mediating intrapulse energy flows. We also study the hydrodynamic response following filamentation, with the intent of engineering the response to construct a variety of neutral gas waveguides. In a proof-of-concept experiment, we demonstrate that a transverse array of filamenting pulses can be used to inscribe two distinct types of waveguides into the air: acoustic and thermal waveguides. These waveguides can be used to guide very high average power laser beams or as remote atmospheric collection lenses. HYDRODYNAMIC AND ELECTRODYNAMIC IMPLICATIONS OF OPTICAL FEMTOSECOND FILAMENTATION by Nihal Jhajj Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2017 Advisory Committee: Professor Howard Milchberg, Chair Professor James Drake Professor Ki-Yong Kim Professor Daniel Lathrop Professor Phillip Sprangle © Copyright by Nihal Jhajj 2017 Acknowledgements I am deeply grateful for the opportunity provided to me by my advisor, Prof. Howard Milchberg, to work and learn in his group. Howard leads by example with his passion for physics and indefatiguable work ethic. I owe much to his guidance, and the confidence he has placed in me as a scientist. My good friend and colleague, Eric Rosenthal, was there with me from the beginning. He was often the first person I turned to when I needed help, staying up with me for long nights of data taking, and sharing in the ups and downs of being a grad student - his companionship made the everyday reality of working in the lab worthwhile. I must also thank Jared Wahlstrand for being the senior guy in the lab who showed me the ropes. Jared was always generous with his time when I came to him with questions. More than a few ideas in this dissertation are the direct result of brainstorming sessions I had with the “small lab crew”, including Eric and Jared, but also Sina Zahedpour, Arman Fallahkair, and our newest addition, Ilia Larkin. I’ve had the pleasure of working with Ilia over the past few years, and I’m happy to know that the future of the experiment is in capable hands. I’d also like to thank my other colleagues: John Palastro, Yu-Hsin Chen, Brian Layer , Sung Yoon, Andrew Goers, Jennifer Elle, George Hine, Linus Feder, Bo Miao, Fatholah Salehi, Daniel Woodbury, and Robert Schwartz for all the assistance and useful discussion. I’m grateful to the IREAP administrative and facilities staff; in particular Nolan Ballew and Jay Pyle for helping me out with the occasional machining project, and to Bryan Quinn for all the assistance in maintaining and upgrading the facilities in the lab. ii Finally, I’m deeply indebted to my girlfriend, Dina Genkina, for keeping me sane over these years, and to my mother, Inga Jhajj, father, Inderjit Jhajj, and sisters Tess and Tara Jhajj, without your love and support I would not have been able to start this process, much less finish it. I dedicate my thesis to you. iii Table of contents Acknowledgements ....................................................................................................... ii Table of contents .......................................................................................................... iv List of figures ............................................................................................................... vi Chapter 1: Introduction ................................................................................................. 1 1.1 Dissertation outline ............................................................................................. 1 1.2 Linear optics........................................................................................................ 3 1.2.1 Maxwell’s equations .................................................................................... 3 1.2.2 Linear polarization response ........................................................................ 4 1.2.3 Wave propagation in linear media ............................................................... 6 1.3 Nonlinear optics ................................................................................................ 14 1.3.1 The anharmonic oscillator .......................................................................... 14 1.3.2 Formalism for nonlinear optics .................................................................. 16 1.3.3 Optical Kerr effect ..................................................................................... 18 1.3.4 Ionization ................................................................................................... 21 1.3.5 Nonlinear polarization ............................................................................... 25 1.4 Filamentation of high power optical pulses ...................................................... 27 1.4.1 Filamentation summary ............................................................................. 27 1.4.2 Optical collapse and collapse arrest ........................................................... 28 1.4.3 Core/reservoir model of filamentation ....................................................... 31 1.4.4 Spectral broadening and self-steepening ................................................... 33 1.4.5 Modulational instability and multiple filamentation.................................. 34 1.4.6 Long timescale gas response to filamentation ........................................... 35 Chapter 2: Optical beam dynamics in a gas repetitively heated by femtosecond filaments ...................................................................................................................... 38 2.1 Introduction ....................................................................................................... 38 2.2 Experimental setup............................................................................................ 39 2.3 Results and discussion ...................................................................................... 41 2.3.1 Beam deflection ......................................................................................... 41 2.3.2 Density hole evolution ............................................................................... 46 2.4 Conclusion ........................................................................................................ 49 Chapter 3: Demonstration and analysis of long-lived high power optical waveguiding in air ............................................................................................................................ 50 3.1 Overview ........................................................................................................... 50 3.2 Direct imaging of the acoustic waves generated by femtosecond filaments in air ................................................................................................................................. 51 3.2.1 Introduction ................................................................................................ 51 3.2.2 Single mode filament acoustic response .................................................... 51 3.2.3 Multi-mode filament acoustic response ..................................................... 54 3.2.4 Identifying the guiding mechanism behind the single filament acoustic guide ...................................................................................................................

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