PROPAGATION DYNAMICS OF SPATIO-TEMPORAL WAVE PACKETS Thesis Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree of Master of Science in Electro-Optics By Qian Cao UNIVERSITY OF DAYTON Dayton, Ohio August, 2014 PROPAGATION DYNAMICS OF SPATIO-TEMPORAL WAVE PACKETS Name: Cao, Qian APPROVED BY: Andy Chong, Ph.D. Joseph Haus, Ph.D. Advisor Committee Chairman Committee Member Assistant Professor, Department of Professor, Electro-Optics Graduate Physics Engineering Program Partha Banerjee, Ph.D. Committee Member Professor, Electro-Optics Graduate Engineering Program John G. Weber, Ph.D. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean Dean, School of Engineering School of Engineering ii c Copyright by Qian Cao All rights reserved 2014 ABSTRACT PROPAGATION DYNAMICS OF SPATIO-TEMPORAL WAVE PACKETS Name: Cao, Qian University of Dayton Advisor: Dr. Andy Chong We measured the three-dimensional (3D) propagation dynamics of the Airy-Bessel wave packet, inculding its intensity and phase evolution. Its non-diffraction and non-dispersive features were verified. Meanwhile, we built a spatial light modulator (SLM) based wave packet shaping system to generate other types of wave packets such as Airy-Airy-Airy and dual-Airy-Airy-rings. These wave packets were also measured in 3D. The abrupt 3D autofocusing effect was observed on dual-Airy- Airy-rings. iii To my family, my advisor and committee members and the time in University of Dayton. iv ACKNOWLEDGMENTS First of all, I want to express my thank to my advisor, Prof. Andy Chong. Although the time when I became his student it was the second year of his professor career, he taught and guided me in the world of science in such an experienced way. Without his guidance cannot I become so interested in physics. His enthusiasm in science, his broad knowledge and the encouragement is invaluable in my research. At the same time, I want to thank my committee members, Prof. Joseph Haus and Prof. Partha Banerjee for their guidance and patience. It was my fortune and pleasure to work in Dr. Chong’s ultrafast laser group. I sincerely thank Chenchen Wan, Xin Huang and Peiyun Li, the group members, who have contributed a lot in my research. Without their help and company, I will not have the courage to accomplish this work. Finally I sincerely thank my family. I am indebted forever for their priceless love and support. They have been asking about the progress of my thesis for long. I believe as I finish the thesis writing, the story will come to a happy ending. v TABLE OF CONTENTS ABSTRACT . iii DEDICATION . iv ACKNOWLEDGMENTS . v LIST OF FIGURES . vii 1. INTRODUCTION . 1 1.1 Organization of the thesis . 1 1.2 Introduction . 2 2. THEORETICAL BACKGROUND . 4 2.1 Optical Airy wave . 4 2.1.1 Airy pulse . 5 2.1.2 Airy beam and other types of Airy wave . 9 2.2 Bessel beam . 11 3. THREE-DIMENSIONAL MEASUREMENT SYSTEM . 14 3.1 Mechanism and mathematical background . 14 3.2 Experimental configuration . 17 3.3 Temporal phase retrieval . 20 4. MEASUREMENT RESULTS . 22 4.1 Propagation dynamics of Airy-Bessel wave packet . 22 4.1.1 Experiment parameters . 23 4.1.2 3D intensity before propagation . 24 4.1.3 3D intensity after propagation . 26 4.1.4 Temporal phase retrieval . 27 4.2 Measurement of Airy-Airy-Airy wave packet . 28 4.3 Measurement of dual-Airy-Airy-rings wave packet . 30 5. CONCLUSIONS . 34 BIBLIOGRAPHY . 35 vi LIST OF FIGURES 2.1 Airy pulse simulation . 7 2.2 Airy pulse propagation simulation under the influence of normal dispersion . 8 2.3 Airy beam simulation . 9 2.4 dual Airy pulse simulation . 10 2.5 Bessel beam simulation . 12 2.6 Axicon to generate Bessel beam . 13 3.1 Conceptual sketch of the measurement system . 15 3.2 Experimental setup for Airy-Bessel wave packet . 18 3.3 Experimental setup for general spatio-emporal wave packet . 19 3.4 Conceptual sketch of temporal phase retrieval . 21 4.1 Experiment parameters for Airy-Bessel measurements . 23 4.2 Results of the Airy-Bessel wave packet before propagation . 25 4.3 Results of the Airy-Bessel wave packet after propagation . 26 4.4 Temporal phase results for Airy-Bessel wave packet . 27 4.5 Experimental parameters for Airy-Airy-Airy measurements . 28 4.6 Results of the Airy-Airy-Airy wave packet . 29 vii 4.7 Temporal phase retrieval of Airy-Airy-Airy wave packet . 30 4.8 Experimental parameters for dual-Airy-Airy-rings measurements . 31 4.9 Results of the dual-Airy-Airy-rings wave packet at the Fourier plane . 32 4.10 Results of the dual-Airy-Airy-rings wave packet at the autofocus plane . 32 viii CHAPTER 1 INTRODUCTION The main theme of this thesis is the study of the propagation dynamics of spatio-temporal wave packets. The Airy-Bessel wave packet is the main wave packet to be studied in the thesis. Other wave packets such as Airy-Airy-Airy and dual-Airy-Airy-rings are also investigated. 1.1 Organization of the thesis There are be five chapters in this thesis. Chapter 1 is the introduction to the research on optical spatio-temporal wave packets. It ex- plains why they are an important research subject. This chapter gives an initial description of the measurement techniques used in this thesis and how they differ from conventional pulse measure- ment techniques. Finally, it ends with a brief description of wave packets specific to those studied in this thesis. Chapter 2 is the theoretical background for the spatio-temporal wave packets. Airy pulses, Bessel beams and other types of optical Airy waves are discussed in this chapter. For an Airy pulse, its mathematical form and unique properties such as self-healing and self-acceleration is explained. All the contents are in the words of optics to make it straightforward to understand how to realizes Airy pulses optically. For Bessel beams, the origin of the non-diffracting property is explained. Other optical realizations of Airy waves are introduced in the last section of this chapter. 1 Chapter 3 is the discussion around the three-dimensional (3D) measurement system. Firstly, the mathematics and the experimental configuration of this 3D measurement technique is briefly introduced. There are two different setups presented. One of them is used to generate the Airy- Bessel wave packet and measure its intensity profile in 3D. The other one is used to generate wave packets such as Airy-Airy-Airy and dual-Airy-Airy-rings. These two wave packets are measured in 3D and presented in the measurement results chapter. Finally the process of temporal phase retrieval is explained. This temporal phase retrieval technique is accurately a byproduct of the 3D measurement. Although some assumption must be made to access the temporal phase retrieval, this method can reveal the temporal phase signature with a good agreement with theoretical predictions. The temporal phase results are also presented in the measurement results chapter. Chapter 4 presents the 3D measurement results, as well as the temporal phase retrieval of the Airy-Bessel wave packet and the Airy-Airy-Airy wave packet. As the main theme of this thesis, the propagation dynamics of Airy-Bessel wave packet is studied in details covering from the experi- mental parameters to the 3D intensity profile and the temporal phase profile. For an Airy-Airy-Airy wave packet, its 3D intensity profile and its temporal phase is shown. For a dual-Airy-Airy-rings wave packet, to the best of our knowledge, it is the first time that such wave packet is experimentally generated. The 3D autofocusing effect is observed and measured in 3D. Chapter 5 states the conclusions, as the last chapter of this thesis. 1.2 Introduction Spatio-temporal wave packets have demonstrated their potential in the field of nonlinear sci- ence, plasma generation [1, 2], laser machining [3] and other scientific researches [4]. Combining some specific pulse shape and beam profile, these wave packets can have unique properties such as self-acceleration [5], self-healing [6], lateral acceleration [7], non-diffracting [8–10] and abrupt 2 autofocusing [11]. With these properties, spatio-temporal wave packets can serve as a powerful tool in various applications. Itself has also become an interesting research topic. To utilize and study those wave packets, it is necessary to learn how to measure them. Conven- tional measurement techniques include auto-correlation [12], cross-correlation and charge-coupled devices (CCD) camera. They are easy to implement. However, spatio-temporal coupled wave pack- ets cannot be resolved by these methods. To overcome this, methods based on frequency-resolved optical gating (FROG) [13] and some other techniques with nonlinear processes [14] are developed. But these methods have restrictions on the type of the wave packets, wave packets’ energy and their spectrum bandwidth. These restrictions make the measurement scenarios highly limited. Later on, an interferometric measurement system based on noncollinear first order cross corre- lation is suggested [15–17]. This system can measure 3D intensity profile of spatio-temporal wave packets at various wavelengths. Recently its capability to measure the temporal phase is demonstrat- ed [18]. The 3D measurements in this thesis are all achieved by using this measurement technique. Conventional methods will be used as a supplement and for comparison purpose. The wave packets to be studied in this thesis are Airy-Bessel, Airy-Airy-Airy and dual-Airy- Airy-rings. An Airy-Bessel wave packet has been studied as a “linear light bullet” since it can propagate without dispersion or diffraction in the linear regime [19].