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ABSTRACT

Multi-pulse Nonlinear Optical Spectroscopy and Light-matter Interactions in Layered Materials

Brian Alexander Ko, Ph.D.

Mentor: Marlan O. Scully, Ph.D.

The interaction between light and matter is one that underscores many applications from solar energy conversion to optical sensing of biological materials. The use of multiple pulses to study these interactions are especially useful in understanding the nonlinear optical properties of materials.

Transition metal dichalcogenides such as molybdenum disulfide (MoS2) are attractive materials due to the existence of a direct excitonic resonance that can be used to enhance nonlinear optical phenomena, such as Raman spectroscopy. Here, we have investigated four-wave mixing

(FWM) processes in bulk MoS2 using a multiplex coherent anti-Stokes Raman spectroscopy setup.

The observed FWM signal has a resonance at approximately 680 nm, corresponding to the energy of the A excitonic transition of MoS2. This resonance can be attributed to the increased third-order nonlinear susceptibility near the excitonic transition. This phenomenon shows the potential of

MoS2 as a substrate for enhancing FWM processes.

Understanding how particles and light interact in a liquid environment is vital for optical and biological applications. The interaction between two femtosecond pulses and MoS2 nanoparticles suspended in liquid is studied. The laser pulses induce bubble formation on the surface of a nanoparticle and a nanoparticle aggregate then forms on the surface of the trapped bubble.

Two-dimensional organometallic lead halide perovskites are generating great interest due to their optoelectronic characteristics, such as a direct band gap in the visible regime. However, the presence of defect states within the crystal structure can affect these properties, resulting in changes to their emission and the emergence of nonlinear optical phenomena. Here, we have investigated the effects of the presence of defect states on the nonlinear optical phenomena of the hybrid perovskite (BA)2(MA)2Pb3Br10. When two pulses are incident on a perovskite flake, FWM occurs, with peaks corresponding to the defect energy levels present within the crystal. The longer lifetime of the defect state, in comparison to that of virtual transitions, allows for a larger population of electrons to be excited by the second pump photon, resulting in increased FWM signal at the defect energies. This technique has the potential to detect defect energy levels in bulk crystals using FWM. Multi-pulse Nonlinear Optical Spectroscopy and Light-matter Interactions in Layered Materials

Brian Alexander Ko, B.S.

A Dissertation

Approved by the Department of Physics

Dwight P. Russell, Ph.D., Interim Chairperson

Submitted to the Graduate Faculty of Baylor University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

Approved by the Dissertation Committee

Marlan Scully, Ph.D., Chairperson

Ho Wai Howard Lee, Ph.D.

Zhenrong Zhang, Ph.D.

Truell Hyde, Ph.D.

Jonathan Hu, Ph.D.

Accepted by the Graduate School December 2020

J. Larry Lyon, Ph.D., Dean

Page bearing signatures is kept on file in the Graduate School.

TABLE OF CONTENTS

LIST OF FIGURES ...... vii

LIST OF TABLES ...... ix

ACKNOWLEDGMENTS ...... x

ATTRIBUTIONS ...... xii

CHAPTER ONE ...... 1 Introduction ...... 1 Enhanced Four-wave Mixing Process Near the Excitonic Resonances of Bulk MoS2 ...... 2 Multi-pulse Laser-Induced Bubble Formation and Nanoparticle Aggregation Using MoS2 Nanoparticles ...... 4 Resonant Degenerate Four-wave Mixing at the Defect Energy Levels of 2D Organic-inorganic Hybrid Perovskite Crystals ...... 9

CHAPTER TWO ...... 13 Degenerate Multiplex Coherent anti-Stokes Raman Spectroscopy Setup ...... 13 Derivation of Spontaneous Raman Cross-Section ...... 13 Selection Rules for Raman Transitions ...... 15 Degenerate Multiplex Coherent Anti-Stokes Raman Spectroscopy Setup ...... 17

CHAPTER THREE ...... 21 Enhanced Four-wave Mixing Process Near the Excitonic Resonances of Bulk MoS2 ...... 21 Abstract ...... 21 Introduction ...... 21 Methods...... 23 Results ...... 25 Degenerate Four-wave Mixing on Bulk MoS2 ...... 25 Discussion ...... 31 Degenerate Four-wave Mixing at the Excitonic Resonance ...... 31 Thickness Dependence of Four-wave Mixing ...... 32 Calculation of the Third-order Nonlinear Susceptibility ...... 33 Acknowledgments...... 35

CHAPTER FOUR ...... 36 Multi-pulse Laser-Induced Bubble Formation and Nanoparticle Aggregation Using MoS2 Nanoparticles ...... 36 Abstract ...... 36

Introduction ...... 36 Results ...... 39 Laser-Induced Cavitation and Nanoparticle Aggregation ...... 39 Laser-Induced Bubble Rotation and Convection ...... 42 Nanoparticle Aggregation ...... 44 Pulse Dependence ...... 45 Discussion ...... 49 Pulse Dependence of Bubble Formation...... 49 Bubble Heating ...... 50 Comparison with Other Nanoparticles ...... 52 Methods...... 55 Acknowledgments...... 57

CHAPTER FIVE ...... 58 Resonant Degenerate Four-wave Mixing at the Defect Energy Levels of 2D Organic-inorganic Hybrid Perovskite Crystals ...... 58 Abstract ...... 58 Introduction ...... 59 Methods...... 62 Results ...... 65 Discussion ...... 70 Acknowledgments...... 73

CHAPTER SIX ...... 74 Conclusion ...... 74 Enhanced Four-wave Mixing Process Near the Excitonic Resonances of Bulk MoS2 ...... 74 Multi-pulse Laser-Induced Bubble Formation and Nanoparticle Aggregation Using MoS2 Nanoparticles ...... 74 Resonant Degenerate Four-wave Mixing at the Defect Energy Levels of 2D Organic-inorganic Hybrid Perovskite Crystals ...... 75

APPENDIX ...... 77

BIBLIOGRAPHY ...... 85

LIST OF FIGURES

Figure 2.1. Energy Level Diagram for Raman Scattering, Coherent Anti-Stokes Raman Scattering (CARS), and Degenerate Multiplex CARS ...... 19

Figure 2.2. Degenerate Multiplex Coherent anti-Stokes Raman Spectroscopy Setup ...... 20

Figure 3.1. Four-wave Mixing on a MoS2 Flake ...... 23

Figure 3.2. Atomic Force Microscopy of MoS2 Flake ...... 24

Figure 3.3. Schematic of the Multiplex Femtosecond Coherent Anti-Stokes Raman Spectroscopy Setup ...... 25

Figure 3.4. Four-wave Mixing Spectra from a MoS2 Flake ...... 26

Figure 3.5. Spectrum Obtained from Individual Pulses from a MoS2 Flake ...... 27

Figure 3.6. Photoluminescence Intensity Dependence for Individual Pulses ...... 28

Figure 3.7. Four-wave mixing Spectra of the MoS2 Flake with different bandpass filters placed in the Supercontinuum Pulse Path ...... 30

Figure 4.1. Bubble Formation and Nanoparticle Agglomeration Timeline ...... 41

Figure 4.2. Frame-by-frame images of nanoparticle movement in the presence of a laser-induced cavitation bubble ...... 43

Figure 4.3. Frame-by-frame images of a MoS2 Nanoparticle Attaching onto the Surface of a Cavitation Bubble ...... 43

Figure 4.4. Selected frames of a MoS2 Nanoparticle Attaching to a Nanoparticle Aggregate ...... 45

Figure 4.5. Supercontinuum Transmission Intensity Measurement to Detect Bubble Formation ...... 47

Figure 4.6. Scatter Plot of Power Combinations to Determine Pulse Dependence of Bubble Formation ...... 48

Figure 4.7 Absorption Spectra of Nanoparticles Used in the Experiment ...... 54

Figure 4.8. Experimental Setup and Characterization of Homemade MoS2 and Al Nanoparticles ...... 57

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Figure 5.1. Degenerate Four-wave Mixing at the Defect Energy Levels of (MA)2(BA)2Pb3Br10...... 62

Figure 5.2. Scanning Electron Microscope and 3D Laser-scanning Microscope Image of (MA)2(BA)2Pb3Br10 flake ...... 63

Figure 5.3. Energy-dispersive Spectroscopy of (MA)2(BA)2Pb3Br10 flake ...... 64

Figure 5.4. Experimental setup for Degenerate Four-wave Mixing of (MA)2(BA)2Pb3Br10...... 65

Figure 5.5. Degenerate Four-wave Mixing and Confocal Laser-scanning Microscopy of (MA)2(BA)2Pb3Br10 Flake ...... 67

Figure 5.6. Dependence of Two-photon Absorption and Four-wave Mixing Emissions on Individual Pulses ...... 68

Figure 5.7. Four-wave Mixing Signal Intensity Dependence for Pump and Supercontinuum Pulses ...... 69

Figure A.1. Four-wave Mixing Spectra of MoS2 Obtained from Additional Flake Locations ...... 78

Figure A.2. Dependence of Four-wave Mixing Signal on Pulse Power ...... 79

Figure A.3. Supercontinuum Spectra at Different Locations ...... 79

Figure A.4. B Excitonic Resonance of MoS2 ...... 80

Figure A.5. Additional Bubble Formation Timeline ...... 81

Figure A.6. Additional Supercontinuum Transmission Intensity Measurement ...... 82

Figure A.7. Four-wave Mixing Spectra Obtained at Additional Locations of the (MA)2(BA)2Pb3Br10 Flake ...... 83

Figure A.8. Four-wave Mixing Spectra Obtained from Another (MA)2(BA)2Pb3Br10 Flake ...... 83

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LIST OF TABLES

Table 4.1. Nanoparticles Investigated for bubble Formation Events ...... 53

Table 5.1. EDS Elemental Composition of (MA)2(BA)2Pb3Br10 Flake ...... 64

Table 5.2. Measured Defect State Energies and Possible Defects in (MA)2(BA)2Pb3Br10 ...... 72

ACKNOWLEDGMENTS

I first would like to thank my mentor Dr. Marlan Scully. He has provided patient support throughout my time as a graduate student. Thank you for showing me the importance of discourse and multiple viewpoints in research.

Thank you to Drs. Zhenrong Zhang and Howard Lee for providing direction in my work as a graduate student.

Thank you to my dissertation committee and a special thanks to Dr. Truell Hyde and Dr. Jonathan Hu. You have provided some new discussion and potential applications for my work.

Thank you to the Baylor Physics Department, especially to Dr. Gerald Cleaver,

Marian Nunn-Graves, and Chava Baker for the logistical support that has been provided throughout my time here.

Finally, thank you to my parents, Alexander and Belen Ko, as well as my brothers, Michael, Mervin, Brandon, and Brad. Without your continued support throughout these years, I never would have finished this journey.

ATTRIBUTIONS

Chapter Three is published in Photonics Research as “Enhanced Four-wave Mixing

Process near the Excitonic Resonances of Bulk MoS2.” This publication has five contributing authors: myself (Brian Ko), Alexei Sokolov, Marlan Scully, Zhenrong Zhang, and Ho Wai Howard Lee. I performed sample fabrication, data collection, analysis, and wrote the manuscript. Drs. Zhang and Lee designed, conceived, and supervised the project.

Dr. Sokolov provided valuable suggestions and insights in analysis of the collected data, especially on determination of thin film interference effects in our sample. Dr. Scully provided oversight of the project as well as discussion on the results of the project.

Chapter Four will be published in Scientific Reports as “Multi-pulse Laser-Induced

Bubble Formation and Nanoparticle Aggregation Using MoS2 Nanoparticles.” This publication has six contributing authors: myself, Weigang Lu, Alexei Sokolov, Ho Wai

Howard Lee, Marlan Scully, and Zhenrong Zhang. I performed data collection and analysis. Dr. Lu synthesized the homemade MoS2 and Al solutions. Dr. Zhang and Dr. Lee designed and conceived the project. Dr. Zhang, Dr. Lee, and Dr. Scully supervised the project. Dr. Sokolov provided valuable insight on analysis of the collected data. All authors wrote the manuscript.

Chapter Five is in preparation to be published as a manuscript titled “Resonant

Degenerate Four-wave Mixing at the Defect Energy Levels of 2D Organic-inorganic

Hybrid Perovskite Crystals” This work has eight authors: myself, Keith Berry, Zhaojun

Qin, Alexei Sokolov, Jonathan Hu, Marlan Scully, Jiming Bao, and Zhenrong Zhang. I

xi prepared substrates for the perovskite flakes, performed data collection, and analyzed the data. The perovskite crystals were fabricated by Zhaojun Qin. Dr. Berry, Dr. Zhang, Dr.

Sokolov, and Dr. Hu provided valuable insight and support in analysis of the data. Dr.

Scully, Dr. Zhang, and Dr. Hu supervised the project. Dr. Bao provided guidance and discussion, especially on the properties of perovskite.

xii

CHAPTER ONE

Introduction

The interaction between light and matter is a field that underscores many applications. The study of how photons interact with matter is the basis of the energy conversion industry, where the properties of the material can affect the light-conversion efficiency[1]. In optical sensing applications, photons can interact with biological material to provide a host of data, from species identity[2, 3] and composition to the effects of the environment on the sample[4]. Light can also interact with matter in synthesis applications, such as the formation of nanoparticles[5] and nanostructures[6-10], usually through ablation and optical tweezing[11].

In this Chapter, I will address the background motivations of Chapters Three through Five. First, Chapter One will address previous experiments on light-matter interactions with molybdenum disulfide and its various applications. Then, I will discuss the various light-matter interactions that can take place in nanoparticle solutions, such as laser ablation in liquids and optical trapping. Finally, I will discuss the novel optical and electrical properties of organometallic perovskites and the effects of defects in the crystal structure on these properties. In each section, I will also discuss the previous applications of the method utilizing multiple photons, such as third-harmonic generation, two-photon absorption, and four-wave mixing.

In Chapter Two, the optical setup used in Chapters Three through Five will be discussed as a primer. In that Chapter, the coherent anti-Stokes Raman spectroscopy

(CARS) technique will be discussed and the advantages of the degenerate multiplex CARS scheme utilized throughout this work will be addressed.

Enhanced Four-wave Mixing Process near the Excitonic Resonances of Bulk MoS2

Molybdenum disulfide (MoS2) is a transition metal dichalcogenide consisting of S-

Mo-S sheets bonded through Van der Waals forces. As a substrate, MoS2 is generating interest due to its optical[12-15], electrical[16, 17], and catalytic[18, 19] properties. As a bulk crystal, MoS2 has an indirect bandgap of approximately 1.29 eV, but in the monolayer limit, MoS2 has a direct bandgap of 1.88 eV at the K point[20].

The presence of a direct excitonic resonance in MoS2 has led to its study in a variety of experiments as a tunable emitter. Liu, et al, were able to enhance the spontaneous excitonic emission from a MoS2 monolayer by coupling the monolayer to a one- dimensional silicon nitride photonic crystal[21], showing that these devices are a possible platform for solid-state cavity quantum electrodynamics. Similarly, Li et al. modulated the photoluminescence of MoS2 by coupling the exciton to the plasmonic resonance from graphene quantum dots, producing a red-shifted photoluminescence[22]. Li et al. were also able to perform hot electron injection from Au nanoparticles into the monolayer flake, inducing n-doping within the MoS2 flake[23]. The exciton binding energy increased, causing a redshift in the absorption. Yin et al., fabricated Ti/Au electrodes on a flake of monolayer MoS2, creating a phototransistor that exhibited greater photoresponsivity than that exhibited by 2D graphene-based devices[24]. Lee et al, fabricated a silver bowtie array on MoS2 monolayers to create a localized surface plasmon resonance to tune the emission of the MoS2 layer[25]. The bowtie structure produces a high electric field enhancement within the gap between the triangular sections, resulting in plasmon-exciton coupling,

2 increasing the MoS2 photoluminescence emission. Butun et al., used an Ag nanodisk array on MoS2 to enhance the photoluminescence emission of MoS2 by using the plasmonic resonance of the Ag nanodisk array to enhance the excitation field[26].

A variety of methods of coupling photonic structures to the exciton of MoS2 have been developed to modulate its nonlinear optical properties. Li et al. simulated different geometries for nano-groove arrays that can enhance the absorption of MoS2 monolayers, achieving up to 61.48% absorption in monolayer MoS2 with the ability to tune the peak wavelength by change groove height and spacing[27]. Janisch et al. used a nanocavity formed by a structure of MoS2-alumina-aluminum layers, leading to a 70% increase in absorption over bare MoS2 [28]. Similarly, the absorption of MoS2 can be enhanced by integrating MoS2 samples with resonant photonic structures in the form of GaN nanopillars, as was done by Huang et al [29]. The resulting film displayed a 70% broadband absorption due to leaky mode coupling.

The excitonic resonance of MoS2 has also led to its use as an enhancement platform for nonlinear optical phenomena. For example, Li et al., created core-shell nanoparticles consisting of a MoS2 shell around a gold nanosphere to observe the light-matter interactions between the curvature of the shell and the plasmonic effect of the Au core[30]. On the interface between the Au core and the MoS2 shell, the electric field strength is increased due to the plasmon-exciton coupling, which can be used to enhance the Raman scattering and photoluminescence emission on these nanoparticles. Zhou et al. examined the effects of van der Waals interactions between monolayer MoS2 and other two-dimensional crystals on the Raman modes of the monolayer[31]. They observed a 14 cm-1 shift in the 2D peak of graphene, highlighting the capability of MoS2 as a fingerprinting tool for van der Waals

3 heterostructures. Li et al., manipulated the spin-orbit coupling of light with metal- dielectric-metal plasmonic structures to investigate the MoS2 exciton-plasmon interaction[32]. They found the surface plasmon polaritons coupled to the MoS2 exciton enhanced the exciton photoluminescence by an order of magnitude.

Even with the great amount of interest in MoS2 for its optical properties, there are shortcomings in the application of MoS2 monolayers for nonlinear optical phenomena. The presence of a direct band gap can lead to radiative electron-hole recombination, resulting in a strong photoluminescence signal that can disturb other signals, such as Raman spectra[33]. Moving to a bulk sample of MoS2 quenches the excitonic photoluminescence emission while still maintaining the direct excitonic transition, which can enhance third- order nonlinear optical phenomena such as four-wave mixing[34].

In Chapter Three, the degenerate four-wave mixing signal from a bulk MoS2 flake was enhanced at wavelengths near its excitonic resonances. The enhancement occurs due to an increased third-order nonlinear susceptibility that occurs due to the large concentration of free carriers induced by transitions between the valence and conduction bands[34].

Multi-pulse Laser-Induced Bubble Formation and Nanoparticle Aggregation Using MoS2 Nanoparticles

Light-matter interactions in liquids are particularly interesting due to its potential in biological applications. Nanoparticles are especially useful as their geometry can lend them properties that are vastly different from their bulk form. Studies using nanoparticles in liquids have shown the potential to enhance nonlinear optical phenomena, such as

Raman spectroscopy[35], as well as agglomeration and manipulation of nanoparticles to form enhancing structures[6].

Laser ablation in liquids is a well-known nanoparticle fabrication method in which a high-energy pulsed or continuous wave laser is focused onto a metal or semiconductor target, forming a solution of nanoparticles. Depending on the parameters of the incident laser, such as pulse duration and wavelength, the characteristics of the created nanoparticles can be controlled. Mafuné et al. observed laser-assisted dissociation of gold nanoparticles by focusing a 532 nm pulsed laser on a gold target[8]. As the number of incident pulses increases, the size of the produced gold nanoparticles decreases due to rapid heating and fragmentation of the nanoparticles. Intartaglia et al. utilized laser ablation in liquids on a Si target in water to produce luminescent Si quantum dots that are suitable for biomedical applications. Lalayan was able to synthesize GaAs and CdS quantum dots using a pulsed 1064 nm laser[36]. Laser ablation in liquids has also been used to create alloyed nanoparticles by focusing a laser on a solution of two different particles. For example,

Hodak et al., focused a 532 nm nanosecond laser onto a solution of fabricated Au-Ag core- shell nanoparticles, melting the nanoparticles and forming alloyed nanoparticles.[37] The combination of core-shell and alloyed nanoparticles in solution can be used in all-optical data-storage devices due to the contrast in spectral features between the two types of particles.

During laser ablation in liquids, the rapid heating of the target results in the creation of a cavitation bubble, which also has been studied for its potential applications. Zharov, et al. used laser-induced microbubbles to selectively target cancer cells for nanophotothermolysis[38]. By selectively exciting Au nanoparticles in close proximity,

5 bubble formation phenomena can overlap on the surface of a breast cancer cell, resulting in lysing of the cell at laser intensities over two orders of magnitude lower than with isolated suspended nanoparticles. Yan et al, utilized an excimer laser on a Zn target in an ethanol-water solution to create a solution of dispersed nanoclusters with some assembled into hollow nanoparticles[39]. In a water-only solution, no hollow nanoparticles were created, due to the decreased lifespan of cavitation bubbles produced in the water-only solution. The laser-induced cavitation bubble can also be optically trapped and heated to produce convection currents within the solution, as shown in the work by Namura et al[40].

The heating of the bubble creates a surface tension gradient on the surface of a bubble, resulting in convection currents around the bubble that can be used to sort nanoparticles based on their size. Setoura et al. observed a similar convection flow by focusing a CW laser on a single Au nanoparticle[41].

Laser ablation in liquids is also accompanied with laser-induced aggregation or agglomeration of the created nanoparticles, forming nanostructures in the liquid. These nanostructures can be used to increase the surface-to-analyte contact within the sample, enhancing nonlinear optical phenomena such as surface-enhanced Raman scattering.

Zhang et al. observed nanoparticle agglomeration in a solution of gold nanoparticles using a 532 nm continuous wave laser[10]. Modulation of beam shape and beam power showed that the agglomeration matches the beam shape and that the size of the agglomerate increases with the incident power. Harris et al. fabricated colloidal crystals made of gold nanospheres using a 514 nm laser that were then formed into an array by moving the laser focus across a glass slide[42]. The assembly was facilitated by localized heating of the nanoparticles as no particles were observed in areas without laser irradiation. Au-Ag

6 nanoparticle colloids were formed under exposure to a picosecond laser by Serkov et al[43]. The formation of aggregates consisting of both Au and Ag nanoparticles was attributed to an induced charge distribution from laser-induced thermionic emission from the nanoparticles.

The focusing of a laser pulse in a liquid also produces a force gradient that can be used to trap particles within the focal point of the laser[11]. The optical trapping effect can be used to fabricate nanostructures in liquids, as seen in the work by Pauzauskie et al. on

GaN and SnO2 nanowires[44]. By using the laser to fuse wires together and manipulate their free ends, complex structures can be formed. Characterization of nanowires and other nanoparticles can be done using optical trapping by studying their motion within the trap, as performed by Reece et al[45]. By observing their position relative to the trapping center, they were able to establish nanowire length ranges in which trapping efficiency was constant. Naumenko et al, created gold nanoparticle micropatterns on a glass slide by direct laser writing[6], in which a fs laser is focused onto a droplet of a solution of gold nanoparticles and raster-scanned, creating a line pattern. The line pattern was then used as a surface-enhanced Raman spectroscopy substrate and an enhancement of one order of magnitude over bare glass was observed. The optical trapping force produced by a laser can be enhanced by using polarized light and nanostructures. Wilson et al. observed a trapping force four orders of magnitude greater than previously reported by using linearly polarized light and a one-dimensional periodic grating with grooves running perpendicular to the incident polarization[46].

Multi-pulse light-matter interactions in liquids are especially important as the utilization of multiple pulses can make certain experiments easier or reduce potential

7 thermal damage of the sample. Multi-pulse schemes are especially useful in biological applications, as avoiding thermal damage is paramount to in vivo studies. McDougall et al. achieved optical injection of a gold nanoparticle into a hamster ovary cell by first positioning the particle on top of the cell using a 1064 laser then using a 780 nm fs pulsed laser to optically inject the particle into the cell for surface-enhanced optical processes[47].

Even after optical injection, the ovarian cell continued to function as normal. Similarly,

Farias used multi-laser optical tweezers to allow macrophages to engulf quantum dots as fluorescent markers[48]. Using two lasers allowed them to control the optical trapping gradient more accurately. Simultaneously with the trapping field, a third laser was utilized as an excitation source for two-photon absorption studies. The macrophages survived quantum dot injection and optical trapping.

In Chapter Four, the complex dynamic processes of dual laser-induced agglomeration of suspended nanoparticles are investigated. When two femtosecond pulses are incident on a solution of MoS2 nanoparticles, laser-induced cavitation occurs when a nanoparticle passes through the focal point, forming a cavitation bubble. The incident lasers then induce heating on the bubble, creating convection currents that guide the nanoparticles in solution towards the bubble, attaching onto the surface. Using suspended nanoparticles instead of a metal or semiconductor target reduces the required energy for bubble formation and subsequent aggregation. Other nanoparticles such as Al nanosheets and polystyrene beads are also studied using this scheme.

Resonant Degenerate Four-wave Mixing at the Defect Energy Levels of 2D Organic-Inorganic Perovskite Crystals

Organometallic lead halides perovskites, such as MAPbBr3 and MAPbI3, are semiconductors that are receiving great interest due to their high reported energy conversion efficiency[1] and ease of fabrication that make them attractive materials in the photovoltaic industry[49, 50]. Their tunable bandgaps in the visible regime demonstrate their promise as emitters and detectors. Park et al. investigated the optoelectronic properties of cesium lead halide perovskite nanowires, reporting low-threshold microlasing within the wires[51]. Past threshold, the nanowires emit at 530 nm and behave as a Fabry-Perot resonator. Guo et al. studied the photoluminescence emission produced by MAPbBr3, observing two photoluminescence peaks – a narrow emission at 580 nm and a broad emission at 620 nm[52]. The broad 620 nm peak is only observed in the orthorhombic phase due to the presence of manifolds of energy levels near the band gap, showing that charges decay via defect sites at the surface of the perovskite. Fluorescence intermittency between neighboring perovskite nanoparticles was observed by Wen et al[53]. The intermittency occurs due to photoexcited charge migration and accumulation that results in

Auger nonradiative recombination, in which the energy dissipates as a phonon to neighboring particles. Wei et al. produced an x-ray detector using MAPbBr3 perovskite crystals[54]. By increasing the charge extraction efficiency of the single perovskite crystals by oxidizing the surface for passivation of surface defects, a twelve-fold increase in photoluminescence intensity and a larger radiative recombination lifetime was observed.

This work showed the potential of perovskites as a low-cost alternative x-ray detector with a higher sensitivity than that of silicon.

The presence of a tunable band gap in perovskite crystals has also made it an attractive platform for higher order optical studies, such as two-photon absorption and four- wave mixing. Walters et al. also studied the two-photon absorption mechanism in perovskite crystals[55]. When pumping a MAPbBr3 crystal with an 800 nm laser, a strong emission at 2.21 eV was observed, showing that the perovskite crystal can be used a photodetector by applying a voltage across the crystal. Zhang et al. attempted to control the cavity structure of perovskite microlasers by fabricating different structures such as nanorods and two-dimensional microplates[56]. One-dimensional nanorods behaved as

Fabry-Perot resonators, while the 2D microplates exhibited whispering gallery mode resonances when pumped with a near-infrared pulsed laser beam. The third-order nonlinear optical properties of organometallic perovskites were investigated by Kalanoor et al. using the z-scan technique[57]. They observed a similar nonlinear refractive index as those observed for ferroelectrics and other semiconductors commonly used for optical switches.

Li et al. observed temperature dependence within the two-photon second harmonic generation signal produced in a hybrid perovskite consisting of butylammonium (BA) and formamidinium (FA) lead bromide[58]. As the temperature increases, the hybrid perovskite transitions into a ferroelectric phase, resulting in symmetry breaking and quenching of the SHG signal.

However, perovskites are prone to defects in their crystal structure, which affects their energy conversion efficiency by introducing nonradiative recombination pathways[49]. Crystal structure defects can take on the form of vacancies, interstitials, or antisites. Interstitials occur when multiple atoms occupy the same lattice point, while antisites occur when atoms or ions swap places on the lattice. The presence of these defect

10 states can affect the emission properties of the perovskite. Musiienko et al. studied the defect level activation energy and capture cross section using photo-Hall effect spectroscopy[59]. Similarly, Cui et al. observed a quenching of a trap-induced photoluminescence when annealing a MAPbI3 film, resulting in a high conversion efficiency and subdued photocurrent hysteresis of perovskite solar cells[50]. In their measurements, they found that the presence of defects can enhance the electron recombination if the defect levels are sufficiently empty, but once defect levels are filled, nonradiative recombination occurs. In some cases, the presence of defects can also introduce new emission pathways, leading to its use as an emitter. Haris et al. created hybrid perovskites by synthetically controlling the structure and dimensionality of ethylenediammonium lead bromide perovskites[60]. The 1D chain structure exhibited a white light continuum emission, while the 2D sheet emitted its characteristic 410 nm band gap photoluminescence. The white light continuum of the 1D chain structure arises due to the formation of self-trapped excitons, in which excitons couple to lattice distortions.

Extrinsic defects, such as doping, can also be performed to tune the emission of a perovskite. For example, Nazim et al. observed a shift in the photoluminescence emission wavelength when a perovskite was doped with KMnO4[61].

In Chapter Five, the nonlinear optical properties of a 2D hybrid organic-inorganic perovskite crystal, (MA)2(BA)2Pb3Br10, is examined using two femtosecond pulses – one narrowband pump pulse and a broadband supercontinuum pulse. When the two pulses are incident on the crystal, four-wave mixing occurs, with noticeable peaks in the signal at wavelengths corresponding to the defect energy levels. The enhancement occurs by coherently exciting charge carriers into defect states, which have longer recombination

11 lifetimes than that of virtual states[62-64]. As a result, the population of carriers are much higher than that in the virtual state, leading to enhancement. The FWM signal intensity is also observed to increase with the thickness of the perovskite crystal due to the increased presence of defects in the optical path. The increased presence of defects also leads to more instances of nonradiative recombination, which quenches the two-photon photoluminescence signal. This multi-pulse FWM scheme has the potential to detect the defect binding energies of a semiconductor crystal under ambient conditions.

CHAPTER TWO

Degenerate Multiplex Coherent Anti-Stokes Raman Spectroscopy Setup

Derivation of the Spontaneous Raman Cross-section

In the interaction picture, the Hamiltonian for a molecule-field interaction is defined as

† † 퐻 = ħ휈|휈⟩⟨휈| + ħ휔0|0⟩⟨0| + ∑푖 ħ휔푖|푖⟩⟨푖| + ħ휈푝푎푝푎푝 + ħ휈푠푎푠 푎푠 (2.1) where |휈⟩ denotes vibrational wavefunctions of the molecule, |0⟩ is the ground state wavefunction, |푖⟩ denotes virtual transitions at energy ħ휔푖, and the last two terms are the interaction terms between the field and molecule. The potential in the interaction picture is defined as[65]

′ 푖(휔푗− 휔푗′)푡 † 푖휈푝푡 −푖휈푝푡 † 푖휈푠푡 −푖휈푠푡 푉(푡) = ħ ∑푗 ≠ 푗′ 푔푗,푗′|푗⟩⟨푗 |푒 [푎푝푒 + 푎푝푒 + 푎푠 푒 + 푎푠푒 ] (2.2) where gj,j’ is the coupling coefficient between states j and j’ and defined as

ħ휈푘 푑푗푗′∙ 푒̂푘 푔푗,푗′ = − (2.3) √2휋휖0 ħ where djj’ is the electric-dipole transition matrix. In the Raman scattering scheme, a pump photon with energy ħ휈푝 is absorbed by the molecule and a Stokes photon with energy ħ휈푠 is emitted, or

|0, 푛푝, 푛푠⟩ → |휈, 푛푝 − 1, 푛푠 + 1⟩ = |휈⟩ (2.4)

The probability of this transition is defined as

2 푃0→휈 = |⟨휈|푈(푡)|0⟩| (2.5)

Using time-dependent perturbation theory

1 푡 1 푡 푡′ 푈(푡) = 1 + ∫ 푉(푡′)푑푡′ + ∫ 푑푡′ ∫ 푑푡′′ 푉(푡′)푉(푡′′) + ⋯ (2.6) 푖ħ 0 (푖ħ)2 0 0

The transition shown in equation 2.4 can occur in two ways: (1) The pump photon absorbed before the Stokes photon is emitted or (2) the Stokes photon is emitted before the pump photon is absorbed. Both pathways are possible, so the transition probability can be written as

2 ⟨휈|푑휈푖 ∙ 푒̂푠|푖⟩⟨푖|푑푖0 ∙ 푒̂푝|0⟩ ⟨휈|푑휈푖 ∙ 푒̂푝|푖⟩⟨푖|푑푖0 ∙ 푒̂푠|0⟩ 휈 휈 ( + ) 1 푝 푠 | ∆휔푖−휈푝 ∆휔푖+휈푠 | 푃0→휈 = 2 2 2 |∑푖,푠 | (2.7) ħ 4휖0푉 푒푖(Δω− Δν)푡−1 × 푛 (푛 + 1) Δω− Δν √ 푝 푠 where Δωi = ωi – ω0, Δω = ν - ω0, and Δν = 휈푝 − 휈푠. Because the sum over all Stokes photon emissions can be expressed as

푉 ∑ = 2 ∫ 푘2푑푘 푑훺 (2.8) 푠 (2휋)3 푠 푠

Equation 2.7 can be rewritten as

2 ⟨휈|푑휈푖 ∙ 푒̂푠|푖⟩⟨푖|푑푖0 ∙ 푒̂푝|0⟩ ⟨휈|푑휈푖 ∙ 푒̂푝|푖⟩⟨푖|푑푖0 ∙ 푒̂푠|0⟩ ( + ) 1 휈 휈 푑훺 ∆휔 −휈 ∆휔 +휈 푑푃 = 푝 푠 ∫ 푘2푑푘 |∑ 푖 푝 푖 푠 | (2.9) 0→휈 ħ2 2휖2푉 (2휋)3 푠 푠 | 푖 | 0 2sin2((Δω− Δν)푡/2) × 푛 (푛 + 1) (Δω− Δν) √ 푝 푠

The spontaneous Raman cross-section can be related to the transition probability by

푑휎 lim 푑푃0→휈 = 푡→∞ 푉 (2.10) 푑훺 푑훺푛푝푐

At large time t, the transition probability (2.9) becomes

2 2휋 휈 휈3 푑훺√푛 (푛 +1) ⟨휈|푑 ∙ 푒̂ |푖⟩⟨푖|푑 ∙ 푒̂ |0⟩ ⟨휈|푑휈푖 ∙ 푒̂푝|푖⟩⟨푖|푑푖0 ∙ 푒̂푠|0⟩ 푑푃 = 푝 푠 푝 푠 ∫ 푘2푑푘 |∑ ( 휈푖 푠 푖0 푝 + )| (2.11) 0→휈 ħ2 휖2푉 (2휋)3 푠 푠 푖 ∆휔 +휈 0 ∆휔푖−휈푝 푖 푠

And substituting 2.11 into 2.10 leads to the spontaneous Raman cross-section

2 푑휎 푘 푘3 ⟨휈|푑 ∙ 푒̂ |푖⟩⟨푖|푑 ∙ 푒̂ |0⟩ ⟨휈|푑휈푖 ∙ 푒̂푝|푖⟩⟨푖|푑푖0 ∙ 푒̂푠|0⟩ = 푝 푠 |∑ ( 휈푖 푠 푖0 푝 + )| (2.12) 푑훺 8휖2휋2ħ2 푖 ∆휔 +휈 0 ∆휔푖−휈푝 푖 푠

The 푑푗푗′ ∙ 푒̂푙 terms indicate that the Raman cross-section depends on the angle between the dipole moment of the atom or molecule and either the polarization of the absorbed pump photon or the polarization of the emitted photon.

Selection Rules for Raman Transitions

Vibrational modes in a molecule can be approximated using a simple harmonic oscillator potential.

푉(푟) = 1/2 휇휔2푅2 (2.13) where µ is the reduced mass of the dipole, ω is the frequency of the vibrational mode, and

R is the displacement from equilibrium (R = r-re). This leads to the Schrodinger equation for a simple harmonic oscillator:

−ħ2 푑2 1 ( + 휇휔2푅2) 휓 = 퐸휓 (2.14) 2µ 푑푅2 2

Working in the Born-Oppenheimer approximation, which assumes that the vibrational, rotational, and spin wavefunctions are independent components[66], the Schrodinger equation yields vibrational wavefunctions of the form

푅2 0 − |휓푣 ⟩ = 푁푣퐻푣(푅)푒 2 (2.15) where Hv are the Hermite polynomials of order v (the vibrational quantum number) and

Nv is an orthogonality constant. The induced dipole moment by an electric field is:

휇 = 훼 ∙ 푬 (2.16) where α is the polarizability.

The probability of a transition from vibrational state vi to vf is given by

0 0 ⟨휓푣푓 |µ|휓푣푖⟩ (2.17)

Expanding µ about equilibrium (R = 0),

2 푑훼 푑훼 2 휇(푅) = 훼0퐸 + 퐸 | 푅 + 퐸 2 | 푅 … (2.18) 푑푅 푅=0 푑 푅 푅=0

Inserting 2.18 into equation 2.17 yields:

2 0 0 0 0 푑훼 0 0 푑 훼 0 2 0 ⟨휓푣 |µ|휓푣 ⟩ = 훼0퐸 ⟨휓푣 |휓푣 ⟩ + 퐸 | ⟨휓푣 |푅|휓푣 ⟩ + 퐸 2| ⟨휓푣 |푅 |휓푣 ⟩ … (2.19) 푓 푖 푓 푖 푑푅 푅=0 푓 푖 푑푅 푅=0 푓 푖

Using the orthogonality relation for Hermite polynomials

∞ −푅2 푛 ∫−∞ 퐻푛(푅)퐻푚(푅)푒 푑푅 = √휋2 푛! 훿푚푛 (2.20)

The first term in the right side of equation 2.19 is nonzero only if 푣푓 = 푣푖, corresponding to Rayleigh scattering. Converting the second term to integral form yields:

∞ 2 ⟨휓0 |푅|휓0 ⟩ = 푁 퐻 (푅)푟푁 퐻 (푅)푒−푅 푑푟 (2.21) 푣푓 푣푖 ∫−∞ 푣푓 푣푓 푣푖 푣푖

Using the recurrence relation for Hermite polynomials

1 푅퐻 (푅) = 푛퐻 (푅) − 퐻 (푅) (2.22) 푛 푛−1 2 푛+1 the integral can be rewritten as:

∞ 1 2 ⟨휓0 |푅|휓0 ⟩ = ∫ 푁 푁 퐻 (푅) [푣 퐻 (푅) − 퐻 (푅)] 푒−푅 푑푅 (2.23) 푣푓 푣푖 −∞ 푣푖 푣푓 푣푓 푖 푣푖−1 2 푣푖+1

Using the orthogonality rule of equation 2.20, equation 2.23 is non-zero only if

푣푓 = 푣푖 ± 1 표푟 ∆푣 = ±1 (2.24)

This is the traditional selection rule for a simple harmonic oscillator and indicates that, under this approximation, only the fundamental modes of vibration are Raman active[67]. However, moving to a second-order approximation of the transition dipole

16 moment (the quadratic term of equation 2.18), and using the recurrence relation for

Hermite polynomials (equation 2.22) results in:

∞ 3푛+1 1 2 ⟨휓0 |푅2|휓0 ⟩ = ∫ 푁 푁 퐻 (푅) [푣 (푣 )퐻 (푅) − 퐻 (푅) + 퐻 (푅)] 푒−푅 푑푅 (2.25) 푣푓 푣푖 −∞ 푣푖 푣푓 푣푓 푖 푖−1 푣푖−2 2 푣푖 4 푣푖+2

Using the orthogonality condition, equation 2.25 is non-zero only if

푣푓 = 푣푖, 푣푖 ± 2 표푟 ∆푣 = 0, ±2 (2.26)

This shows that, due to the second-order d2α/dR2 terms in equation 2.18, the previously forbidden overtone modes (Δv = ±2) are no longer forbidden.

Multiplex Degenerate Coherent Anti-Stokes Raman Spectroscopy Setup

Four-wave mixing (FWM) is a third-order nonlinear optical process in which three photons (pump, Stokes, and probe) interact in a medium to produce a fourth (FWM). One common form of FWM is difference frequency generation, in which the output photon has energy equal to the sum of two photon minus the third. Coherent anti-Stokes Raman scattering is a difference frequency generation process in which the frequency difference between the pump and Stokes photons corresponds to the vibrational mode of the target molecule[68]. As a result, the sample is coherently excited into the vibrational mode by the laser pulses. The probe photon then interacts with this coherently excited population, resulting in signal intensities much greater than in the normal Raman scheme.

Compared to spontaneous Raman spectroscopy, CARS offers a number of advantages. Because of the ability to coherently excite electrons into a vibrational mode,

CARS can measure much smaller concentrations of samples, giving it potential application in toxicology measurements[69, 70]. The enhanced signal intensity also allows CARS measurements to obtain measurements with lower acquisition times, facilitating en vivo microscopy of biological samples. In fact, live mice tissue was imaged using CARS

-1 microscopy by Evans et al by setting the Raman shift to 2845 cm for the lipid CH2 symmetric stretch[71]. CARS also produces anti-Stokes spectra, allowing for lower wavelength excitation that avoids fluorescence from the substrate or the sample that can overpower the Raman signal [35].

However, CARS does come with distinct disadvantages. The requirement of three photons with different wavelengths necessitates three lasers, resulting in a much higher cost of implementation. The requirement of temporal and spatial overlap of all three photons as well as phase matching also makes CARS more difficult to implement. To circumvent these issues, degenerate CARS, in which the pump and probe photons are supplied by the same pulse, has been developed, reducing the required number of lasers to two[72], lowering the cost of implementation and the difficulty of establishing temporal and spatial overlap.

One other disadvantage of conventional CARS is its inability to measure multiple vibrational modes without modulating the Stokes wavelength. To overcome this difficulty, a supercontinuum (SC) Stokes pulse can be implemented to simultaneously create multiple populations of excited electrons in different vibrational modes at the cost of signal intensity

– a method known as multiplex or broadband CARS[73-75]. The SC Stokes pulse can be supplied by using a separate laser[73] or by pumping a photonic crystal fiber (PCF)[74,

75]. By combining the degenerate CARS technique with a photonic crystal fiber to produce a supercontinuum Stokes pulse, it is possible to perform CARS using only a single laser while simultaneously have the ability to capture the entire anti-Stokes spectrum up to the limit of the supercontinuum pulse (Figure 2.1).

Figure 2.1. Energy diagram for Raman scattering, coherent anti-Stokes Raman scattering (CARS), and degenerate multiplex CARS.

In our CARS setup (Figure 2.2), a continuous wave Nd:YAG laser (Spectra Physics

Millenia EV15, 532 nm) pumps a Ti:Sapphire oscillator (Spectra Physics Tsunami) to create femtosecond pulses centered at 800 nm (~30 nm full width at half maximum, 100 fs duration, 80 MHz repetition rate). The pulse train from the Tsunami is split into two pulse trains by a 3 nm band pass filter centered at 800 nm. One pulse train is centered at 800 nm with a FWHM of 3 nm; the reflected pulse is manipulated to pump a photonic crystal fiber

(PCF) producing a SC with bandwidth starting from approximately 500 nm to 1100 nm.

The narrowband pulse continues on to become the pump/probe pulse, while the SC passes through an 800 nm long pass filter to ensure a Stokes excitation between the pump/probe and SC. The two pulses are recombined at the razor-edge long pass filter (RELP) so that they travel collinearly for ease of spatial overlap. Prior to the RELP, a linear polarizer is placed in each pulse train to optimize their polarization for maximum CARS intensity.

Temporal overlap is achieved by using the two translation stages prior to recombination to adjust their path lengths. A beta barium borate (BBO) crystal is placed to further optimize the temporal and spatial overlap. When the two pulses pass through the BBO crystal, second harmonic generation (SHG) occurs for both pulses, producing two spatially- resolved signals. Spatial and temporal overlap is achieved when a third, sum-frequency generation (SFG) signal appears between the two SHG signals, as SFG is only possible when the two pulses are overlapped. After spatial and temporal overlap are achieved, the pulses are directed into the focusing objective to the sample. The excitation laser pulses are then filtered out using two short pass filters and the resultant spectra is collected with a spectrometer (Horiba iHR 550).

Figure 2.2 Schematic of degenerate multiplex coherent anti-Stokes Raman spectroscopy setup. PCF, photonic crystal fiber; RELP, razor-edge long pass.

CHAPTER THREE

Enhanced Four-wave Mixing Process near the Excitonic Resonances of Bulk MoS2

This chapter is published as: Ko, B. A., et al., Enhanced Four-wave Mixing Process near the Excitonic Resonances of MoS2. Photonics Research, 2019. 7(3): p.251-259.

Abstract

Two-dimensional materials are generating great interest due to their unique electrical and optical properties. In particular, transition metal dichalcogenides such as molybdenum disulfide (MoS2) are attractive materials due to the existence of a direct band gap in the monolayer limit that can be used to enhance nonlinear optical phenomena, such as Raman spectroscopy. Here, we have investigated four-wave mixing processes in bulk

MoS2 using a multiplex coherent anti-Stokes Raman spectroscopy setup. The observed four-wave mixing signal has a resonance at approximately 680 nm, corresponding to the energy of the A excitonic transition of MoS2. This resonance can be attributed to the increased third-order nonlinear susceptibility at wavelengths near the excitonic transition.

This phenomenon could open the path to using MoS2 as a substrate for enhancing four- wave mixing process such as coherent anti-Stokes Raman Spectroscopy.

Introduction

Molybdenum disulfide (MoS2) is a transition metal dichalcogenide that is generating great interest due to its optical[12-15], electrical[16, 17], and catalytic[18, 19] properties. Bulk MoS2 consists of layers of S-Mo-S sheets bonded through van der Waals forces. In bulk form, MoS2 is a semiconductor with an indirect bandgap of approximately

1.29 eV in the Γ valley. However, in the monolayer limit, the indirect bandgap energy

21 increases and MoS2 becomes a direct bandgap semiconductor with a bandgap of 1.88 eV at the Κ point[20]. This indirect-to-direct bandgap transition has been studied for its optical effects such as photoluminescence in the monolayer limit[76] and Raman enhancement[77,

78].

The advance of MoS2 monolayer production methods such as micromechanical exfoliation and chemical vapor deposition has led to an increase in the use of MoS2 thin films to explore various nonlinear optical phenomena[79-81], such as Raman spectroscopy, where charge transfer interactions have been observed to enhance the Raman signal[78].

However, while monolayer MoS2 has been studied intensively for its ability to enhance nonlinear optical processes, it does have shortcomings. In the Raman enhancement case, the photoluminescence signal of MoS2 disturbs the Raman signal, resulting in low enhancement of Raman shifts at or near the direct bandgap energy (659 nm)[78].

Monolayer MoS2 fabrication methods also suffer from low yield, making it difficult to implement commercially. By increasing the layer count and turning MoS2 into an indirect bandgap semiconductor, the photoluminescence signal becomes quenched while still maintaining the A and B excitonic resonances[76]. Raman spectroscopy measurements capitalizing on the electronic or excitonic resonances of various substrates and samples have been extensively performed, from gases[82] to nanoparticles[83]. In this paper, we present our findings on the observation of the excitonic photoluminescence in bulk MoS2 via four-wave mixing (FWM). We observe an enhancement of degenerate four-wave mixing near the direct excitonic resonances of MoS2 using a broadband supercontinuum

(SC) coherent anti-Stokes Raman spectroscopy setup (Figure 3.1). Previous studies on

MoS2, especially that of Li et al., have demonstrated nonlinear optical phenomena such as

22 sum frequency generation (SFG) and four-wave mixing[84]. However, our results are performed on bulk MoS2 substrates, much thicker than the few-layer substrates typically studies. Our results also highlight the enhancement of degenerate four-wave mixing that has not been observed previously. These results show the potential of the exitonic resonances of bulk MoS2 for the enhancement of nonlinear optical phenomena.

Figure 3.1. Four-wave mixing on an MoS2 flake. Two pulses (ωp and ωSC) are incident on an MoS2 flake. Two photons of the pump pulse (ωp) and one photon of the supercontinuum pulse (ωSC) interact to produce a fourth (ωFWM).

Methods

The MoS2 flakes were prepared with adhesive tape via mechanical exfoliation and deposited onto a glass slide[85]. Atomic force microscopy (AIST-NT; 40 nm tip diameter) was performed on the flake at the two locations measured to determine flake thickness and layer count (Figure 3.2). The measurements determined the minimum thickness of the

MoS2 flake to be 120 nm, with the majority of the flake having a thickness of roughly 290

23 nm. This corresponds with a layer count between 200 and 600, firmly within the bulk regime.

Figure 3.2. (a) Atomic force microscope (AFM) image of MoS2 flake for the region of interest. (b) Cross section of the MoS2 flake along the white line in (a).

The optical measurements were performed using a multiplex coherent anti-Stokes

Raman spectroscopy setup (CARS-KT, Newport Optics) previously described in Chapter

Two and shown in Figure 3.3. Pulse energies for pump and SC pulses before the focusing objective onto the sample were calculated from dividing the measured average power

(Thorlabs PM100D power meter with S132C sensor) by the repetition rate of the Tsunami

Ti:sapphire oscillator and found to be approximately 6.2 pJ (39 MeV) and 250 pJ (1.56

GeV), respectively. While the SC pulse has over 40 times as much pulse energy as the pump pulse, the bandwidth of the SC pulse is also over 40 times larger than that of the pump. As a result, the pulse energy near a given ωSC is comparable to that of the narrowband pump pulse. The sample was placed on a 3D translation stage, and a camera was used to position the flake normal to the SC pulse in the focal spot. The pump pulse was then manipulated to spatially and temporally overlap with the SC pulse. Spectra at multiple locations on the MoS2 flake were obtained by moving the flake using the 3D translation stage.

Figure 3.3. Schematic of the multiplex femtosecond coherent anti-Stokes Raman spectroscopy setup. The laser provides 50 fs pulses with an 80 MHz repetition rate. RELP: razor-edge long-pass filter.

Results

Degenerate Four-wave Mixing on Bulk MoS2

Two different locations and thicknesses of the MoS2 flake are investigated as depicted in the optical microscope image (Figure 3.4a). The orange dot corresponds to a thickness of 120 nm, and the blue dot has a thickness of approximately 290 nm. The resultant four-wave mixing spectra at these two locations are shown in Figures 3.4b and

3.4c, respectively. Additional spectra from the MoS2 flake for different locations are shown in Appendix A. These spectra are characterized by three regions. The green peaks

-1 correspond to the -634 cm A1g + LA(M) Raman mode that appear in bulk MoS2[77, 86].

The blue region shows a peak at approximately 680 nm with relatively stable peak position as thickness and location on the flake are varied. Lorentzian peak fitting was used to determine individual peak intensities, starting with fitting with the red region. The peak ratio of the 680 nm blue peak to the red peak after Lorentzian fitting is larger for the 290

25 nm location. The red region shows a large variance in peak position as the excitation location is moved across the flake.

Figure 3.4. Four-wave mixing spectra from a MoS2 flake. (a) Optical microscope image of the MoS2 flake. Two different locations with different thicknesses are investigated (blue, 290 nm; orange, 120 nm). FWM signal obtained from the (b) orange spot and (c) blue spot in (a).

Single pulse excitation experiments were performed to rule out potential mechanisms for the observed signal (Figure 3.5). For each region, when the SC pulse train is blocked and only the pump pulse is allowed to reach the sample, the signal obtained is completely quenched, showing that the process is not the result of two-photon absorption.

If two-photon absorption was the driving process for this spectrum, the observed spectra in Figures 3.4b and 3.4c would be observed if either of the two pulses was incident on the flake[81]. However, when the pump pulse is blocked and the SC is incident on the sample, a resulting spectrum similar to the ones shown in Figure 3.4 is obtained but with lower intensity. We attribute this to leakage of the SC pulse through the short-pass filters after the sample.

Figure 3.5. Spectrum obtained at the two locations depicted in Figure 3.4a by blocking individual pulses. Unblocked spectrum (both pulse trains) are shown in black, supercontinuum only (pump blocked) in blue, and pump only (supercontinuum blocked) in red.

To determine the effects of individual pulses on the observed spectrum, a variable neutral density filter was placed in the path of either r pulse train to control the pulse energy without modifying the spectral character of the pulse. Average power was recorded, and delay stages were modified between measurements to adjust peak temporal overlap as the pulse energy was changed (Figure 3.6). As incident power is changed, there is no noticeable shift in the spectral character of the resultant signal (insets in Figure 3.6). The measurements were performed at the location with a 290-nm-thick MoS2 spot since it provides a more well-defined peak at 680 nm than the thinner section. Spectra obtained using variable input powers were analyzed by Lorentzian fitting to obtain the peak area of the 680 nm peak and plotted with respect to average incident power of the pulses as shown in Figures 3.6a and 3.6b (red dots). The results were then fitted via polynomial fitting, and the intensity dependence due to the relation between the intensity of an observed spectrum and the intensities of the incident pulses was described as

푚 푛 퐼푆푝푒푐푡푟푢푚 ~ 퐼푝푢푚푝퐼푆퐶 (3.1)

27 where m and n are the number of photons from the pump and SC pulses required to produce the observed signal, respectively. As seen in Figure 3.6b, the observed signal has a linear dependence on the SC intensity, indicating that one SC photon is required. In contrast, a quadratic dependence on the incident intensity of the narrowband pump is observed (Figure

3.6a), indicating that two pump photons are required in the emission process. A linear component was also observed, possibly due to a low amount of transmission through the short-pass filters after the MoS2 flake. This process was repeated for the 120-nm-thick location, and the results were consistent with that of the 290-nm-thick location. This indicates that the observed spectrum results from a third-order, four-wave mixing process.

Figure 3.6. Photoluminescence intensity dependence for (a) pump and (b) supercontinuum pulses on the 290 nm section of the MoS2 flake. Insets show the photoluminescence spectrum as pulse power is modulated. Enlarged insets are shown in Appendix A.2.

With the required number of photons from each pulse train known, the four-wave mixing relation for the observed signal was obtained by modifying the SC spectrum into a narrowband pulse and varying its wavelength range using different bandpass filters (850 nm, 900 nm, 950 nm, 1000 nm; 10 nm FWHM). These bandpass filters were placed in the path of the SC before the razor-edge long-pass filter, and temporal overlap was readjusted

28 with each filter for peak signal intensity (Figure 3.3). The resultant four-wave mixing signal changes to a narrow peak in the presence of a bandpass filter because the range of the SC pulse is restricted to a narrow band. The resultant spectra are shown in Figure 3.7. With the 850 nm bandpass filter, the resultant FWM peak is located at 768 nm, while with the

900 nm filter, the FWM peak is found at 730 nm. These measurements confirm that the four-wave mixing relation for the observed signal is

휔퐹푊푀 = 2휔푝푢푚푝 − 휔푆퐶 (3.2)

The pump wavelength was determined to be approximately 807 nm during these measurements. This four-wave mixing relation has multiple analogous excited state diagrams. To distinguish these processes, we would need to determine through which electronic state coherent propagation of the observed process is occurring, using for example a three-pulse four-wave mixing process. A third pulse train obtained by splitting the pump pulse into two pulses with a beam splitter, along with an additional delay line, is necessary[87]. Our experimental setup is not capable of discerning this due to the lack of a third pulse train. Interestingly, this is the same four-wave mixing frequency relation as that of coherent anti-Stokes Raman scattering. However, the observed spectra outside the green CARS region in Figure 3.4, especially the 680 nm peak in the blue region of Figure

3.4, do not correspond to the excitation of a known Raman mode of MoS2[77]. Therefore, the resultant spectra occur due to a property of MoS2 not related to its vibrational modes.

Because of the observed four-wave mixing relation, one possible cause for the variation of the red peak in Figure 3.4 is shifts in the SC intensity at wavelengths that would produce the observed peaks. The SC spectra at the two locations shown in Figure 3.4a were

Figure 3.7. Four-wave mixing spectra of the MoS2 flake with different bandpass filters placed in the supercontinuum pulse path.

measured by removing the short-pass filters used to remove the two incident pulses after the sample and directly measuring the SC pulse spectrum (see Appendix A). A neutral density filter was placed near the spectrometer in order to prevent signal saturation of the spectrometer without affecting the overall character of the observed SC spectrum. The SC spectrum while on the 120-nm-thick portion of the MoS2 flake is characterized by a broad background signal with peaks at 855 nm, 870 nm, 882 nm, 900 nm, and 942 nm. When moving to the 290-nm-thick portion, the background for the SC pulse changes, but the positions of the peaks of the SC remain relatively unchanged. Moreover, the relative intensity ratios of these peaks varied depending on the thickness of the flake. This confirms that thin film interference effects occur within the flake. These thin film interference effects occur because nd ~ λ/2, where n is the refractive index of MoS2, d is the thickness of the flake, and λ is the wavelength of the incident light. The layered structure of the MoS2 flake, which can be viewed as multiple MoS2 flakes of intermediate thicknesses stacked together,

30 causes varying interference rates for different wavelengths of the SC pulse[88]. The interference effects are affected by the layer-layer spacing of the flake at that position, as well as the angle of incidence of the laser pulses, such that small translations across the flake can change the interference rate. As a result, the spectrum of the SC pulse changes with its location on the flake. These modified SC pulses then interact with the 800 nm pump pulse to produce different non-resonant four-wave mixing signals as the location is changed. However, the relatively stable peak position of the 680 nm peak in Figures 3.4b and 3.4c implies that this peak is unaffected by thin film interference effects. This leads to the conclusion that this peak is determined by the intrinsic properties of MoS2, such as the direct excitonic transitions within the semiconductor.

Discussion

Degenerate Four-wave Mixing at the Excitonic Resonance

From previous works on the band structure of MoS2[12-15, 20, 89], MoS2 has direct excitonic resonances of 1.88 eV and 2.04 eV at the Κ point, called the A and B excitons, respectively. In the monolayer limit, the A exciton becomes lowest energy transition between bands, and MoS2 becomes a direct bandgap semiconductor. As layer count increases, MoS2 becomes an indirect bandgap semiconductor with a bandgap between 1.3 eV and 1.6 eV[20]. However, the direct excitonic resonances are mostly unchanged in energy in the bulk limit because the direct resonances are dependent on the localized d orbitals of the MoS2 atoms, making them less sensitive to layer thickness[90]. Near these resonance, light-induced transitions between the conduction and valence bands generate a large concentration of free carriers that exhibit the spatial variations of the incident electric

31 field, resulting in perturbations of the refractive index that can lead to an increase of several orders of magnitude of the third-order susceptibility[34]. This increased Χ(3) value leads to an increased intensity of the measured four-wave mixing signal, resulting in the peak observed in the blue-colored region near 680 nm (1.88 eV, A exciton) in Figure 3.4.

Similarly, we also observe a second, but much weaker, peak centered at approximately 595 nm, corresponding to the B exciton of MoS2 (2.04 eV) (Figure A.4). This signal is weaker due to the higher energy requirement of the B exciton and the lower SC intensity at the wavelength required for the four-wave mixing process at 2.04 eV. Likewise, higher energy excitons, such as the C and D excitons that arise through transitions between the deep- valence bands and the conduction band[91], do not play a large role as the four-wave mixing condition requires a Stokes wavelength well outside the range of our SC pulse.

These resonances can be used to enhance four-wave mixing process on the surface of the flake by creating large electric fields at wavelengths near the bandgap to induce localized surface plasmons[92].

Thickness Dependence of Four-wave Mixing

Starting with the coupled-wave equations for degenerate four-wave mixing with the undepleted pump and slowly varying envelope approximations, the wave equations become[93]

푑푎 푑푎 푠 = −푖훾(푎∗ + 2푎 ) 푎 = −푖훾(푎∗ + 2푎 ) (3.3) 푑푧 푎 푠 푑푧 푠 푎 where

2 2 (3) 3ℏ휂0휔푝푎푝훸 훾 = 2 (3.4) 휀0푐푛

(3) where η0 is the vacuum impedance and χ is the third-nonlinear susceptibility of the semiconductor. Solving the coupled-wave equations yields

∗ 푎푎(푧) = −푖훾푎푠푧 (3.5)

Therefore,

2 휔푝 2 ∗ 푎푎 ~ 3 푎푝푎푠푧, (3.6) 휔푎 where z is the thickness of the material. Because the intensity I is proportional to |푎|2, we predict a quadratic dependence on the thickness of the MoS2 flake. Wang et al. observed that the intensity of the third-harmonic generation (THG) signals from MoS2 displayed a quadratic dependence on flake thickness and that the THG was quenched in the monolayer limit[90]. Similarly, we also observe the four-wave mixing photoluminescence peak to be quenched when measuring a commercial solution of MoS2 nanoparticles with thicknesses generally at or near a monolayer. The relative intensity of the 680 nm FWM peak was also observed to be higher for the 290 nm portion of the flake, even with the decreased transparency of the higher thickness.

Calculation of the Third-order Nonlinear Susceptibility

The third-order nonlinear susceptibility in a semiconductor at photon energies near the bandgap for a short laser pulse (pulse duration τL) is[34]:

2 (3) 휂훼푛푐푒 휏퐿 휒 = ∗ 3 (3.7) 16휋ħ푚푒ℎ휔푎

∗ Where 푚푒ℎ is the effective electron-hole mass, n is the refractive index, α is the absorption coefficient of MoS2, η is the quantum efficiency of carrier generation (of order unity), and

τL is the incident pulse duration.

∗ For the A excitonic resonance of MoS2 at 680 nm, 푚푒ℎ is 0.24245 me[94], n is

7 -1 15 5.878[95], α is 2.0215 x 10 m , and τL is 35 x 10 s. Substituting into the above equation yields the upper bound for χ(3), assuming a quantum efficiency of 1:

푚2 휒(3) = 2.04 × 10−19 (3.8) 푉2

Using the absolute intensity of the 680 nm peak observed on the 290 nm area, we can derive the average power generated by the four-wave mixing process:

푃 퐶표푢푛푡푠 푃ℎ표푡표푛푠 푒푛푒푟푔푦 (3.9) 퐹푊푀 ~ × × 푠 푐표푢푛푡 푝ℎ표푡표푛

Substituting the absolute intensity for the 680 nm peak and accounting for absorption by the flake, we get an average power of 4.6 x 10-11 W.

The average power of a laser pulse can be related to its irradiance I via:

3 1 휋 푃̅ = ( )2 ƒ휏푊2퐼 (3.10) 푖 8 ln 2 푖

Where ƒ is the repetition rate, τ is the pulse duration, and W is the spot size. Likewise, the irradiance can be expressed via the field amplitude ε:

|휀 |2 퐼 = 푛 휖 푐 푖 (3.11) 푖 푖 0 2

Substituting 3.11 into 3.10 yields:

2 푃̅푖 = 푘푛푖|휀푖| (3.12)

Where

3 1 휋 푚2퐶 푘 = ( )2 ƒ휏푊2휖 푐 = 2.522 × 10−19 (3.13) 16 ln 2 0 푉 푠

For 80 MHz repetition rate, 35 fs pulse duration, and 7.5 μm spot size.

Also, for a four-wave mixing process, the FWM field amplitude is related to the incident field amplitudes via:

푖 휔퐹푊푀 (3) 2 휀퐹푊푀 = 휒 |휀푃| 휀푆퐶 (3.14) 4 2푛퐹푊푀푐

Thus,

1 1 1 ̅ (3) 8 푘 푐 1 푃퐹푊푀 2 2 2 휒 = ( ) 푛푃푛 푛 (3.15) 휔퐹푊푀푑 푃̅̅̅푝̅ 푃̅푆퐶 푆퐶 퐹푊푀

Substituting experimental conditions and indexes of refraction for the three wavelengths[95] results in:

푚2 휒(3) = 1.8278 × 10−19 (3.16) 푉2

Which is in general agreement for the bulk nonlinear susceptibility at the A exciton with previous experimental works by Wang et al.[90] and Woodward et al.[96] as well as Soh et al.’s theoretical work[97]. Our results on enhanced photoluminescence via excitonic resonances of MoS2 could open the path for enhancing four-wave mixing processes of

MoS2 for optical sensing and imaging applications such as coherent anti-Stokes Raman spectroscopy.

Acknowledgments

The authors would like to thank Dr. Zhe He at Texas A&M University for help with the atomic force microscopy measurements.

CHAPTER FOUR

Multi-pulse Laser-Induced Bubble Formation and Nanoparticle Aggregation using MoS2 Nanoparticles

This Chapter is published as: Ko, B. A., et al., Multi-pulse Laser-Induced Bubble Formation and Nanoparticle Aggregation using MoS2 Nanoparticles. Scientific Reports. 10: p. 15753.

Abstract

Understanding of how particles and light interact in a liquid environment is vital for optical and biological applications. MoS2 has been shown to enhance nonlinear optical phenomena due to the presence of a direct excitonic resonance. Its use in biological applications is predicated on knowledge of how MoS2 interacts with ultrafast (<1 ps) pulses. In this experiment, the interaction between two femtosecond pulses and MoS2 nanoparticles suspended in liquid is studied. We found that the laser pulses induce bubble formation on the surface of a nanoparticle and a nanoparticle aggregate then forms on the surface of the trapped bubble. The processes of formation of the bubble and the nanoparticle aggregation are intertwined.

Introduction

The interaction between light and matter in liquids is a field of study that is vital for the advancement of biomedical[98-102] and optical sensing applications[11, 36, 103-

107]. Nanoparticles are especially useful for studying light-matter interactions due to their properties that differ from their macroscopic source. For example, Wang, et. al., used gold nanoparticles to induce a high-speed liquid flow by inducing an ultrasonic photoacoustic effect using a pulsed laser[107]. With metal nanoparticles, laser pulses have been used to

36 manipulate particles for controlled transport[11], allowing for localized light absorption for photothermal applications.

Laser ablation and laser-induced agglomeration are two light-matter interaction processes in liquid that are often related. Laser ablation in liquids has been studied extensively for its ability to create nanoparticles, in which a high-energy pulsed or continuous wave laser is focused onto a solid metal target, ablating the target and creating nanoparticles in solution[8, 9, 36, 103-105, 108]. The cavitation bubble formed in the process is also useful for a variety of applications, especially as a precursor to laser-induced agglomeration of nanoparticles dispersed in liquid. In laser-induced agglomeration, the optical tweezing effect induced by subsequent laser pulses aggregates the suspended nanoparticles to form structures[109]. Depending on the particle properties, such as shape and composition, nanostructures in the liquid medium can be formed. Laser-based agglomeration of nanoparticles has been shown using gold nanoparticles fabricated via laser ablation in liquids[10, 109]. The aggregates formed via ablation and agglomeration can be used to enhance nonlinear optical phenomena[110]. However, these techniques are limited in their scale due to the high pulse energy requirement for the synthesis of nanoparticles, with many of these experiments requiring pulse energies in the mJ regime[36, 103-105, 108]. The high pulse energy requirement gives these techniques high potential for damage of the surrounding material.

Different approaches have been developed to bypass the high pulse energy requirement for laser-induced agglomeration and minimize damage to surrounding material. One method is to use nanoparticles already suspended in a liquid, which reduces the required laser power, and the size and shape of the nanoparticles can be more accurately

37 controlled prior to aggregation. Another method is to use multiple low-energy laser pulses with different wavelengths as the cavitation bubble formed prior to agglomeration can be optically trapped by the second laser pulse[111, 112]. Optical trapping, in which a focused laser beam creates a force gradient that can trap a nanoparticle within the focus of the laser[11], is a tool that is useful for manipulating nanoparticles and creating structures[10].

However, single laser beam traps have some shortcoming in terms of fine control of the trapped particle. To circumvent this, double-laser optical traps have been developed[113,

114], using two lasers to trap an object. The second laser has been utilized to perform localized excitation for spectroscopic applications such as Raman and fluorescence spectroscopy[114] as well as to provide finer control of the optical force gradient[113].

In this paper, we investigate the complex dynamic processes of dual laser-induced agglomeration of suspended nanoparticles in liquid. Molybdenum disulfide (MoS2) is a transition metal dichalcogenide that has been extensively studied for its optical[12-15], electrical[16, 17], and catalytic[18, 19] properties. The presence of a direct excitonic transition[20] in MoS2 allows for the enhancement of nonlinear optical phenomena, making it an attractive candidate as a substrate for optical studies. MoS2 nanoparticles in solution have also been used to enhance nonlinear optical phenomena as they were employed to enhance the coherent anti-Stokes Raman scattering intensity of the surrounding pyridine medium, with a calculated nine orders of magnitude enhancement of the Raman excitation[35]. MoS2 is also nontoxic in bulk form, shown previously by Weng, et. al.[115], making it suitable for optical study of biological samples. However, investigations into how ultrafast (<1 ps) laser pulses affect the behavior of MoS2 nanoparticles in fluids have not been performed, with experiments only performed on

38 mono- and few-layer nanosheets[116]. These investigations are vital to understanding potential interactions that may occur during the integration of multiple femtosecond laser pulses of differing wavelengths with MoS2 nanoparticle solutions.

Here, we image and study the interaction between two low-energy femtosecond laser pulses and suspended MoS2 nanosheets in an ethanol solution. We observed the intertwined interaction of the laser-induced formation of a cavitation bubble and the subsequent agglomeration of MoS2 nanoparticles. Two focused laser pulses – one narrowband pump pulse centered at 800 nm and one broadband supercontinuum pulse

(800-1000 nm) – create a cavitation bubble when a nanoparticle passes through the focal point. As the bubble grows, MoS2 nanoparticles in the solution agglomerate onto its surface, creating a nanoparticle aggregate. Using suspended nanoparticles instead of a metal or semiconductor target reduces the required power for bubble formation and subsequent aggregation. Other nanoparticles, including Al nanosheets and polystyrene beads were also studied using this scheme.

Results

Laser-Induced Cavitation and Nanoparticle Aggregation

Figure 4.1 shows interaction between the incident laser pulses and MoS2 nanoparticle as the particle passes through the laser focus. The incident power for the pump and supercontinuum pulses are 16 mW and 8 mW, respectively. The formation of the bubble begins when a particle (red circle in Figure 4.1a) enters the focus (yellow circle) of the incident laser pulses. The nanoparticle enters the focus due to the optical tweezing effect, in which focused laser pulses or beams create a force gradient trapping particles[11].

Once in the laser focus, the bubble is formed on the surface of the nanoparticle but outside of the focus spot (Figure 4.1b) due to a process similar to laser ablation in liquids[117], except the bubble does not burst due to a lack of cavitation pressure and is allowed to grow in liquid. In the first short period (~25s) of the lifetime of the bubble, the bubble sits just outside of the laser focus (Figure 4.1c). The collision of the downward flow of the nanoparticles with the bubble in solution is counteracting the optical tweezing effect induced by the incident laser pulses. As a result, the bubble repeatedly moves into and out of the bubble focus. During this period, bubble growth is slow, with the diameter growing from approximately 5 um to 9.5 um in 45 seconds for the bubble depicted in Figure 4.1, an increase in diameter of 90%. Nanoparticles begin to attach onto the bubble as they flow towards the focus. After this “out-of-focus” growth period, the bubble then shifts into the focus (Figure 4.1d). The bubble is able to enter the focus because its mass is large enough that the nanoparticle collisions do not impart a large enough change in bubble’s velocity to move it out of focus. When the bubble enters the focus bubble growth is more rapid than the out-of-focus period. In a similar time interval to that of the out-of-focus period, the bubble diameter increases from 9.5 um to 26.5 um, an increase of 178% in diameter (Figure

4.1e). The rate at which nanoparticles attach onto the bubble also increases compared to the out-of-focus period. Once the bubble becomes too heavy or the incident laser pulses are blocked, the bubble falls off, leaving the aggregate created by the attached nanoparticles in the laser focus (Figure 4.1f), and the process repeats. In most situations, the aggregate is then left behind in the focus; otherwise, the aggregate stays attached to the bubble as it falls out of the focus. In the former case, the presence of the aggregate in the laser focus immediately forms a new cavitation bubble in the focus, bypassing the out-of-focus period

(Figure 4.1g). Secondary bubbles also form due to trapped solvent within the aggregate

(Figure 4.1h). These secondary bubbles can then merge with the primary in-focus bubble and further accelerate the bubble growth. The growth process then continues, with either further growth of the nanoparticle aggregate or, in the case that the initial aggregate falls away with the bubble, formation of a new aggregate. An additional timeline of bubble formation for a lower combination of laser power (14.0 mW pump and 10.5 mW SC) is available in Appendix Figure A.5. Temporal overlap of the two lasers is necessary for bubble formation until the SC power is 27 mW, as no bubble formation was observed until the two lasers are close to maximally overlapped as observed through the BBO crystal.

Figure 4.1. (a) A nanoparticle (red circle) flows towards the focused spot of the laser (yellow dotted circle). (b) A cavitation bubble is formed when the nanoparticle enters the laser focus. The bubble is small (~5 µm diameter) and not centered in the laser focus. (c) The bubble has increased in size but is still not centered in the focus. (d) The bubble becomes centered in the laser focus and has become defocused from the camera’s focal region. (e) Bubble has grown and nanoparticles can be seen on the surface of the bubble. (f) The bubble has fallen away from the focus and the nanoparticle aggregate is left behind. (g) A new bubble forms in the focus with the aggregate attached. (h) Trapped ethanol within the aggregate forms additional bubbles. Laser powers are 16 mW and 8 mW for the supercontinuum and pump pulses, respectively. Times are relative to initial bubble formation.

Laser-Induced Bubble Cavitation and Rotation

Video recordings of the entire process show that the formation of the nanoparticle aggregates on the bubble is related to the convection currents that are generated as the bubble is formed and grows in size, both while out of the focal point and in the focal point.

The flow of the nanoparticles in solution follows the convection currents. Figure 4.2 shows the path of the nanoparticles near the bubble by monitoring the positions of the particles using a video camera. An animation depicting frame-by-frame movement of the nanoparticles is available in the Appendix (Movie A.1). The particles travel along a curved path when the bubble and laser pulses are present. The currents are created due to the heating of the bubble by the incident laser pulses. This creates a difference in surface tension between the bubble and the surrounding solvent, creating convection currents within the solvent[40]. The nanoparticles travel along the convection currents towards the bubble and attach themselves to the bubble. Figure 4.3 shows a nanoparticle attaching onto the bubble. In the first frame (Figure 4.3a), the nanoparticle is suspended in the liquid and flows along the convection currents towards the bubble. In the second frame (Figure 4.3b), the nanoparticle attaches onto the bubble. As the particle attaches to the bubble, it imparts torque onto the bubble, causing the bubble to rotate, as shown in Figure 4.3c and 4.3d. The increased rotation of the bubble also further increases the speed of the convection currents, increasing the frequency of nanoparticle collisions onto the bubble surface.

Figure 4.2. Frame-by-frame images of nanoparticle movement in the presence of a laser- induced cavitation bubble. Time between frames is approximately 0.3s. Arrows indicate motion from the previous frame.

Figure 4.3. An MoS2 nanosheet (red circle) attaches onto the surface of the cavitation bubble. Previous locations of the nanoparticle are shown as dotted circles to trach the motion.

Nanoparticle Aggregation

As particles attach onto the surface, the optical tweezing effect of the incident laser pulses manipulates the nanoparticles to aggregate within the beam path. Figure 4.4 depicts a nanoparticle aggregate on the surface of the bubble and the motion of a nanoparticle attaching to the aggregate. The images are taken over the course of 11 frames, with the time between frames is approximately 0.15s. An animation is available in the Appendix

(Movie A.2). The nanoparticle aggregate is centered at the laser focus, with the dark background corresponding to the portion of the bubble where light is not transmitted through to the camera, as seen previously in Figure 4.1e. The nanoparticle, highlighted by the red circle in Figure 4.4, begins near the dark background. Over the course of the animation, the particle moves, via the optical tweezing effect, towards the center until it attaches to the nanoparticle aggregate. Once attached, the particle moves along with the larger aggregate.

Figure 4.4. Selected frames of an MoS2 nanoparticle (red circle) attaching onto a nanoparticle aggregate formed on the surface of a cavitation bubble. The red arrow indicates motion of the nanoparticle from the previous frame. Time between frames is approximately 0.3s.

Pulse Dependence

Supercontinuum intensity measurements were performed to observe the overall bubble formation process on a longer timescale as well as investigate the difference in effects of the two pulses on the process (Figure 4.5). Measurements were conducted by removing one of the short pass filters after the sample and measuring the transmitted intensity of the supercontinuum pulse. A decrease in measured signal indicates the formation of a cavitation bubble, as the transmitted light is scattered away from the original path by the bubble. Similarly, an increase in the measured supercontinuum intensity correlates to the absence of a bubble in the beam focus. To observe the effects of individual pulses on the interaction, a beam block is placed in either the 800 nm pump line or the broadband supercontinuum line to prevent it from reaching the sample. When the sample is first placed in the laser path (t < 3 minutes), the measured supercontinuum signal

45 oscillates due to nanoparticles that are passing through the laser path without forming a bubble. Shortly after, there is a sharp decrease in the supercontinuum intensity, signaling the bubble formation process. As the bubble grows, a larger portion of the supercontinuum light is scattered away from the normal optical path, resulting in a lower transmitted signal.

The center of the bubble also begins to scatter light away from the optical path as nanoparticles aggregate on the surface. When the supercontinuum pulse is blocked for five minutes (red region of Figure 4.5, t ~ 26-31 mins), a sharp increase in the intensity is observed after the supercontinuum is unblocked, meaning that the bubble is no longer in the focus and the light passes through. However, after a few minutes, the supercontinuum intensity decreases, indicating that a new bubble has formed in the focus. When the pump pulse is blocked instead (t ~ 40-45 mins, green region of Figure 4.5), the intensity of the supercontinuum pulse stays low, indicating that the bubble is still in the focus. The slight increase in SC intensity in the green region can be attributed to a reduction in tweezing force from the absence of the pump pulse causing nanoparticles to fall off the surface of the bubble. Similar experiments show that the effect of the supercontinuum pulse is more significant than that of the pump in trapping the bubble in place, as the bubble remains in the laser path while the pump pulse is blocked. In these supercontinuum measurements, we observe a periodic behavior of bubble formation and bubble fall off as the bubble increases in size. The bubble lifetime period appears to be approximately 15 minutes. An additional measurement at different pulse powers is depicted in Appendix Figure A.6.

Figure 4.5. Supercontinuum (SC) transmission intensity measurement performed to determine the effects of individual pulses on the bubble formation process. Bubble formation is characterized by a sharp decrease in the SC intensity. Laser powers used are 27 mW and 6.1 mW for the SC and pump pulses, respectively.

The experiment was conducted with different power combinations between the two incident pulses (pump and SC) to investigate the difference in their effects on the behavior of the bubble. Measurements were performed by placing two neutral density filters, one in each pulse path, in order to control the power of the pulses without modifying their spectral character. The laser properties (center wavelength and bandwidth) of the Ti:Sapphire oscillator were modified in order to control the proportion of pulse power that is reflected by the 3 nm bandpass filter into the photonic crystal fiber to create the supercontinuum pulse while maintaining the wavelength on the 800 nm narrowband pump pulse. Pulse path lengths were adjusted with each measurement to ensure maximal temporal overlap between the pulses. The dependence of bubble formation on the individual pulse power is plotted in

Figure 4.6. Pulse power combinations that resulted in the formation of a bubble are denoted as blue circles, while those that did not form a bubble are shown as red squares. The dashed

47 line in Figure 4.6 corresponds to 24 mW of combined pump and SC pulse power. If the effects of the pump and SC pulses were equivalent, the outcome of bubble formation would not change moving along lines of constant power. Because the outcome changes along the dashed line, the bubble formation process is more dependent on one pulse than the other.

Moreover, because bubble formation is not observed along the dashed line in Figure 4.6 at power combinations with a high pump power contribution, the SC pulse has a larger effect on bubble formation than the pump pulse. The presence of successful bubble formation at

27 mW SC and 0 mW pump power also confirms the greater dependence on the SC pulse.

Figure 4.6. Scatter plot of different power combinations between the narrowband pump and broadband supercontinuum pulses to determine pulse dependences in bubble formation. Power combinations that resulted in bubble formation are denoted as blue circles, while power combinations in which no bubble was observed are depicted as red squares. The black dotted line represents 24 mW of combined laser power.

Statistically, 40 bubble formation events over 8 separate solution samples were measured using a SC power of approximately 27 mW and a pump power of about 10 mW.

Of those 40 bubble formation events, the lifetime of each even varied from approximately

15 minutes to 25 minutes, with the first bubble formation event in a sample set having a longer lifetime than subsequent bubbles.

Discussion

Pulse Dependence of Bubble Formation

From the SC intensity measurements and the pulse power dependence measurements, the SC pulse contributes more to the bubble formation and nanoparticle aggregation processes than the narrowband 800 nm pulse. One possible reason for the greater dependence on the SC pulse is that the tweezing force applied by the SC pulse is greater than that of the 800 nm pulse. The tweezing force gradient applied by a laser pulse with pulse duration τ can be approximated as[118]:

2퐸 푧 푡 2 푧 4 퐹푝푢푙푠푒 = − 2 2 exp (− ( ) ) exp (− ( ) ) (4.1) 휏√휋 (1+(푧/푧푠) ) 휏 푧푠

2 where E is proportional to the pulse energy per cross-section area, and zs = πω0 /λ0 is a distance parameter. From the first term, 2퐸/휏√휋, there is an inverse proportional dependence on the pulse duration. From the time-bandwidth product, the 3 nm FWHM bandwidth 800 nm pulse has a minimum pulse duration of 313 fs. The SC pulse generated by the photonic crystal fiber has a much shorter pulse duration, approximately 100 fs, due to the near-zero dispersion of the PCF. As a result, the maximum amplitude of the tweezing force from the SC pulse is about three times greater than that of the narrowband 800 nm pulse. Thus, the 800 nm pulse alone is unable to trap the bubble in the laser focus, preventing the bubble from growing.

Due to the complex nature of dual-laser bubble formation, many factors can affect the formation and lifetime of the bubble[119], as evidenced by the variation in lifetime in

49 the SC transmission intensity measurements shown in Figure 4.5. Factors such as the increase in pressure caused by the formation of the cavitation bubble[120, 121], changes in the optical force gradient[113], and the surrounding medium can affect the bubble formation[122]. Differences in individual laser powers as well as the spatial and temporal overlap of the two pulses can change the profile of the force gradient of the optical trap and affect the heating of the bubble. The bubble itself can refract the pulses and affect the overlap of the pulses, changing the energy absorption efficiency. Moreover, there is a distinct difference between the first bubble formation event and the ensuing bubble formation events within a sample set, where the formation of the first bubble takes a longer time than the second or the following bubbles. This is attributed to the presence of an aggregate at or near the focal point of the laser, which guarantees that a particle is in the focus to induce the formation of a cavitation bubble.

Bubble Heating

The temperature on the surface of a nanoparticle after laser irradiation of two femtosecond pulses was calculated using the method shown by Burgess, et. al.[123]. The change in surface temperature immediately after irradiation by a square-shaped laser pulse with pulse duration τ is defined as:

1 퐹 휅휏 ∆푇(휏) = 2 ( 0) ( )2 (4.2) 퐾 휋 where F0 is the maximum absorbed power density, K is the thermal conductivity of MoS2

(2.3 W/m K)[124], and κ is the thermal diffusivity of MoS2, defined as:

퐾 휅 = (4.3) 휌퐶푝

3 3 where ρ is the density (5.06 x 10 kg/m ) and CP is the isobaric specific heat[125] (397.125

J/kg K) of MoS2. Substituting these values into equation 4.3 gives the thermal diffusivity

-6 2 of MoS2 as 1.1446 x 10 m /s.

The maximum absorbed power density by a nanoparticle with dimensions of 1 µm can be calculated from the average power of the incident laser pulses. For the combination of 16 mW of SC power and 8 mW of narrowband pump, the combined absorbed power density can be calculated as:

퐹0 = 퐴푆퐶퐼푆퐶 + 퐴푃퐼푃 (4.4) where Ak is the absorbance of MoS2 at the wavelength of the incident light, defined as

푎 푑 퐴 = 푖 (4.5) 푖 2.303 where d is the thickness of the MoS2 nanosheet (~100 nm) and ai is the absorption

-1 coefficient of MoS2 at the wavelength λi . For 800 nm, ap = 87422 cm and for the

-1 wavelength range of the SC pulse, aSC ≈ 60000 cm [126]. Thus, AP = 0.3796 and ASC ≈

0.2605. The total power density on an MoS2 nanosheet Ii, is defined by

푃̅ 퐼 = 푖 (4.6) 푖 푓휏퐴 where 푃̅푖 is the average power of the laser pulse, 푓 is the repetition rate of the laser (80

MHz), and A is the beam waist at the focal point (5 µm). Inserting these values into equations 4.5 and 4.6 and substituting into equation 4.4, the maximum absorbed power density F0 is

9 2 퐹0 = 4.58 × 10 푊/푐푚 (4.7)

Substituting all values into equation 4.2 yields the surface temperature shift of an MoS2 nanosheet by a single laser pulse as

1 2 푊 푚 2 (4.58 ×1013 ) (1.1446 × 10−6 )(5 ×10−14푠) 푚2 푠 3 ∆푇(휏) = 2 푊 ( ) = 5.37 × 10 퐾 (4.8) (2.3 ) 휋 푚 퐾

It also shows the role of the 800 nm pump pulse, in that MoS2 has a higher absorption coefficient at 800 nm than in the IR regime of the SC, allowing for more efficient heating of the bubble than with just the SC pulse alone. However, after initial bubble formation, due to the lensing effect of the bubble on the laser light as well as the pulsed nature of the irradiation, the irradiated spot cools down between pulses, preventing optical breakdown of the nanoparticles trapped on the surface of the bubble.

Comparison with Other Nanoparticles

The bubble formation experiment was performed using nanoparticles of different geometries and compositions in order to determine the cause of bubble formation and nanoparticle aggregation. Commercial MoS2 flakes (2D Semiconductors) 1 to 10 layers in thickness with sizes on the order of 10 nm were studied to determine if the bubble formation was caused due to the composition of the nanoparticles. Al nanosheets were tested due to its similar geometry and absorption properties to the homemade MoS2 nanoparticles – 200-

1000 nm span with ~100 nm thickness with a flat rectangular shape and low absorption in the IR regime. Polystyrene spheres (500 nm and 1um diameter) and Ag nanorods (diameter

50 nm, length 1-2 um) with size on the same order to the homemade MoS2 nanoparticles were also selected to determine shape dependence. The results of these experiments are shown in the Table 4.1. From the table, only aluminum nanosheets with size of about 1 micron, were able to create a suspended bubble in the laser focus. Thus, a flat flake shape with a span on the order of 1 square micron is necessary to create a bubble. This is possibly due to the flat nanosheets acting as a surface like that of the metal targets used in laser

52 ablation in liquids experiments[36, 98, 103-105, 108]. The dependence on the nanoparticle geometry could imply that the bubble formation process is possible with other nanoparticle compositions if the nanoparticles are flat and rectangular.

Table 4.1 Nanoparticles Investigated for Bubble Formation Events Nanoparticle Shape Size Bubble Formation MoS2 (homemade) Nanosheet 400-500 nm, >10 nm thickness Yes MoS2 (commercial) Nanosheet 10-100 nm, <5 nm thickness No Aluminum Nanosheet 1-2 µm, 50-100 nm thickness Yes Silver Nanorod 1-2 µm length, 50 nm radius No Polystyrene Nanosphere 499 nm radius No Polystyrene Nanosphere 1.053 µm radius No

Absorption spectra for each nanoparticle were also taken to determine if the bubble formation event has a plasmonic origin. The absorption spectra can be found in Figure 4.7.

For MoS2, both homemade and commercial MoS2 solutions exhibit absorption peaks at approximately 680 and 600 nm, corresponding to the A and B excitons, respectively[33].

They also have a broader absorption peak at approximately 400 nm, corresponding to the

C and D excitons. Absorption measurements of the aluminum nanoparticle solution show that the nanoparticles have a relatively flat absorption spectrum with little features in the visible to near-infrared regime. Ag nanorods show a plasmonic absorption peak at approximately 400 nm with a long tail in the visible regime. 500 nm diameter polystyrene beads exhibit an absorption peak at approximately 300 nm with a long tail in the visible.

The 1 um polystyrene beads exhibit a broad absorption peak centered at 418 nm. Because the commercial MoS2 nanoparticles did not create a cavitation bubble while having an identical absorption spectrum to the homemade nanoparticles, it can be determined that the bubble formation did not occur due to a resonance. If the bubble formation was caused by a plasmonic resonance, then both the homemade and the commercial MoS2 solutions would

53 have produced a cavitation bubble. This is further confirmed with the lack of an absorption peak in the visible or near-infrared regime for the aluminum nanoparticles.

Figure 4.7. Absorption spectra of nanoparticles used in the experiment. MoS2 absorption peaks in the inset correspond to the A (680 nm) and B (600 nm) excitons for the commercial (red) and homemade (black) solutions. PS: polystyrene.

The observed MoS2 nanoparticle aggregation can be used in nonlinear optical studies as a potential enhancer of optical signals such as Raman scattering by increasing the amount of analyte-surface contact within the focal point of the laser. The increased analyte-surface contact can also be used to increase light-based catalysis between the nanoparticle and the sample. The low pulse energy requirements (<1 nJ combined pulse energy) of this aggregation scheme, which does not require the ablation of a metal target which requires pulse energy on the order of mJ[36, 103-105], make it possible to use with photo-sensitive samples with reduced chance of damaging the sample. Because of the capability of MoS2 to enhance nonlinear optical phenomena and its nontoxicity in bulk form, MoS2 nanoparticle aggregates can be especially useful in biological applications,

54 such as creating localized points of increased light absorption. In this study, we have demonstrated the above technique can be done using MoS2, allowing for the use of light- assisted transport of MoS2 nanoparticles for applications such as nanostructure fabrication for samples that are incompatible with traditional metal substrates. The overall bubble formation process is similar to the donut-shaped object that was observed by Zhang, et. al., using gold nanoparticles on glass in liquid[10]. However, Zhang and co. suggest that the donut-shaped object is a nanoparticle aggregate. In our experiment, due to the merging event shown in Figure 4.1g, we determine that the donut-shaped object is a bubble, with the dark ring seen in the image caused by the scattering of incident light away from the camera.

Methods

To study the interaction between light and the nanoparticles suspended in liquid, the experiment was conducted using a broadband femtosecond coherent anti-Stokes Raman spectroscopy setup[127] previously described in Chapter Two and depicted in Figure 4.8a.

Video and images were taken using a CCD camera (IDS uEye 2240) placed after the filters.

For taking the image with the camera, a white light source was placed before the sample and directed using a glass slide to the sample collinear to the laser pulses. Supercontinuum spectra for intensity measurements were collected using a spectrometer (Horiba iHR 550).

MoS2 nanosheets were prepared using the lithium-intercalation/exfoliation method[128]. First, 0.5g MoS2 powder was immersed in 5 ml of 1.6 M n-butyl lithium solution (0.1 g/mL) and stirred for 48 hours in an argon protected container to produce Li- intercalated MoS2 (LixMoS2). LixMoS2 was filtered and washed repeatedly with hexane to remove excess lithium and organic residues. Then the LixMoS2 powder was dispersed in

TM 100 mL Nanopure water (18.3 MΩ). Subsequently, LixMoS2 was exfoliated via bath ultrasonication and the MoS2 nanosheets were separated through centrifugation. The nanosheets are then transferred into a clean cuvette and placed in a solution of pure ethanol.

Scanning electron microscope (SEM) images of the prepared MoS2 nanosheets are shown in Figure 4.8b. The nanosheets are irregular flakes in shape with an average size of 300-

400 nm and thickness of several layers (~10 nm). Aluminum nanosheets[129] were prepared via ultrasonication of commercial aluminum foil in ethylene glycol. The Al nanosheets were separated through centrifugation to remove the ethylene glycol and placed in a solution of pure ethanol. An SEM image of the Al nanoparticles are shown in Figure

4.8c. The Al nanosheets are irregular sheets. The diameters of the Al sheets are ~200–1000 nm and the thicknesses are ~50–200 nm. The commercial MoS2 nanosheets were purchased from 2D Semiconductors in an ethanol solution. The commercial MoS2 nanosheets consist of monolayer to few-layer MoS2 and have sizes roughly 50 nm in diameter. The two polystyrene bead solutions were purchased from Polysciences, Inc., and are spherical in shape with radii of 1.053 µm and 0.499 µm. The polystyrene bead solutions were diluted with additional ethanol to increase transmission.

Absorption measurements were conducted using a spectrophotometer (Agilent

8453) equipped with deuterium and tungsten lamps. First, a quartz cuvette filled with pure ethanol is used as a blank, then 0.1 mL of nanoparticle solution in ethanol was measured.

Because of differences in sample concentration, relative absorption measurements are compared between samples.

Figure 4.8. (a) Experimental setup. A femtosecond laser (800 nm, 100 fs, 30 nm FWHM) is split into two pulses using a bandpass filter. The narrow, transmitted pulse supplied the 800 nm pulse, while the reflected light pumps a photonic crystal fiber (PCF) to create the broadband supercontinuum pulse. (b) Transmission electron microscope of homemade MoS2 nanoflakes. (c) Scanning electron microscope of homemade Al nanoparticles.

Acknowledgments

The authors would like to thank the Center for Microscopy and Imaging at Baylor

University for use of their facility.

CHAPTER FIVE

Resonant Degenerate Four-Wave Mixing at the Defect Energy Levels of 2D Organic-inorganic Perovskite Crystals

Abstract

Two-dimensional organometallic lead halide perovskites are generating great interest due to their optoelectronic characteristics, such as a high energy conversion efficiency and a direct band gap in the visible regime. However, the presence of defect states within the two-dimensional crystal structure can affect these properties, resulting in the changes to their band gap emission as well as the emergence of nonlinear optical phenomena. Here, we have investigated the effects of the presence of defect states on the nonlinear optical phenomena of the hybrid perovskite butylammonium methylammonoium lead bromide, (BA)2(MA)2Pb3Br10. When two pulses, one narrowband pump pulse centered at 800 nm, and one supercontinuum pulse with bandwidth from 800-1100 nm, are incident on a bulk perovskite flake, degenerate four-wave mixing occurs, with peaks corresponding to the energy levels of the defect states present within the crystal. The longer carrier lifetime of the defect state, in comparison to that of virtual transitions that take place in non-resonant four-wave mixing processes, allows for a larger population of electrons to be excited by the second pump photon, resulting in increased FWM signal at the defect energy levels. This technique shows the potential application of detecting defect energy levels in bulk crystals using four-wave mixing.

Introduction

Organometallic lead halide perovskites, such as methylammonium lead bromide

(MAPbBr3), are layered semiconductors that have seen a great increase in interest due to their optoelectronic characteristics[52, 130-136]. Their high energy conversion efficiency, as high as 20%[1], and ease of production have made them promising candidates in photovoltaic (PV) applications such as thin film solar cells[49, 50]. Their band gaps, which are tunable in the visible regime by changing the doping concentration, demonstrate the promise of halide perovskites as light emitters, either as microlasers[56, 131] or diodes[55,

137-139]. Their ease of manufacturing via solution-based processes have also made them attractive alternatives to traditional power conversion materials [139-141]. The acceleration in research interest in organometallic lead halides has led to additional novel uses of the material, such as humidity sensing [142] and NH3 gas detection [134]. However, these samples are prone to defects in their crystal structure, affecting their energy efficiency by introducing nonradiative recombination pathways [49].

Defects within a crystal structure are abnormalities in the regular structure. Intrinsic defects can take on the form as simple atomic vacancies or interstitials or as more complex antisites (two atoms switch locations)[143-146]. Extrinsic defects can come in the form of doping the crystal, substituting one atom with that of the dopant[147-151]. Both of these types of defects cause changes to the density of states (DOS) of the crystal, fundamentally changing the band structure and subsequent emission properties[49, 50, 59, 60, 134, 135,

144, 152-157]. Defects within the crystal structure of organometallic perovskites can lead to a variety of phenomena, including the introduction of nonradiative recombination pathways for the electron-hole pairs to decay into, leading to a quenching of the

characteristic bandgap emission[135]. In the photovoltaic industry, these phenomena are a hindrance to the conversion efficiency of the PV cell. In other applications, the formation of defect energy levels can lead to its use as an emitter[50, 60, 148, 158]. Defect levels have longer lifetimes, on the order of nanoseconds[62], than that of virtual levels, allowing for the enhancement of nonlinear optical phenomena, such as four-wave mixing. Four- wave mixing (FWM) in semiconductors has been well established to study light-matter interaction and the coupling between electronic states that occur within the crystal, such as the excitonic coherence of GaN[159], the dynamics of excitonic broadening in perovskites[160, 161], and our previous work on FWM at the excitonic resonance of

MoS2[127]. FWM processes are attractive techniques due to the decreased linear absorption, as the wavelengths typically used in FWM experiments are of lower energy than the band gap of the material. However, non-resonant four-wave mixing (NR-FWM) can disturb and overpower the resonant signal. The NR-FWM signal arises due to excitation of electrons into short-lived (<1 ps) virtual states[63, 64] which then are further excited by another pump photon to be emitted as an anti-Stokes signal. The presence of defects allows for coherent excitation of electrons into the defect levels so it is no longer non-resonant, but instead reveals the property of the material.

Current experimental methods of optical detection of the defects present within a crystal are limited to mainly low-temperature studies, such as those done on CdTe[162] and MoS2[163] as well as perovskite materials[52, 135], or photoemission studies such as angle-resolved photoemission spectroscopy (ARPES) that require ultra-high vacuum

(UHV) conditions. Previous FWM experiments on perovskites have shown that weak exciton-carrier interactions prevents the enhancement of excitonic FWM signal that is tied

60 to excitation-induced dephasing[161]. Other FWM experiments on perovskites have shown that below-bandgap excitation leads to spectral broadening of the excitonic emission due to an increased number of inter- and intra-band FWM combinations that can contribute to the emission[164]. However, the correlation of the defect states in perovskites with their nonlinear optical phenomena has not been reported.

In this experiment, two incident pulses – one narrowband pump pulse centered at

800 nm and a broadband supercontinuum pulse from 800-1100 nm – are utilized to study the nonlinear optical properties of flakes consisting of the organometallic perovskite butylammonium methylammonium lead bromide (BA)2(MA)2Pb3Br10 (Figure 5.1). By coherently exciting carriers into the defect states in our experiment, defect states detection can be performed in ambient conditions, as a larger population of charge carriers is excited.

Furthermore, the use of a supercontinuum pulse allows for simultaneous measurement of multiple defect levels via four-wave mixing, as the broadband nature allows for multiple defect levels to be resonantly filled. When the two pulses are temporally and spatially overlapped, degenerate four-wave mixing occurs. The resultant FWM signal increases with sample thickness due to the increased presence of defect sites within the optical path. These defect states enhance the FWM emission by providing a longer carrier lifetime than virtual electronic transitions.

Figure 5.1. Degenerate four-wave mixing at the defect energy levels of (MA)2(BA)2Pb3Br10. Two photons of the pump pulse and one photon of the supercontinuum pulse interact to produce a fourth pulse. In the presence of defect levels, the beat frequency of the two pulses (ωP – ωSC) can be resonant with the energy level of a trap state or the four-wave mixing relation 2ωP – ωSC is equal to the energy of a donor state, resulting in increased emission at that energy.

Methods

Butylammonium methylammonium lead bromide, (BA)2(MA)2Pb3Br10, crystals were synthesized by dissolving the precursors PbO (0.59 mmol, 131.7 mg, Sigma-Aldrich),

BABr (0.19 mmol, 29.3 mg, Sigma-Aldrich), and MABr (0.4 mmol, 44.8 mg, Greatcell

Solar) in an acid mixture consisting of 0.9 ml HBr (Sigma-Sigma Aldrich) and 0.1 ml

H3PO2 (Sigma-Aldrich) in a 10 ml glass vial. Using a magnetic stir rod, the vial was heated to 393 K in an oil bath[140]. After the precursors are completely dissolved and the solution becomes transparent, the stirring is stopped and the solution was cooled at a rate of 2 K/min, during which crystals are formed. The crystals are collected via filtration and the residual solvent was removed via a vacuum pump. (BA)2(MA)2Pb3Br10 flake samples were prepared using the mechanical exfoliation method with adhesive tape on the as-synthesized crystals and deposited onto a glass slide. To facilitate observation of the perovskite flake using a scanning electron microscope (SEM) while simultaneously allowing for nonlinear transmission measurements, a thin layer of indium tin oxide was deposited via RF

62 magnetron sputtering (K-Lab ITO target, 50 W, 45s deposition time, 5.0 mTorr process pressure) prior to application of the perovskite flake. The flake shown in Figures 5.2 and

5.5, as well as its satellite flakes, were studied in order to observe the interaction of the two incident pulses with a perovskite flake of different thicknesses. SEM revealed that the flake was macroscopically flat outside of step edges (Figure 5.2a). To determine the thickness of the perovskite flake, a 3D laser scanning microscope (3D-LSM) was utilized (Olympus

LEXT OLS5000). The 3D-LSM map (Figure 5.2b) showed that the large flake and its surrounding satellite flakes are divided into three distinct categories (Figure 5.2c) – the majority of the large flake measuring approximately 8-9 um in thickness (region 1), a small region of the large flake measuring between 5.0 and 7.0 um in thickness (region 2), and the thin satellite flakes measuring approximately 1.3 um (region 3). Election diffraction spectroscopy (EDS) measurements were taken using a scanning electron microscope

(Figure 5.3a) to determine whether there are any compositional differences between the regions (Figure 5.3b). The EDS measurements revealed that the flake has uniform composition throughout. Table 5.1 lists the elemental composition of the perovskite flake.

Figure 5.2. (a) Scanning electron microscope (SEM) image of representative (BA)2(MA)2Pb3Br10 flake. (b) 3D Laser-scanning microscope image of representative flake, showing the thickness of the flake. (c) Cross-section of the flake along the arrows drawn in (d).

Figure 5.3. Energy-dispersive Spectroscopy (EDS) of (MA)2(BA)2Pb3Br10 Flake. (a) EDS scan of (MA)2(BA)2Pb3Br10 flake. The EDS image shows that the flake has uniform composition even with at regions with different thickness. (b) EDS spectrum of the flake depicted in (a). Elemental composition of the perovskite flake is shown in Table 5.1.

Table 5.1. EDS Elemental Composition of (MA)2(BA)2Pb3Br10 Flake Element Weight % Atomic % Net Int. Error % K ratio C K 6.14 16.18 16.40 10.38 0.0095 N K 2.22 5.01 6.70 11.09 0.0037 O K 18.56 36.74 174.80 9.18 0.0426 Br L 24.60 9.75 741.50 1.94 0.1958 Si K 25.54 28.80 1128.60 5.64 0.1540 Pb M 22.96 3.51 358.40 2.00 0.1516

The optical measurements were performed using a multiplex coherent anti-Stokes

Raman spectroscopy[127] setup previously described in Chapter Two and shown in Figure

5.4. The pulse powers for the pump and SC pulses used in this experiment were 3.7 mW and 10.3 mW, respectively. For pulse power dependence measurements, a variable neutral density filter is placed in one of the pulse trains before the RELP to attenuate the pulse.

Figure 5.4. Experimental setup for Degenerate Four-wave Mixing of (MA)2(BA)2Pb3Br10. A femtosecond laser (800 nm, 100 fs, 30 nm FWHM) is split into two pulses using a bandpass filter. The narrow, transmitted pulse supplied the 800 nm pulse, while the reflected light pumps a photonic crystal fiber to create the broadband supercontinuum pulse.

Results

The two-photon absorption and four-wave mixing spectra were obtained at various points on the perovskite flake and its surrounding flakes as depicted in the optical image

Figure 5.4a. The three spots chosen in Figure 5.5a correspond to the three distinct regions shown in the 3D-LSM image of Figure 5.2a. The representative spectra shown in Figure

5.4b are characterized by two separate phenomena – a green emission centered at approximately 525 nm with a shoulder at 485 nm and a red emission starting from approximately 650 nm until the cutoff from the short-pass filters (785 nm) that block the incident pulses. The green emission is due to two-photon absorption [140] and the red emission is attributed to FWM (see below). The red emission is characterized by many small peaks in the spectra and the positions of these peaks stays roughly constant as the excitation location is changed. Additional spectra taken at other locations on this flake, as well as locations on other flakes are shown in Figures A.7 and A.8, respectively. The optical image of the perovskite flake and its surrounding satellite flakes can be divided into

65 three areas as shown in the LSM image in Figure 5.2c – one broad area covering the majority of the perovskite sample measuring 8-9 um in thickness (red dot), one small region on the bottom-left corner of the perovskite flake measuring 5-6.4 um in thickness (green dot), and smaller outlying flakes (blue dot) measuring 0.5-1.5 um in thickness – and each area is characterized by the presence of the green emission, the red emission, or both. On the majority of the flake (red region in Figure 5.2c), the red emission (Figure 5.5b) is present and is much larger than the nearly nonexistent green emission, while on the thinner satellite flakes (blue region in Figure 5.2c), only the green emission is visible, with the red emission quenched. Only on the areas with the intermediate thickness (green region in

Figure 5.2c), occupying a small portion on the bottom left and the upper portion of the large flake in Figure 5.5a, is where both the red and green emissions are present. Figures

5.5c and 5.5d show the confocal laser scanning microscopy (CLSM, 405 nm excitation) image of the perovskite flake and its surrounding flakes and the photoluminescence spectra at the three locations depicted in Figure 5.5a. The CLSM spectra also shows a stronger 485 nm peak than the 525 nm peak for the blue and green spots, most likely due to band filling of the 525 nm exciton due to the increased absorption at the 405 nm excitation of the

CLSM[154].

Figure 5.5. (a) Optical microscope image of the (BA)2(MA)2Pb3Br10 flake. Three different locations with different thicknesses are investigated (red: 8.7 µm, green: 5.5 µm, blue: 1.5 µm). (b) Four-wave mixing (FWM, red region), and two-photon absorption (TPA, green region) signal obtained from the locations marked in (a). The TPA signal is visible at the green and blue spots and quenched at the red spot, while the FWM is visible at the red and green spots and quenched at the blue spot. (c) Confocal laser-scanning microscope (CLSM) image of perovskite flake in (a). (d) CLSM spectra at the three locations marked in (a).

Single pulse excitation experiments were performed to investigate the process behind the green and red emissions. These were performed by simply blocking either of the two pulse trains and measuring the resulting spectra (Figure 5.6). The green spot on

Figure 5.5a was chosen due to the easily visible presence of both the green and red signals.

From these measurements, it is evident that the green emission observed is two-photon absorption, as the pump pulse is able to produce the same emission, although at a lower intensity[55, 130]. The contribution from the supercontinuum pulse to the two-photon emission is small. Confocal laser scanning microscopy (CLSM) was performed to study the excitonic emission of the representative flake and its satellite flakes (Figure 5.5c). 67

Similar to the results shown in Figure 5.5b, the CLSM spectra in Figure 5.5d shows that the thin satellite flakes exhibit a stronger photoluminescence emission than that of the larger flake. This is due to the increased linear absorption in optical path that comes with a thicker sample, resulting in a decreased TPA coefficient[130, 165]. Moreover, a thicker sample contains more defect sites which produce more non-radiative recombination pathways for electron-hole pairs, further resulting in reduced photoluminescence. The two- photon absorption peak position (525 nm) indicates that the flake has a bandgap of 2.39 eV which agrees with previous reports[140]. However, the red emission is not observed in either case where one of the two pulse trains are blocked, showing that the red emission is not caused by two-photon absorption. Furthermore, the red emission is only seen when both pulses are on the flake. With either the pump only or the SC only, the red emission is not observed.

Figure 5.6. Dependence of the two-photon absorption (TPA) and four-wave mixing (FWM) emissions on individual pulses. The TPA emission requires only the pump pulse, while the FWM (625-775 nm) emission requires both pulses.

With both pulse trains required to create the red emission observed in Figure 5.5b, power dependence measurements were taken to determine the number of photons of each pulse required to make the red emission. In these measurements, the power of one pulse train is kept constant, while the power of the other pulse is modulated using a variable neutral density filter placed in its path. Temporal and spatial overlap were optimized each time the variable neutral density filter is modulated to ensure maximum resultant signal.

The results of these power dependence measurements are shown in Figure 5.7. The pump power dependence measurement (Figure 5.7a) revealed a quadratic dependence of the resultant signal on the pump power, indicating that the process requires two pump photons.

On the other hand, modulation of the supercontinuum power (Figure 5.7b) showed a linear power dependence, indicating a single supercontinuum photon is used in the process. This confirms that the phenomenon creating the red emission is a third-order, four-wave mixing process.

Figure 5.7. Four-wave mixing (FWM) signal intensity dependence for (a) pump and (b) supercontinuum (SC) pulses at the green location of the (BA)2(MA)2Pb3Br10 flake. The quadratic dependence of the FWM signal on the pump power corresponds to the process requiring two pump photons, while the linear dependence on the SC power indicates a single SC photon is used.

The 3D-LSM scan for sample thickness (Figure 5.2b) and the FWM/TPA emission seen at the three locations depicted in Figure 5.5 indicate that FWM signal intensity increases with sample thickness while the TPA intensity decreases as the thickness increases. On the red spot in Figure 5.5a, with measured thickness 8.7 µm, the FWM/TPA intensity ratio is 555, while on the blue spot (1.5 µm), the FWM/TPA ratio is 0.1. On the green spot (thickness 5.5 µm), where both FWM and TPA are easily visible, the FWM/TPA intensity ratio is 1.7.

Discussion

Based on the 3D-LSM measurements of the perovskite flake thickness (Figure 5.2a) and the increased FWM to TPA intensity ratio of the red region in Figure 5.2b, both the

TPA and the FWM processes are affected by the thickness of the flake. The quenching of the two-photon absorption process as the thickness of the material increases has been previously attributed to the increased presence of defects within the sample[130, 135, 165,

166]. The presence of these defect sites introduces intermediary energy levels between the valence and conduction bands. As a result, when the incident pulses excite an electron from the valence to the conduction band, the rate of nonradiative recombination into these defect states increases. Thus, the characteristic excitonic emission is quenched for thicker samples.

In addition to the quenching of the two-photon absorption process, our results show that the increased presence of the defects in thicker perovskite samples can lead to increased four-wave mixing signal at these defect energy levels. In non-resonant four-wave mixing the energy difference ωp – ωs is only a virtual state; the lifetime of these virtual states is much shorter than that of a vibrational mode (i.e. Raman) or an excitonic resonance

(i.e. TPA) that is intrinsic to the sample. In a thin sample, the presence of a defect site within the laser path is low. As a result, the efficiency of FWM process within the organometallic perovskite is low. However, as the thickness and the number of defects present within the illuminated portion of the sample increases, the energy difference between the pump and supercontinuum pulses becomes resonant with one of the defect states, resulting in a longer-lived state. Because the defect energy state has a longer lifetime than a virtual level, the FWM process is enhanced as more charge carriers are available at the defect energy level (Figure 5.1). Furthermore, as the supercontinuum pulse is a broadband pulse, multiple defect energy levels can be excited, allowing for the determination of multiple defect energy levels with a single measurement, as evidenced by the multiple peaks in the red emission seen in the red region of Figure 5.2b.

Thin film interference, where internal reflections within the flake can cause variations in the spectrum of the SC pulse, was ruled out by comparing the overall shape of the FWM spectra obtained at different locations on the flake but within the same thickness regime. In thin film interference, the layered structure of the perovskite flake can make the flake be viewed as multiple flakes of intermediate size stacked together, which would cause varying interference rates depending on the wavelength of the supercontinuum pulse. These interference effects would then cause large shifts in the shape of the overall resultant spectra even through small translations of the focal point on the flake. However, on examination of the resultant spectra shown in Figures 5.5b and A.7b on the red region with thickness 8-9 um in Figure 5.2a, the shape of the resultant spectra stays relatively constant even with a translation of over 100 um across the flake. This rules out that the

FWM signal is caused by thin film interference and instead is dependent on the intrinsic characteristics of the perovskite flake.

The binding energy of the defect levels present in the sample can be simply derived by calculating the difference in energy between the incident pump pulse (800 nm, 1.55 eV) and the resultant emission spectrum. From the spectra obtained in the red region of Figure

5.2, the observed peaks are shown to be located at 675 (1.84 eV), 690 (1.80 eV), 720 (1.72 eV), and 740 (1.68 eV) nm. In the proposed FWM scheme, the energy values of these defect states would be 0.29 eV, 0.25 eV, 0.17 eV, and 0.13 eV above the valence band or below the conduction band as FWM measures the energy difference. Various donor and acceptor defect levels have been calculated through DFT calculations on the band structure of the perovskite with the presence of defects [143, 145, 146]. Based on previous DFT calculations of MAPbBr3 conducted by Mannodi-Kanakkithodi et al., Shi et al., and Motti et al., the defect energy levels observed in this experiment would correspond to deep defects located in the band between the valence and conduction bands[143, 145, 146].

Table 5.2 lists the possible defects within the crystal structure that would create these calculated defect levels. Of these potential defects, the most stable in terms of formation energy are bolded. Because the energy values correspond so closely to that calculated by previous DFT calculations, the defects seen are most likely attributed to defects in the

MAPbBr3 structure instead of the more stable BAPbBr3n structure[136].

Table 5.2. Measured Defect State Energies and Possible Defects in (BA)2(MA)2Pb3Br10 Wavelength Measured Energy Possible Defect Source 675 nm 0.29 eV Bri(+/-)[145], Pbi(+/2+)[146], PbMA(+/0)[143] 690 nm 0.25 eV VPb(0/2-)[145], VPb(-/2-)[143]

720 nm 0.17 eV VPb(-/2-)[145]

740 nm 0.13 eV VMA(0/-)[143, 146], Bri(0/-)[145]

This method, to our knowledge, is the first to correlate the defect energy levels with the FWM signal produced. This method is capable of measuring the defect levels of a bulk semiconductor while avoiding the high linear absorption that comes with the increased layer count. In fact, the signal intensity of four-wave mixing processes increases linearly with sample thickness, making it more suitable for analysis of bulk crystals. Also, by utilizing two laser pulses, both with photon energies lower than the characteristic bandgap energy, the induced photoluminescence that can disturb nearby defect level measurements is separated from the emission created by the defect levels. Previously, defect level measurement using laser pulses was limited to low temperature studies such as those performed by Zázvorka et al. on CdTe[162] and by Guo et al. and Zhang et al. on perovskites[52, 135]. This method can obtain the defect levels at room temperature by coherently exciting molecules into the defect state and obtaining the defect levels before thermal excitation of the electrons out of the defect states can occur[162].

Acknowledgments

The authors would like to thank the Center for Microscopy and Imaging at Baylor

University for use of their facilities. The authors would also like to thank Olympus

Corporation for use of their 3D laser-scanning microscope.

CHAPTER SIX

Conclusion

Enhanced Four-wave Mixing Process near the Excitonic Resonances of Bulk MoS2

A photoluminescence-like signal from bulk MoS2 was observed via four-wave mixing. Pulse power dependence measurements confirmed the four-wave mixing relation between the broadband SC and the 800 nm pump pulse. The signal arises due to the increased third-order nonlinear susceptibility near excitonic resonances in semiconductors as light-matter interactions cause perturbations in the refractive index at wavelengths near these resonances. From these measurements, a third-order nonlinear susceptibility on the order of 10-19 m2/V2 is calculated, in agreement with other measurements performed previously. This opens the path to using bulk MoS2 for nonlinear optical processes as increasing the layer count quenches the photoluminescence peak while retaining the excitonic resonances that create the photoluminescence. This provides a strong case for resonant Raman enhancement using bulk MoS2.

Multi-pulse Laser-induced Bubble Formation and Nanoparticle Aggregation using MoS2 Nanoparticles

The interaction between MoS2 nanoparticles and ultrafast laser pulses was studied.

Laser-induced aggregation of suspended MoS2 nanosheets in an ethanol solution was observed using two low-power ultrafast pulses – one narrowband pulse centered at 800 nm and a broadband supercontinuum pulse with wavelength from 800 nm to 1000 nm. The pulses induce heating of the surrounding ethanol solvent when a nanoparticle passes

74 through the focal point, creating a bubble. The bubble is then heated by the incident laser pulses to create convection currents that draw nanoparticles towards the bubble. Optical tweezing traps the bubble and nanoparticles into the laser focus, where aggregation occurs.

When the bubble falls off, the aggregate is left behind to be used. The process is dependent on the geometry of the nanoparticles, with only flat nanoflakes producing a bubble and forming an aggregate. This aggregation scheme can be used as an alternative to coinage metals such as gold and silver in nanoparticle aggregation studies for use with sensitive samples.

Resonant Degenerate Four-wave Mixing at the Defect Energy Levels of 2D Hybrid Organic-inorganic Perovskite Crystals

The relation between the thickness of an organometallic perovskite flake, and the increased number of defects within the flake, and the ratio between the two-photon absorption and four-wave mixing signal intensities are measured using temporal and spatially-overlapped pulses – one narrowband pulse at 800 nm and a broadband supercontinuum pulse with wavelength 800-1100 nm. As the thickness of the flake increases, the two-photon absorption process is inhibited by the increased number of defect states within the flake that allow for nonradiative recombination of electron-hole pairs that are excited by the incident pulses. However, the increased number of defects creates real energy levels that are resonant with the pump-supercontinuum energy difference ωp – ωs, resulting in longer lived states. The longer carrier lifetimes result in an increased number of electrons in these decay states, resulting in an increased four-wave mixing signal as the thickness of the flake increases. This four-wave mixing scheme can be used to identify defect energy levels within a semiconductor by using two pulses that are of lower energy

75 than the characteristic band gap, resulting in lower thermal absorption and thus, thermal decomposition of the sample.

APPENDIX

Figure A.1. Four-wave mixing spectra obtained at additional locations from a MoS2 flake. (a) Optical microscope image of MoS2 flake. (b) Four-wave mixing spectra obtained from locations A-C in (a). (c) Four-wave mixing spectra obtained from locations D-F in (a).

Figure A.2. Dependence of four-wave mixing signal on pulse energy. Spectra (solid lines) and fitted peaks (dashed lines) of the MoS2 flake as the power of each pulse is modulated.

Figure A.3. Measured spectrum of the supercontinuum pulse incident on the (a) blue and (b) orange spots in Figure 3.4a. Spectra were obtained by blocking the pump pulse and removing the short-pass filters that block the incident pulses.

Figure A.4. B excitonic resonance of MoS2 at the blue spot of Figure 3.4a. The energy of the B exciton corresponds to a wavelength of approximately 600 nm.

Figure A.5. Additional timeline of cavitation bubble formation and nanoparticle aggregation of MoS2 nanoparticles. Optical camera images captured at different times showing the light-matter interaction between MoS2 nanosheets and two femtosecond laser pulses. Times are relative to initial bubble formation. (a) A nanoparticle (red circle) flows towards the focused spot of the laser (yellow dotted circle). (b) A cavitation bubble is formed when the nanoparticle enters the focus. The bubble is small (~5 µm diameter) and not centered in the focus. (c) The bubble becomes centered in the focus and also becomes defocused from the camera’s focal region. (d) Bubble increases in radius once centered in the focus. (e) Bubble has grown and nanoparticles can be seen on the surface of the bubble. (f) The bubble has fallen away from the focus and the nanoparticle aggregate is left behind. Laser power is 14 mW and 11.2 mW for the supercontinuum and pump pulses, respectively.

Figure A.6. Transmitted supercontinuum intensity through a laser-induced cavitation bubble. Supercontinuum (SC) intensity measurement to detect bubble formation and observe the effects of individual pulses on bubble formation. Laser powers are 26.5 mW and 11.6 mW for the SC and pump pulses, respectively. A decrease in the SC intensity corresponds to the formation and presence of a bubble in the laser path. When the SC pulse is blocked (red region), the bubble falls off, indicated by the increase in SC intensity immediately after the red region. When the pump pulse is blocked (green region), the SC signal is unchanged, though there is a small perturbation in the SC signal intensity.

Figure A.7. Four-wave mixing and two-photon photoluminescence spectra obtained at additional locations of the (MA)2(BA)2Pb3Br10 flake. (a) Optical microscope image of (MA)2(BA)2Pb3Br10 flake. (b) Four-wave mixing spectra obtained at positions A-D marked on (a). (c) Four-wave mixing and two-photon absorption spectra obtained at positions E-G marked on (a). Dotted lines correspond to peak positions in Figure 5.5.

Figure A.8. Four-wave mixing and two-photon absorption spectra from an additional (MA)2(BA)2Pb3Br10 flake. (a) Optical Image with red emission of (MA)2(BA)2Pb3Br10 flake. (b) FWM and single pulse dependence spectra from location depicted in (a).

Movie A.1. Animation of Convection Current Generated via Laser Heating of a Bubble. Video animation showing the travel of MoS2 nanoparticles suspended in an ethanol solution near a laser-induced cavitation bubble. The heating of the cavitation bubble creates differences in surface tension near the surface of the bubble, inducing convection currents that the nanoparticles flow along. Colored circles highlight the nanoparticles and the arrows mark their displacement from the previous frame. Animation is taken over the course of 1.2s at 8 frames/second.

Movie A.2. Animation of MoS2 Nanoparticle Attaching to the Nanoparticle Aggregate. Video animation of Figure 4.4, in which an MoS2 nanoparticle attaches onto the nanoparticle aggregate. The red circle indicates the position of the nanoparticle and the red arrows denote the displacement from the previous frame. Video was taken at 8 frames/second.

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