Photoelectron and photoion spectroscopy of atoms,
nanoparticles, and nanoplasmas irradiated withstrong femtosecond laser fields
byDaniel D. Hickstein
M.Phil, University of Cambridge, 2008
B.A., Pomona College, 2007

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Program in Chemical Physics
2014This thesis entitled:
Photoelectron and photoion spectroscopy of atoms, nanoparticles, and nanoplasmas irradiatedwith strong femtosecond laser fields
written by Daniel D. Hickstein
has been approved for the Program in Chemical Physics

Henry C. Kapteyn

David M. Jonas

Date

The final copy of this thesis has been examined by the signatories, and we find that both thecontent and the form meet acceptable presentation standards of scholarly work in the above
mentioned discipline.

iii
Hickstein, Daniel D. (Ph.D., Chemical Physics)
Photoelectron and photoion spectroscopy of atoms, nanoparticles, and nanoplasmas irradiated withstrong femtosecond laser fields
Thesis directed by Professors Margaret M. Murnane and Henry C. Kapteyn

Modern femtosecond lasers can produce pulses of light that are shorter than the vibrational
periods in molecules and have electric fields stronger than the Coulomb field that binds electronsin atoms. These short-pulse lasers enable the observation of chemical reactions, the productionof attosecond bursts of high-energy photons, and the precision-machining of solid materials withminimal heat transport to the material. In this thesis, I describe three experiments that provide new
insight into strong-field (∼1014 Watts/cm2 ) femtosecond laser-matter interactions in three important
regimes. First, I discuss the strong-field ionization of gas-phase atoms, identify a new structure in
the photoelectron angular distribution of xenon gas, and explain this structure by developing an
intuitive wave interference model. Second, I describe a new method to perform photoelectron andphotoion spectroscopy on single, isolated nanoparticles and demonstrate this technique by observing
the directional ion ejection that takes place in the laser ablation of nanostructures. Finally, I
present the first experimental observations of shock wave propagation in nanoscale plasmas. Thesefindings will guide future efforts to probe the structure and dynamics of atoms and molecules on
the femtosecond timescale, design nanomaterials that enhance light on the subwavelength scale, andproduce high-energy ions from plasmas.

Acknowledgements

The work in this thesis would not have been possible if it were not for the assistance of many,
many people. My heartfelt thanks goes
• To the best family ever: my parents, Mary and Dennis, and my brother, Matt.
• To Laura Johnson for her love and support.
• To Margaret Murnane and Henry Kapteyn for being the best advisors anyone could ask for.
• To my mentors in the Kapteyn–Murnane Group, especially Predrag Ranitovic, Xibin Zhou, andWei Xiong.
• To Curtis Stevens, Katie Johnson, and Daisy Johnson for their support and company on the trails.
• To my labmates in the KM Group, past and present, especially Jennifer Ellis, Franklin Dollar,
Chengyuan Ding, Paul Arpin, Matt Seaberg, Dan Adams, Tenio Popmintchev, Tory Carr, Craig
Hogle, Ellen Keister, Robynne Lock, Chris Mancuso, Bosheng Zhang, Tingting Fan, Ming-Chang
Chen, Bill Peters, Patrik Grychtol, Michael Gerrity, Wen Li, Chan La-o-vorakiat, Stefan Witte,and Stefan Mathias.
• To the staff of the JILA Instrument Shop, who do the impossible nearly every day, especiallyHans Green, David Alchenberger, Blaine Horner, Kim Hagen, Ariel Paul, Todd Asnicar, and Kels
Detra.
• To the JILA Computing Team, especially J. R. Raith, who magically make dealing with a room
full of angry Windows computers tolerable.

v• To Brad Baxley for his beautiful illustrations that are scattered throughout this thesis.
• To our talented collaborators, who made this work possible, especially Kyle Schnitzenbaumer,
Molly Wilker, Gordana Dukovic, Brett Palm, Jose Jimenez, Pedro Campuzano–Jost, Jim Gaffney,Mark Foord, Steve Libby, Ymkje Huismans, Marc Vrakking, Xiao-Min Tong, Ofer Kfir, Oren
Cohen, Avner Fleischer, Luis Miaja-Avila, Carlos Hernandez-Garcia, Andreas Becker, and George
Petrov.
• To Mikhail Ryazanov and Hanna Reisler at USC for their help with the BASEX Abel transform.
• To our wonderful undergraduate students: Robbie Wright, Jennifer Li, Ethan Scott, Maithreyi
Gopalakrishnan, and Leigh Martin.
• To the staff at KMLabs who were always quick to provide advice and assistance, especially Xiaoshi
Zhang, Mike Walls, Daisy Raymondson, Neil Anderson, and Sterling Backus.
• To professors David Jonas, Agnieszka Jaron-Becker, Ralph Jimenez, W. Carl Lineberger, forserving on my thesis committee and for their help and advice throughout my years at JILA.
• To the professors at Pomona College that inspired me to pursue a PhD: Dan O’Leary, Wayne
Steinmetz, and Alfred Kwok.
• To my previous research mentors, who taught me how to work in a lab: Jacqui Cole (Cambridge),
Dan O’Leary (Pomona College), Liz Donley (NIST), Brant Weinstein (NICHD), and Paul Liu(NHGRI).
• To Jason Haas, Hillary Smith, and Julie Phillips, for teaching me how to write.

Contents

1 Introduction
1.1

1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.1

Seeing the invisible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1.2

Femtosecond lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.1.3

The velocity map imaging (VMI) spectrometer . . . . . . . . . . . . . . . . .

3

1.1.4

Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4Electron dynamics in strong femtosecond laser fields . . . . . . . . . . . . . . . . . .

7

1.2.1

The three step model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

1.2.2

Strong field ionization with mid-IR fields . . . . . . . . . . . . . . . . . . . .

9

1.3

Localized light absorption in nanoparticles . . . . . . . . . . . . . . . . . . . . . . . .

10

1.4

Shock waves in nanoplasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

1.2

Motivation

2 Apparatus and methods

12

2.1

Experimental summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.2

Femtosecond laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.2.1

Chirped pulse amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.2.2

Light sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.2.3

Optical parametric amplifier (OPA) . . . . . . . . . . . . . . . . . . . . . . .

14

2.2.4

Delay line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

Velocity map imaging spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

2.3

vii

2.4

2.3.1

Concept and history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

2.3.2

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

2.3.3

Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

2.3.4

Abel transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

Nanoparticle aerosol source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

2.4.1

Atomizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

2.4.2

Electrostatic classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

2.4.3

Aerodynamic lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

2.4.4

Light scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

2.4.5

Single particle experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

3 Electron dynamics in strong field ionization

30

3.1

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

3.2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

3.2.1

Zeptosecond waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

3.2.2

HHG and SFI in the mid-IR. . . . . . . . . . . . . . . . . . . . . . . . . . .

32

3.3

Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

3.4

Photoelectron angular distributions from UV to mid-IR . . . . . . . . . . . . . . . .

35

3.5

Plane-spherical wave model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

3.6

Inner spider structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

3.7

Measurement of the quantum tunnel distance . . . . . . . . . . . . . . . . . . . . . .

42

3.8

Conclusion

43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Plasma Explosion Imaging

45

4.1

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

4.2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

4.2.1

Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

4.2.2

Experimental approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

viii
4.2.3

Summary of findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

4.3.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

4.3.2

Electron microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

4.3.3

Photoion spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

Case studies of nanoscale light enhancement . . . . . . . . . . . . . . . . . . . . . . .

57

4.4.1

NaCl crystals: nanofocusing in dielectric nanomaterials . . . . . . . . . . . .

57

4.4.2

TiO2 nanoclusters: light interaction with a particle ensemble . . . . . . . . .

58

4.4.3

50 nm gold nanoparticles: field enhancement at the surface . . . . . . . . . .

59

4.4.4

17 nm gold nanospheres: asymmetric hot-spots . . . . . . . . . . . . . . . . .

60

4.5

Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

4.6

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

4.3

4.4

5 Shock Waves in Nanoplasma

62

5.1

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

5.2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

5.3

Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

5.4

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

5.5

Hydrodynamic Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

5.6

Conclusion

71. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Conclusion and outlook

72

6.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

6.2

Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

6.2.1

Strong-field ionization of gas-phase atoms and molecules . . . . . . . . . . . .

72

6.2.2

Plasma Explosion Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

6.2.3

Shock waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

6.3

ix

6.4

6.3.1

Extreme ultraviolet probe of nanomaterials . . . . . . . . . . . . . . . . . . .

76

6.3.2

Magnetron sputtering nanoparticle source . . . . . . . . . . . . . . . . . . . .

77

Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A Multiple Scattering Structures Appendix

79

81

A.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

A.2 Details of the Plane-Spherical Wave Model . . . . . . . . . . . . . . . . . . . . . . .

81

A.3 Calculating the modulation frequency . . . . . . . . . . . . . . . . . . . . . . . . . .

83

A.4 Extracting the experimental multiple rescattering cutoff . . . . . . . . . . . . . . . .

85

A.5 Intensity dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

B Plasma Explosion Imaging Appendix

89

B.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

B.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

B.2.1 Photoion spectroscopy and aerosol generation . . . . . . . . . . . . . . . . . .

89

B.2.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

B.2.3 Transmission electron microscopy . . . . . . . . . . . . . . . . . . . . . . . . .

90

B.2.4 Finite-difference time-domain (FDTD) simulations . . . . . . . . . . . . . . .

91

B.3 Photoelectron Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

B.4 Plasma Explosion Mass Spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . .

93

B.4.1 Mass spectrum of a single nanoparticle . . . . . . . . . . . . . . . . . . . . . .

93

B.4.2 Time-of-flight experimental details . . . . . . . . . . . . . . . . . . . . . . . .

94

C Shock Waves in Nanoplasmas Appendix

96

C.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

C.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

C.3 Dependence of shock formation on particle size . . . . . . . . . . . . . . . . . . . . .

98

C.4 Effect of laser intensity on nanoplasma formation . . . . . . . . . . . . . . . . . . . .

99

x
C.5 Time-dependence of shock formation rate . . . . . . . . . . . . . . . . . . . . . . . . 101
C.6 Hydrodynamic simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
C.7 Plasma quasi-neutrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

References

107Figures

1.1

Edgerton’s “Bullet Through Apple” . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.2

Various sizes of CdSe quantum dots . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.3

The three-step model of high harmonic generation (HHG) . . . . . . . . . . . . . . .

8

2.1

Femtosecond light sources from the UV to the mid-IR. . . . . . . . . . . . . . . . . .

15

2.2

A typical femtosecond pump-probe experiment . . . . . . . . . . . . . . . . . . . . .

16

2.3

Schematic of the velocity map imaging (VMI) spectrometer . . . . . . . . . . . . . .

19

2.4

Photograph of the VMI electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

2.5

Alignment of the gas jet to the skimmer . . . . . . . . . . . . . . . . . . . . . . . . .

22

2.6

The atomizer and differential mobility analyzer (DMA) . . . . . . . . . . . . . . . .

26

2.7

The aerodynamic lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

3.1

Illustration of photoelectron rescattering . . . . . . . . . . . . . . . . . . . . . . . . .

30

3.2

Summary of multiple rescattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

3.3

The plane-spherical wave (PSW) model . . . . . . . . . . . . . . . . . . . . . . . . .

36

3.4

Comparison of experiment, simulations, and simple PSW theory . . . . . . . . . . .

37

3.5

Multiple scattering of the electron with the ion . . . . . . . . . . . . . . . . . . . . .

40

3.6

Measurement of the quantum tunnel distance . . . . . . . . . . . . . . . . . . . . . .

43

4.1

Illustration of plasma explosion imaging (PEI) in a single nanoparticle . . . . . . . .

45

4.2

Summary of PEI in four nanostructures . . . . . . . . . . . . . . . . . . . . . . . . .

47

4.3

Apparatus for PEI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

xii
4.4

Electron microscopy of nanoparticles collected at the interaction region. . . . . . .

52

4.5

Photoion angular distributions (PADs) from individual nanostructures . . . . . . . .

55

4.6

Position of the centers of mass of the PADs . . . . . . . . . . . . . . . . . . . . . . .

56

4.7

Finite-difference time-domain (FDTD) simulations . . . . . . . . . . . . . . . . . . .

57

4.8

Summary of nanoscale light absorption revealed through PEI . . . . . . . . . . . . .

61

5.1

Illustration of laser-driven shock wave in a nanoplasma . . . . . . . . . . . . . . . . .

62

5.2

Apparatus for imaging shock waves in individual nanoplasmas . . . . . . . . . . . . .

65

5.3

Experimental observation of shock waves in individual nanoplasmas . . . . . . . . .

66

5.4

Control of shock wave formation using two laser pulses . . . . . . . . . . . . . . . . .

68

5.5

Mechanism for shock formation, revealed by hydrodynamic simulations . . . . . . . .

70

6.1

Photoelectrons from circularly polarized driving lasers . . . . . . . . . . . . . . . . .

74

6.2

Schematic of the NanoGen50. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

A.1 Electron trajectories that produce interference structures. . . . . . . . . . . . . . . .

84

A.2 Procedure for determining the inner-spider cutoff . . . . . . . . . . . . . . . . . . . .

86

A.3 The positions of the inner-spider cutoffs. . . . . . . . . . . . . . . . . . . . . . . . . .

87

A.4 Effect of the laser intensity on inner spider structures . . . . . . . . . . . . . . . . . .

88

B.1 Comparison of photoelectron and photoion distributions from single nanoparticles .

93

B.2 Mass spectrum of a single nanoparticle explosion . . . . . . . . . . . . . . . . . . . .

95

C.1 Nanoplasma explosions of NaCl nanoparticles with a single pulse. . . . . . . . . . . .

98

C.2 Effect of particle diameter of the formation of shock waves. . . . . . . . . . . . . . .

99

C.3 Ion yield and shock wave formation versus laser intensity. . . . . . . . . . . . . . . . 100
C.4 The fraction of ions in the shock controlled with two-pulse delay. . . . . . . . . . . . 101
C.5 HYDRA simulations at various two-pulse delays. . . . . . . . . . . . . . . . . . . . . 102
C.6 Scaling of the shock with laser intensity using HYDRA. . . . . . . . . . . . . . . . . 103

List of Abbreviations

ATI

Above Threshold Ionization

ADK

Ammosov, Delone, and Krainov [1] – an estimate of tunnel ionization rates

BBO

Beta Barium Borate – a nonlinear crystal

CCD

Charge-Coupled Device – the type of sensor in many digital cameras

CoM

Center of Mass

CPA

Chirped Pulse Amplification

DMA

Differential Mobility Analyzer - A device that produces a size-selected aerosol

EUV

Extreme Ultraviolet (light)

eVElectron Volt - unit of energy, 1 eV ≈ 1.602 × 10−19 J

FDTD

Finite-Difference Time-Domain – a simulation method

HHG

High-Harmonic Generation – a method for producing EUV and SXR light

HYDRA

A radiation hydrodynamic code developed at Livermore National Lab

IR

Infrared (light)

JILA

The Institute formerly known as the Joint Institute for Laboratory Astrophysics

MCP

Microchannel Plate – a detector of electrons, ions, and photons

OPA

Optical Parametric Amplifier

PAD

Photoelectron (or Photoion) Angular Distribution

PEI

Plasma Explosion Imaging

PES

Photoelectron Spectroscopy

psig

pounds per square inch gauge – a unit of pressure in excess of atmospheric pressure

ii
PSW

Plane Spherical Wave – a model for SFI presented in this thesis

PVP

Polyvinylpyrrolidone – an organic compound

SFI

Strong Field Ionization

SXR

Soft X-ray

TDSE

Time-Dependent Schrödinger Equation

ToF

Time of Flight

UV

Ultraviolet

VMI

Velocity Map Imaging

VMIS

Velocity Map Imaging Spectrometer

Thesis Outline

This thesis describes three studies, each based on a different publication, and each presented
in a separate chapter:• Chapter 3 is based on a 2012 Physical Review Letter [2] titled “Direct Visualization of LaserDriven Electron Multiple Scattering and Tunneling Distance in Strong-Field Ionization” anddescribes the strong-field ionization of atomic gases using femtosecond laser pulses ranging
from 262 to 2000 nm. Additional information is presented in Appendix A.
• Chapter 4 is based on a 2014 ACS Nano Article [3] titled “Mapping Nanoscale Absorption of
Femtosecond Laser Pulses using Plasma Explosion Imaging” and discusses how strong laser
pulses can induce a directional ion ejection in nanostructures, revealing the absorption of
femtoseond pulses on the nanometer scale. Additional information presented in Appendix B.
• Chapter 5 is based on a 2014 Physical Review Letter [4] titled “Observation and Control of
Shock Waves in Individual Nanoplasmas” and presents an experiment where two laser pulses
are used to convert a nanoparticle into a rapidly expanding nanoplasma and subsequently
drive a shock wave through the expanding nanoplasma. Additional information is presented
in Appendix C.

The introduction (Chapter 1) provides a general motivation for femtosecond laser science andnanoscience (Section 1.1) and a brief motivation for each study (Sections 1.2, 1.3, and 1.4). Chapter 2
provides a detailed discussion of the apparatus and techniques used in this thesis, describing the
femtosecond laser systems (Section 2.2), the Velocity Map Imaging Spectrometer (Section 2.3), andiv
the nanoparticle aerosol source (Section 2.4). After the studies presented in Chapters 3, 4, and5, Chapter 6 provides a brief synopsis of the findings and presents ideas for future experimentsthat build upon the developments made in this Thesis. Appendices A, B, and C present additional
information relating to Chapters 3, 4, and 5 respectively.

Additional works
In addition to the works highlighted in this thesis, the author was a co-author on the following
studies that will be covered in the theses of other JILA graduate students.
• A complete description of the 2013 Nano Letter [5] titled “Photoelectron Spectroscopy of
CdSe Nanocrystals in the Gas Phase: A Direct Measure of the Evanescent Electron Wave
Function of Quantum Dots” will be presented in the thesis of Jennifer Ellis.
• A complete description of a submitted paper [6] titled “Strong Field Ionization Tomography
with Two-color Circularly Polarized Femtosecond Laser Fields” will be presented in thethesis of Chris Mancuso.
• A complete description of a submitted paper [7] titled “Electron transfer dynamics in gasphase and solvated quantum dots” will be presented in the thesis of Jennifer Ellis.
• A complete description of a forthcoming paper titled “Extreme ultraviolet photoelectron
spectroscopy of nanoparticles” will be presented in the thesis of Jennifer Ellis.

Copyright
All images, figures, and illustrations are the work of the author unless otherwise noted. Text
and figures are Copyright 2014 Daniel Hickstein unless noted.

Chapter 1

Introduction

1.1

Motivation

1.1.1

Seeing the invisible

One goal of science is to take things that are invisible to human perception and make themvisible. This takes many forms, from using statistics to “see” the evolution of genetic diseases
across many generations, to using an electron microscope to inspect the nanometer-scale (10−9 m)
structures that provide the color of a butterfly wing [8]. Objects and phenomena can be “invisible”
to human perception for many different reasons. For example, the object may be too small to see
with the naked eye, or it may be too large to observe all at once. Alternatively, a process may bedifficult to observe because it occurs on a timescale much longer than a human lifetime, or takes
place in a split second. The use of new technology to observe such otherwise invisible phenomena
allows for breakthroughs in our understanding.
A particularly striking example of how scientists use technological advances to visualize thenatural world in revolutionary ways is the work of Harold Edgerton in the 1930s through the 1960s.
Among numerous innovations, Edgerton pioneered the use of the xenon flashlamp for high-speed
photography. The xenon flashlamp provides bursts of light lasting only 1 microsecond (µs), several
orders of magnitude faster than the fastest mechanical shutter. Since a rifle bullet only travels∼1 mm per µs, this flashlamp allowed Edgerton to take photographs of speeding bullets impacting
various objects as if they were motionless (Figure 1.1).

2

Figure 1.1: Edgerton’s iconic 1964 photograph “Bullet Through Apple” [9]. Using a
carefully timed xenon flashlamp in a completely dark room, Harold Edgerton was able to photographa rifle bullet passing through and apple with microsecond time resolution. c 2010 MIT. Courtesyof MIT Museum

1.1.2

Femtosecond lasers

Femtosecond lasers generate bursts of light with durations on the timescale of a few 10s of femtoseconds (1 fs = 10−15 s). Thus, they allow for the examination of processes that are ∼100,000,000
times shorter than those that can be resolved using the xenon flashlamp that produced the “Bullet
Through Apple” photograph. Light moves only ∼300 nm per fs, meaning that even an object moving
at the speed of light would be blurred by only 3 µm when photographed using a 10 fs pulse froma femtosecond laser.1 Thus, a femtosecond laser allows any macroscopic object to be photographedwith negligible motion blur, even if it is moving extremely fast. Indeed, the speed of light implies
that the only processes that can fully utilize the impressive time resolution of a femtosecond laser
pulse occur on the nanometer length scale or smaller. For example, a carbon–oxygen single-bond(∼145 pm) has a vibrational stretching period of ∼30 fs, indicating that femtosecond lasers can beused to study chemical reactions on a timescale comparable to the movements of nuclei. Electrons
1 Of course, this ignores relativistic effects.

3(being less massive than nuclei) can move somewhat faster, but electron motion on the nanometerscale is another phenomena that can now be observed with femtosecond laser pulses.
Because a femtosecond laser produces light in such short bursts, the light field can also be
extremely intense, allowing unusual regimes of laser-matter interactions to be studied using table-top
scale devices. When focused, a 40 fs pulse from an amplified titanium-doped sapphire (Ti:sapphire)laser can easily reach intensities in excess of 1014 W/cm2 , an intensity regime where the electric fieldof the laser pulse becomes comparable to the Coulomb field binding electrons to atoms. These intense
femtosecond laser pulses enable fascinating and useful phenomena on the nanoscale. For instance,electrons can be ripped from atoms, accelerated in the laser field, and returned to the atom to createhigh-energy photons in a process called high harmonic generation (HHG, Section 1.2.1) [10–12]. In
addition, high-density plasmas may be generated on the timescale of only a few femtoseconds. This
thesis focuses on finding new methods to use femtosecond lasers to study the motion of electrons
and nuclei that take place when intense femtosecond laser fields irradiate atoms, nanoparticles, andnanoplasmas.

1.1.3

The velocity map imaging (VMI) spectrometer

Unfortunately, one cannot simply take a photograph of objects on the nanometer or picometerscale (see Section 1.3). In order to observe electron and chemical dynamics in materials, we utilizea velocity-map imaging (VMI) spectrometer, a device that detects the momentum of the electrons
and ions that are generated when a laser pulse irradiates an atom, molecule, or nanoparticle. The
VMI spectrometer was developed nearly 20 years ago and has proven itself as a straightforward, yethighly flexible, tool for observing both chemical and electronic structure. The VMI spectrometer canrecord the complete momentum distribution of either photoelectrons or photoions, which provides
the flexibility to study a wide range of processes, including the attosecond dynamics of electrons
driven by a strong laser field (Chapter 3), ion ejection in laser-ablated nanoparticles (Chapter 4), andthe picosecond dynamics of shock waves propagating through a dense laser-produced nanoplasma(Chapter 5).

4
Though the VMI spectrometer can now be considered a mature technology, the field has been
re-invigorated by utilizing new light sources and new samples. This thesis presents three different examples of how combining femtosecond light sources and nanostructured targets with a VMI
spectrometer led to new observations. First (Chapter 3), we record the photoelectron spectra fromatoms and molecules using strong-field femtosecond lasers with wavelengths ranging from 266 nm
to 2000 nm. While each of these wavelengths has been explored individually in the VMI, this constitutes the first efforts to systematically study the effects of strong laser fields across such a large
wavelength range. Second, we replace the typical gas-jet source with a nanoparticle aerosol sourcethat can inject high-concentration nanoparticles into the interaction region of the VMI spectrometer
while minimizing the amount of background gas present. This technique allows us to study the
directionality in ion ejection from nanoparticles of different compositions and morphologies (Chapter 4). Third, we use the VMI to explore the regime of single, expanding nanoplasmas (Chapter 5)
by using one femtosecond laser pulse to transform a nanoparticle into a nanoplasma and a second
laser pulse to drive shock waves through the nanoplasma.

1.1.4
1.1.4.1

Nanoparticles
Nanomaterials: a frontier of science and technology

Historically, technologies have existed to observe matter on the scale of bulk materials as wellas on the scale of atoms and molecules. However, the nanometer scale has remained largely elusive
to measurement and manipulation until recently, where technological advances have made it possible
to observe and fabricate materials on the nanometer scale. The nanoscale is especially interesting,because this is where materials undergo the transition from atomic- or molecular-like properties tobulk-like properties, a regime that is not completely understood and currently represents a frontierof science. Often, the properties of nanomaterials are somewhere between the properties of theconstituent atoms and the bulk material, but frequently the nanomaterials exhibit properties thatare entirely unexpected – and potentially very useful!
For example, a macroscopic sphere of gold has the usual color and luster that we expect from a5
piece of bulk gold. However, a solution of 50-nm diameter gold spheres suspended in water is not goldcolored, but instead appears a deep blood-red color. In a more spectacular example, nanocrystalsof semiconductor materials (quantum dots or QDs) fluoresce vivid colors under ultraviolet illumination and the color of the fluorescence can be tuned, simply by varying the size of the nanoparticles(Figure 1.2), which is easily achieved during synthesis. Their unusual properties have made nanomaterials prime candidates to enable breakthrough technologies as diverse as inexpensive photovoltaic
panels, cancer treatments, and efficient catalysts.

Figure 1.2: Cadmium selenide quantum dots (CdSe QDs). (left) Each vial contains the samechemical composition (CdSe QDs and toluene), but the different sizes cause the nanocrystals to
fluoresce different colors. The bandgap increases with decreasing particle size, so the vials on theleft contain the smallest QDs (largest bandgap) and the vials on the right contain the largest QDs(smallest bandgap). Image courtesy of NN-Labs Inc. (right) An illustration of CdSe quantum dotsshows the individual atoms clustered into faceted nanocrystals.

1.1.4.2

Nanoparticles in vacuum

Motivated by the unusual (and, in many cases, unexplained) properties and numerous applications of nanomaterials, there is a pressing need for spectroscopies that probe the fundamental
physics of nanoparticles and nanostructures. However, almost all previous studies on nanoparticles
have been conducted on nanoparticles that are in close physical contact with other materials, such as
nanoparticles suspended in a liquid solvent, nanoparticles embedded in a bulk material, or nanoparticles attached to a surface. All such studies face the fundamental limitation that any observed
effect cannot be unambiguously attributed to the nanoparticle itself, since it could be a result of
the interaction between the nanoparticle and the solvent/substrate/surface. Most of these exper-6
iments also study the same nanoparticles over a long period of time (multiple laser shots), so theparticles may become damaged, charged, or stuck in a long-lived excited state. Most importantly,
studying nanoparticles that are in contact with other materials prevents the use of many powerfulspectroscopies that can only take place with isolated particles in high-vacuum conditions, such as
photoelectron spectroscopy and photoion spectroscopy.
One notable exception to this generalization is a handful of pioneering efforts that have usedphotoemission spectroscopy to study QDs attached to metal surfaces [13–15]. While these studies
have produced valuable insights into the electronic structure and dynamics of QDs, they are fundamentally limited in that they must always ensure good electronic contact between the nanoparticle
and the metal substrate in order to return electrons to the nanoparticle to counteract the charging
that takes place through the photoionization process. When there is good electrical contact between
the nanoparticle and the surface, the electronic wavefunction of the nanoparticle is likely distorted
from its original state and the measurement cannot be interpreted as a faithful representation of the
intrinsic wavefunction of the nanoparticle.
In contrast to previous efforts, we study “gas phase” nanoparticles that are isolated in vacuum.
It may be argued that these studies are not relevant to the practical applications of nanoparticles,
which involve nanoparticles that are embedded in bulk materials, attached to a surface, or suspended
in a liquid. However, the motivation for studying nanoparticles in the gas phase is to gain an understanding of the fundamental properties of the particles and how those properties can be accurately
calculated using theoretical models. Just as studying molecules in the gas-phase provided the benchmark for the computational chemistry methods that have, in turn, revolutionized our understandingof chemical reactions in solution, it is possible that the study of nanoparticles in vacuum will provide
similar benchmarks for theoretical methods that simulate properties on the nanoscale. In addition,by comparing how the properties of nanoparticles change as they are moved from the gas-phase to
the condensed phase, we can gain insight into one of the most important topics in nano-science: hownanomaterials interact with their environment.
In order to investigate the inherent (unperturbed) electronic structure of nanomaterials, we7choose to work with a collimated beam of isolated nanoparticles that are flying through a highvacuum chamber. Fortunately, many years ago, researchers in the field of atmospheric science
had the same desire to study sub-micron aerosol particles in the absence of carrier gas.2 Thesescientists designed an “aerodynamic lens,” a tube containing several small orifices, that “focuses”
a nanoparticle aerosol, forming a collimated beam of nanoparticles, while leaving the carrier gas
divergent, enabling the separation of the nanoparticles from the gas. Thus, through an unusual
combination of techniques and apparatus borrowed from physical chemistry (the VMI spectrometer),
optical physics (femtosecond laser pulses), and atmospheric science (the aerodynamic lens), we havemade some of the first measurements of the femtosecond dynamics of isolated nanoparticles.

1.2

Electron dynamics in strong femtosecond laser fields

This section provides a broad picture of the motivations for the study of strong-field ionization(SFI) using UV through mid-IR lasers presented in Chapter 3.

1.2.1

The three step model

The interaction of strong laser fields (∼1014 W/cm2 ) with atoms and molecules is of greatscientific and technological interest because of two related phenomena: high-harmonic generation(HHG) [10] and strong field ionization (SFI) [16]. HHG makes it possible to use tabletop lasers togenerate coherent beams of extreme ultraviolet (EUV) and soft X-ray (SXR) light, [11, 12, 17–19]
and it has found applications across a broad range of science. For example, HHG makes it possible
to observe chemical reactions in real time [20–22], to uncover correlated thermal [23] and magnetic
dynamics [24] in materials with elemental specificity, and for coherent imaging on the nanometerscale near the wavelength limit [25, 26]. Similarly, recent studies have revealed that the photoelectron
distribution from SFI records information about molecular structure [27–29], suggesting that it may
serve as a new technique for understanding molecular dynamics. Both HHG and SFI result fromtunnel-ionization of an electron from an atom or molecule (Figure 1.3). The free electron is then2 Interestingly, these efforts also used photoion spectroscopy techniques, though not with femtosecond lasers or
angle-resolved detectors.

8
accelerated to high velocities in the laser field [30]. HHG occurs when the electrons that are driven
back towards the parent ion by the laser field recombine radiatively with the parent ion, emitting
high-energy photons. SFI corresponds to those electrons that do not recombine; however, they may
still re-encounter their parent ion and scatter.

Step 1: Tunnel ionization
Electron energy
Coulomb+laser

Energy (eV)40

Step 2: Propagation

Step 3: Recombination

40

40

20

20

0

0

0

20

20

20

40

40

40

20

1

0

1

Distance (nm)

2

1

0

1

Distance (nm)

2

1

0

1

Distance (nm)2

Figure 1.3: The semi-classical three-step model of high harmonic generation (HHG).
The blue line shows the combined energy of the laser and Coulomb potential, which is changing
as a function of time. The green line shows the total energy of the electron (kinetic energy plus
potential energy of the laser field) plotted as a function of the distance from the ion. (a) In thepresence of a strong laser field (in this case 1 × 1014 W/cm2 ), the Coulomb potential of an atom (ormolecule) is strongly deformed. Under these conditions, a valence electron can tunnel through thebarrier and emerge into the continuum (Step 1). (b) In Step 2, the free electron is now driven by thelaser field, first away from the ion and then (depending on the phase of the field when the electron
tunnels) driven back towards the ion. (c) In Step 3, the electron recombines with the ion emitting
a high-energy photon. In the case of strong-field ionization (SFI), the electron does not recombine,
but can scatter from the ion.

This semi-classical model of tunnel ionization, propagation in the laser field, and recombination with the ion is known as the “three-step model”. The three-step model ignores the Coulomb
potential during the propagation of the electron and only includes the Coulomb potential during
the recombination/rescattering step. Consequently, the three-step model is more accurate in cases
where the electron are driven a long distance from the ion, making the influence of the Coulomb
potential on the propagation of the electron negligible.

9
1.2.2

Strong field ionization with mid-IR fields

The three-step model makes an important prediction about HHG: the highest possible (cutoff)photon energy (Ecutoff ) scales with the ponderomotive potential (Up ) as [30]
Ecutoff ≈ 3.2Up + Ip ,(1.1)

where Ip is the ionization potential of the atom (or molecule) and the pondermotive potential isgiven by [31]:Up =e2 E 2=4me ω 2



9.337 × 10−14eV(W/cm2 )(µm)



Iλ2 ,

(1.2)

where e is the electron charge, E is the laser electric field, me is the electron mass, w is the angularfrequency of the laser, I is the intensity of the laser (in W/cm2 ), λ is the wavelength of the laser (inµm), and Up is in terms of eV.
The important practical implication of Equations 1.1 and 1.2 is that the cutoff energy of highharmonic generation can be increased either by increasing the laser intensity or increasing the laser
wavelength. In practice, a critical ionization level of the gas cannot be exceeded without a severe lossof conversion efficiency, and so the laser intensity cannot be increased past a certain level [12]. Thus,
the only available method for scaling HHG to higher photon energies is to use longer wavelength
driving lasers. Indeed, recent experiments have demonstrated that driving lasers in the mid-IR cangenerate photon energies past 1 keV [19] and that driving lasers with wavelengths of 2.0 µm or
longer can easily generate isolated attosecond pulses [32]. However, the mechanisms of HHG in the
mid-infrared region are not fully understood.
SFI is the “sister process” to HHG, since it corresponds to electrons that tunnel ionize in thesame manner and are driven in the same strong laser field, but do not recombine with the atom
or molecule. Historically, a careful analysis of SFI has built the foundation for understanding the
HHG process. In Chapter 3, we continue this tradition, by observing structures in the photoelectron
angular distributions using mid-IR driving lasers. These structures correspond to the multiple
rescattering of field-driven electrons with the ion, a process that has recently been suggested as apossible avenue for generating zeptosecond waveforms [33].

10

1.3

Localized light absorption in nanoparticles

This section provides the broad motivations for the study of Plasma Explosion Imaging (PEI)
presented in Chapter 4.
The ability to focus light tightly is immensely useful, enabling numerous innovations in scienceand technology, including high-resolution microscopy, spectroscopy of small objects, and precisionlaser-machining. Considering the wide-ranging applications of a small focus, it is not surprising thatan incredible amount of effort has been expended to manufacture lenses that minimize aberrations
and laser light sources that exhibit good mode quality. However, there is a fundamental lower limit
to the diameter of the focus (d) that can be achieved:d=

λ,2n sin θ(1.3)

where λ is the wavelength of the light, θ is the half-angle of the lens, and n is the index of refractionof the medium. Equation 1.3 serves as a limit for how localized a certain wavelength of light can be.
Unless, of course, you cheat.
Equation 1.3 applies for lenses and curved mirrors which attempt to focus light at a distance, but
nanoparticles can be used to “cheat” this limitation by locally enhancing the light field, sometimes
by many orders of magnitude. The most famous example of this enhancement is probably the strong
enhancement of the electric field that takes place at the surface of metal nanoparticles and allows
the surface enhanced Raman spectroscopy technique (SERS) to evaluate the Raman spectrum of
single molecules [34, 35]. More recent studies have successfully utilized the subwavelength focusing of“photonic nanojets” that form behind transparent nanospheres irradiated with laser light to machine
features on the sub-wavelengths scale [36]. However, despite the numerous applications of local-fieldenhancement in nanostructures, there are no techniques to evaluate the local field enhancementthat takes place when an intense femtosecond laser pulse irradiates a single, isolated nanostructure.
Chapter 4 presents the development of a high-repetition-rate technique capable of observing the
local field enhancement that takes place in a range of different nanostructures.

11

1.4

Shock waves in nanoplasmas

This section provides the motivations for the study of shock waves in nanoplasmas presented
in Chapter 5.
When an intense (>1014 W/cm2 ) femtosecond laser pulse is focused into a material, the material
is rapidly converted into a plasma and high energy electrons, ions, and electrons are ejected. This
is not only useful as a way to study an extreme state of matter using tabletop scale apparatus, but
can also serve as a source of high-energy electrons, ions, and photons. The energy of the emitted
photons and particles depends on how much of the laser energy can be transferred into the material
and how confined the interaction can be made. In order to generate the highest energy interaction,
the majority of the laser energy must be coupled into a very small area. This sounds straightforward,
but it is not. For example, gas targets are not appropriate because they are not dense enough toabsorb the laser light in a small area. Solid surfaces also present a problem, because they are quickly
converted to a plasma, at which point they become metallic and reflect most of the laser pulse.
Nanoplasmas, which are formed by laser-irradiating isolated nanoparticles, can serve as theperfect solution, since they are both highly absorbing of laser light [37] and can localize that lighton an extremely small scale. The absorbed laser energy is then trapped in the nanoplasma andcannot dissipate, leading to much higher plasma temperatures. Previous experiments have obsered
the ejection of ions with kinetic energies exceeding 1 MeV [38], and even nuclear fusion [39] inlaser-irradiated nanoplasmas. With this motivation, theoretical studies suggested that shock waves
could be driven through these nanoplasmas [40–42] and that these shock waves could be used tofurther enhance the energies of the ejected nanoparticles. However, in the intervening decade,no experimental obvervation of shock waves propagating through nanoplasmas has taken place.
Chapter 5 discusses the first experimental observation of shock waves propagation withing a single
nanoplasma and demonstrates how a second “heating” laser pulse can be used to tailor the plasma
density profile to optimize the yield of quasi-monoenergetic ions.

Chapter 2

Apparatus and methods

Hofstadter’s Law: It always takes longer than you expect, even when you take into
account Hofstadter’s Law.
–Douglas Hofstadter

2.1

Experimental summary

The experiments presented in this thesis explore different physical phenomena, but share several techniques and apparatus in common. In particular, all of the experiments were completedusing similar femtosecond laser systems and the same velocity map imaging (VMI) spectrometer.1
The studies involving nanoparticles and nanoplasmas were conducted using the same nanoparticle generation and delivery system. Thus, this chapter provides a description of the femtosecond
laser systems (Section 2.2), the VMI spectrometer (Section 2.3), and the nanoparticle aerosol source(Section 2.4).

2.2

Femtosecond laser system

2.2.1

Chirped pulse amplification

In order to study processes on the femtosecond timescale, we use femtosecond laser pulses
obtained from titanium-doped sapphire (Ti:sapphire) laser systems. Ti:sapphire is a material especially suited for the generation of high-intensity femtoseond pulses due to its broad gain bandwidthand high thermal conductivity. Kerr-lens modelocked Ti:sapphire oscillators operate with repetition
1 It should be noted that, while the laser systems are similar, two different laser systems were used. In addition,
the spectrometer evolved over the course of the studies presented in this thesis, such that it now contains very few of
its original parts.

13
rates of 80 to 100 MHz and generate ∼10 fs pulses with pulse energies on the nJ scale. This allows
the focused laser to achieve peak field intensities of <1013 W/cm2 , even with diffraction-limited
focusing. This laser field is still weak compared to the Coulomb field. To move into the strong-fieldregime, the laser intensity must be increased by at least an order of magnitude.
To decrease the repetition rate and increase the average power (thereby greatly increasing theenergy per laser pulse), we use a Ti:sapphire amplifier system. The amplifier cannot directly amplify
the 10 fs pulses from the oscillator, since attempting to do so would expose the Ti:sapphire crystal topeak laser intensities above its damage threshold. Instead, amplifiers are designed around the principle of chirped pulse amplification (CPA). In the CPA scheme, the pulses from the oscillator first passthrough a grating-based stretcher which frequency disperses the laser pulses in time (“temporally
chirps” the pulses) until they have a duration of more than 100 ps [43]. A Pockels cell then selects
a single pulse from the 80–100 MHz pulse train and allows this pulse to proceed to the Ti:sapphire
crystal. The pulse is then amplified by passing through the Ti:sapphire crystal many times. Afterthe pulse energy has been increased, the ∼100 ps pulse can then be recompressed to 20–50 fs bypassing through a grating-based compressor, which compensates the temporal chirp introduced by
the stretcher. The pulse typically cannot be compressed to the original 10 fs pulse duration that it
emerged from the oscillator due to the gain-narrowing of the spectral bandwidth that takes place inthe amplifier.
In the experiments presented in this thesis, two different laser amplifier systems were used.
The strong-field ionization experiments (Chapter 3) were completed using a two-stage multipass
amplifier (KMLabs Red Dragon). The nanoparticle experiments (Chapters 4 and 5) utilized abreakthrough high-pulse-energy one-stage regenerative amplifier: the KMLabs Wyvern HE [44, 45].
At first glance, the laser systems seem very similar: the Red Dragon produced 7 mJ, 25 fs pulses at
1 kHz, and the Wyvern HE produces 8–10 mJ,2 40 fs pulses, also at 1 kHz. However, the advantageof the single-stage regenerative amplifier (Wyvern HE) over the two-stage multipass amplifier is
2 While the Wyvern HE is capable of producing pulse energies of 10 mJ, the output mode quality (M 2 ≥ 1.3)

is not as good compared to operation at 8 mJ (M 2 ≈ 1.2). Because a good mode is important for the subsequent
frequency conversion steps and minimizes the risk of damage to the optical systems of both the amplifier and theexperiment, the amplifier was typically operated near 8 mJ for the experiments described in this thesis.

14seen in the reliability of the laser system. The >95 percent up-time of the Wyvern HE is a breakthrough achievement in 10-mJ-class laser systems and was crucial for successfully obtaining datafrom nanoparticles. More information about the Wyvern HE is presented in Ref 44, as well as in
the PhD thesis of Chengyuan Ding [45], who designed and build the amplifier in cooperation with
Xiaoshi Zhang and other staff at KMLabs, Inc.

2.2.2

Light sources

A unique aspect of the study of SFI of atomic gases presented in Chapter 3 is that the study was
conducted using a wide range of driving laser wavelengths, ranging from the deep-UV at 267 nm, tothe mid-IR at 2000 nm. The Ti:sapphire laser can only be tuned over a narrow range near 800 nm, so
the other wavelengths must be generated using non-linear light conversion techniques (Figure 2.1).
The 400 nm pulses were generated using a beta-barium borate (BBO) crystal, with a thickness of
200 µm. The 267 nm light was generated from sum-frequency generation of 400 nm and 800 nm
light in a second BBO crystal. A calcite plate is placed in the beam to compensate for the small
time-delay between the 400 nm and 800 nm pulses. The mid-IR pulses at 1300 nm and 2000 nm
are generated using parametric amplification techniques described in the following section. This
unusually large range of laser wavelengths allowed us to explore how the physics of SFI scale withthe driving laser wavelength.

2.2.3

Optical parametric amplifier (OPA)

The optical parametric amplifier (OPA) system used to generate the mid-IR light in Chapter 3
converts the 800 nm output of the Ti:sapphire laser system into mid-IR light at 1300 nm and2000 nm. The OPA [44, 46] was designed and built at JILA by Matt Seaberg, Paul Arpin, andStefan Witte and adapted to the higher pulse energies and longer pulse durations of the Wyvern HE
by Chengyuan Ding, Tingting Fan, and Wei Xiong.
Recent experiments have demonstrated that high harmonic generation (HHG) can generatemuch higher photon energies when longer laser wavelengths are used to drive the process [12, 47].

BBO	
  calcite	
  λ/2	  BBO	
  

BBO	
  

15

267	
  nm	
  
400	
  nm	
  
800	
  nm	
  

Ti:sapphire	
  laser	
  

OPA	
  

1300	
  nm	
  
2000	
  nm	
  

Figure 2.1: Femtosecond light sources from the UV to the mid-IR. An unusually large
range of wavelengths were available for the experiments described in this thesis. The 800 nm pulses
were obtained directly from the amplifier, and 400 nm pulses were obtained through generation of
the second harmonic in a BBO crystal. The 267 nm pulses were generated through sum-frequency
generation in a second BBO crystal. The 1300 nm and 2000 nm mid-IR pulses were obtained using
an optical parametric amplifier (OPA).

Using a driving laser wavelength of 3900 nm, Popmintchev and coworkers [19] were able to generate
photon energies in excess of 1 keV. But the advantages of mid-IR driving lasers are seen well before
3900 nm – a 1300 nm driving laser can generate soft X-ray light to the carbon edge at 285 eV [47],and 2000 nm light has recently been shown to generate single attosecond pulses when appropriate
phase-matching conditions are used [32]. This breakthrough in using longer wavelength driving
lasers for HHG motivated the construction of the OPA and motivates the studies of strong-field
ionization using longer driving wavelengths presented in Chapter 3.

2.2.4

Delay line

The time-resolved experiments presented in Chapter 5 were completed using a simple Mach–
Zehnder-geometry delay-line setup similar to that shown in Figure 2.2. The dichroic mirrors used toseparate and recombine the 400 and 800 nm light were obtained from Lattice Electro-Optics. The
translation stage is a model NST-100 from Thorlabs and was controlled in concert with the VMI
camera using Matlab 2012b (32-bit version). In Figure 2.2, a single lens is shown focusing both

1	
  

16
beams into the interaction region of the VMI. However, in practice separate lenses were typicallyplaced in each beam in order to independently control the focal spot size, as well as to correct for
chromatic aberration.

Detector	
  Delay	
  stage	
  
BBO	
  

Photoelectrons	
  
or	
  
Photoions	
  Waveplate	  	
  Polarizer	  Ti:sapphire	
  laser	
  

Lens	
  

Gas	
  jet	
  Figure 2.2: A typical femtosecond pump-probe experiment. The Ti:sapphire amplifier produces 25–40 fs pulses of 800 nm light (red beam). In this example, a BBO crystal converts the 800
nm light to 400 nm. Dichroic mirrors are used to split and later recombine the two laser pulses.
A waveplate and polarizer placed in each arm are used to control the intensity of each beam. A
motorized delay stage in the 800 nm arm is used to control the relative path length and thereby
control the relative time delay of the two pulses. In the velocity-map imaging (VMI) spectrometer,
the intense laser pulses ionize atoms/molecules in a gas jet (or nanoparticles in a particle beam) andthe electrons (or ions) are projected onto a microchannel-plate–phosphor-screen detector by a static
electric field.

2.3

Velocity map imaging spectrometer

2.3.1

Concept and history

The concept of charged particle imaging is refreshingly simple - charged particles (either electrons or ions) are simply projected onto a position sensitive detector using an electric field, making
a two-dimensional picture of the momentum distribution. The field of photoion imaging was born in1987 when Chandler and Houston [48] used a position-sensitive detector to record the angle-resolved
ion momentum distribution resulting from the dissociation of CH3 I by a 266 nm laser pulse. Dueto its simple implementation and powerful capabilities, photoion imaging became a popular method
for studying gas-phase chemical reactions. In the mid-1990s, the first photoelectron images wererecorded by Helm [49] and Bordas [50].

17
Eppink and Parker [51] improved upon the methods of Chandler and Houston by implementing an electrostatic lens that could compensate for the extended interaction region formed by theintersection of the ionizing radiation with the particle beam. Since this method maps the velocity ofeach particle to position on the detector irrespective of the exact location where the particle originated, this method was termed Velocity Map Imaging (VMI) and the apparatus has become known
as a VMI spectrometer. The VMI spectrometer provides an additional advantage over the original
photoion spectrometer invented by Chandler and Houston [48]; by removing the metal meshes thatall previous studies had placed between the interaction region and the detector, Eppink and Parker
increased the fraction of electrons or ions that reach the detector and further increased the resolutionof the instrument [52].
The standard “Eppink and Parker” VMI geometry consists of three circular electrodes: arepeller plate, an extractor plate that features a hole through which the electrons pass, and aground plate that features a somewhat larger hole. As suggested by the name, the ground plateis typically held at 0 V, though this is not always the case [52]. The relative ratio between therepeller and extractor plates sets the “focus” of the spectrometer. The exact ratios needed for thebest focus depend on the geometry of the spectrometer, and can be used to select between velocity
map imaging mode (repeller-to-extractor ratio of ∼0.75) [52] and spatial imaging mode (repellerto-extractor ratio of ∼0.98) [53, 54]. When the repeller-to-extractor ratio is set somewhere between
these two extremes, the image produced on the VMI is a convolution the spatial and momentum
profiles of the generated electrons.

2.3.2

TheoryComplete treatments of the principles of VMI can be found in numerous sources, with themost eloquent being the original 1997 Review of Scientific Instruments article by Eppink and Parker[51], Whitaker’s 2003 textbook Imaging in Molecular Dynamics [52], and a wonderful 2004 Master’s
thesis by Sara Thorin [55] that provides extensive details on the practicalities of constructing andoperating a VMI spectrometer.

18
In brief, the basic principles of VMI can be understood from a simple analysis of the equationsof motion. Under the assumptions that the acceleration region is small compared to the free-flightregion and that the initial kinetic energy of the particles is small compared to the energy imparted
by the static electric field of the spectrometer,3 the radial position of the electrons on the detector
R is given by [51, 52, 55]s
R ≈ NL

Er
,
qV

(2.1)

where N is a magnification factor particular to the geometry of the spectrometer and the relative
voltages of the electrodes, L is the length of the free-flight region, Er is the radial component of the
kinetic energy of the particle, q is the charge of the particle, and V is the potential through which
the particle is accelerated. If we ignore the terms from the spectrometer, we can express the radial
position of the ions as
r
R∝

Er
,
Z

(2.2)

where Z is the charge number of the particle. This expression makes it clear that the term “velocity
map imaging spectrometer” is something of a misnomer, since particles of the same velocity but
different masses (or different charges) will not map to the same position on the detector. Astute
readers will therefore read the term “VMI spectrometer” as “square-root of kinetic energy divided
by charge imaging spectrometer,” but will accept that fact that the latter term is too cumbersome
for common usage, and would require a more stylish acronym before gaining popularity.
The above theory makes the assumption that the only field acting on the spectrometer is theelectric field of the spectrometer. Any additional fields will affect the trajectory of the particles inthe spectrometer and must be avoided. One of the most problematic is Earth’s magnetic field. Inorder to avoid affects from Earth’s field, a VMI spectrometer must be enclosed within one or morelayers of µ-metal, an alloy (composed primarily of Ni and Fe, with a few percent Cu, Cr, and Mo)
that significantly attenuates magnetic fields. Any parts of the VMI spectrometer that are placed
3 The assumptions of a long free-flight region and slow initial momentum are good approximations in regime ofthreshold-ionization where VMI is typically applied. In the regime of strong-field ionization, higher kinetic energy
electrons are generated, making numerical modeling (using a program such as SIMION [56]) more important to checkthe linearity and resolution of the instrument.

19
within the µ-metal must be non-magnetic in order to avoid introducing any additional magnetic
fields into the VMI or free-flight regions.

2.3.3

Implementation

The VMI spectrometer in the Kapteyn–Murnane group (Figure 2.3) was designed and partiallyassembled in early 2010 by Xibin Zhou, Bosheng Zhang, Predrag Ranitovic, and Chengyuan Ding.
The design of the spectrometer assembly (the electrodes and their support structure) is based largelyon the VMI spectrometer in the Weber lab at JILA [57], which is, in turn, based on the VMI
spectrometers in the Lineberger Group at JILA and Sanov Group at the University of Arizona [58,59]. All of these spectrometers share the standard three-electrode design of Eppink and Parker[51]. In late 2010, the author took over the construction of the VMI spectrometer with the helpof Chengyuan Ding and Predrag Ranitovic. The author designed the gas jet assembly and theskimmer assembly, fixed the virtual leaks caused by non-vented screws and vacuum-incompatible
Kapton tape, and re-designed the electrode support assembly to support voltages up to 5 kV.

(a) VMI Exterior view(b) VMI interior (cut-away) view

Figure 2.3: Schematic of the VMI spectrometer (a) Exterior view of the VMI spectrometer,
showing the ∼500 L/s turbopumps that are used to maintain medium-vacuum (< 10−2 Torr) in
the source chamber (left) and high-vacuum (< 10−6 Torr) in the spectrometer chamber. The XYZ
manipulator on the left side of the apparatus allows for aerodynamic lens (or gas jet) to be positioned
relative to the skimmer that separates the two chambers. (b) Interior view of the VMI spectrometer,
showing the aerodynamic lens forming a collimated beam of nanoparticles. The nanoparticle beam
passes through the tube-skimmer and into the spectrometer chamber. The laser beam ionized thenanoparticles and creates electrons (and often ions) that are projected onto the detector by theelectric field generated by three stainless steel electrodes.

20
2.3.3.1

Spectrometer assembly

The “spectrometer assembly” is the term given to the electrodes, the structure that supports
them, and the µ-metal that surrounds them. This is the part of the instrument that required themost custom machining, and also the most iterations before it was fully operational. Since most VMI
spectrometers only collect electrons with kinetic energies below 10 eV, the electrodes are typicallynot designed to support voltages higher than 1 kV. In contrast, since the strong-field ionization
process can easily produce electrons in excess of 50 eV, this instrument needed to support higher
voltages on the electrodes while avoiding arcing or corona discharge.
In the first iteration, the electrodes were made from copper, since it is a readily machinable
material that is not magnetic. The original copper electrodes could only support ∼2 kV due tothe roughness and contamination of the surface [60]. To increase the supportable potential of theelectrodes to the full 5 kV of the PS350 power supplies (Stanford Research Systems), the copper
electrodes were replaced with stainless steel electrodes. Because some varieties of stainless steel
can be slightly magnetic, it is typically considered an innapropriate for spectrometer construction.
However, new electrodes were made of austenitic stainless steel (Type 316) which is not magnetic.
The electrodes were polished with progressively finer-grit sandpaper up to 2000 grit, but it’s likelythat the electrodes could support even higher voltages with electropolishing.4 Additionally, the holein the ground plate was expanded from 1 inch to 1.5 inches in order to allow higher kinetic energy
photoelectrons to be collected on the detector.
For the experiments presented in Chapter 3, the spectrometer assembly was rotated 90 degrees
from the orientation shown in Figure 2.3b to allow the gas jet to pass through a ∼1 mm hole in
the repeller plate. This allowed the skimmer to be positioned less than 1 inch from the interaction
region, which minimized the expansion of the gas and therefore maximized the gas density probed by
the laser. For the nanoparticle experiments (Chapters 4 and 5), it was deemed undesirable to use ageometry where the nanoparticle beam impacted the detector, since it would likely deposit a spot of
4 Indeed, a new “high energy” VMI assembled in KM-Group features electropolished electrodes and can support
up to 15 kV before arcing.

21

Figure 2.4: The VMI electrodes. This photograph shows the spectrometer assembly with theµ-metal removed to reveal the copper electrodes, which were later exchanged for stainless steel
electrodes. The electrode support structure consists of threaded molybdenum rods (not visible)
surrounded by an inner ceramic tube. One-inch sections of larger diameter tube (the white cylinders)
fit over the inner tubes and provide the appropriate spacing between the electrodes.

nanoparticles in the center of the detector. Thus, for these experiments, the spectrometer assemblyand detector flange were rotated by 90 degrees to the configuration shown in Figure 2.3b. Since
the nanoparticle beam is only slowly diverging after exiting the aerodynamic lens, the additional 2
inches that the beam must pass before reaching the interaction region does not cause an appreciable
decrease in the particle density.

2.3.3.2

Gas jet

For the strong-field ionization experiments described in Chapter 3, the target was gas-phaseatoms and molecules obtained via supersonic expansion of a gas in vacuum. The gas (backing pressure of ∼700 Torr) is introduced into the “source” chamber through a 30 µm nozzle. The expanding
gas then passes through a 300 µm skimmer (Beam Dynamics, Inc. [61]) and into the differentiallypumped “spectrometer” chamber. The gas jet increases the pressure in the source chamber to around10−4 Torr and increases the pressure in the spectrometer chamber to approximately 10−7 Torr, from

22base pressures of 10−9 Torr. The exact pressure in the spectrometer chamber depends on the exact
position of the gas get relative to the skimmer.
The gas jet must be precisely aligned with the skimmer, so that the beam of gas exiting theskimmer will pass cleanly through the small hole in the repeller plate. To achieve good alignment,
the gas jet assembly is mounted on an XYZ manipulator that allows for precise positioning in three
dimensions. It would be very difficult to attempt to align the focused laser beam and the gas
jet simultaneously. Therefore, the gas jet is aligned first, by moving the position to optimize thepressure in the spectrometer chamber. To roughly find alignment, it is possible to simply examine
the pressure in the spectrometer chamber as a function of the gas jet position and align by hand.
Once rough alignment is obtained, fine alignment can be completed by taking small steps in eachdimension transverse to the flow of gas and fitting the resulting pressures to a Gaussian function.
Using this method, the gas jet can be aligned to within a few µm and the gas beam can easily
be found with the focused laser. Further optimization of the gas jet position is then completed by
iteratively moving the gas jet position and the finding the new position of the interaction region

Chamber pressure (10−7 Torr)using the laser.

5
4

a)

Horizontal position

5

Data
Gaussian Fit
mean: -0.266 mm

4

3

3

2

2

1

1

0

6

4 2 0 2 4
Gas jet position (mm)

6

0

b)

22

Vertical position
Data
Gaussian Fit
mean: 27.401 mm

24 26 28 30 32
Gas jet position (mm)Figure 2.5: Alignment of the gas jet to the skimmer. The 30 µm gas jet must be carefullyaligned to the 300 µm skimmer so that the skimmed beam of gas passes directly through theinteraction region. Coarse alignment can be accomplished by moving the gas jet to optimize thepressure in the spectrometer chamber. Precise alignment is achieved by moving the gas jet in small
increments and recording the pressure in the spectrometer chamber as a function of the mircometer
position. This is performed in the horizontal (a) and vertical (b) directions. A Gaussian fit allows
the center point to be precisely extracted.

23
2.3.3.3

Detector

The electrons and ions are detected using a phosphor screen behind two microchannel plates(MCPs) in a chevron stack. Each MCP is biased with up to 1.2 kV per plate5 and ejects manyelectrons each time an electron or ion collides with a channel. The gain is extremely high, such thatup to 107 electrons emerge from the backside of the MCP stack for each electron that impacts thefront of a channel. The electrons that leave the MCP are accelerated onto a phosphor screen, thatconverts the electrons into visible light, with a wavelength that depends on the material coating thephosphor screen. We used two different phosphor screens: P43, which emits at 545 nm and has alifetime of 1 ms, and P47 which emits at 400 nm and has a lifetime of 55 ns [62]. The P43 phosphor
produces more photons per electron impact (it’s “brighter”), but the faster response time of the P47
phosphor makes it more appropriate for time-of-flight studies. The light on the phosphor screen
passes through a f /1.4 camera lens (Fujinon) and is recorded with a CCD camera (Pike 145b, Allied
Vision Technologies).
The assembly that holds the MCP and phosphor is a 75 mm Beam Observation System (BOS75), manufactured by Beam Imaging Solutions (Longmont, CO). Since all of the experiments described in this thesis involved unusually high electron/ion flux, the MCPs were damaged rapidly
and several sets of MCP plates and phosphor screens were used:• The study described in Chapter 3 used two Imaging Grade 60:1 MCP plates and a P47
phosphor screen that were installed in 2011 and replaced in 2012.
• The study described in Chapter 5 used two Detection Grade 40:1 MCP plates and a P43
phosphor screen that were installed in 2012 and replaced in 2014.
• The study described in Chapter 4 used a matched set of two Imaging Grade 60:1 MCP plates
and a P47 phosphor screen. These were installed in mid-2014 and are the MCP plates andphosphor screen that are currently installed as of December 2014.
5 The 60:1 length-to-diameter ratio plates can support 1.2 kV, the 40:1 plates can only support 1.0 kV. Whensetting the voltage across the MCP stack, keep in mind that any voltage divider will obscure the true voltage being
applied to the plates. Most pairs of plates do not have the same resistance, and so a different voltage divider is needed.

24
The phosphor screens (75 mm diameter) were obtained from Beam Imaging Solutions and the MCP
plates (75 mm) were obtained from Photonis, Inc. via Beam Imaging Solutions.

2.3.4

Abel transform

The VMI spectrometer records a 2D projection of the 3D photoelectron (or photoion) angular
distribution (PAD). Several techniques exist for providing the desired full 3D PAD, or, simply a sliceof the 3D PAD. For some experiments where ions are detected, rapid gating of the detector can beused to capture only a small slice of the expanding Newton sphere [52, 63], but this technique cannot
be used for photoelectrons, because the detector gating is not nearly fast enough. Another approachrelies on the fact that sometimes the PAD can be rotated in the laboratory frame, as is the case for
SFI, where a waveplate can be used to rotate the electric field of the laser and consequently rotate
the PAD. If many 2D projections of the PAD are captured at many different angles of rotation, thenthe 3D PAD can be reconstructed using tomographic methods.
However, the vast majority of VMI images are recorded of PADs that exhibit cylindrical symmetry about the laser polarization, and the axis of rotational symmetry lies in the plane of therecorded image. In this case, the Abel transform may be applied. The Abel transform utilizes thecylindrical symmetry of the PAD to provide a 3D reconstruction from the 2D projection recorded by
the VMI spectrometer. While the Abel transform has an exact mathematical definition, it is nearly
impossible to apply because it is extremely sensitive to the noise and imperfect symmetry present
in real-world VMI datasets [52, 64]. Consequently, several different numerical approximations haveemerged to allow 3D PADs to be conveniently reconstructed from experimental VMI data. The
most well-known methods include Vrakking’s Iterative Inversion method [65], the BASEX algorithm[64], and the Polar Onion Peeling (POP) method [66]. While all of these three methods produced
low-noise transforms on our datasets, the BASEX algorithm proved to be the fastest and most convenient,6 and was used to transform the data in Chapter 3. The PADs recorded from nanoparticles
6 Specifically, the BASEX algorithm was the most convenient because the Reisler group at USC kindly provided

the Matlab implementation of the BASEX algorithm, which the author could port to Python. The reconstructionis then scriptable and can be applied to large, multi-image datasets, taking less than 1 second for each 1 megapixel
image.

25(Chapter 4 and 5) do not depend on the laser polarization and do not exhibit cylindrical symmetry,so the Abel transform cannot be used.

2.4

Nanoparticle aerosol source

A high-concentration of isolated nanoparticles in the VMI spectrometer is achieved by preparing
a nanoparticle aerosol and then injecting the aerosol into a high-vacuum chamber via the aerodynamic lens. The integration of aerosol technologies with the VMI spectrometer was enabled througha collaboration with the Jose Jimenez group in the CU Chemistry Department, especially JimenezGroup members Brett Palm and Pedro Campuzano–Jost.

2.4.1

Atomizer

The nanoparticle aerosol is generated using a Collison-type7 atomizer (TSI, Model 3076), whichuses compressed gas to make a fine mist of droplets from a liquid solution (Figure 2.6). As thedroplets evaporate, they leave behind whatever material is suspended or dissolved in the starting
solution. In the case of a colloidal nanoparticle solution, the droplets will contain one or more
nanoparticles, and when they evaporate, will leave behind single nanoparticles or clumps of many
nanoparticles. In the case of a salt solution, the droplet will evaporate to leave behind either asingle crystal or an amorphous clump, depending on the properties of the material. As discussed in
Section 4.3.2, electron microscopy reveals that a solution of NaCl produces mostly single crystals,
though some amorphous clumps can also be seen.
The performance of the atomizer depends on the liquid used and the pressure of the carrier gas.
The recommended operating pressure of the atomizer is 30 psig when air is used as a carrier gas.
We found that the pressure required to generate a high concentration of nanoparticles decreased
with the viscosity of the solvent – both hexane and acetone produced the highest concentrations of
nanoparticles with pressures of about 20 psig. An additional advantage of using lower pressures isthat there is less solvent loss through evaporation. We used several different carrier gases – including
7 Often miswritten as “collision-type”, the Collison-type atomizer is named after W. E. Collison, who presented
the design at a 1932 meeting of the British Medical Association [67].

26
He, N2 , Ar, Ne, and CO2 – and there was not a detectable difference in the particle concentrations
when different gases were used. Thus, different carrier gases could be used depending on which gas
minimized the background signal in the VMI spectrometer.

(a) Atomizer(b) DMA

Figure 2.6: The atomizer and differential mobility analyzer (DMA). (a) The atomizer uses
compressed gas to prepare an aerosol of droplets, which quickly evaporate to leave behind thematerial in solution. (b) The electrostatic classifier and DMA column (the cylindrical steel object
on the right) select only a specific size of particles. Photographs courtesy of TSI, Inc.

A significant problem with the atomizer is that it relies on the evaporation of ∼1 µm diameter
droplets8 to generate nanoparticles. Since we are interested in studying nanoparticles that are 50 nm
or smaller, the vast majority of the volume of a 1 µm droplet must evaporate. In order to generate
nanoparticles that are not coated with a thick layer of contamination, a very high level of solvent
purity is necessary, and the level of solvent purity required increases as the final particle size isdecreased. A striking example of this effect is seen in Chapter 4, where the 50 nm gold nanoparticle
sample is coated with a layer of contamination that is larger than the particle itself. This problem
is compounded as we move to experiments that are more surface sensitive, which causes even a thinlayer of surface contamination to have a large effect. For these reasons, we have plans to switch the
8 The atomizer produces a wide distribution of droplet sizes, which is centered around 1 µm diameter and depends
on the solvent and pressure of the carrier gas.

27
nanoparticle source to a magnetron sputtering source, as discussed in Section 6.3.2.

2.4.2

Electrostatic classifier

Nanomaterials often exhibit properties that vary with the dimensions of the nanoparticle, making it is very useful to be able to prepare a nanoparticle sample with a controllable size. This isachieved by passing the aerosol through a differential mobility analyzer (DMA) column connected
to a control box known as an electrostatic classifier (TSI 3080, Figure 2.6b). Two different DMA
columns were used, a short column optimized for particles ranging from 2 to 150 nm (TSI 3085)
and a long column (borrowed from the Jimenez Group) optimized for particles ranging from 10 to1000 nm (TSI 3081).

2.4.3

Aerodynamic lens

The aerodynamic lens (Figure 2.7) was invented in 1995 by a team at the University of Minnesota [68, 69] and creates a collimated beam of particles from an aerosol. By passing the aerosol
through a series of small orifices, where the diameters and distances are carefully chosen, the aerodynamic forces drive the particles to follow straight paths while leaving the gas divergent at the exitof the lens.
Each aerodynamic lens is designed around a certain flow rate, which is controlled by varying
the pressure at the input of the lens. The lens used in this thesis requires ∼1.5 Torr, which istypical of aerodynamic lenses in general. In order to drop the pressure from atmospheric pressure
to 1.5 Torr, a small flow-limiting “critical orifice” is required. In our preliminary studies, we used athin steel disk-orifice (SPI, Inc.) with a 100 µm hole, as is commonly used in instruments studying
atmospheric aerosols. This achieved the appropriate pressure drop, but it clogged within about one
hour when we used solutions with concentrations of 1 g/L. In order to reduce clogging, we switched
to a glass capillary tube with an inner diameter of 250!µm and a length of about 15 cm, dimensions
that offer a similar conductance to the 100-µm disk-orifice. This tube-style critical orifice increased
the time before clogging to about 20 hours of continuous operation. It is not clear what aspect of

28
the glass tube prevents clogging, since it could be the increased inner diameter of the glass tube,
the smoother microcopic surface of glass compared with steel, the non-reactive chemical nature ofglass, or the long length of the tube, which may produce a less turbulent flow at the tube exit.
When using the aerodynamic lens, we also had problems with clogging the skimmer that separates the source and spectrometer chambers and allows for differential pumping. So, using a similarsolution to the critical orifice, we swapped the thin 300 µm orifice for a long “tube-skimmer”. The
1.5 mm inner diameter of the tube skimmer allowed the ∼0.5 mm nanoparticle beam to pass cleanly
through the skimmer without clogging, and the longer length (35 mm) provided a sufficiently low
conductance to permit effective differential pumping of the spectrometer chamber.

Figure 2.7: The aerodynamic lens. The nanoparticle aerosol enters the left side of the aerodynamic lens (blue) and, after passing through a series of orifices, the aerosol emerges from theright side of the lens as a collimated beam with low divergence. The carrier gas (not shown) is still
divergent and does not pass through the skimmer (right). This allows the laser to interact with aconcentrated beam of nanoparticles in the absence of carrier gas. This drawing is not to scale andthe aerodynamic lens is slightly compressed in the horizontal dimension. The exact dimensions of
the lens used in this study are provided in Table 1 and Figure 1 of Ref. 70.

2.4.4

Light scattering

In order to check that the particle beam is passing through the spectrometer, we implemented
a simple light-scattering experiment. Though the particles are smaller than the wavelength of visible
light, they are still large enough to scatter strongly. Thus, when the particle beam is crossed with agreen laser pointer (5 mW), a faint glow is visible to the naked eye. To improve the sensitivity of themeasurement, we illuminate the particle beam with an unfocused (but collimated) 0.75 W, 532 nm

29laser (Wicked Lasers) and observe the light scattering using a CCD camera. Once the nanoparticle
beam is aligned through the spectrometer, it can easily be intersected by a focused laser beam bylooking at the photoelectron or photoion signal on the VMI spectrometer.

2.4.5

Single particle experiments

The number concentration of nanoparticles emerging from the aerodynamic lens is on the orderof 105 particles/cm3 by the time the nanoparticle beam reaches the interaction region. For manyof the experiments, the volume of the interaction region (the intersection of the laser beam andthe particle beam) is on the order of 10−7 cm3 . In this scenario, there is, on average, less than
one nanoparticle in the focal volume for each laser shot. Thus, most laser shots do not hit ananoparticle. When a laser shot does hit a nanoparticle, there is only a small chance that it will hit
two nanoparticles. This technique allows the observation of a single nanoparticle. The caveat is thatthe interaction of one laser pulse with one nanoparticle needs to produce enough electrons or ionsto produce a reasonable signal. This condition is met when a plasma is formed in the nanoparticle,
as is demonstrated in Chapters 4 and 5 of this thesis.

Chapter 3

Electron dynamics in strong field ionization

This chapter is adapted, with permission, from:• D. D. Hickstein, P. Ranitovic, S. Witte, X.-M. Tong, Y. Huismans, P. Arpin, X. Zhou, K.
E. Keister, C. Hogle, B. Zhang, C. Ding, P. Johnsson, N. Toshima, M. J. J. Vrakking, M.
M. Murnane, and H. C. Kapteyn. Direct Visualization of Laser-Driven Electron Multiple
Scattering and Tunneling Distance in Strong-Field Ionization. Phys. Rev. Lett., 109, 2012,
073004. doi: 10.1103/PhysRevLett.109.073004
c 2012 American Physical Society

Figure 3.1: Illustration of photoelectron rescattering. (a) This numerical simulation of thestrong field ionization of xenon (using a 1300 nm laser) illustrates the numerous interferences thattake place in the field-driven electron wavepacket. Calculation by Xiao-Min Tong, Tsukuba University, art by Brad Baxley, JILA.

31

3.1

Abstract

By systematically recording the photoelectron angular distributions (PADs) resulting from thestrong field ionization of gas-phase atoms and molecules with laser wavelengths ranging from 262 nm
to 2000 nm, we observe distinct structures in the PADs that correspond to the multiple rescattering
the field driven electron with the parent ion. Using a simple scattering-wave model of strong-field
ionization, we show how the interference patterns that result from electron–ion scattering can beunderstood using straightforward methods. The shape of these structures can be associated with thespecific number of times the electron is driven past its parent ion in the laser field before scattering.
Furthermore, a careful analysis of the cutoff energy of the structures allows us to experimentallymeasure the distance between the electron and ion at the moment of tunnel ionization. This work
provides new physical insight into how atoms ionize in strong laser fields, and has implications forfurther efforts to extract atomic and molecular dynamics from strong-field physics.

3.2

Introduction

3.2.1

Zeptosecond waveforms

Recent theoretical work [33] has shown that when the high-harmonic generation (HHG) process is driven with mid-IR lasers, the generated soft X-ray waveforms exhibit modulations on the
zeptosecond timescale, suggesting a possible path for generating laser pulses on the sub-attosecond
timescale. The origin of the zeptosecond modulations is the interference of harmonics generated
from electrons that recombine on the first time they are driven past the ion (the first “revisit”) withelectrons that recombine on subsequent ion revists. Thus, there is considerable motivation to understand the role of this “multiple recscattering” process1 as it may be serve as the next breakthroughin generating the shortest laser pulses. In this chapter, we study strong field ionization (SFI), thecomplementary process to HHG, in order to gain an understanding of multiple rescattering in strong
1 In strong-field physics, even the first time that the electron is driven past the ion is commonly referred to as“rescattering”. The rational for adding “re” is that the tunnel ionization process is assumed to be the first electron–ion“scattering” process.

32
laser fields and investigate how this process changes as we tune the wavelength of the driving laser
over nearly an order-of-magnitude, from the UV to the near-IR.

3.2.2

HHG and SFI in the mid-IR

When an atom or molecule is illuminated with a strong (∼1014 W/cm2 ) femtosecond laser field,
an electron wavepacket will tunnel-ionize and accelerate in the field. Depending on the phase of thelaser field when the electron tunnels, it may be completely turned around and returned to the parention (Section 1.2.1). The returning electron can either recombine with the parent ion, releasing its
kinetic energy as a high-energy photon [10, 16, 71], or elastically scatter from the potential of the ion.
The photons and electrons generated by these strong-field processes have the potential to probe thedynamic structure of molecules and materials on the sub-nanometer length scale and femtosecondto-attosecond time scale. Recent studies have suggested that structures seen in angle-dependent
photoelectron spectra may be useful for determining time-resolved molecular structures [28, 29, 72,73], characterizing attosecond electron wavepackets [74, 75], and studying the dynamics of electron
wavepacket propagation [76, 77]. However, despite extensive analyses [30, 78–81], many features
observed in angle-resolved photoelectron spectra still lack a simple physical explanation.
The recent development of high pulse energy (>1 mJ) femtosecond lasers [82] in the mid-infrared(mid-IR) and angle-resolved detection schemes [51] has enabled new advances in visualizing strongfield physics. Electrons that are ionized in a mid-IR laser field reach higher velocities due to the larger
ponderomotive energy, Up ∝ Iλ2 , where I is the intensity and λ is the wavelength of the driving laser.
The possibility of harnessing the high-energy electrons that are first ionized and then driven back to amolecule by a strong laser field has inspired several theoretical and experimental efforts to use strong
field ionization to probe molecular structure [27, 28, 83, 84]. Recently, Huismans and coworkers [85]used 7 µm mid-IR lasers in combination with angle-resolved detection to observe angular interference
structures in the photoelectron spectra of metastable xenon atoms. They presented a theoreticalmodel that explains these structures based on the difference in phase between the two different
paths that electrons can take to reach the same final momentum: either proceeding directly to

33
the detector, or rescattering from the ion before reaching the detector. In other work, Blaga andcoworkers [86] irradiated atoms and molecules with 1.7–3.4 µm lasers and discovered an unexpected
spike in the (non-angle-resolved) photoelectron energy spectrum that they refer to as the low-energy
structure (LES). Subsequent papers [87–90] proposed various interpretations, but all agree that thislow-energy structure arises from the rescattering of electrons by the parent ion.
In this work, we develop an intuitive model for understanding strong-field ionization as a simple
superposition of plane and spherical photoelectron waves. This approach extends the standard
three-step model of strong field ionization that has provided crucial physical insight into strong
field ionization [91] and high-harmonic generation [92, 93]. We use this model to show that newinterference structures, which we observe in the experimental photoelectron angular distributions
generated by mid-IR lasers, are created by electron trajectories that scatter from the parent ion after
passing by the ion several times (Figure 3.2). The quantum phase accumulated by the electrons
during their oscillatory path between ionization and rescattering is directly imprinted onto thephotoelectron angular distribution. Thus, the shape and spacing of the interference structures
directly corresponds to the specific number of times the electron re-encounters its parent ion before
scattering strongly. Through an analysis of the energy cutoff of these newly observed structures,
we show that when an atom is ionized by an intense laser, the electron emerges at a finite distancefrom its parent ion that corresponds to the far side of the quantum tunneling barrier. Our simple
model thus allows us to uncover valuable physical insight into strong-field electron dynamics that is
not readily extracted from full quantum simulations.

3.3

ExperimentUltrashort (30 fs, 785 nm) laser pulses with a maximal per-pulse energy of 7 mJ are derived froma two-stage multipass Ti:sapphire amplifier (KMLabs Red Dragon) operating at 1 kHz. The second
harmonic (393 nm, ∼40 fs) is generated in a beta-barium borate (BBO) crystal (Eksma Optics).
The third harmonic (262 nm, ∼50 fs) is generated with four-wave mixing of the fundamental andsecond harmonic in a BBO crystal using a collinear geometry (Femtokit FK-800-020, Eksma Optics).

34

Figure 3.2: Summary of multiple rescattering. (a) The photoelectron angular distribution
resulting from the ionization of argon gas with a 1300 nm, 7.5 × 1013 W/cm2 , 40 fs laser pulse. The
primary spider structure (minima shown with white lines) results from interferences between directly
ionized electrons and those that are driven back to scatter from the Coulomb potential of the ion
before reaching the detector. (b) The newly observed inner spider structure (minima shown with
red lines) results from electron trajectories that scatter from the Coulomb potential on their second
re-encounter with the ion, and the interfere with unscattered trajectories. (c–g) Simple laser-driven
electron dynamics during ionization explain the primary and inner spider structures. Artwork by
Ellen Keister and Daniel Hickstein. Adapted with permission from Ref. 2. c 2012 American PhysicalSociety

An optical parametric amplifier [44] generates ultrafast pulses at 1300 nm (∼1.3 mJ) and 2000 nm(∼0.8 mJ) with pulse durations of ∼40 fs.
The laser pulses are focused into the velocity map imaging (VMI) spectrometer to achieve peakintensities ranging from 5×1013 to 5×1014 W/cm2 . The focused laser beam ionizes gas-phase atoms

35
or molecules at a target pressure of approximately 10−2 Torr. Three electrodes arranged in a VMI
geometry [51] drive photoelectrons towards a microchannel-plate–phosphor-screen detection system.
A CCD camera (Pike 145b, Allied Vision Technologies) records the image of the phosphor screen,
which is then Abel inverted using the BASEX algorithm [64] to obtain a 2D slice of the cylindricallysymmetric 3D momentum distribution.

3.4

Photoelectron angular distributions from UV to mid-IR

Photoelectron angular distributions were recorded at various driving laser wavelengths between 262 and 2000 nm, and with intensities ranging from 5 × 1013 to 5 × 1014 W/cm2 . For
driving wavelengths between 393 and 2000 nm, we observe interference structures aligned along thelaser polarization axis (Figure 3.2a). These interference structures were observed by Huismans andcoworkers [85], and interpreted in terms of the interference between laser-driven electron trajectories
that collide with the ion (rescattered electrons) and electron trajectories that proceed directly to thedetector (direct electrons). In this paper, we refer to these angular features as “spider structures”
due to their resemblance to the body and legs of a spider. For driving laser wavelengths of 1300
and 2000 nm, we observe additional “inner spider” structures (Figure 3.2b) at low final momenta
that have more closely spaced fringes. Unlike other low-energy angular structures reported in theliterature [94–96] these inner spider structures are clearly visible through a wide range of intensitiesof the driving laser.

3.5

Plane-spherical wave model

To investigate the origin of both the primary and inner spider structures (Figure 3.2), we apply
a simplified model of the electron-ion recollision process that we call the plane-spherical wave (PSW)
model (Figure 3.3). In this model, the spider structures in the photoelectron angular distribution
are modeled as the interference between a plane-wave electron wavefunction (Figure 3.3a) originating directly from the tunnel ionization of the atom, and a spherical-wave electron wavefunction(Figure 3.3b) that originates from the electron–ion rescattering event. By treating the phase evolu-

36
tion of the quantum wave function during its propagation semiclassically (the so-called intrinsic orquantum phase studied in high-harmonic generation (HHG) [97]), we can reproduce the outer spider
structures (Figures 3.3c, and 3.4).
1.0

a

b

c

d

P (a.u.)

0.5

0.0

0.5

1.0

Plane
0.5

0.0

P

(a.u.)

Spherical
0.5

0.5

0.0

P

(a.u.)PSW Model
0.5

0.5

0.0

P

(a.u.)

Experiment
0.5

0.5

0.0

P

(a.u.)

0.5

Figure 3.3: The plane-spherical wave (PSW) model. The superposition of a plane wave (a)and a spherical wave (b) generates an interference pattern (c) that has the same shape as the spider
structures. The phase of the plane wave is given by Ψplane ∝ eikPk , while the phase of the sphericalwave is given by Ψplane ∝ eikPtotal , where Pk is the momentum parallel to the laser polarization,q
Ptotal = Pk2 + P⊥2 is the total momentum, and k is the modulation frequency of the plane andspherical waves. Only the real part of the complex value is shown in panels (a) and (b) while thesquare of the absolute value is shown in panel (c). (d) The minima of the spider structure calculatedusing the plane spherical model (white lines) match very well with the experimental data across a
broad range of wavelengths and intensities (shown: 1300 nm, 5 × 1013 W/cm2 , 40 fs driving laser).
Adapted with permission from Ref. 2. c 2012 American Physical Society

In addition, by explicitly considering that the electron can pass by the atomic core more thanonce before rescattering, the PSW model can also explain the origin of our newly observed innerspider structures. These inner-spider structures arise from higher-order electron–ion rescattering
events, with a characteristic fringe spacing that depends on the number of electron revisits to thevicinity of the ion before interacting strongly enough to rescatter. Through this interpretation,
we can define a series of higher-order recollision cutoff energies that are a generalization of theponderomotive cutoffs postulated first for HHG [30, 92] and then for strong field ionization [98, 99].
This extremely simple model can reproduce the gross features of our experimental photoelectron
angular distributions across a very broad range of wavelengths, providing valuable physical insight
into strong-field ionization physics.

37
1.5
1.0

Experimental photoelectron spectra

a)

b)

c)

d)

e)

1300 nm2000 nmP (a.u.)

0.5
0.0
0.5
1.0

262 nm

1.5
1.5
1.0

393 nm785 nmTime-Dependent Schrödinger Equation (TDSE)

g)

f)

h)

i)

j)

1300 nm2000 nmP (a.u.)

0.5
0.0
0.5
1.0
1.5
1.5
1.0

267 nm

400 nmk)l)

800 nmPlane-spherical wave (PSW) model

m)

n)

o)

1300 nm2000 nm

0.5

0.5

P (a.u.)

0.5
0.0
0.5
1.0
1.5

262 nm
0.5

P

0.0(a.u.)

393 nm
0.5

0.5

P

0.0

(a.u.)

785 nm
0.5

0.5

P

0.0

(a.u.)

0.5

P

0.0

(a.u.)

0.5

P

0.0

(a.u.)

0.5

Figure 3.4: Comparison of experiment, time-dependent Schrödinger equation (TDSE)
simulations, and simple PSW theory. (a-e) The experimental photoelectron angular distributions at ∼1014 W/cm2 demonstrate how the ionization process moves from the multiphoton regime
at short wavelengths to the tunneling regime at longer wavelengths. The spider structures can bemost clearly seen at 1300 nm, though they are also visible at 800 and 2000 nm. (f-j) The spider
structures also appear in the numerical TDSE simulations, which also reveal how the alternating
nodal structure in the multiphoton-like ionization at 262 and 400 nm morphs into the spider structures at longer wavelengths. (k-o) The spectra simulated using the plane-spherical wave (PSW)
model (see Figure 3.3) show remarkable agreement with the TDSE and experiment despite ignoring
the effects from the ionization step and simplifying the interaction with the Coulomb potential to asingle scattering step. The lines drawn on all of the plots correspond to the minima of the spider
structures as predicted by the PSW model.

38
To develop the PSW model, we begin with the three-step (recollision) model of strong-field
HHG, which starts with tunneling ionization of an electron from the neutral atom in the presence ofa strong laser field (Figure 3.2c). Next, the electron moves under the influence of the driving field,
first being accelerated away from the parent ion and then driven back towards the ion (Figure 3.2d).
Depending on the phase of the laser field when the electron tunnels, the electron may return to thevicinity of the parent ion, or it may drift away. Recently it has been shown that the spider structures
can be reproduced by completing numerical trajectory simulations assuming that electrons born with
low transverse momentum can scatter elastically from the ion (Figure 3.2e), a method referred to as
the generalized strong-field approximation (GSFA) [85].
The PSW model (Figure 3.3) further simplifies the computationally intensity GSFA model toby treating the revisiting electrons as a simple plane wave in the final momentum space and treating
the rescattered electrons as a spherical wave in the final momentum space. In the PSW model, theonly thing that needs to be calculated is the spatial modulation frequency of the plane and sphericalwaves on the detector, i.e., the dependence of the phase of the electron on the final momentum. In
the Lewenstein model [93, 97] the phase of an ionized electron is e−iS/h̄ , where S is the semiclassicalaction, given by
Z t
S(p, t, tb ) =tb
p(t0 )2+ Ip dt,0
2me

(3.1)

where Ip is the ionization potential of the atom or molecule, me is the mass of the electron, tb is
the time the electron tunnels into the continuum, and p(t0 ) is the momentum. Thus, the probabilityof observing an electron at some position on the detector can be found by integrating all of theclassical trajectories that reach the same final momentum and adding them coherently. In practice,
this means that the Equation 3.1 must be integrated up until the time when the electron rescattersfrom the ion, after which both electrons take identical paths to the detector. In the PSW model,
the situation is further simplified because the calculation need only be completed in one dimension:
along the component of electron momentum in the direction of the laser polarization direction (Pk ).
This analysis is shown in Figure 3.5b, which plots the action S versus Pk , accumulated in the time
between ionization and the time at which the electron returns to the ion core at its lowest recollision

39
velocity . The slope of this line corresponds to the modulation frequency of the plane and sphericalwaves in the PSW model, which, in turn, determines the spacing of the interference fringes in the
spider structure. To simplify the analysis, we make the approximation that this slope is stepwise
constant.
This simple procedure generates interference patterns that quantitatively reproduce the spacing
and shape of the spider structures seen in the experimental data. As shown in Figure 3.2a, thepredicted minima are in excellent agreement with the experimentally observed interference minima.
This agreement is achieved with no fitting parameters – the structures are generated from firstprinciples with minimal computational effort. The calculation requires only the wavelength andintensity of the driving laser and the ionization potential of the atom. This shows that, although theshape and spacing of the spider structures do not depend strongly on the structure of the atom ormolecule, the PSW model suggests that structural information will be encoded in the momentumdependent ratio between the plane wave and the spherical wave.

3.6

Inner spider structures

In addition to reproducing the shape of the primary spider structures, the PSW model alsooffers a simple explanation for the inner spider structures (Figure 3.2b). By examining Equation 3.1
and Figure 3.3b, it is clear that there is a relationship between the different amounts of time thatthe various electron trajectories spend in the continuum and the spacing of the spider structuresthat are generated. Using this relationship, we can explain the experimentally observed inner spider
structures as resulting from electrons that spend significantly more time in the continuum before
rescattering. More specifically, we conclude that the distinct inner spider structures are createdby electrons that re-encounter the ion a specific number of times before scattering from the ion.
Electron trajectories that arrive at the detector with low final momenta correspond to electrons
that are ionized near the peak of the laser field and can revisit their parent ion more than once
(Figure 3.5a). The PSW model allows us to easily compute the spacing of the spider structures thatwould result from each type of trajectory and compare this spacing to the experimental photoelectron40
angular distribution (Figure 3.5f).

Position (nm)

5

100

a

Action, S/h (cycles)

10

0
5

5 revisits
4 revisits
3 revisits
2 revisits
1 revisit

10
15
20

1.0

0

5

10

c Argon

15

Time (fs)1300 nm

20

25

30

b

2000 nm1300 nm
785 nm

80
60
40
20
0
0.0

0.2

0.4

0.6 0.8
P (a.u.)d Xenone Xenon4 Revists (top)& 2 Revisits
boundaries
0.5 0.0 0.5
P (a.u.)0.5 0.0 0.5
P (a.u.)2000 nm

TDSE

1.0

1.2

f XenonPSW

P (a.u.)

0.5
0.0
0.5
1.0

2 Revisits
boundary
0.5 0.0 0.5
P (a.u.)0.5 0.0 0.5
P (a.u.)Figure 3.5: Multiple scattering of the electron with the ion. (a) Depending on when an
electron is born into the continuum, it will be driven past the ion a specific number of times. (b)Quantum phase obtained by integrating each electron trajectory from when it is born to when it
revisits the ion for the second-to-last time versus the final momentum parallel to the laser polarization(Pk ). The frequency of the plane and spherical waves is given by the slope of this graph. The steps
at low momenta correspond to regions of multiple rescattering. (c) Experimental photoelectron
distribution from argon ionized by a 1.3 µm, 7.5×1013 W/cm2 laser shows a clear boundary between
the high momentum region where only one revisit is possible and the low-momentum region where
scattering can take place during a subsequent revisit. (d) Photoelectron distribution from xenon
using a 2.0 µm, 5 × 1013 W/cm2 laser displays clear boundaries that correspond to the second andforth revisits. (e) TDSE calculations reproduce the low-momenta structures in xenon. (f) Singlecycle PSW model, including scattering on the first revisit (outer spiders) as well as the second andforth revisits (inner spider structures). Adapted with permission from Ref. 2. c 2012 American
Physical Society

This simple picture provides insight into the physics of the recollision interaction. Simple

41classical calculations (Figure 3.5a) show that subsequent revisits of the ionized electron to the coretake place with lower velocities. Since slower trajectories will be more influenced by the Coulomb
potential, it is reasonable to assume that the main scattering event will take place during one of the
final two laser-driven re-encounters with the ion, since these two re-encounters take place with thelowest velocity. The second to last encounter occurs with lower velocity since the oscillation anddrift directions are opposite. By carefully measuring the spacing of the inner spider structure in
the experimental photoelectron spectra and comparing with the results of the simple PSW model(Figure 3.2g), we can conclude from our data that scattering on the second-to-last re-encounter does
indeed play the most significant role. In other words, if an electron makes three passes near theion in the longitudinal direction, it is most likely to scatter strongly on the second pass. Thus, we
can reproduce the experimental spider structures by integrating each electron trajectory from thetime that the electron tunnels into the continuum to the time that it re-encounters the ion for thesecond-to-last time (Figure 3.5b).
For high-final-momenta trajectories, there is no change in the resulting photoelectron distribution, since these trajectories encounter the ion only once. Thus, the main spider structures are preserved at high final momenta, in good agreement with experiment. However, for low-final-momenta
trajectories, the spacing of the spider structure becomes narrower in discrete steps that correspondto the classical boundaries between trajectories that are driven past the ion multiple times andscatter on the second-to-last revisit.2 The calculated spacing of the spider structure inside the firstboundary (Figure 3.5f) is approximately half the frequency of that outside, in good agreement withexperiment (Figure 3.5c).
2 One might object to the term “multiple rescattering” to describe the process of scattering on a high-order revisit,since it seems to imply that the electron is scattering many times from the ion, while the model proposed above
only incorporates one scattering step. However, considering the electron trajectories in a classical model: in order tointeract with the Coulomb potential of the ion strongly on a high-order revisit, the electrons must undergo a slightangle change on the first revisit so that it may then pass more closely to the ion on a later revisit. Thus, while we model
the multiple rescattering process as only involving one strong scattering step, it is necessarily a more complicatedprocess of soft “Coulomb focusing” on low-order revisits followed by strong scattering on subsequent revisit.

42

3.7

Measurement of the quantum tunnel distanceThe cutoff energies for various numbers of revisits can be easily calculated using classical mechanics (Figures 3.1c-f). If we assume that electrons tunnel at x = 0 and ignore the effect of the
Coulomb potential after ionization, then electrons with kinetic energy greater than 0.09 Up willrevisit only once, electrons with energy between 0.09 and 0.06 Up will revisit three times (scatteringon the second revisit), and electrons with energy less than 0.06 Up will revisit five or more times(scattering on the forth, or subsequent even-numbered revisit). However, the predicted position of
the cutoff is slightly lower than that observed in the experimental photoelectron spectra unless thefinite tunnel distance is taken into account.
The tunnel distance results from the fact that electrons will be born into the continuum at a
finite distance from the atom, which is dictated by the strength of the electric field and the ionization
potential of the species (Figure 3.6a). The tunnel distance varies with the laser electric field, but
at the peak of a laser field of intensity 5 × 1013 W/cm2 , it is on the order of 5 Å for most atoms.
If this finite tunnel distance is considered, the classical boundaries move to slightly higher energies,
and are in better agreement with the experimental data (Figures 3.6b and A.3). To our knowledge,
this is the first example where the finite tunnel distance inherent in strong-field ionization can beextracted from an experimental observable.
Interestingly, this simple model offers a straightforward explanation for the spike-like low-energy
structure (LES) observed in previous time-of-flight studies [86, 87]. The location of the cutoff energy
for three revisits matches perfectly with the position of the LES, which was found to scale with theqI
Keldysh parameter γ = 2Upp as γ −1.8±0.1 . Our simple model provides further insight, showing
that, when the tunnel distance is taken into account, the cutoff energy for two revisits (Ecutoff ) also
depends on the ionization potential of the atomic species as
Ecutoff ∝ 0.06 Ip γ −1.8 ,(3.2)

in perfect agreement with the experimental results (Figure 3.6). If we make the incorrect approximation that the electron originates at the position of the ion, then we would predict a γ 2 scaling. Thus,

43

Figure 3.6: Measurement of the quantum tunnel distance. (a) In the presence of a strong
laser field (5 × 1013 W/cm2 ), the atomic Coulomb potential is deformed, enabling tunnel ionization,
where the tunneling distance is determined by strength of the laser field and the ionization potentialof the atom. (b) By examining the classical equations of motion, we plot the theoretical cutoff
between trajectories that revisit the ion once and those that rescatter several times (lines). If thetunnel distance is included, the theoretically predicted multiple rescattering cutoffs agree with theexperimentally observed cutoffs (points). If the tunneling distance is ignored (simple theory, dashedline), the theory no longer agrees with the data. The experimental intensity was calibrated from the2Up cutoff and was assumed to be 10%. The error in the energy of the multiple rescattering cutoff
was assumed to be 0.02 atomic units of momentum. Adapted with permission from Ref. 2. c 2012
American Physical Society

by observing a deviation from the γ 2 scaling, we observe this tunnel distance distance in our data.
Other theoretical work has found that electrons that reach the turning point of their field-driven
oscillation while in close proximity to the ion will result in a low-energy spike in the photoelectron
distribution [100]. This further supports the notion that our predicted cutoff for the inner spider
structures corresponds to the position of the peak in low energy electrons.

3.8

Conclusion

In conclusion, by generalizing the well-known three-step strong field ionization model using asimple plane-spherical wave model, we can intuitively explain the experimental photoelectron angular
distributions of atoms ionized in strong laser fields. We show that newly observed low-energy features
display clear signatures that an electron can pass by its parent ion more than once before strongly

44
scattering from it. Furthermore, the data show that when an atom is ionized by an intense laser,
the electron emerges at a finite distance from its parent ion that corresponds to the far side of thequantum tunneling barrier. These new observations and physical explanations will inform futurestudies that seek to extract femtosecond-resolved structural information from strong-field ionization.

Chapter 4

Plasma Explosion Imaging

This chapter is adapted, with permission, from:• D. D. Hickstein, F. Dollar, J. L. Ellis, K. J. Schnitzenbaumer, K. E. Keister, G. M.
Petrov, C. Ding, B. B. Palm, J. A. Gaffney, M. E. Foord, S. B. Libby, G. Dukovic, J. L.
Jimenez, H. C. Kapteyn, M. M. Murnane, and W. Xiong. Mapping Nanoscale Absorptionof Femtosecond Laser Pulses using Plasma Explosion Imaging. ACS Nano, 8 (9), 2014,
8810. doi: 10.1021/nn503199v
c 2014 American Chemical Society

Figure 4.1: Illustration of plasma explosion imaging (PEI) in a single nanoparticle. A femtosecond laser pulse interacts with a single gold–dielectric composite nanoparticle, ejecting positive
ions, which are recorded by a two-dimensional detector (bottom).

46

4.1

Abstract

This chapter describes the development of a new technique for investigating the interactionof nanostructures with strong laser fields: plasma explosion imaging (PEI). PEI enables the direct
measurement of the highly localized light absorption that takes place in a single nanostructure irradiated by a strong femtosecond laser. By imaging the photoion momentum distribution resulting fromplasma formation in a laser-irradiated nanostructure, PEI maps the spatial location of the highly
localized plasma and thereby images the light absorption on the nanometer scale. This method
probes individual, isolated nanoparticles in vacuum, which allows us to observe how small variationsin the composition, shape, and orientation of the nanostructures lead to vastly different light absorption. In this chapter, we study four morphologically and chemically different nanoparticle samples
with overall dimensions of ∼100 nm and find that each sample exhibits distinct light absorption
mechanisms despite their similar size. Specifically, we observe the following effects:• Subwavelength focusing in single NaCl crystals• Symmetric absorption in TiO2 aggregates• Surface enhancement in dielectric particles containing a single gold nanoparticle• Hot spots in dielectric particles containing multiple smaller gold nanoparticles.
These observations (Figure 4.2) demonstrate how PEI directly reveals the diverse ways in which
nanoparticles respond to strong laser fields, a process that is notoriously challenging to model becauseof the rapid evolution of materials properties that takes place on the femtosecond timescale as asolid nanostructure is transformed into dense plasma.

4.2

Introduction

4.2.1

Background

The interaction of strong (>1013 W/cm2 ) laser fields with bulk materials has widespread applications, including precision machining on the sub-micron scale [101], the “green” synthesis of

47

100	
  nm	
  

Nanopar+cle	
  enhances	
  laser,	  forms	
  localized	
  plasma,	  	
  ejects	
  ions	  Figure 4.2: Summary of PEI in four nanostructures. PEI uses a femtosecond laser pulse toprobe nanoparticles of different compositions, shapes, and orientations. Based on the structure of
the particle, the electric field of the laser pulse is enhanced in a specific region of the nanoparticle.
The location of the light-field enhancement can be deduced based on the direction(s) that ions areejected. Adapted with permission from Ref. 3. c 2014 American Chemical Society

nanoparticles [102], and the production of high-energy electrons, ions and photons [103]. Nanoscale
structures can locally enhance a laser field, often by many orders of magnitude [35], enabling thegeneration of strong laser fields that are localized on the nanometer scale, thus paving the way forbreakthrough techniques and technologies. For example, gold nanoparticles are being designed toseek out cancerous tumors in the body and, when irradiated with a femtosecond laser, produce
shock waves that destroy the tumor with minimal damage to nearby tissues [104, 105]. Additionally,
several preliminary experiments have demonstrated the ability of laser-irradiated nanostructuresto accelerate electrons, suggesting that nanomaterials may enable the fabrication of miniaturizedparticle accelerators [38, 40, 42, 106]. However, transforming these proof-of-principle concepts into
practical technologies requires an advanced understanding of how nanostructures respond to lightfields that are near the damage threshold.
For short-pulse laser intensities near and above the damage threshold (∼3 × 1013 W/cm2 forglass [107], and roughly similar for most other dielectric materials) the interaction of femtosecond
laser pulses with bulk materials is a complex process that is extremely challenging to model. The
difficulties stem largely from the fact that the laser pulse modifies the optical properties of thematerial on the femtosecond timescale [108], requiring a model that incorporates the time-dependent

48
properties of the laser field, the solid material, and the newly formed plasma. Materials that exhibit
nanoscale structure present a further challenge because features smaller than the wavelength of thelight can enhance the electric field on the nanometer scale, and this effect depends strongly on theexact size, shape, and composition of the particle. For example, past work harnessed the abilityof nanostructured targets to efficiently absorb laser light to create bright soft X-ray sources [109],
but the detailed mechanisms of this enhancement could not be understood in detail because of thecomplexity of the interaction. Thus, there is pressing need for a direct measurement technique thatcan provide clear insight into how nanomaterials interact with laser fields.

4.2.2

Experimental approach

Making direct measurements of nanostructures irradiated with strong laser fields presents several experimental hurdles. First, when exposed to strong laser fields, nanostructures are damaged,
and thus a fresh sample is required for each laser shot. Second, nanomaterial samples are rarely
homogeneous, often varying widely in size, shape, composition, and surface roughness. Even small
variations in the morphology of a nanostructure can have a dramatic effect on how the nanostructure
responds to incident light fields. When particles of different sizes and shapes are probed simultaneously, these variations are obscured. Finally, the orientation of asymmetric nanoparticles relative tothe laser propagation and polarization can dramatically influence how they interact with the lightfield.
Here we utilize a method that overcomes the experimental hurdles by imaging the localized
nanoscale plasma that is created when an isolated nanostructure is irradiated with a short (40 fs),
intense (∼3 × 1013 W/cm2 ) laser pulse (Figure 4.3). Instead of working with nanoparticles suspended in liquid solution or deposited on a surface, we employ a flowing aerosol of nanoparticles(Figure 4.3) that provides a fresh nanoparticle for every laser shot, thereby allowing us to use wellestablished angle-resolved-photoion-spectroscopy techniques [2, 4, 51]. Despite probing only a single
nanoparticle each laser shot, many particles can be probed each second through the use of a highrepetition-rate femtosecond laser (1 kHz in this study).

49
Detector	
  

Ions	
  
Aerodynamic	
  Lens	  Nanopar6cle	
  beam	  laser	
  
cond	
  
e
s
o
t
Fem

a)	
  Experimental	
  apparatus	
  Plasma	  forma6on	
  
in	
  a	
  single	
  nanopar6cle	
  Figure 4.3: Experimental apparatus for observing PEI in single nanostructures. (a)The nanoparticle aerosol is introduced into the high-vacuum chamber by an aerodynamic lens that
produces a collimated beam of nanoparticles. The nanoparticle beam is crossed with a tightly focused
40 fs laser pulse that interacts with a single nanoparticle. (b) When the nanoparticle encountersa region of high laser intensity (>1014 W/cm2 ), it is completely transformed into a plasma thatthen ejects ions in all directions. (The apparent lack of ions in the center of the detector is a resultof an inhomogeneous detector response.) (c) When the particle encounters a region of low laser
intensity, a plasma is formed only in a localized region of the particle, and ions are ejected in a
specific direction that depends on the structure, composition, and orientation of the particle. The
photoions are collected by a velocity-map-imaging spectrometer and provide information about the
localized electric fields in the nanoparticle. Adapted with permission from Ref. 3. c 2014 American
Chemical Society

A key aspect of our approach is the use of laser intensities slightly below the plasma formationthreshold of the bulk material; this creates a localized nanoplasma only within a specific region of ananostructure. This method contrasts with previous studies [4, 38], which used laser intensities highenough to field-ionize the entire nanoparticle, creating a uniform plasma throughout the particle.
Despite using laser intensities below the bulk plasma formation threshold, we do observe (localized)
plasma formation in the nanoparticles. The formation of plasma at sub-threshold laser intensities
occurs because of nanoscale field-enhancements, whereby the nanoparticle itself enhances the laser
field in localized regions. Thus, while the average laser intensity is below the plasma formationthreshold, some regions of the nanoparticle can experience light fields higher than threshold, and aplasma is formed only in these regions of the nanoparticle. The heated plasma is rapidly ejected50
outwards from the surface of the nanoparticle, producing ions with momenta that correspond to
the location of the plasma in the nanoparticle. Since we record a two-dimensional image of theangular distribution of the ions using an angle-resolved imaging detector, we refer to this techniqueas “plasma explosion imaging”. In the following examples, we show how PEI can be used to gain
insight into the unusual and unintuitive light-absorbing properties of nanomaterials with a range ofcompositions and morphologies.

4.2.3

Summary of findings

Using this newly developed PEI technique, we observe dramatic differences in how nanoparticles of different compositions and shapes respond to intense laser fields. Specifically, we observe
subwavelength focusing in NaCl, symmetrical absorption in aggregates of TiO2 particles, and highly
localized light absorption in gold–dielectric hybrid nanostructures. Surprisingly, we find that we canmodel light absorption in this strong-field regime using the finite-difference time-domain (FDTD)
method, which has seen great success in modeling low-intensity light–nanoparticle interactions. Thisagreement suggests that many of the useful nanoscale optical effects that exist at low laser intensities(such as subwavelength focusing and plasmonic effects) will extend into the near-damage-threshold
regime where they might be expected to breakdown. By demonstrating the nano-optical effects
present at laser intensities near and above the material damage threshold, we pave the way for future developments that utilize the unique ability of nanoparticles to absorb, scatter, and focus lightin the high-intensity regime.

4.3

Results and Discussion

4.3.1

Overview

A complete description of the sample preparation and experimental apparatus is found in
Section B.2 (and Chapter 2) and is briefly summarized here. To perform photoion spectroscopy on
isolated nanostructures, we employ an aerodynamic lens [70, 110, 111], which produces a collimatedbeam of nanoparticles from a nanoparticle aerosol and leaves the carrier gas divergent. A skimmer

51
then allows us to separate the carrier gas from the high-concentration beam of nanoparticles andthereby maintain high vacuum 1 × 10−6 Torr in the photoion spectrometer. The particle beam isirradiated with tightly focused, intense (∼3×1013 W/cm2 ), 785 nm, 40 fs laser pulses. Because of thetight focusing of the laser and the narrow width of the particle beam, the volume of the interaction
region is only ∼10−7 cm3 (see Section B.2.1). Since the particle density is ∼105 particles/cm3 , only
one laser shot in ∼100 will hit a nanoparticle. Statistically, those pulses that do hit a nanoparticle,
typically hit only one nanoparticle. The photoions produced from the laser-irradiated nanoparticles
are collected by a VMI photoion spectrometer [2, 4, 5, 51, 108], which produces images of the ion
momentum distribution.
To develop a broad understanding of how nanostructures of different shape and size interact
with laser fields near the damage threshold, we prepared a range of nanoparticle aerosols startingwith four different aqueous solutions: NaCl dissolved in water, ∼5 nm TiO2 nanoparticles suspended
in water, 50 nm gold nanospheres suspended in water, and 17 nm gold nanospheres suspended inwater. The nanoparticle aerosols were generated from the aqueous solutions using a compressedgas atomizer, which produces droplets with an average diameter of ∼1 µm. Before entering thevacuum chamber, the droplets evaporate to leave single crystals (when using a salt solution) or
aggregated nanostructures (when using a colloidal solution) consisting of one or more nanoparticles.
The concentration of the material in solution determines the average diameter of the crystals (orthe average number of nanospheres per aggregate).

4.3.2

Electron microscopy

To understand the morphology of the various nanostructures, we performed transmission electron microscopy (TEM) on nonirradiated nanostructures collected at the exact point where theywould be probed by the laser. The TEM images reveal that the nanostructures that emerge fromthe aerodynamic lens are often quite different from the structures that exist in the solution phase(Figure 4.4). The NaCl solution produces particles with an average diameter of ∼100 nm (Figure 4.4a). Since crystal faces are clearly visible in many of the particles, we conclude that most of

52
the nanoparticles are single crystals of NaCl, consistent with previous studies of salt aerosols [112].
The TiO2 particles present as 50–100 nm aggregates of ∼5 nm TiO2 particles (Figure 4.4b). The
aggregates form because many ∼5 nm TiO2 crystals are present in a single droplet. As the droplet
evaporates, the nanoparticles clump into larger aggregates.

(a)

(b)

NaCl

100 nm(c)

Gold, 50 nm

100 nmTiO2

100 nm(d)

Gold, 17 nm

100 nmFigure 4.4: Transmission electron microscopy (TEM) images of nanoparticles collected
at the interaction region. (a) The aqueous NaCl solution evaporates to form single crystals. (b)The solution of TiO2 nanoparticles produces 50–100 nm diameter aggregates of ∼5 nm particles. (c)The solution of 50 nm gold nanoparticles produces hybrid nanostructures consisting of a single gold
nanoparticle (dark polygons) residing near the surface of a sphere of polyvinylpyrrolidone (PVP, graycircles). d) The solution of 17 nm gold nanoparticles also generates hybrid gold–PVP nanostructures,
but these nanostructures contain numerous 17 nm gold nanospheres. Adapted with permission from
Ref. 3. c 2014 American Chemical Society

The morphology of the aerosol particles generated from the aqueous solutions of gold nanospheresis surprising; heterogeneous nanostructures are clearly seen in the TEM images (Figure 4.4c and d).
For the solution of 50 nm gold nanospheres, the aerosol particles typically consist of one 50 nm gold
nanosphere embedded near the surface of a ∼100 nm sphere of lower-density material. The lowerdensity material is polyvinylpyrrolidone (PVP), an organic polymer that is added to the solution

53
by the manufacturer in a similar concentration to that of the nanospheres and serves to keep thenanospheres dispersed in solution.
The solution of 17 nm gold nanospheres also displays a heterogeneous morphology with gold
spheres embedded in PVP (Figure 4.4d). However, the number concentration of the gold nanospheresis much higher, and the aerosol particles generated from this solution often contain ten or more gold
nanospheres. Thus, while the composition of the 17 nm and 50 nm gold nanospheres samples issimilar in aqueous solution, the aerosol particles display starkly different morphologies. Interestingly,
for both the 50 nm and 17 nm gold nanosphere samples, the gold nanospheres are almost invariably
located towards the outside of the PVP nanosphere.

4.3.3

Photoion spectroscopy

As shown in Figure 4.3, a collimated beam of nanostructures is introduced into the VMI spectrometer via the aerodynamic lens, and individual nanostructures are probed with femtosecond laser
pulses. Though the focused laser has a Gaussian intensity profile, the full-width at half-maximum
is on the order of 20 µm which is very large compared to the ∼100 nm dimensions of the nanostructures used in this study and means that each nanoparticle experiences a laser field that is almost
perfectly homogeneous over the dimensions of the nanoparticle. When the laser intensity exceeds∼5 × 1013 W/cm2 , the laser delivers enough energy to create a plasma in the entire nanoparticle(Figure 4.3b). In contrast, at intensities near 3 × 1013 W/cm2 , a plasma is formed only in a small
region of the particle (Figure 4.3c). Since it is these localized plasma cases that provide information
about the local-field enhancement, they are the focus of this work. Creating primarily localized
plasmas is achieved by keeping the laser intensity in a range such that only the most intense regionsof the laser focus are capable of creating a plasma in a nanoparticle.
The mechanism for plasma formation in solid-density materials irradiated with femtosecond
pulses near the damage threshold is typically described as an avalanche ionization process [113–115]. First, a few free electrons are generated through multiphoton or tunnel ionization of thematerial (for conductors, free electrons already exist in the material). Next, these free electrons are

54
driven by the strong laser field and can reach kinetic energies exceeding the ionization threshold.
When an electron impacts an atom, it can remove one or more electrons through electron impact
ionization. The newly liberated electrons can then cause more ionization in an avalanche process.
Both the initial ionization process and the avalanche ionization process scale exponentially withlaser intensity [1] and, therefore, a small increase in the laser intensity in certain regions of thenanoparticle can have a very large effect on the ionization rate, and, in turn, determine if complete
breakdown of the material will occur.
Given the field-driven avalanche breakdown mechanism, it is conceivable that any ionization
within the nanoparticle would create free electrons, which could then ionize neighboring atoms,
initiating rapid ignition over the entire nanostructure. However, the excursion distance of a freeelectron driven by a 785 nm laser field at an intensity of 5 × 1013 W/cm2 is only ∼1 nm. In addition,
we estimate the plasma temperature to be approximately 5 eV [4], which does not provide thethermal electrons enough kinetic energy to propagate more than a few nm during the laser pulse.
Consequently, the free electrons cannot travel to all regions of a 100 nm nanoparticle during theduration of the laser pulse. Rather, at intensities near the damage threshold, avalanche breakdown
stays localized near the region of initial ionization, which is the region that experienced the highest
local field. Thus, the physical location of the localized plasma serves as a map of the locally enhanced
laser field that caused the avalanche breakdown (Figure 4.5).
After the laser pulse is over (<0.1 ps), the region of localized plasma rapidly expands on
the picosecond timescale, attempting to eject ions in all directions [4]. However, those ions that arelaunched inwards (towards the undamaged material) cannot penetrate the material (because of their
low kinetic energy) and do not reach the detector. We observe only ions that are launched away fromthe undamaged regions of the nanostructure. As a result, we can interpret the angular features in thephotoion momentum distribution as a direct result of spatial location of the localized plasma in thenanostructure. The photoelectrons can provide similar information to the photoions (Section B.3),
but with somewhat less resolution due to the increased scattering of the electrons compared to theions. Thus, we choose to study the photoions primarily. Using mass spectrometry (Section B.4),

55

NaCl

a

b

c

d

e

f Average

50
5
0
5

laser

50

g

h

i

j

k

l Average

50

Energy/charge (eV/Z)

TiO2

5
0
5

17 nm Gold50 nm Gold

50

m

n

o

p

q

r Average

50
5
0
5

50

s

t

u

v

w

x Average

50
5
0
5
50

50

5 0 5

50

50

5 0 5

50

50

5 0 5

50

50

5 0 5

Energy/charge (eV/Z)

50

50

5 0 5

50

50

5 0 5

50

Figure 4.5: Photoion angular distributions (PADs) from individual nanostructures showions ejected in different directions. The laser propagates from left to right and is polarized
in the vertical direction, although no polarization dependence is observed in this study. (a–e) The
photoions from ∼100 nm NaCl crystals are ejected in the laser propagation direction, suggestinga focusing effect. (g–k) The ions from TiO2 aggregates are typically centered around zero kinetic
energy, indicating mostly symmetric plasma formation. (m–q) Ions from 50 nm gold nanoparticles
embedded in a larger PVP sphere eject ions with directions that depend on the orientation of thenanostructure. (s–w) Photoions from 17 nm gold–PVP nanostructures eject ions in the direction
opposite of the laser propagation, indicating absorption of laser energy on the front (illuminated)side of the nanoparticle. The averaged images (f,l,r,x) correspond to 70, 869, 419, and 108 particles
respectively, and reveal general trends, but conceal the diversity of the individual particles, especiallyin the case of the 50 nm gold sample. Adapted with permission from Ref. 3. c 2014 American
Chemical Society

we confirm that the photoions that reach the detector are primarily from the nanoparticles and notfrom other sources, such as the background gas.
For all of the nanostructure samples investigated, we observe considerable hit-to-hit variations in
the photoion angular distributions (Figure 4.5), reflecting the differences in the shape, composition,and orientation of the particles. Despite the hit-to-hit variations, we can easily spot general trends
in the direction of ion ejection in the four samples presented here. These trends are summarized in
Figure 4.5, and confirmed via the center-of-mass distributions presented in Figure 4.6. To understand56
the physical origin of the localized light absorption in each nanostructure, FDTD methods were used
to simulate the interaction of 785 nm femtosecond pulses with the nanomaterials (Figure 4.7 andSection B.2).

Energy/charge (eV/Z)

Energy/charge (eV/Z)

15

a

b

NaCl

10

TiO2

5
0
5

laser

10
15
15

c

laser

d

Gold, 50 nm

10Gold, 17 nm

5
0
5
10
15

laser
15

10

laser
5

0

5

10

Energy/charge (eV/Z)

15

15

10

5

0

5

10

Energy/charge (eV/Z)

15

Figure 4.6: Position of the center of mass (CoM) of each PAD for the various nanoparticle
samples. The position of each dot indicates the CoM of the photoion distributions and larger sizes
correspond to higher ion yield. (a) NaCl particles act as lenses, focusing the light onto the backside of
the particle and ejecting ions primarily in the laser propagation direction. (b) TiO2 undergoes plasma
formation over the entire particle, generating plasma explosions that are largely symmetric about
zero kinetic energy. (c) The 50 nm gold nanosphere samples produces composite nanostructuresconsisting of gold nanospheres embedded in a dielectric material. A plasma is preferentially formedin the gold nanosphere and explodes outward, ejecting ions in a direction that depends on theorientation of the nanostructure, but not on the laser polarization or propagation directions. (d) The
17 nm gold nanosphere sample forms aggregate nanostructures consisting of many gold nanospheresthat absorb mainly on the illuminated face and eject ions opposite the direction of laser propagation.
Adapted with permission from Ref. 3. c 2014 American Chemical Society

57

Figure 4.7: Finite-difference time-domain (FDTD) simulations of the electric field intensity inside of the various nanostructures. The laser propagates from left to right andthe colorscale is in units of the incident field intensity. Plasma formation is most likely to occur
near the regions of highest electric field. (a) In the NaCl particles, the laser field is enhanced byapproximately 10% on the side opposite of the light source. (b) In the TiO2 aggregates, the highest
electric field is in the regions between the TiO2 particles and does not have a preference for thelaser polarization or laser propagation directions. (c) For the 50-nm-gold–PVP nanostructures, theelectric field is enhanced substantially near the surface of the gold nanoparticle, which ignites localized plasma formation in the dielectric material. (d) In the 17-nm-gold–PVP nanostructures, thelight field is greatly enhanced in hot spots between the nanospheres, and higher fields are seen on
the illuminated side of the nanostructure. Adapted with permission from Ref. 3. c 2014 American
Chemical Society

4.4

Case studies of nanoscale light enhancement

4.4.1

NaCl crystals: nanofocusing in dielectric nanomaterials

In the case of the ∼100 nm NaCl crystals, ion ejection is observed almost exclusively in theforward direction, i.e., the direction of laser propagation (Figures 4.5a and 4.6a). This effect is the
opposite of what is expected for an opaque macroscopic object, which would absorb light primarily

58
on the illuminated side and eject material back towards the laser. It is also different from whatis expected at laser intensities well above the damage threshold, where the high electron densities
would cause the resulting plasma to act like a metal, again absorbing energy on the surface facing
the laser. Instead, we observe that a ∼100 nm NaCl crystal acts like a lens, focusing the light onto
itself and forming a plasma on the back side. Of course, strictly speaking, we cannot apply theterm focusing in this case, since geometric optics does not describe the interaction of light with
objects smaller than the wavelength. However, numerous studies of photonic nanojets [116–120]
have confirmed the ability of nanoparticles to concentrate visible light on length scales far smaller
than the wavelength, a phenomenon referred to as subwavelength focusing.
Indeed, our FDTD simulations confirm the subwavelength focusing of the NaCl particles, revealing a ∼10% increase of the light intensity on the backside of the particle compared to the front
side (Figure 4.7a). While this increase is relatively modest compared to the intense lensing observedin micron-sized dielectric particles [117], our experiment is operated in a regime very close to thethreshold for plasma formation, and a small increase in intensity can have dramatic effects on thehighly nonlinear plasma formation process.

4.4.2

TiO2 nanoclusters: light interaction with a particle ensemble

The overall size of the TiO2 aggregates is similar to the NaCl crystals (both are ∼100 nm
in diameter). However, in contrast to NaCl, the ion ejection from the TiO2 particles is generally
symmetric about zero kinetic energy (Figures 4.5b and 4.6b). This effect cannot be explained by adifference in the material properties, because both TiO2 and NaCl are transparent materials witha bandgap larger than the photon energy. Given this similarity, one would expect TiO2 to exhibit
the same subwavelength focusing that takes place in NaCl. The different response must then be
due to the fact that the large TiO2 aggregates are composed of many ∼5 nm crystals instead of asingle large crystal. Our FDTD simulations (Figure 4.7b) reveal considerable enhancement of theelectric field between the 5 nm TiO2 nanoparticles, but show no preference for the front or back of
the 100 nm aggregate. There are two effects that cause the lack of focusing in the TiO2 aggregates.

59First, the strong enhancement between adjacent ∼5 nm TiO2 particles likely overpowers any small
focusing effect that is seen within the TiO2 particles. Second, the TiO2 particles are significantly
smaller than the NaCl nanoparticles (5 nm versus 100 nm diameter) and therefore they are further
from the regime of geometric optics and will experience a more homogeneous internal field. Thus,by simply changing from a single crystal to a similarly sized aggregate of smaller particles, we cancompletely change the light absorption properties of the material, even at a scale much smaller than
the wavelength of the light.

4.4.3

50 nm gold nanoparticles: field enhancement at the surface

The gold–nanosphere–dielectric hybrid nanostructures are of particular interest, because the
50 nm and 17 nm gold nanoparticle samples are identical in chemical composition but exhibit vastlydifferent properties because of their different morphologies. For 50 nm gold nanostructures, the ion
explosions are directional, but the direction is random with respect to the laser (Figures 4.5c and4.6c). Explosions were observed in the direction of laser propagation, in the opposite direction, andin orthogonal directions, all with equal probability. Thus, the direction of the explosion is not set
by the laser, but by the spatial orientation of the nanostructure.
Gold nanoparticles are well known to enhance the electric field at their surface [116, 121–123], and this enhancement likely ignites the plasma formation process in the vicinity of the gold
nanosphere. Additionally, being metal, the gold particles already have conduction band electrons,
which are freely driven by the laser and absorb energy through collisions with the ions. Thus, theheating of the gold nanosphere will begin before the laser pulse has reached maximum intensity,
in contrast to the PVP, which must be ionized before it can strongly absorb energy from the laser
pulse. Both of these effects lead to a strong absorption of laser energy in the immediate vicinity of
the gold nanosphere, which leads to a localized plasma formation. This localized plasma creates adirectional ion ejection in a direction set by the orientation of the nanostructure. This rationalizationis confirmed by the FDTD simulations (Figure 4.7c), which reveal that the laser field is enhancedby more than 200% near the surface of the gold nanoparticle.

60
4.4.4

17 nm gold nanospheres: asymmetric hot-spots

Interestingly, the 17-nm-gold–PVP hybrid nanostructures display completely different behavior
than 50 nm gold nanostructures; for the 17 nm sample, the ions are ejected primarily in the backwards(opposite of the laser propagation) direction (Figures 4.5d and 4.6d). The difference stems from thefact that the 50 nm sample produces nanoparticles that contain only one gold nanosphere, whilethe 17 nm sample produces PVP nanoparticles that contain numerous 17 nm gold spheres. Since
the 17 nm spheres are located in close proximity to one another (Figure 4.3d), the electric field canbe enhanced by nearly an order of magnitude in the regions between the gold nanospheres (Figure4.7d). It is likely that the plasma formation takes place in the PVP in the electric field hot spots[124] between the gold nanoparticles. The FDTD calculations reveal that these hot spots are mostpronounced on the illuminated side of the aggregate, suggesting that plasma will preferentially formon this face of the particle. In analogy to geometric optics, it appears that the gold nanoparticles
on the illuminated side are blocking the light from reaching the back side of the particle.

4.5

Future directions

In this study we focused on laser intensities near the ablation threshold and, consequently, wewere able to successfully simulate the laser ablation process using numerical methods that ignore
the changes in the material properties that take place at high laser intensities such as the nonlinear
refractive index or the excitation of charge carriers to the conduction band. It is likely that such
effects begin to dominate as the laser intensity is increased. Future studies could utilize the plasma
explosion imaging technique to search for these nonlinear effects at laser intensities well above theplasma formation threshold. Indeed, a close examination of Figure 4.3b reveals that, while the highintensity explosion of the nanoparticle ejects ions in all directions, it is not completely homogeneous.
Thus, the plasma explosion imaging method can likely provide information about laser–nanoparticle
interactions at intensities well above the damage threshold.

61

4.6

Summary

We have demonstrated a new technique called plasma explosion imaging, where we use strong
femtosecond laser fields to create a localized plasma within isolated nanoparticles and use the momentum of the ejected ions to infer the location of this plasma within individual nanoparticles. The
location of the plasma indicates where the electric fields are enhanced in the particle and provides
a map of the nanoscale light absorption at laser intensities near the damage threshold. We apply
this novel method to observing sub-wavelength focusing in NaCl, symmetric plasma formation in
TiO2 clusters, and highly localized plasmaformation in gold–dielectric hybrid nanostructures. Figure 4.8 presents a summary of the different light absorption mechanisms observed in the various
nanostructures. In the future, this method can be easily extended to more complex nanostructuresand higher laser intensities, providing further insight into the interaction of strong laser fields withnanomaterials.
Par9cle	  morphology	
  

100	
  nm	
  NaCl	  Crystal	  Aggregate	
  of	
  	
  
TiO2	
  crystals	
  

50	
  nm	
  gold	  sphere	
   Many	
  17	
  nm	
  gold	  in	
  dielectric	
  spheres	
  in	
  dielectric	
  

Nano	
  lensing	  Symmetric	
  absorp3on	
  Surface	  enhancement	  Laser	  Ion	
  distribu3on	
  reveals	
  nanoscale	
  op3cs	  Asymmetric	
  hot	
  spots	  Figure 4.8: Summary of nanoscale light absorption revealed through PEI. While all particles presented here have similar diameters (∼100 nm), they absorb light in different ways, form
a localized plasma in different locations, and exhibit different characteristic photoion distributions,which indicate the light absorption mechanism for a single isolated nanoparticle. Adapted withpermission from Ref. 3. c 2014 American Chemical SocietyChapter 5

Shock Waves in Nanoplasma

This chapter is adapted, with permission, from:• D. D. Hickstein, F. Dollar, J. A. Gaffney, M. E. Foord, G. M. Petrov, B. B. Palm, K. E.
Keister, J. L. Ellis, C. Ding, S. B. Libby, J. L. Jimenez, H. C. Kapteyn, M. M. Murnane,
and W. Xiong. Observation and Control of Shock Waves in Individual Nanoplasmas. Phys.
Rev. Lett., 112 (11), 2014, 115004. doi: 10 . 1103 / PhysRevLett . 112 . 115004 c 2014
American Physical Society

Figure 5.1: Illustration of laser-driven shock wave in a nanoplasma. A beam of ∼100 nm
NaCl crystals is crossed by two laser pulses (400 nm and 800 nm). The first pulse forms a nanoplasma
and the second drives a shock wave through the nanoplasma.

63

5.1

Abstract

In a novel experiment that images the momentum distribution of individual, isolated 100-nmscale plasmas, we make the first experimental observation of shock waves in nanoplasmas. We
demonstrate that the introduction of a “heating” pulse prior to the main laser pulse increases
the intensity of the shock wave, producing a strong burst of quasi-monochromatic ions with anenergy spread of less than 15%. Numerical hydrodynamic calculations confirm the appearance ofaccelerating shock waves, and provide a mechanism for the generation and control of these shockwaves. This observation of distinct shock waves in dense plasmas enables the control, study, andexploitation of nanoscale shock phenomena with tabletop-scale lasers.

5.2

Introduction

Nanoscale plasmas (nanoplasmas) offer enhanced laser absorption compared to solid or gas
targets [37], enabling high-energy physics with table-top-scale lasers. Indeed, previous experimental
studies have observed the production of high-energy ions [38], and even nuclear fusion [39] in laserirradiated nanoplasmas. For more than a decade, theoretical studies have predicted that shockwaves can be generated in nanoplasmas, and that these nanoplasma shock waves might allow for
the practical generation of quasi-monoenergetic high-energy ions, neutrons from fusion processes, orultrafast X-ray bursts [40–42].
In an analytical study, Kaplan, Dubetsky, and Shkolnikov [40] find that shocks should be acommon phenomenon in expanding nanoplasmas, requiring only a plasma density distribution thatis highest in the center and decays smoothly towards the edges. Similarly, Peano et al. [41, 125] usednumerical simulations to show that the density profile of the precursor nanoplasma would dictate theproperties of the shock. In particular, they demonstrated that a weak laser pulse could be used toshape the density profile to so that a second, stronger laser pulse could produce more intense shockwaves. However, until this work, nanoplasma shock waves have eluded experimental observation.
In contrast to the theoretical studies, which model a single nanoplasma, previous experimental

64
studies of nanoplasmas [38, 126] used laser focal volumes that contained many particles, thereby
simultaneously irradiating nanoparticles of different sizes and with different laser intensities. As weshow in this work, the kinetic energy of the shock wave depends on the plasma size and the laser
intensity. Thus, studies that probe many nanoparticles simultaneously would create an ensemble ofshock waves with different kinetic energies, thereby obscuring their identification as shocks.
In this chapter, by imaging individual laser-irradiated nanoparticles, we remove the size andintensity averaging present in previous studies, which allows us to clearly observe nanoscale plasma
shock waves. Furthermore, we demonstrate that these shock waves can be controlled by using alaser pulse to shape the plasma density profile. Finally, we present hydrodynamic simulations thatprovide a mechanism for the generation and control of shock waves in nanoplasma.

5.3

Experiment

Our observation of shock waves in nanoplasma is enabled by a unique experiment (Figure 5.2)
that can detect photoions from the nanoplasma generated from a single laser-irradiated nanoparticle. Nanocrystals of NaCl, KCl, KI, or NH4 NO3 with diameters of ∼100 nm are created using acompressed-gas atomizer and introduced into the vacuum chamber using an aerodynamic lens. A
plasma is formed via illumination of a particle with a tightly focused 40-fs laser pulse (wavelength ofeither 400 nm or 800 nm) with an intensity that is adjusted between 3×1013 and 4×1014 W/cm2 . The
angle-resolved energy distribution of the ions created by the expanding nanoplasma is recorded using
a velocity-map-imaging (VMI) photoion spectrometer [2, 5, 51, 127] that records a two-dimensional
projection of the photoion angular distribution (PAD).
Because the laser focal spot is small compared to the spacing between the nanoparticles, weprobe, on average, one nanoplasma every 40 laser-shots (see Section 2.4.5). In all laser-irradiatednanoparticle experiments, each nanoparticle will experience a different laser intensity dependingon where it is located in the laser focus, which leads to intensity averaging effects if each PAD
contains ions from many nanoparticles, as was the case in previous nanoplasma studies [38, 114,
128]. However, in this experiment, each PAD corresponds to a single particle and, although the65

Detector	  Posi8ve	
  ions	  Electrodes	  Aerodynamic	
  lens	
  

400	
  nm	
  and	
  800	  nm	  	
  laser	
  pulses	
  Nanopar8cle	
  beam	  Plasma	  explosion	
  from	  single	
  nanopar8cle	
  Figure 5.2: Apparatus for imaging shock waves in individual nanoplasmas. An aerodynamic
lens focuses nanoparticles into a high-vacuum chamber where they are irradiated by a series of twotime-delayed laser pulses. The first pulse creates an expanding nanoplasma, while the second pulse
further heats the plasma, causing a pressure increase, which leads to shock wave formation. The
resulting photoion momentum distribution is projected onto a microchannel-plate detector using
three electrodes in a velocity-map-imaging geometry [51]. Art by Brad Baxley, JILA. Adapted withpermission from Ref. 4. c 2014 American Physical Society

intensity cannot be precisely controlled for each particle, no intensity averaging takes place within
a single PAD. This allows for the observation of previously undiscovered physical processes, eventhose that are exquisitely sensitive to laser intensity, particle size, or particle composition.

5.4

Results and Discussion

In our experiment, when the peak laser intensity is below 5 × 1013 W/cm2 , the PADs contain
only 100 or fewer ions, corresponding to the ionization of the residual N2 and H2 O gas that flows
with the particles through the aerodynamic lens. However, when the laser intensity is increased
above ∼5 × 1013 W/cm2 , we observe some PADs that contain more than 104 ions, indicating plasma
formation in a single nanoparticle (Figure C.3). Indeed, in this intensity regime, solid nanoparticles
are rapidly (<1 ps) converted into dense nanoplasmas through the following mechanism [113–115].
First, the strong laser field causes some of the atoms to ionize through tunnel ionization [126],
liberating about one electron per atom within a few tens of femtoseconds [1]. These free electrons

66
are accelerated by the strong laser field and then drive further rapid ionization through electron
impact ionization [114]. The electrons continue to be driven by the laser field and absorb energy
through collisions with the ions [129], reaching high temperatures.
When the laser intensity is increased above ∼1 × 1014 W/cm2 , shock waves appear in approximately 10% of the nanoparticle PADs (Figures 5.3 and C.3). Each shock wave manifests as a sharp
ridge on top of a broad photoion distribution. The ion kinetic energy of each shock ranges from
15 eV/Z to 50 eV/Z, where Z is the charge state of the positive ion. However, each individual shock

50 (a)No shockIon energy, x-direction (eV/Z)

Ion energy, x-direction (eV/Z)

is quasi-monoenergetic, with an energy spread of less than 15% (Figure 5.3b).

50 (b)

5
0
5

50

50

5

0

5

5
0
5

50

50

Experiment
1-Gaussian fit

10

0

0

10

20

30

40

50

Ion energy, x-direction (eV/Z)

515 (d)

0550Experiment
2-Gaussian fit

Full-width at half maximum: 13%

10

5

50

Ion energy, z-direction (eV/Z)

Ion yield (arbitraty units)

Ion yield (arbitraty units)

Ion energy, z-direction (eV/Z)
15 (c)

Shock

5
0

0

10

20

30

40

50

Ion energy, x-direction (eV/Z)

Figure 5.3: Experimental observation of shock waves in individual nanoplasmas. (a) The
photoion angular distribution (PAD) from a single NH4 NO3 nanoparticle irradiated with a pulse of
400 nm light followed by pulse of 800 nm light typically displays a broad ion distribution. Here thelaser propagates in the z-direction (right-to-left) and is linearly polarized in the x-direction. The
angular features are due to the inhomogeneous response of the imaging detector. (b) If the particle
size, laser intensity, and laser pulse time-delay are tuned appropriately, a sharp shock wave (orange
and yellow) appears in addition to the broad ion distribution. (c) The radial energy distributionof the typical nanoplasma explosion can be fit by a single broad Gaussian function. (d) The shock
wave manifests as an additional sharp peak, which can be fit by a second Gaussian function with anarrow energy spread. Adapted with permission from Ref. 4. c 2014 American Physical Society

67
The formation of the shock waves is sensitive to both the physical size and chemical composition of the particle. We observe that larger nanoparticles are more likely to create shock waves(Figure C.2), which can be explained by the fact that larger nanoplasmas absorb more energy fromthe laser field [37]. Using a single laser pulse, shocks are observed in a variety of compounds, including KI, NaCl, and KCl, and the threshold laser intensity required to create shocks scales roughlywith the ionization potential of the compounds (Figure C.3), as expected for the onset of tunnel
ionization [1], and in agreement with the relative ionization yields observed in single-particle mass
spectroscopy experiments [130]. For NH4 NO3 , the compound with the highest ionization potential
in this study, no shocks are observed in the single-pulse experiment (Figure 5.3), making it the ideal
example case for demonstrating the two-pulse shock generation scheme.
Two laser pulses with an appropriate relative time delay can be used to create shock waves
in all of the nanoparticles investigated in this study, including NH4 NO3 . The likelihood of shock
formation depends critically on the time delay between the first and second pulses. The minimal timedelay for shock creation coincides with the peak in the total photoion yield, which occurs around
7 ps (Figure 5.4a). Similarly, the maximum time delay for shock production occurs near 45 ps,corresponding to the end of the enhanced ion yield. Previous studies [128, 131] observed a similar
dependence of the photoion yield on time delay during the two-pulse irradiation of nanoparticles(although they did not observe shocks) and attributed this behavior to the increased absorption of
the second laser pulse caused by the expansion of the plasma following the first laser pulse.
The expansion of our nanoplasma into the vacuum is significantly slower than previous studies
due to the large size of the nanoparticles and can be estimated using the ion sound speed [126]rvexpand =

ZkTe
,
mi

(5.1)

where Z is the charge of the ions, mi is the mass of the ions, and kTe is the electron temperatureof the plasma. A 100 nm diameter particle composed of N+ ions (mass of 14 Da each) with atemperature of 10 eV would double in size in 6 ps, in good agreement with the 7 ps delay for shock
wave formation.

20 (a) No shock
Shock
Moving average (x2)1510800 nm first
400 nm second

4068

1.0 (b)

400 nm first
800 nm second

50

Ion energy distribution, x-direction20
020Time delay (picoseonds)

40

Ion yield, offset (arb. units)

Total photoion yield (arb. units)

Ion yield and shock formation versus two-pulse delay

0.8
0.6
0.4
0.2

40 ps
30 ps
20 ps
10 ps

0.0
0 10 20 30 40 50 60 70 80
Ion kinetic energy (eV/Z)

Figure 5.4: Control of shock wave formation using two laser pulses. (a) Each dot indicatesa single nanoplasma explosion of an individual NH4 NO3 nanoparticle as a function of the delay
between the 400 nm and 800 nm laser pulses. The first pulse forms a slowly expanding nanoplasma,
and the second pulse causes a rapid pressure increase inside of the nanoplasma, which leads to theformation of a shock wave. When the delay between the two pulses is greater than 7 ps, shockwaves are formed. The ion yield is higher when the 400 nm pulse precedes the 800 nm pulse because
the 800 nm pulse is more effective at heating the expanded nanoplasma. (b) As the relative timedelay between the laser pulses is increased, the shocks become more pronounced. For comparison
purposes, we display shocks with energies ∼50 eV, though the shocks from different nanoparticles
range between ∼15 and 50 eV. Adapted from [4]. c 2014 American Physical Society

After the nanoparticle is irradiated by the first laser pulse, the resulting plasma expands, andits density assumes a radial profile that decays smoothly into vacuum. Energy absorption peaks
when the electron density of the plasma is near the critical density [126, 132], the density at whichelectrons in the plasma are driven resonantly by the laser field. As the plasma expands, the volumeof plasma near the critical density expands, enhancing energy absorption. Eventually, the entire
nanoplasma drops below the critical density and light absorption is diminished. Thus, the arrival
time of the second pulse relative to the first determines the amount of energy absorbed. The similar
timescale of ion yield enhancement and shock formation suggests that the two effects share a common
mechanism: the expansion of the plasma between the first and the second pulses is crucial for theformation of shocks in the two-pulse experiment.
The time delay between the laser pulses not only determines the presence of shocks, but also
determines the fraction of ions that become part of the shock wave. The shocks produced with time

69
delays of ∼10 ps involve a small fraction of the ions, while the shock generated using time delays of>15 ps contain a much larger fraction of the total ions (Figures 5.4b and C.4). This indicates thatthe first pulse is shaping the plasma density to achieve a density profile that is better optimized forshock wave propagation and generation of quasi-monoenergetic ions. Thus, this demonstrates that
it is possible to control shock waves in plasmas by actively sculpting the plasma density profile using
a femtosecond laser pulse.

5.5

Hydrodynamic Simulations

To investigate the mechanism for shock formation we employ numerical hydrodynamic simulations using the radiation hydrodynamics code HYDRA [133]. Complete simulations details are
discussed in Section C.6. In brief, we simulate the interaction of two time-delayed laser pulses(each with an intensity of 4.9 × 1014 W/cm2 with a 100 nm diameter nanoparticle composed of
NaCl. A prominent shock waves is observed for time delays between 5 and 35 ps (Figures 5.5 andC.5). In addition, the hydrodynamic simulations accurately reproduce measured ion kinetic energies.
The good agreement between simulated and observed ion energies indicates that the hydrodynamic
calculations capture of the physics of the plasma expansion.
The hydrodynamic calculations suggest a simple mechanism for shock formation (Figure 5.5).
After the first pulse expands the cluster, the second laser pulse is absorbed in a relatively thinshell at the critical density (Figure 5.5a). The resultant heating produces a localized pressure
increase that drives material away from the absorption region (Figure 5.5b). This shock wave
reflects from the center of the plasma, resulting in a population of high-velocity ions at small radius(Figure 5.5b). These ions drive an outward-moving shock (Figure 5.5c), and the associated density
increase produces a peak in the ion kinetic energy distribution (Figure 5.5d). The energy of the shockis determined both by the energy imparted by the laser and the work required for the high-velocity
ions to accelerate the material ahead of them as they move to large radius. Similar to previous
theoretical predictions [40, 42, 134] of shock formation in the Coulomb explosion of small clusters,
the shock formation occurs when faster particles towards the interior of the plasma overrun slower

10-1

Initial plasma density (0 ps)
Light absorbed in thinlayer near critical density
After first
pulse (19 ps)

10-2

Pressure wave
moves inward

10-3 0

100

200

300

400

500

Ion density (x1022 particles/cm3 )

10-3
10-4

Shock propagates

100 ps500

1000

Radius (nm)1500

10-3 070

Before second pulse (19 ps)
After second pulse (30 ps)
Pressure wave
reflects from center,then moves outward

10-2

Wave moves outward,
shock forms
50 ps
80 ps

10

Second pulse: creates pressure wave
(b)
0

10-1

Radius (nm)After second pulse: shock wave forms
10-1 (c)10-2

Ion density (x1022 particles/cm3 )

100

(a)

Number of ions per eV

Ion density (x1022 particles/cm3 )101

First pulse: expands plasma

100

200

300

400

500

Radius (nm)At
detector:shock
manifests as peak107 (d)Shock accelerates,
50 ps then equilibrates
80 ps
100 ps
106

105

101

102

Ion kinetic energy (eV)Figure 5.5: The mechanism for two-pulse shock wave formation, as revealed by numericalhydrodynamics simulations using HYDRA [133]. (a) The first laser pulse creates a plasma,
which expands into the surrounding vacuum. A small single-pulse shock wave can be seen near
230 nm. Near 270 nm, energy from the second laser pulse is preferentially absorbed (red shaded
region) in a layer just below the critical density (nc = 1.7 × 1021 cm−3 at 800 nm). (b) The heatingfrom the second laser pulse creates a pressure wave that moves inwards, reflects from the center,and then moves outwards. (c) The pressure wave moves outwards supersonically and accelerates
slower material in front of it, creating a shock wave, which is seen as a small step in the ion density
distribution. (d) In the kinetic energy distribution of the ions, the shock wave is a sharp peak whichis accelerated by the pressure gradient, eventually settling at a final kinetic energy of a few 10s of eVafter ∼100 ps. It is this asymptotic kinetic energy distribution that is recorded by the spectrometerin the experiment. In this simulation, both laser pulses are modeled as 50 fs, 800 nm pulses withintensities of 4.9 × 1014 W/cm2 . Adapted with permission from Ref. 4. c 2014 American PhysicalSociety

particles in the exterior of the cluster. However, in this case, the velocity differential is caused by
the preferential absorption of light near the critical density, which creates a ridge of high pressure.
In contrast to studies conducted in the Coulomb explosion regime, where the shock is formed on thetimescale of 100 fs, the shocks in these hydrodynamic explosions take ∼50 ps to form.
Interestingly, the hydrodynamic simulations show a shock wave that accelerates as it moves

71
outwards (Figure 5.5c), which is most easily seen by the temporal increase in energy of the peakin the ion distribution (Figure 5.5d). In the simulations, the shock velocity increases by more than
twofold during this acceleration period. The mechanism for such shock acceleration is well known,and stems from the radially decreasing density profile in the background plasma. In the classic
Sedov-Taylor–Waxman-Shvarts [135] analysis of the problem, acceleration is seen for steep density
gradients. Simple dimensional analysis scaling laws [136], which describe the asymptotic behaviorof the shock, are in good agreement with the simulated shock acceleration once we account for
the fact that our plasma density is rapidly decreasing with time. Accelerating shock waves areof great interest in astrophysics and, consequently, experiments have been proposed to investigate
such shocks in the laboratory setting [137]. We believe that this study is the first realization ofsuch an experiment and could serve as a versatile platform for studying shocks propagating throughcustomizable density gradients.

5.6

Conclusion

Here we presented the first measurements of individual nanoplasmas, demonstrating a new
method for studying laser-plasma interactions, which can be implemented using a tabletop apparatus and at a high repetition rate. By characterizing the momentum distribution of individual
nanoplasmas, we make the first observation of plasma shock waves on the nanometer scale, confirming a decade of theoretical predictions [40, 42, 134]. By adjusting the time delay between twolaser pulses, the creation and strength of the shock wave was varied in a controllable manner. Furthermore, because these shocks are produced in plasmas with temperatures of just ∼10 eV, thisexperiment potentially enables a compact, inexpensive method for studying a relatively unexplored
regime of low-temperature nanoplasmas.

Chapter 6

Conclusion and outlook

Science is what we understand well enough to explain to a computer.
Art is everything else we do.
–Donald Knuth

6.1

Overview

This section summarizes the work presented in this thesis, provides an outlook for future workthat can expand on the presented results, and provides a brief summary of new research directions
that will be pursued. First, Section 6.2 summarizes each of the three main experiments and provides
ideas for future experiments that could expand upon each of these results. Section 6.3 provides abrief description of several new experiments that are in the process of being constructed and could
serve as fruitful avenues for future research.

6.2

Outlook

6.2.1

Strong-field ionization of gas-phase atoms and molecules

Chapter 3 demonstrated how changing the wavelength of the driving laser can provide new
insight, even when using a “classic” experimental technique. In the presented study, the mid-IR
driving lasers provided a clear picture of electron dynamics in the continuum, in good analogy
to the higher-energy HHG that is also enabled with mid-IR driving lasers. The discovery of new
physics using mid-IR driving lasers in the VMI suggests that using a VMI to study the strong-field
ionization process will continue to yield breakthroughs as long as the parameter space continues to

73
be expanded.
The most obvious extension of the study would be to increase the wavelength of the driving laser
to greater than 2.0 µm and see if additional features appear in the photoelectron spectrum. Whiledriving laser wavelengths up to 7 µm [85, 138] have been explored, many of these were completedwith low laser intensities and with species exhibiting exceptionally low ionization potentials, such as
metastable xenon species [85]. Neutral atoms have been probed using driving laser wavelengths up
to 3.7 µm [86], but only one-dimensional photoelectron spectra have been collected. High-quality
angle-resolved photoelectron images using driving laser wavelengths longer than 2.0 µm are stilllacking. It is possible that in the near future, the high-repetition rate optical parametric chirped
pulse amplifier (OPCPA) that is in development in a collaboration between the Kapteyn–Murnane
Group and KMLabs will provide sufficient pulse energies for strong-field ionization at 3.0 µm [139].
In addition to simply changing the wavelength of the driving laser, the polarization can also
be changed to provide insight into different physics. Recently, the generation of circularly polarized
XUV light from the HHG process has been accomplished through the mixing of counter-rotating
circularly polarized 400 nm and 800 nm laser fields [140–142], thus demonstrating the importance of
unusual polarization states of the driving laser for the HHG process. The laser field that results fromthe mixing of the circularly polarized 400 nm and 800 nm light (Figure 6.1) drives electrons twodimensional trajectories [140, 143, 144], which opens the exciting possibility that the angle of electron
tunneling and the angle of electron rescattering/recombination may be separated, allowing for the
extraction of molecular structure using either HHG or SFI. Indeed, in a forthcoming publication [6],we demonstrate that two-color circularly polarized fields can enable electron recattering when thefields are counter-rotating, but not when the fields are co-rotating.
In addition, more careful collection, analysis, and interpretation of PADs resulting from thestrong-field ionization using previously explored wavelengths can continue to yield insight. For example, while Chapter 3 discusses the low energy structure (LES), more recent studies have identified
two additional structures: the very low energy structure (VLES) and the zero energy structure (ZES,
which is not actually at zero kinetic energy) and attributed them to more complicated processes in-74

Figure 6.1: Photoelectrons from circularly polarized driving lasers. When counter-rotating
circularly polarized 400 nm and 800 nm laser fields are mixed, the resulting field takes on a three-leaf
clover shape, exhibiting three-fold symmetry. The 3D PAD can be reconstructed by rotating the
PAD in the lab frame and collecting 2D projections at different angles.

volving the motion of electrons under the influence of the Coulomb potential of the ion [145–147].
Also, new analysis techniques have revealed that molecular structure information can be extracted
even from one-dimensional photoelectron spectra using mid-IR driving lasers [29]. Exciting developments such as these demonstrate that the field of strong field ionization is far from being completely
understood and will likely produce exciting insights for many years to come.

6.2.2

Plasma Explosion Imaging

Chapter 4 discusses the development of the Plasma Explosion Imaging (PEI) technique andapplies it to four representative nanostructures. The obvious follow-up experiment would be to apply the PEI method to many more nanostructures and see how the results change. Additionally, theexperiments could be completed in a time-resolved fashion, where a pump pulse is used to create achange in the geometry of optical properties of the material. This technique could potentially evaluate the evolution of the linear and nonlinear optical properties of the material on the femtosecond
timescale.

75
6.2.3

Shock waves

The primary question posed by the study of shock waves in nanoplasmas presented in Chapter 5
is how the physics would scale with the laser intensity, and if higher intensity lasers could be used togenerate very high energy ions, as was seen with smaller nanoplasmas [38] and proposed theoretically[41, 42]. While the laser intensity can easily be increased, the difficulty is that our VMI cannot
observe electrons past ∼100 eV and even the “highest energy” VMI cannot work past 330 eV [148].
Thus, studies that attempt to observe higher energy shock waves from nanoplasmas will need touse other techniques such as time-of-flight. However, time-of-flight provides a different mapping of
kinetic energy and ion mass, and it might make the shock wave more difficult to observe.
An alternative method for understanding all manners of phenomena is to probe the plasma withhigh-energy photons. While visible and even ultraviolet light is generally not high-energy enoughto penetrate into a dense plasma, EUV and X-ray photons are above the plasma frequency and canpenetrate into a nanoplasmas. A 2014 theory paper by Peltz and coworkers [149] indicates thattime-resolved X-ray scattering experiments will provide new insight into nanoplasmas.
Another important question for determining if nanoplasma shock waves will be a practicalsource of electrons, ions, and photons is if the shock wave can be made directional. In Chapter 5, theshocks are largely spherically symmetric, ejecting ions in all directions. However, some asymmetryis still seen in the directionality of the shock wave, suggesting that it may be possible to control the
direction of high-energy ion ejection by controlling the characteristics of the particle from which theplasma is formed. It is possible that the principles that control the directional ion ejection in PEI
will carry over to the shock-wave formation regime. For example, it may be possible to use speciallyshaped micro or nanoscale structures to ensure that a shock wave primarily ejects ions in a specificdirection.

76

6.3

Future Directions

In the following sections I provide an outline of a few of the future experiments that are planned
for the VMI spectrometer and the nanoparticle aerosol source.

6.3.1

Extreme ultraviolet probe of nanomaterials

When the idea to study nanoparticles using a VMI at JILA was first conceived, the goal was
to attempt to image the exciton orbitals of quantum dots (QDs). These orbitals are called the 1S,
1P, etc. orbitals and there is an open question of what symmetry the photoelectron distribution will
have when ionizing from these states. In Ref. 5, we used 400 nm light to excite a 1S exciton in CdSe
QDs and 267 nm light to liberate the excited electron. However, in these experiments there was an
overwhelming amount of secondary electrons and these obscured the primary photoelectrons, whichwere also at low kinetic energies. The same problem is encountered in photoemission from surfaces
and the solution is to move to higher photon energy light sources, in the EUV. The EUV light does
not cut down on secondary electron emission, but it does move the primary electrons to much higher
kinetic energies so that they may be distinguished from the secondary electrons. Thus, with thehope of providing a clear picture of the exciton orbitals in quantum dots, we are now using EUV
light from HHG as a probe for the photoelectron spectroscopy experiment.
Moving to a HHG source has several disadvantages – the primary one being the low flux –but offers several important advantages that may lead to breakthrough results. First, as mentioned
above, XUV light is extremely surface sensitive, since electrons that are excited below the surface
will likely scatter and not emerge as primary electrons. This is a curse and a blessing, because
it dramatically decreases the photoelectron yield compared to lower photon energies, but it allows
us to study processes on surfaces. Most importantly, the light generated using the HHG process
constitutes some of the shortest laser pulses ever generated. Generating isolated attosecond pulses
typically requires mid-IR driving lasers [32], but at driving laser wavelengths in the visible and nearIR, the attosecond pulse trains are locked to the phase of the driving laser. Due to this phenomena,

77
sub-femtosecond processes can be studied even when the overall duration of the pulse train is many
femtoseconds.

6.3.2

Magnetron sputtering nanoparticle source

As mentioned in Section 2.4.1, The atomizer generates nanoparticles that have a layer of contamination dictated by the purity of the solvent. Even for the most pure solvents available, thenanoparticles are still covered by many atomic layers of contamination at a minimum. Since theEUV light is a surface sensitive probe, it is not meaningful to study atomizer-generated nanoparticles using EUV light. Consequently, we are exploring alternative methods of introducing isolated
nanoparticles into the spectrometer. One possible method would be electrospray ionization, where ahigh voltage is used to atomize a liquid solution of nanoparticles into the vacuum. While electrosprayhas been highly successful at obtaining high-purity molecules and nanoparticles into a vacuum, theparticles are charged, preventing the study of neutral nanoparticles.
Currently, the most promising method for introducing a stream of high-purity nanoparticles inthe VMI spectrometer appears to be a Haberland-type [150, 151] magnetron-sputtering nanoparticle source (Figure 6.2). This device utilizes a traditional DC magnetron sputtering target, which
produces free atoms from bulk material using a magnetically confined plasma. While a typicalmagnetron sputtering source produces the atoms directly into a high-vacuum chamber where they
are used to produce thin-film coatings, a Haberland-type nanoparticle source places the magnetronsource in a chamber with ∼1 Torr argon gas, which extends for a few inches before incorporating
an orifice into a high-vacuum chamber. As the atomic vapor traverses the argon-filled chamber,the atoms aggregate into nanoparticles and the size of the nanoparticles depends on the pressureof gas in the chamber and the length of the interaction region. After exiting into the high vacuum
chamber, the aggregation stops and a freely expanding source of ultra-pure nanoparticles is achievedin high-vacuum conditions. Some of the nanoparticles are charged, but a significant fraction are
neutral.
The magnetron sputtering source offers several additional advantages in addition to the purity of

78

Figure 6.2: Schematic of the NanoGen50. The device uses the DC magnetron sputtering
technique to transform a pure solid target (semiconductor or metal) into an atomic vapor. As
the atoms pass through the condensation zone, they aggregate into nanoparticles, which then passthrough the exit orifice and into the VMI spectrometer. c 2014 Mantis Deposition, used withpermission.

the nanoparticles. It offers smaller nanoparticles, higher nanoparticle concentrations, better stability,
and automated control over the particle size and parameters. Regarding the smaller size of thenanoparticles, the magnetron sputtering nanoparticle source can generate particles with diameters
ranging from 2 to 20 nm, in contrast to the atomizer that has difficulty producing nanoparticles below
100 nm without serious contamination issues. The 2 to 20 nm size regime is much more interesting
than the 100s of nm size regime because it is in the sizes of a few nm where most materials transition
from atomic or cluster-like behavior to bulk behavior. Indeed, most QDs have sizes that are between
2 and 10 nm.
The concentration of the nanoparticle beam is also higher for the magnetron sputtering source,with the caveat that the source is divergent and therefore the particle concentration depends on the
distance between the source and the interaction region. We estimate that the particle concentration
at the exit of a commercial magnetron sputtering nanoparticle source (NanoGen50, Mantis Deposition, Figure 6.2) is approximately 109 particles/cm3 and that the device can be arranged to bring79
107 particles/cm3 to the interaction region of the VMI spectrometer. It may be possible to couple
the magnetron sputtering nanoparticle source to an aerodynamic lens and generate a collimatednanoparticle beam, thereby increasing the particle concentration in the interaction region. However,an aerodynamic lens that is specially designed for the smaller particles generated by the magnetron
sputtering source would be required.

6.4

Conclusion

This thesis described how velocity map imaging photoelectron and photoion spectroscopy canbe extended to study a wide variety of phenomena, including strong-field electron dynamics inatoms, local field enhancement in single, isolated nanoparticles, and shock wave propagation in
nanoplasmas. Specifically, several important developments were highlighted, including• The first observation of the “inner spider” structures in strong-field ionization. (Chapter 3).
• The development of an intuitive model (the plane-spherical wave model) that can explain
the most prominent interference structures observed in the strong-field ionization of atoms
and molecules (Chapter 3).
• The realization that a VMI spectrometer can be used to probe individual nanoparticles at
a high repetition rate (Chapters 4 and 5).
• The invention of a new technique for observing the local-field enhancement in nanostructures
called plasma explosion imaging (Chapter 4).
• The first observation of shock waves in nanoscale plasmas, a discovery that confirmed a
decade of theoretical work (Chapter 5).
• The presentation of a clear path towards the experimental observation of attosecond dynamics in isolated, ultrapure metal and semiconductor nanocrystals (Chapter 6).
These result presented in this thesis answered many questions (for instance, they explained
the origin of the famous “low energy structure” [86] and confirmed the 2003 prediction of shock80
waves in nanoplasmas [40]) but they posed more questions, including the feasibility of utilizing thenanoplasma shock waves to accelerate high-energy ions, the applicability of the PEI technique toother laser-intensity regimes, and the scaling of the inner-spider structures with longer wavelength
driving lasers. Future studies at JILA will extend these new techniques to utilize HHG as an XUVlight source and use small, ultra-pure nanoparticles generated in vacuum to make the measurementsof electron dynamics in nanoparticles on the attosecond timescale.

Appendix A

Multiple Scattering Structures Appendix

This chapter is adapted, with permission, from the Supplemental Material for:• D. D. Hickstein, P. Ranitovic, S. Witte, X.-M. Tong, Y. Huismans, P. Arpin, X. Zhou, K.
E. Keister, C. Hogle, B. Zhang, C. Ding, P. Johnsson, N. Toshima, M. J. J. Vrakking, M.
M. Murnane, and H. C. Kapteyn. Direct Visualization of Laser-Driven Electron Multiple
Scattering and Tunneling Distance in Strong-Field Ionization. Phys. Rev. Lett., 109, 2012,
073004. doi: 10.1103/PhysRevLett.109.073004
c 2012 American Physical Society

A.1

Overview

This appendix provides additional details about the multiple scattering structures described in
Chapter 3 that result from the strong-field ionization of noble gases with strong femtoseond laser
pulses in the mid-IR region. Section A.2 describes the implementation of the PSW model, Section A.3
explains the analysis of the classical trajectories that is used to calculate the modulation frequencyof the plane and spherical waves, Section A.4 elaborates on the method used to extract the multiple
rescattering cutoffs from the experimental data, and Section A.5 discusses the dependence of the
TDSE results on the laser intensity.

A.2

Details of the Plane-Spherical Wave ModelIn the plane-spherical wave model, we aim to reproduce the angle and spacing of the spider
structures from first principles using a simple superposition of two waves. We represent the part of

82
the electron wavepacket that does not scatter from the ion as an elliptical Gaussian wavepacket withplane phase (Ψplane ), while the part of the wavepacket that does scatter from the ion is represented as
an elliptical Gaussian wavepacket with spherical phase (Ψspherical ). We call these elliptical Gaussian
wavepackets the “plane wave” and the “spherical wave” respectively. The plane and spherical waves
are written as
  2

P⊥
P2
Ψplane = Aplane exp −eiP ·f ,2 + 2σ 2
2σ⊥
  2

P⊥
P2
Ψspherical = Aspherical exp −+eiPtotal ·f ,
2
2σ⊥
2σ 2

(A.1)
(A.2)

where Aplane and Aspherical are the amplitude of the plane and spherical waves, P⊥ and P are
the components of the final momentum perpendicular to and parallel to the laser polarization,
Ptotal is the total final momentum and is equal topP⊥2 + P 2 , σ⊥ and σ determine the width of

the wavepacket in the P⊥ and Pk directions, and f is the modulation frequency of the plane andspherical waves.
The frequency f is not the same as the spacing of the spider structures, but the shape (andfrequency) of the spider structures is a function of f . Since we are only concerned with reproducing
the interference pattern, σ⊥ and σ are set empirically, to match the width and height of theexperimental photoelectron distribution. The observed photoelectron interference pattern is given
as the superposition of Ψplane and Ψspherical asΨtotal = Ψplane + Ψspherical ,(A.3)

where both wavefunction are complex.
The above superposition produces interference patterns that look quite similar to the spider
structures seen in the experimental photoelectron spectra as well as the TDSE calculations. The
only parameters used are the amplitudes of the plane and spherical waves (Aplane and Aspherical ) andthe width and height of the wavepackets (σ⊥ and σ ), but these only control the overall shape ofthe generated electron distribution and do not affect the shape or frequency of the spider structures.
The modulation frequency waves (f ) is determined through a quasi-classical analysis of the electron
trajectories. To observe the spider structure interference, f must be the same for the plane wave

83
and the spherical wave. If f is different for the plane wave and spherical wave, qualitatively different
interference patterns are observed.

A.3

Calculating the modulation frequency

In a path-integral approach, we can understand the interference of particles by examining thevarious trajectories by which a particle can reach a certain point and summing those trajectories
coherently (Figure A.1). The amplitude of each trajectory is equal, but the phase of each trajectoryis given by e(iS/h̄) , where S is the action given by Equation 3.1. Thus, we can re-create the complete
photoelectron angular distribution by integrating all of the trajectories that can reach each point in
the final momentum space. Indeed, this is the approach employed in the CCSFA model presented
by Huismans and coworkers [85].
In the long-wavelength limit (where the electron wave packet enjoys a long sojourn in thecontinuum and spreads significantly), only electrons that tunnel with very low transverse momentum
return close enough to the ion to be significantly affected by the Coulomb potential. Thus, we makethe approximation that the rescattered electrons have zero transverse momentum until they scatterfrom the Coulomb potential. We also assume that the scattering will be elastic and can occur inany direction with equal probability.
To calculate the action from Equation 3.1, it at first seems necessary to integrate each trajectoryfrom the time that an electron tunnels into the continuum to the time that the electron reaches
the detector. However, the situation simplifies because any two electrons that have the same vector
momentum at the same point in time will accumulate the same action from that point onward. Oncethe rescattered trajectory scatters from the Coulomb potential, it now has the same momentum as
the corresponding revisiting trajectory and we may stop integrating Equation 3.1. By integrating
Equation 3.1 for both the revisiting and rescattered trajectories from the time that the electrons
tunnel to the time that the rescattering trajectory reaches the ion and rescatters, Huismans [85] andBian [152] were able to reproduce the spider structure using this generalized SFA model.
Here we further simplify the generalized SFA model by treating the revisiting electrons as a

Position (nm)

84

40

a

20

12

0

34

20

2. Revisiting
3. Direct

40
0
2.0

P (a.u.)

1.5

c

5

10

15

Time (fs)
Rescattered

20

25
2.0
1.5

d

b

20
10
0
10
20
30
40

1. Direct
4. Revisiting

30

revisiting

0

Revisiting

trajectory
without
rescattering
5
10

1.5

1.0

1.0

0.5

0.5

0.5

0.5 0.0 0.5
P (a.u.)0.0

0.5 0.0 0.5
P (a.u.)15

20

Time (fs)
Rescattered+ revisiting
2.0

1.0

0.0

rescattered0.0

e

0.5 0.0 0.5
P (a.u.)Figure A.1: Electron trajectories that produce photoelectron interference structures.
(a) Electrons from the 1st and 3rd quarter cycles are driven away from the ion, never to return.
Electrons from the 2nd and 4th quarter cycles are first driven away from and then back to thevicinity of the ion. (b) The spider structures result from interferences between trajectories thatpass the ion without rescattering and trajectories that pass the ion closely and are scattered by
the Coulomb potential. (c) Phase of the rescattered trajectories calculated by integrating Equation
3.1 between tunneling and rescattering events. (d) Phase of the revisiting trajectories calculated
by integrating Equation 3.1 between tunneling and rescattering event - the phase accumulated islinear with the longitudinal momentum. (e) Interferences between the rescattering and revisiting
trajectories creates the spider structures. (insets in panels c,d,e) Sketches of the 2D trajectories
corresponding to the rescattered and revisiting trajectories. Adapted with permission from Ref. 2.
c 2012 American Physical Society

simple plane wave in the final momentum space and treating the rescattered electrons as a sphericalwave in the final momentum space. The modulation frequency of each wave is related to theaction accumulated according to Equation 3.1, as discussed below. Although we are dealing witha scattering problem, this plane-spherical wave approximation is not obvious since we are making
the approximation in the final-momentum space as opposed to real space. Initially, it is not clear
why the revisiting electrons should resemble a plane wave on the detector and why the rescatteredelectrons can be treated as a spherical wave. However, after completing a generalized SFA analysis of

85
the interference patterns (Figure A.1e) and examining the revisiting (Figure A.1d) and rescattered(Figure A.1c) contributions separately, we see that they do indeed resemble a plane wave anda spherical wave. The wavefront curvature that might be expected in the wavefunction for therevisiting electrons has been compensated since the electrons are turned around by the laser field.
To calculate the modulation frequency (f ) needed for the plane-spherical wave model, we simply
calculate the action (using Equation 3.1) for a range of trajectories that correspond to P from 0 to
2UP . By assuming that trajectories that can rescatter on a subsequent revisit will scatter on thesecond, fourth, sixth, etc. revisit, we stop integrating Equation 3.1 at different times and obtain theplot shown in Figure 3.5b. Thus, the procedure for creating a complete PSW calculation consistsof three steps. First, a series of classical trajectories corresponding to a range of P are flown andthe action is calculated along each one from the time that the electron tunnels into the continuum
to the time that the electron returns to the ion. Next, we make a plot of the action versus the
final momentum and fit a line to the nearly-linear curve. The slope of this line is the modulation
frequency (f ) needed for the plane-spherical wave model. Finally, we use Equation A.3 to create
the 2D photoelectron momentum distribution, estimating the amplitude and shape of the Gaussian
wave packet to best fit the experimental data.

A.4

Extracting the experimental multiple rescattering cutoff

In order to estimate the quantum-mechanical tunneling distance, we measured the position of
the multiple rescattering cutoff across a broad range of laser wavelengths and intensities. Though it isreasonably easy to visually estimate the cutoff of the inner spider structures in the 2D photoelectron
spectra, a more quantitative definition is desirable to ensure sufficient precision. We identified thecutoff of the inner spider structures by looking closely at the inner spider structure closest to Pk = 0.
That is, we looked at the first set of “spider legs” closest to the central maxima.
Since the colormap and contrast of the 2D image can cause influence the appearance of the 2D
photoelectron angular distribution, we took 1D lineouts across the 2D spectra at various values ofP⊥ (Figure A.2). When the lineout is taken across the inner spider structure, additional maxima and86
minima are seen that correspond to the inner spider fringes. The cutoff of the inner spider structure
was defined as the value of P⊥ where these maxima and minima can no longer be identified. In
Figure A.2b, the red line is above the cutoff and the green line is below. Using this method, we
can identify the cutoff to the nearest 5 pixels (0.018 atomic units of momentum). For displaying
the error range in Figures A.3 and 3.6b, we set the error equal to 0.02 atomic units of momentum.
The relative intensity of the experimental photoelectron distributions was measured using a power
meter and the absolute intensity was calibrated from the 2Up cutoffs and comparison with the TDSE
results (Figure 3.4).

b)a) Ar 2000 nm(a.u.)

0.5
0.0
0.5
1.0
0.5

no max or min

Intensity (arbitrary units)

1.0

180 mW
0.0(a.u.)

max
min
max
min

0.5

0.4

0.2

0.0

0.2

(atomic units)

0.4

Figure A.2: The procedure for determining the cutoff of the inner spider structures inthe experimental 2D photoelectron momentum distributions. a) For this PAD, the innerspider structure extends from about Pk = 0.25 to 0.45 atomic units. The colored lines correspondto the lineouts shown on the right. The lineouts are integrated over 3 pixels (0.01 atomic units ofmomentum) of P⊥ to reduce noise. We are only concerned with the inner spider legs that appear
closest to Pk = 0. Adapted with permission from Ref. 2. c 2012 American Physical Society

A.5

Intensity dependence

The TDSE calculation presented in Figure 3.5e was not averaged over the focal volume of thelaser. Fortunately, focal-volume averaging does not dramatically affect the appearance of the main
spider structures or the inner spider structures for two reasons. First, as shown in Figure A.4d, theyield from calculations performed at 5.5×1013 W/cm2 is an order of magnitude larger than the yield

87
1.0

Ar 1300 nm

Ar 1300 nm

Ar 1300 nm

Ar 2000 nm

Ar 2000 nm

40 mW

50 mW

60 mW

150 mW

160 mW

Ar 2000 nm

Ar 2000 nm

Ar 2000 nm

Ar 2000 nm

Xe 2000 nm

170 mW

180 mW

190 mW

230 mW

40 mW

Xe 2000 nm

Xe 2000 nm

Xe 2000 nm

Xe 2000 nm

0.5
0.0
0.5
1.0
1.0
0.5
0.0
0.5
1.0
0.6
0.4
0.2
0.0
0.2
0.4
0.6

50 mW

0.2

0.0

0.2

0.5

90 mW
0.0

0.5

0.5

100 mW
0.0

0.5

0.5

110 mW
0.0

0.5

Figure A.3: The positions of the inner-spider cutoffs. The high Pk cutoff of the inner spider
structures was found using the 1D inspection method shown in Figure A.2 and the error was set
to be ±0.02 atomic units of momentum. The upper and lower error-boundaries are shown withyellow lines on the 2D photoelectron momentum distributions shown above. The position of theinner spider cutoff found using the 1D corresponds to the apparent position of the cutoffs in the
2D spectra. The upper and lower bounds (yellow lines) correspond to the upper and lower limits
indicated with error bars in Figure 3.6b. Adapted with permission from Ref. 2. c 2012 American
Physical Society

from 4.5 × 1013 W/cm2 . This large difference is due to the highly non-linear nature of the strongfield ionization process as well as the fact that the calculations and experiments were performed well
below ionization saturation. Additionally, Figures 3.6a–c show that the spider structures do notsignificantly change shape or angle with a reasonable change in intensity. The inner spider structure

88
can be clearly seen to extend to higher kinetic energy at higher laser intensity, but the shape of thestructure at low energy remains the same. Thus, both the primary and inner spider structures arerobust to the focal volume averaging that takes place in the experiment.

Figure A.4: Dependence of the inner spider structures on the intensity of the driving
laser. (a-c) The photoelectron angular distributions calculated using TDSE for xenon using a
2000 nm driving laser at various laser intensities. The color scales have been adjusted to show the
spider structures. The spider structures extend to higher energies at higher laser intensity, but theshape of the spider structure does not change significantly with intensity. (d) The angle-integrated
photoelectron yield plotted on the same scale reveals that the photoelectron yield quickly increases
with intensity. Figure by Xiao-Min Tong, Tsukuba University. Adapted with permission from Ref. 2.
c 2012 American Physical SocietyAppendix B

Plasma Explosion Imaging Appendix

This chapter is adapted, with permission, from the Supporting Information for:• D. D. Hickstein, F. Dollar, J. L. Ellis, K. J. Schnitzenbaumer, K. E. Keister, G. M.
Petrov, C. Ding, B. B. Palm, J. A. Gaffney, M. E. Foord, S. B. Libby, G. Dukovic, J. L.
Jimenez, H. C. Kapteyn, M. M. Murnane, and W. Xiong. Mapping Nanoscale Absorptionof Femtosecond Laser Pulses using Plasma Explosion Imaging. ACS Nano, 8 (9), 2014,
8810. doi: 10.1021/nn503199v
c 2014 American Chemical Society

B.1

Overview

This appendix provides additional details about the plasma explosion imaging (PEI) techniquedescribed in Chapter 4. Section B.2 provides details about the experimental methods, the nanoparticle samples, and the FDTD simulations. Section B.3 compares the photoelectron distributions
to the photoion distributions from PEI in single nanoparticles, and Section B.4 describes single
nanoparticle mass spectrometry experiments that confirm that the observed ions result from thenanoparticle itself and not from the background gas in the spectrometer chamber.

B.2

Methods

B.2.1

Photoion spectroscopy and aerosol generation

To perform velocity-map-imaging spectroscopy on nanostructures, we first generate a nanoparticle aerosol, consisting of isolated nanoparticles suspended in N2 gas. The aerosol enters a low-

90
vacuum chamber through an aerodynamic lens (Aerodyne Research) [70, 111] that collimates theparticles into a ∼0.5 mm beam, but leaves the carrier gas divergent. The collimated particle beam
passes through a 1.5 mm skimmer and enters the photoion spectroscopy chamber, which is maintained at 10−6 Torr (base pressure 10−8 Torr). The particles are then irradiated by an intense(∼3 × 1013 W/cm2 ), 785 nm, 40 fs laser pulse, derived from a Ti:sapphire regenerative amplifier(KMLabs Wyvern HE) operating at 1 kHz.
The laser is focused using a 40 cm lens to reach an approximate diameter of 20 µm, which –considering the width of the particle beam (0.05 cm) – provides an interaction volume of approximately 10−7 cm3 . Because the density of the nanoparticles is only ∼105 particles/cm3 , the hit rateis ∼0.01 particles per laser shot. The photoions originating from the laser-irradiated nanoparticles
are imaged by a velocity-map-imaging (VMI) spectrometer [51], which projects the expanding ion
distribution onto an microchannel-plate–phosphor detector. The angular-resolved momentum distribution of the ions is then recorded using a CCD camera (Allied Vision Technologies) operatingat ∼15 Hz. The exposure time of the camera is adjusted to ensure that each frame consists of only
one particle hit.

B.2.2

Materials

We obtained pure NaCl from Sigma Aldrich and ∼5 nm TiO2 nanoparticles from US Research
Nanomaterials. The 50 and 17 nm gold nanospheres were obtained from Nanocomposix, Inc. All
samples were used as received, except for dilution in ultrapure (>15 MΩ resistivity) water. The
liquid samples are converted into an aerosol using a Collison-type compressed-gas atomizer (TSI)
backed with 30 psig of N2 carrier gas.

B.2.3

Transmission electron microscopy

To characterize the nanoparticles probed by the laser, we performed transmission electron
microscopy (TEM) on particles collected in the high vacuum chamber. TEM grids were inserted
into the chamber using a magnetically coupled linear actuator (Kurt J. Lesker, Inc.) passing through91
an airlock. The TEM grids were positioned at the exact position where the laser crosses that particle
beam, and high-velocity particles were collected on the grids for 10 to 30 seconds. TEM images wereobtained using a Phillips CM100 Transmission Electron Microscope.

B.2.4

Finite-difference time-domain (FDTD) simulations

To understand the results obtained with photoion spectroscopy, we employed finite difference time domain (FDTD) simulations implemented in the FDTD Solutions [153] software package(Lumerical, Solutions Inc.) to simulate the interaction of the laser field with the nanoparticles.
We simulated the interaction of a 40 fs pulses with a central wavelength of 785 nm with several
different structures that are representative of the actual geometry of our nanoparticles. The TiO2
particles were simulated as a collection of 6 layers of 5 nm dielectric spheres with n = 2.523 (therefractive index of TiO2 at 785 nm [154]). The NaCl nanocystals were simulated as 100 nm diameter
dielectric spheres with n = 1.536 (the refractive index of NaCl [155] at 785 nm). The gold–PVP
heterostructures were simulated as 50 or 17 nm gold spheres embedded in a dielectric sphere withn = 1.4 (the approximate index of PVP at near-IR wavelengths [156]). The wavelength-dependent
complex refractive index of gold was treated according to the Palik [157] model.

B.3

Photoelectron Distributions

The above analysis focused only on the photoion angular distributions (Figure 4.5). However,the VMI spectrometer can easily collect photoelectron angular distributions simply by applying
negative (instead of positive) potentials to the electrodes. Similar to the photoion distributions,the photoelectron distributions from individual nanoparticles are also frequently asymmetric about
zero kinetic energy (Figure B.1), with similar directional preferences as the photoion distributions.
In contrast, the photoelectron distributions exhibit a peak near zero kinetic energy, which is absent in the photoion distributions. In addition, the asymmetry is typically less pronounced in thephotoelectron distributions than in the photoion distributions.
These two qualitative differences between the photoelectron and photoion distributions are92both explained by the large difference in mass between electrons and ions, which has two principal
effects. First, because the electrons are significantly lighter than the ions, they undergo significantly
more scattering in the expanding plasma and the angular ejection caused by the localized plasma
formation is partially obscured. Second, the near-zero energy peak in the photoelectron distribution
is a result of atoms left in excited states that are subsequently ionized by the electric field of thespectrometer. A recent study of nanoplasmas formed in xenon clusters with extreme ultraviolet
radiation [158] has observed a similar low-energy peak and attributed it to electrons in high-lying
atomic Rydberg states that are detached by the electric field on the spectrometer [159].
Initially, it might be assumed that an electric-field-induced separation of weakly bound electron–
ion pairs would result in a field-ionized electron angular distribution that is an exact replica of theion distribution. However, this is not the case due to the differences in masses between the electron
and the ion. If we consider an electron–ion pair moving transverse to the detector with kinetic
energy Ei , and assume that both the electron and ion will maintain the same transverse velocity
when separated, then the energy of the electron is given by

Ee =

me
Ei
mi

(B.1)

e
where mmi is the ratio of the masses of the electron and the ion. For example, if a gold ion is travellingat 80 eV (roughly the edge of the detection range of our VMI) then the field-ionized electron will
have a kinetic energy of only 0.0002 eV. Thus, while the ions may have a wide range of kinetic
energies, any field-ionized electrons will arrive as part of the low-energy peak.
Photoelectron spectra were not collected for the samples presented above, but photoion andphotoelectron spectra were collected under identical conditions for a sample of ∼25 nm gold nanoparticles prepared via the citrate synthesis as described by McFarland and coworkers [160]. The 25 nm
gold nanoparticle sample exhibits directional ion ejection characteristics that are very similar to the
50 nm gold nanoparticle sample described in the manuscript. We infer that the excess sodium citratefrom the nanoparticle synthesis is acting in a very similar fashion to the PVP in the case of the
50 nm gold nanoparticle sample. The laser intensity used for the photoelectron/photoion imaging

93of the 25 nm gold nanoparticle sample (Figure B.1) is ∼3 × 1013 W/cm2 , which is the same as usedin Figure 4.5.

b

c

d

e

f

50

Ions

5
0
5
50

Electrons

g

h

i

j

k

l

50
5
0
5

laser
50

5 0 5

Energy/charge (eV/Z)

a

50
50

50

5 0 5

50

50

5 0 5

50

50

5 0 5

Energy/charge (eV/Z)

50

50

5 0 5

50

50

5 0 5

50

Figure B.1: Comparison of photoelectron and photoion distributions from single
nanoparticles. Photoions (top) and photoelectrons (bottom) from a sample of 25 nm gold nanoparticles prepared via the citrate synthesis. The photoion and photoelectron distributions were collected
separately and do not correspond to the same nanoparticle, but they are plotted next to one anotherto demonstrate the correspondence of the angular ion ejection. This gold nanoparticle sample behaves similarly to the 50 nm gold nanosphere sample discussed in the Chapter 4, ejecting electrons
and ions at a specific, but random, angle due to the random orientation of each nanoparticle. The
electrons exhibit the same qualitative behavior to the ions with respect to the angle of ion ejection.
However, the electrons are ejected to lower kinetic energies, show somewhat less asymmetry in general, and feature a sharp peak near zero kinetic energy, differences that can be explained in termsof the significant mass difference between the electrons and the ions. Adapted with permission from
Ref. 3. c 2014 American Chemical Society

B.4

Plasma Explosion Mass Spectrometry

B.4.1

Mass spectrum of a single nanoparticle

Above, we make the assumption that the ions reaching the detector correspond to atoms thatwere originally found in the nanoparticle. However, it is conceivable that the plasma formation
process would eject numerous electrons that would, in turn, collide with background gas particles(N2 ), creating additional ions. A representative mass spectrum corresponding to a nanoplasma
formed in a single potassium iodide (KI) nanoparticle (Figure B.2) demonstrates that the majorityof the ions observed on the detector correspond to the plasma formation process. The main ion
species resulting from the ablation of the KI particles are K+ , I+ , C+ , and H+ . The predominanceof K+ and I+ is due to the KI sample used in the experiment. The increased relative abundance of94
K+ compared to I+ is a result of the higher ionization potential of I compared to K.
The observation of H+ results from a thin film of water that adheres to the nanoparticle sample
even after passing through a diffusion dryer and into the vacuum chamber. Indeed, the small, poorly
resolved peaks around 16–18 Da may correspond to H2 O+ (18 Da), OH+ (17 Da), and O+ (16 Da).
The C+ peak (12 Da) likely corresponds to the contamination of the sample with a small amount ofmethanol, which is used to clean the atomizer between samples. Indeed, there is a broad peak near
32 Da which could correspond to CH3 OH+ .
Most importantly, we do not observe significant ionization of the background gas. The basepressure of the spectrometer chamber when the nanoparticle source is not in use is ∼10−8 Torrand increases to ∼10−6 Torr when the experiment is running, demonstrating that the majority ofthe background gas during the experiment comes from the nanoparticle source, which used N2 as acarrier gas. The insignificant role of the background gas is evidenced by the lack of ions with masses
corresponding to N+ (14 Da) or N+
2 (28 Da). Thus, the mass spectrum of a single KI nanoparticle
demonstrates that the ions that reach the detector are due to the atoms in the nanoparticle itself,
and not from the background gas.

B.4.2

Time-of-flight experimental details

The mass spectrum was collected using the same MCP–phosphor detector as for the VMI
images, except that the voltage drop across the phosphor screen was monitored. Acquiring timeof-flight information on the ions is experimentally challenging, because each plasma explosion caneject more than 10,000 ions, which is far greater than typical mass spectrometry that generally
detects just 1 ion per laser shot. Thus, instead of the time-to-digital converter typically used inmass spectrometry, we recorded the mass spectrum using a high-performance digitizer card (Acqiris
U1084A, Agilent Technologies) that sampled the voltage drop across the detector at 0.5 ns intervals
with 8-bit precision. Still, the data acquisition is complicated due to the low dynamic range of thissingle-shot sampling method and the severe ringing in the electronics due to the extremely high ion
yield. Nevertheless, we are able to observe plasma explosions from single nanoparticles at the full95
repetition rate of the laser (1 kHz). We observe many of the same trends seen in the VMI images.
For example, there is a large range of photoion yields, which correspond to nanoparticles of different
sizes and different intensities in the laser focus.

1

Ion yield (arb units)

150

10

Mass to charge ratio (Da/e)

H+ (1 Da)abundance: 19.8%
K+ (39 Da)
abundance: 50.4%

100

C+ (12 Da)abundance: 20.3%

50
0
0.0

100

0.5

I+ (127 Da)abundance: 9.4%

1.0
1.5
2.0
2.5
Time of flight (microseconds)

3.0

Figure B.2: Mass spectrum of a single nanoparticle explosion. The photoion mass spectrum
corresponding to plasma formation in a single, representative potassium iodide (KI) nanoparticle
demonstrates that the observed ions originate from the nanoparticle itself (K+ and I+ ) and not fromthe background gas (N2 ). The H+ and C+ peaks likely correspond to a layer of water and methanolthat forms on the surface of the particle. The prominence of the H+ peak is over-emphasized by
the severe electronic ringing that takes place due to the intensity of the ion signal. The relative
abundance of each peak is expressed in terms of total identified ions; the labeled peaks account for
more than 75% of all positive ions detected. Adapted with permission from Ref. 3. c 2014 American
Chemical SocietyAppendix C

Shock Waves in Nanoplasmas Appendix

This chapter is adapted, with permission, from the Supplemental Material for:• D. D. Hickstein, F. Dollar, J. A. Gaffney, M. E. Foord, G. M. Petrov, B. B. Palm, K. E.
Keister, J. L. Ellis, C. Ding, S. B. Libby, J. L. Jimenez, H. C. Kapteyn, M. M. Murnane,
and W. Xiong. Observation and Control of Shock Waves in Individual Nanoplasmas. Phys.
Rev. Lett., 112 (11), 2014, 115004. doi: 10 . 1103 / PhysRevLett . 112 . 115004 c 2014
American Physical Society

C.1

Overview

This appendix provides additional details about the observation of nanoplasma shock waves
described in Chapter 5. Section C.2 provides a description of the apparatus and techniques used tocreate and observe the shock waves. Section C.3 presents data showing that larger nanoparticles havea higher likelihood of producing shock waves. Section C.4 discusses the effect of the laser intensity on
the total ion yield and the shock formation rate when using a single laser pulse. Section C.5 describes
how the time delay between two laser pulses can be used to optimize the shock production rate.
Section C.6 presents additional details about the HYDRA hydrodynamics simulations and discusses
how the kinetic energy of the shock waves might increase at higher laser intensities. Section C.7
explains why the expansion larger nanoplasmas must be treated as a net-neutral hydrodynamic
expansion in contrast to the expansion smaller nanoplasmas which can be understood as a Coulomb
explosion.

97

C.2

Experimental Details

The experimental apparatus consists of a nanoparticle aerosol source coupled to a velocity-mapimaging (VMI) photoion spectrometer [2, 5, 51] as described in Section 2.3. Starting with an aqueous
solution, a compressed-gas atomizer (TSI model 3076) generates an aerosol consisting of dropletswith an average diameter of approximately 1 µm. The water in the droplets then evaporates, leaving
behind nanocrystals with a diameter that depends on the sample concentration. The nanocrystals
are typically 100 nm in diameter, and have approximately spherical shape [161]. Samples of NaCl,
KI, KCl, and NH4 NO3 were obtained from Fisher Scientific and diluted in ultrapure (>18 MΩ
resistivity) water. The samples were diluted to the same volume concentration (0.12%) to assurethat the aerosol particles of different compositions would be the same size. The nanocrystals arefocused using an aerodynamic lens (Aerodyne Research) [70], which uses a series of ∼2 mm apertures
to collimate the nanocrystal aerosol into a ∼0.5 mm beam.
The collimated aerosol beam passes through a 1.5 mm diameter skimmer and into the differentially pumped photoionization chamber, which reaches a pressure of 10−6 Torr (base pressure
10−9 Torr). The nanoparticles are then ionized by an intense (∼1014 W/cm2 ), 800 nm, 40 fs laser
pulse, derived from a Ti:sapphire regenerative amplifier (KMLabs Wyvern HE) operating at 1 kHz.
The pre-pulse contrast is greater than 250:1 as measured with a photodiode, and the pulse energies
are varied between 5 to 100 µJ.
The 10 mm laser beam is focused with a 30 cm lens to reach an estimated FWHM focal spot
diameter of 25 µm. The resulting volume of the interaction region (assuming a 0.5 mm collimatedaerosol beam) is 2.5 × 10−7 cm3 . With an estimated aerosol density of 105 particles/cm3 , the laser
pulse will interact with a particle every ∼40 laser pulses, for an average of 25 hits per second at a
1 kHz repetition rate. Thus, even with millisecond exposure times, we can identify the photofragments originating from a single nanocrystal. The actual hit rate observed experimentally depends
on the volume of the laser focus that is above the threshold intensity for plasma formation and thus
depends on the power of the incident laser beam.

98
For the two-pulse experiment, a BBO crystal is used to generate ∼40 fs pulses of 400 nm light.
The 400 nm and 800 nm pulses were delayed in time using a computer-controlled motorized delay
stage placed in the 800 nm arm of a Mach–Zehnder interferometer. The photoions are accelerated
towards the microchannel-plate phosphor detector using three electrodes in a velocity-map-imaging
geometry [51], and the photoion distribution is recorded using a CCD camera (Allied Vision Technologies). The data is recorded at ∼15 Hz. A series of PADs is shown in Figure C.1.

Ion kinetic enegy (eV/Z)

20 a

b

c

d

e

g

h

i

j

0
20
20 f
0
20
20 0 20

20 0 20 20 0 20 20 0 20
Ion kinetic enegy (eV/Z)

20 0 20

Figure C.1: Nanoplasma explosions of NaCl nanoparticles with a single 800 nm laser
pulse. Panels a and f show no particles, while panels b, d, h, i, and j show diffuse plasma explosions. Frames c, e, and g display shock waves that were generated from particles subjected to laser
intensities sufficient to initiate shock formation. The center of the frame corresponds to ions withzero kinetic energy, and the laser polarization is in the vertical direction. The laser propagates fromleft to right. Adapted with permission from Ref. 4. c 2014 American Physical Society

C.3

Dependence of shock formation on particle size

For the size-selected experiment, the nanoparticles were passed through a differential mobility
analyser (TSI, models 3081 and 3085). To quantify the relative number of particles created by theatomizer, we used a scanning-mobility particle-sizer (SMPS) consisting of the differential mobility
analyzer connected to a condensation particle counter (TSI, Model 3775). Figure C.2 presents theresults of plasma formation in size-selected nanoparticles, and demonstrates that larger nanoparticles
produce shock waves more frequently. The physical mechanism for this is not entirely clear, but may
be a simple consequence of the fact that a larger nanoparticle contains more atoms and will therefore
have a higher probability of generating enough “seed” electrons to ignite the avalanche breakdown

99
process. The fact that larger nanoparticles exhibit shock waves while the smaller particles do not,could also be a result of hydrodynamic expansions that takes place for larger particles in contrast

6 1e7

0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00

5
4
3
2
1
0
0

20 40 60 80 100 120 140
Particle diameter (nm)Number of shocks per camera exposure

Number or particles (dN/dlogDp, cm−3 )with the Coulomb explosion physics that governs the expansion of smaller particles.

Figure C.2: Effect of particle diameter of the formation of shock waves. With a single
800 nm laser pulse with an intensity of 3 × 1014 W/cm2 , the frequency of creating shocks in NaClparticles increases as the particle diameter becomes larger, even though the concentration of particles
is decreasing for particle sizes larger than ∼60 nm. Larger nanoparticles absorb more energy per
atom and can therefore create shocks throughout a larger region of the laser focal volume. Adaptedwith permission from Ref. 4. c 2014 American Physical Society

C.4

Effect of laser intensity on nanoplasma formation

Figure C.3 shows the effect of increasing the laser intensity on the total ion yield, the rate ofshock wave formation, and the mean energy of the shock waves. The total ion yield shows a rapid
increase with laser intensity, relating to the highly nonlinear nature of the avalanche ionization
process. The appearance and energy of shock waves follow even steeper relationships with the laser
intensity, quickly reaching saturation. Ammonium nitrate has the highest ionization potential of anyof the compounds in this study, and the decrease in the ion yield if readily apparent in Figure C.3a.
Interestingly, ammonium nitrate never displays shock waves when irradiated with a single laser
pulse. However, it is possible that the laser intensity was simply not high enough to crease shock

100

2.5
2.0

a)

KI (7.2 eV)
KCl (8.3 eV)
NaCl (9.2 eV)
AN (~11 eV)

1.5
1.0
0.5
0.0
0.0

0.20
0.15

0.5

1.0

b)

1.5 2.0 2.5 3.0 3.5
Laser intensity (1014 W/cm2 )

4.0

4.5

KI (7.2 eV)
KCl (8.3 eV)
NaCl (9.2 eV)
AN (~11 eV)

0.10
0.05
0.00
0.0

Mean energy of shock (eV)

Shocks per camera exposure

Ion yield (arbitrary units)

waves in ammonium nitrate.

0.5

35
30 c)
25
20
15
10
5
0
0.0 0.5

1.0

1.5 2.0 2.5 3.0 3.5
Laser intensity (1014 W/cm2 )

4.0

4.5

KI (7.2 eV)
KCl (8.3 eV)
NaCl (9.2 eV)
AN (~11 eV)

1.0

1.5 2.0 2.5 3.0 3.5
Laser intensity (1014 W/cm2 )

4.0

4.5

Figure C.3: Ion yield and shock wave formation versus laser intensity. (a) The ion yieldsuddenly increases with laser intensity, which is typical for avalanche ionization [114]. The thresholdlaser intensity increases with the ionization potential of the species (shown in parenthesis). The
ionization potentials were obtained from the NIST webbook [162], except for NH4 NO3 (ammonium
nitrate, AN), which does not have a documented ionization potential, but is expected to have one
similar to other compounds featuring a nitrate (–NO3 ) moiety: between 11 and 12 eV. (b) The
number of shocks generated per camera exposure increases rapidly at a threshold intensity, quickly
saturating. (c) The average energy of the shocks increases with laser intensity until reaching an
asymptotic value of ∼30 eV/Z. Notably, Ammonium nitrate requires higher laser intensity to achieve
comparable ion yields and does not show any shocks in this one-pulse experiment. Adapted withpermission from Ref. 4. c 2014 American Physical Society

101

C.5

Time-dependence of shock formation rate

Figure C.4 reveals the rate of shock formation increases rapidly and quickly saturates as thetime-delay between the laser pulses is increased. Additionally, the minimum time-delay required tomake shocks is slightly longer when the 800 nm laser pulse arrives first. It’s likely that the 800 nm
pulse does not deposit as much energy into the plasma and causes the plasma to expand more slowly,
therefore taking slightly longer to become highly absorbing of the subsequent 400 nm pulse. It’s
possible that a series of three or more laser pulses can be used to shape the plasma density profile
in order to further optimize the rate of shock production.

Fraction of ions in shock (percent)

Fraction of ions in shock versus two-pulse delay
Average
Average +/- standard error
15
800 nm first
400 nm second

400 nm first
800 nm second

10

5

0

40

20

0
Time (picoseconds)

20

40

Figure C.4: The fraction of ions in the shock controlled with two-pulse delay. Each dot
corresponds to a single shock wave generated from a NH4 NO3 nanoparticle. The relative number ofions in each shock wave compared to the total number of ions is estimated by fitting the ion distribution with two Gaussian functions (Figure 5.3d): one wide Gaussian for the broad “background”
ions and a narrow Gaussian for the ions in the shock wave. At time delays of 10 ps, the shock waves
do not contain many ions compared to the background. However, the fraction of ions in the shockis enhanced at an optimal time delay around 30 ps. Adapted with permission from Ref. 4. c 2014
American Physical Society

102

C.6

Hydrodynamic simulations

To investigate the mechanisms for shock wave formation, hydrodynamic simulations were performed using version 9.0 of the HYDRA radiation-hydrodynamics code [133] for NaCl nanoparticlesof 100 nm radius. These simulations were completed by Dr. Jim Gaffney at Lawrence Livermore
National Laboratory. The HYDRA calculations were performed in 1D, by assuming spherical symmetry, using the 3D version of HYDRA. We note that this version of HYDRA, which uses finite
elements methods (rather than finite difference methods) for transport calculations, is more appropriate for these plasmas. Simulations used an adaptive one (radial) dimensional Lagrangian mesh,which uses a smaller grid zones near regions of rapidly changing plasma density. Thus, the calculations give a reliable description of sharp spatial features (such as shock waves). Furthermore, thecalculations include models for laser energy deposition via inverse bremsstrahlung (IB) along withaccurate equation of state and thermal transport quantities.

Ion energy spectrum
Ion yield (ions/eV)

105

5 ps

10 ps

20 ps

104

103

101
100
Ion kinetic energy (eV)Figure C.5: HYDRA simulations at various two-pulse delays. Hydrodynamic simulations
completed using the HYDRA [133] radiation-hydrodynamics code reveal that two time-delayed
800 nm laser pulses, both with intensities of 4.9 × 1014 W/cm2 , will generate quasi-monoenergetic
shocks in the ion kinetic-energy spectrum only when the time delay is less than ∼35 ps. The shock
does not show up as a sharp peak for the time delay of 5 ps, but when the time delay is increased to
10 ps, the shock displays as a sharp peak, in agreement with experimental findings. Adapted withpermission from Ref. 4. c 2014 American Physical Society

103
The hydrodynamic calculations confirm that a shock wave is produced in the expanding nanoplasma and that this shock manifests as a step in the plasma density as well as a spike in the ion
kinetic energy distribution (Figures 5.5, C.5, and C.6). The simulations indicate that the simulated
spike in the ion kinetic energy distribution is quite sensitive to the parameters of the laser pulse;in this work we have chosen intensities to match the experimentally observed ion energy of ∼20 eVwith the 20 ps delay between the two laser pulses. This results in a simulated laser intensity of
5 × 1014 W/cm2 which is consistent with the estimated experimental laser intensity.

Ion energy spectrum

Ion yield (ions/eV)

105

Second pulse: 0.79 x 1014 W/cm2
Second pulse: 5.00 x 1014 W/cm2
Second pulse: 5.50 x 1014 W/cm2
Second pulse: 11.0 x 1014 W/cm2

104

103
101

Ion kinetic energy (eV)102

Figure C.6: Scaling of the shock with laser intensity using HYDRA. The ion kinetic energy
distribution from two laser pulses delayed by 20 ps as calculated by hydrodynamic simulations using
the HYDRA software [133]. The intensity of the first pulse is 4.9 × 1014 W/cm2 . Increasing theintensity of the second pulse from 0.79×1013 W/cm2 to 1.1×1015 W/cm2 increases the energy of thequasi-monoenergetic ions produced by the shock wave by about 5 times. However, the shape of thepeak in the ion distribution is extremely sensitive to the laser intensity, with ∼10% changes in thelaser intensity transforming a single sharp peak into three broad peaks. Adapted with permission
from Ref. 4. c 2014 American Physical Society

The simulations start with a +1 ionized plasma, making the approximation that the initial
ionization of cold material occurs very rapidly. Using the Ammosov, Delone, and Krainov (ADK)
ionization model [1] we calculate that for our laser parameters, initial ionization of the particle
occurs well before the peak of the laser pulse, after which IB becomes the dominant process and the
HYDRA will model the plasma adequately. The small size of the nanoparticles combined with therelatively high temperatures created by the second laser pulse mean that the thermal electron mean

104
free path is larger than the spatial mesh zone size, making non-local energy transport important. A
model for non-local energy transport is implemented in HYDRA [163], and we include this in thepresented simulations.
The HYDRA calculations make two additional approximations: 1) that the net charge ofthe plasma is small and 2) that the electron energy distribution can be described by a Maxwellian
distribution. Both of these approximations are valid in the regime of the large nanoparticles and subpicosecond laser pulses used in this study. Regarding the first approximation, we show (Section C.7)
that due to the low laser intensities used in this study, only a small fraction of the electrons will
be able to leave the plasma during the laser pulse. Therefore, the plasma is nearly net-neutral andcan be modeled as a hydrodynamic expansion. The second approximation, that the electrons energy
distribution can be described as Maxwellian, is valid because the excited electrons will thermalize
on a very rapid timescale compared to the picosecond timescale of the HYDRA simulations. The
electron thermalization time can be estimated from the electron-electron energy exchange rate [164]:
3/2

τ = 3.44 × 105

Teseconds,
Ne λ

(C.1)

where Te is the electron temperature, Ne is the density of the electrons, and λ ≈ 3 is the Coulomb
Logarithm [164]. Electron thermalization will be the slowest at the time of the second pulse, whenelectron temperatures are high and the plasma is lower density than during the first pulse. In theregion of high-pressure that drives the observed shock, typical simulated conditions are Te = 20 eV
and Ne = 5 × 1021 cm−3 . The timescale for electron thermalization is then ∼0.6 fs, very fastcompared to the hydrodynamic motion of interest in this study.
Consistency between the simulated velocity distribution and the experimentally recorded velocity distribution has been checked by numerically propagating the velocity distribution towards a“detector” using a simulated electric field. This analysis used the simulated velocity profile taken
80 ps after the second laser pulse, the point at which we estimate the VMI field separates electron
and ion clouds, allowing the ions to propagate to the detector without further interactions. The true
process of image formation is complex, and has not yet been modeled, however we have confirmed

105that sharp structures in VMI images correspond to peaks in the kinetic energy distribution. Thatis, the VMI works the way it usually does, even for expanding plamas.

C.7

Plasma quasi-neutrality

In contrast to most previous studies of nanoplasmas [38, 41, 114, 125, 128, 134], this study uses∼100 nm nanoparticles (containing on the order of 107 atoms) versus <10 nm noble gas clusters(containing on the order of 103 or 104 atoms). One important effect of this size difference is thatthe most of the electrons in these larger plasmas cannot escape the plasma, producing a nanoplasmathat has a small charge imbalance (a quasi-neutral plasma). There are several reasons for thisdifference. First, the excursion distance for laser-field-driven electrons is comparatively smaller forlarger nanoplasmas – much less than the cluster radius – preventing the majority of electrons frombeing driven outside of the ion cloud by the laser field. Second, even if a very small fraction of theelectrons leave the plasma, a massive charge builds up, preventing the majority of the electrons fromescaping the nanoplasma.
Here we estimate the fraction of electrons that can leave the nanoplasma ∆Ne /Ne , based onenergy considerations. When free electrons are driven out of the cluster by the laser electric field,
the charge imbalance creates a potential well. If too many electrons leave the cluster, the potential
energy Epot due to excess charge will become larger than the kinetic energy of the escaping electrons
Ekin , which will prevent further electron escape. One can estimate Ne /Ne by equating Epot to Ekin ,assuming that the excess charge is uniformly distributed within the cluster. Since the potential
energy is given by
N e2 ∆Ne,
4πε0 R Ne

(C.2)

e2
≈ 100 eV,
4πε0 aBohr(C.3)

Epot =and taking
Ekin = 4
we get∆Ne
4R
4R[a.u.]=== 10−3 ,Ne
N aBohr
N

(C.4)

106
which corresponds to 0.1% of the electrons leaving the cluster. It should be noted that the small
kinetic energy of the electrons (∼100 eV, due to the low laser intensity) plays an important role forkeeping the electrons inside the cluster. The electrons are simply not energetic enough to overcome
the potential barrier, which arises due to charge imbalance.
The predicted 0.1% ionization for large clusters is in sharp contrast to small noble gas clusters
used in previous studies. As an example, for R = 5 nm (94 a.u.), N = 104 , and Ekin ≈ 1 KeV, we
get
∆Ne
40R
(40)(94)≈ 0.4,=≈Ne
N aBohr104(C.5)

i.e. ∼40% of the electrons leave the cluster. This analysis reveals why small clusters become highly
charged and undergo fast Coulomb explosion while larger clusters remain quasi-neutral and undergo
a slow hydrodynamic expansion.

References[1]

M. V. Ammosov, N. B. Delone, and V. P. Krainov. Tunnel ionization of complex atoms andof atomic ions in an alternating electromagnetic field. Sov. Phys. JETP, 64, 1986, 1191–1194.
url: http://www.jetp.ac.ru/cgi-bin/dn/e\_064\_06\_1191.pdf (cited on pages i, 54,
65, 67, 103).

[2]

D. D. Hickstein, P. Ranitovic, S. Witte, X.-M. Tong, Y. Huismans, P. Arpin, X. Zhou, K.
E. Keister, C. Hogle, B. Zhang, C. Ding, P. Johnsson, N. Toshima, M. J. J. Vrakking, M.
M. Murnane, and H. C. Kapteyn. Direct Visualization of Laser-Driven Electron Multiple
Scattering and Tunneling Distance in Strong-Field Ionization. Phys. Rev. Lett., 109, 2012,
073004. doi: 10.1103/PhysRevLett.109.073004 (cited on pages iii, 30, 34, 36, 40, 43, 48,
51, 64, 81, 84, 86–88, 97).

[3]

D. D. Hickstein, F. Dollar, J. L. Ellis, K. J. Schnitzenbaumer, K. E. Keister, G. M. Petrov, C.
Ding, B. B. Palm, J. A. Gaffney, M. E. Foord, S. B. Libby, G. Dukovic, J. L. Jimenez, H. C.
Kapteyn, M. M. Murnane, and W. Xiong. Mapping Nanoscale Absorption of Femtosecond
Laser Pulses using Plasma Explosion Imaging. ACS Nano, 8 (9), 2014, 8810. doi: 10.1021/
nn503199v (cited on pages iii, 45, 47, 49, 52, 55–57, 61, 89, 93, 95).

[4]

D. D. Hickstein, F. Dollar, J. A. Gaffney, M. E. Foord, G. M. Petrov, B. B. Palm, K. E.
Keister, J. L. Ellis, C. Ding, S. B. Libby, J. L. Jimenez, H. C. Kapteyn, M. M. Murnane, andW. Xiong. Observation and Control of Shock Waves in Individual Nanoplasmas. Phys. Rev.
Lett., 112 (11), 2014, 115004. doi: 10.1103/PhysRevLett.112.115004 (cited on pages iii,
48, 49, 51, 54, 62, 65, 66, 68, 70, 96, 98–103).

[5]

W. Xiong, D. D. Hickstein, K. J. Schnitzenbaumer, J. L. Ellis, B. B. Palm, K. E. Keister,C. Ding, L. Miaja-Avila, G. Dukovic, J. L. Jimenez, M. M. Murnane, and H. C. Kapteyn.
Photoelectron Spectroscopy of CdSe Nanocrystals in the Gas Phase: A Direct Measure of
the Evanescent Electron Wave Function of Quantum Dots. Nano Lett., 13, 2013, 2924. doi:
10.1021/nl401309z (cited on pages iv, 51, 64, 76, 97).

[6]

C. Mancuso, D. D. Hickstein, P. Grychtol, O. Kfir, X.-M. Tong, R. Knut, F. Dollar, D. Zusin,
M. Gopalakrishnan, C. Gentry, E. Turgut, J. L. Ellis, M.-C. Chen, A. Fleischer, O. Cohen,
H. C. Kapteyn, and M. M. Murnane. Strong Field Ionization Tomography with Two-color
Circularly Polarized Femtosecond Laser Fields. Submitted, 2014 (cited on pages iv, 73).

REFERENCES
[7]

108

J. L. Ellis, D. D. Hickstein, K. J. Schnitzenbaumer, M. B. Wilker, B. B. Palm, J. L. Jimenez,
G. Dukovic, H. C. Kapteyn, M. M. Murnane, and W. Xiong. Electron transfer dynamics in
gas-phase and solvated quantum dots. In preparation, 2014 (cited on page iv).

[8]

Z. Han, S. Niu, C. Shang, Z. Liu, and L. Ren. Light trapping structures in wing scales ofbutterfly Trogonoptera brookiana. Nanoscale, 4 (9), 2012, 2879. doi: 10.1039/c2nr12059c(cited on page 1).

[9]H. E. Edgerton. Bullet Through Apple. Edgerton Digital Archives, MIT Museum, Cambridge MA, 1964. url: http://edgerton-digital-collections.org (cited on page 2).

[10]

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, andC. K. Rhodes. Studies of multiphoton production of vacuum-ultraviolet radiation in the raregases. J. Opt. Soc. Am. B, 4 (4), 1987, 595–601. doi: 10.1364/JOSAB.4.000595 (cited on
pages 3, 7, 32).

[11]

C. G. Durfee, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn.
Phase Matching of High-Order Harmonics in Hollow Waveguides. Phys. Rev. Lett., 83 (11),1999, 2187. doi: 10.1103/PhysRevLett.83.2187 (cited on pages 3, 7).

[12]

T. Popmintchev, M.-C. Chen, P. Arpin, M. M. Murnane, and H. C. Kapteyn. The attosecond
nonlinear optics of bright coherent X-ray generation. Nature Phot., 4 (12), 2010, 822–832.
doi: 10.1038/nphoton.2010.256 (cited on pages 3, 7, 9, 14).

[13]

L. Miaja-Avila, J. Yin, S. Backus, G. Saathoff, M. Aeschlimann, M. Murnane, and H.
Kapteyn. Ultrafast studies of electronic processes at surfaces using the laser-assisted photoelectric effect with long-wavelength dressing light. Phys. Rev. A, 79, 2009, 030901. doi:
10.1103/PhysRevA.79.030901 (cited on page 6).

[14]

Z. Xie, T. Z. Markus, G. Gotesman, Z. Deutsch, D. Oran, and R. Naaman. How Isolated
Are the Electronic States of the Core in Core/Shell Nanoparticles? ACS Nano, 5 (2), 2011,
863–869. doi: 10.1021/nn102002x (cited on page 6).

[15]

H. Borchert, D. V. Talapin, C. McGinley, S. Adam, A. Lobo, A. R. B. de Castro, T.
Moller, and H. Weller. High resolution photoemission study of CdSe and CdSe/ZnS coreshell nanocrystals. J. Chem. Phys., 119 (3), 2003, 1800–1807. doi: 10 . 1063 / 1 . 1580096(cited on page 6).

[16]

P. Agostini, F. Fabre, G. Mainfray, G. Petite, and N. Rahman. Free-Free Transitions Following
Six-Photon Ionization of Xenon Atoms. Phys. Rev. Lett., 42 (17), 1979, 1127–1130. doi:
10.1103/PhysRevLett.42.1127 (cited on pages 7, 32).

[17]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov,Y. Liu, D. Attwood, and C. Jacobsen. Generation of spatially coherent light at extreme
ultraviolet wavelengths. Science, 297, 2002, 376. doi: 10.1126/science.1071718 (cited on
page 7).

[18]

A. Rundquist, C. G. Durfee, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C.
Kapteyn. Phase-Matched Generation of Coherent Soft X-rays. Science, 280, 1998, 1412. doi:
10.1126/science.280.5368.1412 (cited on page 7).

REFERENCES
[19]

109

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A.
Gaeta, C. Hernández-Garcı́a, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H.
C. Kapteyn. Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared
femtosecond lasers. Science, 336, 2012, 1287. doi: 10 . 1126 / science . 1218497 (cited on
pages 7, 9, 15).

[20]

E. Gagnon, P. Ranitovic, X.-M. Tong, C. L. Cocke, M. M. Murnane, H. C. Kapteyn, and A.
S. Sandhu. Soft X-ray-driven femtosecond molecular dynamics. Science, 317, 2007, 1374–8.
doi: 10.1126/science.1144920 (cited on page 7).

[21]

W. Li, X. Zhou, R. Lock, and S. Patchkovskii. Time-Resolved Dynamics in N2O4 Probed
Using High Harmonic Generation. Science, 322, 2008, 1207–1211. doi: 10.1126/science.
1163077 (cited on page 7).

[22]

X. Zhou, P. Ranitovic, C. W. Hogle, J. H. D. Eland, H. C. Kapteyn, and M. M. Murnane.
Probing and controlling non-BornOppenheimer dynamics in highly excited molecular ions.
Nature Phys., 8 (3), 2012, 232–237. doi: 10.1038/nphys2211 (cited on page 7).

[23]

K. Hoogeboom-Pot, D. Nardi, J. N. Hernandez-Charpak, E. Anderson, X. Gu, R. Yang,
H. Kapteyn, and M. Murnane. A New Regime of Nanoscale Thermal Transport: Collective
Diffusion Counteracts Dissipation Inefficiency. ArXiv preprint, 2014, 1407.0658. doi: 10 .
1364/UP.2014.10.Thu.E.1 (cited on page 7).

[24]

C. La-O-Vorakiat, E. Turgut, C. A. Teale, H. C. Kapteyn, M. M. Murnane, S. Mathias,
M. Aeschlimann, C. M. Schneider, J. M. Shaw, H. T. Nembach, and T. J. Silva. Ultrafast
Demagnetization Measurements Using Extreme Ultraviolet Light: Comparison of Electronicand Magnetic Contributions. Phys. Rev. X, 2 (1), 2012, 011005. doi: 10.1103/PhysRevX.
2.011005 (cited on page 7).

[25]

R. Sandberg, A. Paul, D. Raymondson, S. Hädrich, D. Gaudiosi, J. Holtsnider, R. Tobey,
O. Cohen, M. Murnane, H. Kapteyn, C. Song, J. Miao, Y. Liu, and F. Salmassi. Lensless
Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams. Phys. Rev.
Lett., 99 (9), 2007, 098103. doi: 10.1103/PhysRevLett.99.098103 (cited on page 7).

[26]

M. D. Seaberg, D. E. Adams, E. L. Townsend, D. a. Raymondson, W. F. Schlotter, Y. Liu,
C. S. Menoni, L. Rong, C.-C. Chen, J. Miao, H. C. Kapteyn, and M. M. Murnane. Ultrahigh
22 nm resolution coherent diffractive imaging using a desktop 13 nm high harmonic source.
Opt. Express, 19 (23), 2011, 22470–9. doi: 10.1364/OE.19.022470 (cited on page 7).

[27]

C. I. Blaga, J. Xu, A. D. DiChiara, E. Sistrunk, K. Zhang, P. Agostini, T. A. Miller, L. F.
DiMauro, and C. D. Lin. Imaging ultrafast molecular dynamics with laser-induced electron
diffraction. Nature, 483 (7388), 2012, 194–197. doi: 10.1038/nature10820 (cited on pages 7,
32).

[28]

J. Xu, Z. Chen, A.-T. Le, and C. D. Lin. Self-imaging of molecules from diffraction spectraby laser-induced rescattering electrons. Phys. Rev. A, 82 (3), 2010, 033403. doi: 10.1103/
PhysRevA.82.033403 (cited on pages 7, 32).

REFERENCES
[29]

110

J. Xu, C. I. Blaga, K. Zhang, Y. H. Lai, C. D. Lin, T. a. Miller, P. Agostini, and L. F.
DiMauro. Diffraction using laser-driven broadband electron wave packets. Nature Comm., 5,2014, 4635. doi: 10.1038/ncomms5635 (cited on pages 7, 32, 74).

[30]

P. B. Corkum. Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett.,
71 (13), 1993, 1994–1997. doi: 10.1103/PhysRevLett.71.1994 (cited on pages 8, 9, 32, 36).

[31]

D. L. Andrews and A. A. Demidov. An Introduction to Laser Spectroscopy. 2nd.
Springer Science and Business Media, 2002, p. 281 (cited on page 9).

[32]

M. C. Chen, C. Hernández-Garcı́a, C. Mancuso, F. Dollar, B. Galloway, D. Popmintchev,
P. C. Huang, B. Walker, L. Plaja, A. Jaron-Becker, A. Becker, T. Popmintchev, M. M.
Murnane, and H. C. Kapteyn. Generation of Bright Isolated Attosecond Soft X-Ray Pulses
Driven by Multi-Cycle Mid-Infrared Lasers. Proc. Natl. Acad. Sci., 2014, E2361–E2367. doi:
10.1073/pnas.1407421111. arXiv: 1401.0240 (cited on pages 9, 15, 76).

[33]

C. Hernández-Garcı́a, J. A. Pérez-Hernández, T. Popmintchev, M. M. Murnane, H. C. Kapteyn,
A. Jaron-Becker, A. Becker, and L. Plaja. Zeptosecond High Harmonic keV X-Ray Waveforms Driven by Midinfrared Laser Pulses. Phys. Rev. Lett., 111 (3), 2013, 033002. doi:
10.1103/PhysRevLett.111.033002 (cited on pages 9, 31).

[34]

N. Felidj, J. Aubard, G. Levi, J. R. Krenn, A. Hohenau, G. Schider, A. Leitner, and F. R.
Aussenegg. Optimized surface-enhanced Raman scattering on gold nanoparticle arrays. Appl.
Phys. Lett., 82 (18), 2003, 3095. doi: 10.1063/1.1571979 (cited on page 10).

[35]

E. C. L. Ru, E. Blackie, M. Meyer, and P. G. Etchegoin. Surface Enhanced Raman Scattering
Enhancement Factors : A Comprehensive Study. J. Phys. Chem. C, 111, 2007, 13794–13803.
doi: 10.1021/jp0687908 (cited on pages 10, 47).

[36]

V. K. Valev, D. Denkova, X. Zheng, A. I. Kuznetsov, C. Reinhardt, B. N. Chichkov, G.
Tsutsumanova, E. J. Osley, V. Petkov, B. De Clercq, A. V. Silhanek, Y. Jeyaram, V. Volskiy,
P. a. Warburton, G. a. E. Vandenbosch, S. Russev, O. a. Aktsipetrov, M. Ameloot, V. V.
Moshchalkov, and T. Verbiest. Plasmon-enhanced sub-wavelength laser ablation: plasmonic
nanojets. Adv. Opt. Mat., 24 (10), 2012, OP29–35. doi: 10.1002/adma.201103807 (cited on
page 10).

[37]

G. M. Petrov, J. Davis, A. L. Velikovich, P. Kepple, A. Dasgupta, and R. W. Clark. Dynamics
of a Xe cluster plasma produced by an intense ultrashort pulse KrF laser. Phys. Plasmas,
12 (6), 2005, 063103. doi: 10.1063/1.1928367 (cited on pages 11, 63, 67).

[38]

T. Ditmire, J. W. G. Tisch, E. Springate, M. B. Mason, N. Hay, J. P. Marangos, and M. H.
R. Hutchinson. High Energy Ion Explosion of Atomic Clusters: Transition from Molecular to
Plasma Behavior. Phys. Rev. Lett., 78, 1997, 2732. doi: 10.1103/PhysRevLett.78.2732(cited on pages 11, 47, 49, 63, 64, 75, 105).

[39]

T. Ditmire, J. Zweiback, V. P. Yanovsky, T. E. Cowan, and G. Hays. Nuclear fusion from
explosions of femtosecond laser-heated deuterium clusters. Nature, 398, 1999, 489–492. doi:
10.1038/19037 (cited on pages 11, 63).

REFERENCES
[40]

111

A. E. Kaplan, B. Y. Dubetsky, and P. L. Shkolnikov. Shock Shells in Coulomb Explosionsof Nanoclusters. Phys. Rev. Lett., 91 (14), 2003, 143401. doi: 10.1103/PhysRevLett.91.
143401 (cited on pages 11, 47, 63, 69, 71, 80).

[41]

F. Peano, R. A. Fonseca, J. L. Martins, and L. O. Silva. Controlled shock shells and intracluster fusion reactions in the explosion of large clusters. Phys. Rev. A, 73 (5), 2006, 053202.
doi: 10.1103/PhysRevA.73.053202 (cited on pages 11, 63, 75, 105).

[42]

F. Peano, R. A. Fonseca, and L. O. Silva. Dynamics and Control of Shock Shells in the
Coulomb Explosion of Very Large Deuterium Clusters. Phys. Rev. Lett., 94 (3), 2005, 033401.
doi: 10.1103/PhysRevLett.94.033401 (cited on pages 11, 47, 63, 69, 71, 75).

[43]

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn. High power ultrafast lasers.
Rev. Sci. Instrum., 69 (3), 1998, 1207. doi: 10.1063/1.1148795 (cited on page 13).

[44]

C. Ding, W. Xiong, T. Fan, D. D. Hickstein, T. Popmintchev, X. Zhang, M. Walls, M. M.
Murnane, and H. C. Kapteyn. High flux coherent super-continuum soft X-ray source driven
by a single-stage, 10mJ, Ti:sapphire amplifier-pumped OPA. Opt. Express, 22 (5), 2014,
6194. doi: 10.1364/OE.22.006194 (cited on pages 13, 14, 34).

[45]

C. Ding. Bright Coherent Ultrafast Tabletop Light Sources Development and the Application
on EUV to Soft X-Ray Absorption Spectroscopy. University of Colorado PhD Thesis, 2014.
url: http://jila.colorado.edu/publications/theses (cited on pages 13, 14).

[46]

G. Cerullo and S. De Silvestri. Ultrafast optical parametric amplifiers. Rev. Sci. Instrum.,74, 2003, 0034–6748. doi: 10.1063/1.1523642 (cited on page 14).

[47]

M.-C. Chen, P. Arpin, T. Popmintchev, M. Gerrity, B. Zhang, M. Seaberg, D. Popmintchev,
M. M. Murnane, and H. C. Kapteyn. Bright, Coherent, Ultrafast Soft X-Ray Harmonics
Spanning the Water Window from a Tabletop Light Source. Phys. Rev. Lett., 105, 2010,
173901. doi: 10.1103/PhysRevLett.105.173901 (cited on pages 14, 15).

[48]

D. W. Chandler and P. L. Houston. Two-dimensional imaging of state-selected photodissociation products detected by multiphoton ionization. J. Chem. Phys., 87 (2), 1987, 1445. doi:
10.1063/1.453276 (cited on pages 16, 17).

[49]

H. Helm, N. Bjerre, M. J. Dyer, D. L. Huestis, and M. Saeed. Images of Photoelectron Formed
in Intense Laser Fields. Phys. Rev. Lett., 70 (21), 1993, 3221. doi: 10.1103/PhysRevLett.
70.3221 (cited on page 16).

[50]

C Bordas, M. Dyer, T Fairfield, H Helm, and K. Kulander. Unexpected product fine-structure
distributions in (3+1)-photon ionization of xenon. Phys. Rev. A, 51 (5), 1995, 3726. doi:
10.1103/PhysRevA.51.3726 (cited on page 16).

[51]

A. T. J. B. Eppink and D. H. Parker. Velocity map imaging of ions and electrons using
electrostatic lenses: Application in photoelectron and photofragment ion imaging of molecularoxygen. en. Rev. Sci. Instrum., 68 (9), 1997, 3477–3484. doi: 10.1063/1.1148310 (cited on
pages 17–19, 32, 35, 48, 51, 64, 65, 90, 97, 98).

REFERENCES
[52]

112

B. J. Whitaker. Imaging in Molecular Dynamics: Technology and Applications (AUser’s Guide). Cambridge, UK: Cambridge University Press, 2003 (cited on pages 17, 18,
24).

[53]

P. Johnsson, A. Rouzée, W. Siu, Y. Huismans, F. Lépine, T. Marchenko, S. Düsterer, F.
Tavella, N. Stojanovic, H. Redlin, A. Azima, and M. J. J. Vrakking. Characterization of a
two-color pump-probe setup at FLASH using a velocity map imaging spectrometer. Optics
Lett., 35 (24), 2010, 4163. doi: 10.1364/OL.35.004163 (cited on page 17).

[54]

M. Stei, J. von Vangerow, R. Otto, A. H. Kelkar, E. Carrascosa, T. Best, and R. Wester.
High resolution spatial map imaging of a gaseous target. J. Chem. Phys., 138 (21), 2013,
214201. doi: 10.1063/1.4807482 (cited on page 17).

[55]

S. Thorin. Design and construction of a velocity map imaging spectrometer. PhD thesis.
Lund, 2004. url: http://old-atto.fysik.lth.se/publications/master/Thorin\_LRAP327.pdf (cited on pages 17, 18).

[56]

D. Manura and D. Dahl. SIMION 8.0. Ringoes, NJ: Scientific Instrument Services, Inc.,
2008. url: http://simion.com/manual/ (cited on page 18).

[57]

C. L. Adams, H. Schneider, K. M. Ervin, and J. M. Weber. Low-energy photoelectron imaging
spectroscopy of nitromethane anions: Electron affinity, vibrational features, anisotropies, andthe dipole-bound state. J. Chem. Phys., 130 (7), 2009, 074307. doi: 10.1063/1.3076892(cited on page 19).

[58]

A. Sanov and W. C. Lineberger. Dynamics of cluster anions: a detailed look at condensedphase interactions. PhysChemComm, 5 (25), 2002, 165. doi: 10.1039/b209239e (cited on
page 19).

[59]

A. Sanov and W. C. Lineberger. Cluster anions: Structure, interactions, and dynamics in the
sub-nanoscale regime. Phys. Chem. Chem. Phys., 6 (9), 2004, 2018. doi: 10.1039/b400524d(cited on page 19).

[60]

R. V. Latham. High Voltage Vacuum Insulation. Academic Press, 1995. doi: 10.1016/
B978-012437175-0/50000-2 (cited on page 20).

[61]

Beam Dynamics Skimmer Specification Sheet. In: Beam Dynamics, Inc. Beam Dynamics,
Inc. url: www.beamdynamicsinc.com/skimmer\_specs2.htm (cited on page 21).

[62] Phosphor Specifications Chart. Beam Imaging Solutions, 2012. url: http : / / www .
beamimaging.com/pscreen.html (cited on page 23).
[63]

D. Townsend, S. Kyoung Lee, and A. G. Suits. Orbital polarization from DC slice imaging:
S(1D2) alignment in the photodissociation of ethylene sulfide. Chem. Phys., 301, 2004, 197–
208. doi: 10.1016/j.chemphys.2003.10.020 (cited on page 24).

[64]

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler. Reconstruction of Abeltransformable images: The Gaussian basis-set expansion Abel transform method. Rev. Sci.
Instrum., 73 (7), 2002, 2634–2642. doi: 10.1063/1.1482156 (cited on pages 24, 35).

REFERENCES
[65]

113

M. J. J. Vrakking. An iterative procedure for the inversion of two-dimensional ion/photoelectron
imaging experiments. Rev. Sci. Instrum., 72, 2001, 4084. doi: 10.1063/1.1406923 (cited on
page 24).

[66]

G. M. Roberts, J. L. Nixon, J. Lecointre, E. Wrede, and J. R. R. Verlet. Toward real-timecharged-particle image reconstruction using polar onion-peeling. Rev. Sci. Instrum., 80 (5),2009, 053104. doi: 10.1063/1.3126527 (cited on page 24).

[67]

K. R. May. The Collison nebulizer: description, performance and application. Aerosol Sci.,
4 (3), 1973, 235. doi: 10.1016/0021-8502(73)90006-2 (cited on page 25).

[68]

P. Liu, P. J. Ziemann, and D. B. Kittelson. Aerosol Science and Technology Generating
Particle Beams of Controlled Dimensions and Divergence: I . Theory of Particle Motion in
Aerodynamic Lenses and Nozzle Expansions. Aerosol Sci. and Tech., 22, 1995, 293–313. doi:
10.1080/02786829408959748 (cited on page 27).

[69]

P. Liu, P. J. Ziemann, D. B. Kittelson, and P. H. McMurry. Generating Particle Beams ofControlled Dimensions and Divergence: II. Experimental Evaluation of Particle Motion in
Aerodynamic Lenses and Nozzle Expansions. Aerosol Sci. and Tech., 22 (3), 1995, 314–324.
doi: 10.1080/02786829408959749 (cited on page 27).

[70]

P. S. K. Liu, R. Deng, K. A. Smith, L. R. Williams, J. T. Jayne, M. R. Canagaratna, K. Moore,
T. B. Onasch, D. R. Worsnop, and T. Deshler. Transmission Efficiency of an Aerodynamic
Focusing Lens System: Comparison of Model Calculations and Laboratory Measurements for
the Aerodyne Aerosol Mass Spectrometer. Aerosol Sci. and Tech., 41, 2007, 721–733. doi:
10.1080/02786820701422278 (cited on pages 28, 50, 90, 97).

[71]

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Maunfray, and C. Manus. Multipleharmonic conversion of 1064 nm radiation in rare gases. J. Phys. B, 21, 1988, L31–L35. doi:
10.1088/0953-4075/21/3/001 (cited on page 32).

[72]

C. T. L. Smeenk, L. Arissian, A. V. Sokolov, M. Spanner, K. F. Lee, A. Staudte, D. M.
Villeneuve, and P. B. Corkum. Alignment Dependent Enhancement of the Photoelectron
Cutoff for Multiphoton Ionization of Molecules. Phys. Rev. Lett., 112 (25), 2014, 253001.
doi: 10.1103/PhysRevLett.112.253001 (cited on page 32).

[73]

S. K. Lee, Y. F. Lin, L. Yan, and W. Li. Laser-induced low energy electron diffraction inaligned molecules. J. Phys. Chem. A, 116 (8), 2012, 1950. doi: 10.1021/jp210798c (cited
on page 32).

[74]

J. Mauritsson, T. Remetter, M. Swoboda, K. Klünder, A. L’Huillier, K. J. Schafer, O. Ghafur, F. Kelkensberg, W. Siu, P. Johnsson, M. J. J. Vrakking, I. Znakovskaya, T. Uphues, S.
Zherebtsov, M. Kling, F. Lépine, E. Benedetti, F. Ferrari, G. Sansone, and M. Nisoli. Attosecond Electron Spectroscopy Using a Novel Interferometric Pump-Probe Technique. Phys.
Rev. Lett., 105, 2010, 053001. doi: 10.1103/PhysRevLett.105.053001 (cited on page 32).

[75]

M. Meckel, A. Staudte, S. Patchkovskii, D. M. Villeneuve, P. B. Corkum, R. Dörner, and M.
Spanner. Signatures of the continuum electron phase in molecular strong-field photoelectron
holography. Nature Phys., 10 (8), 2014, 594. doi: 10.1038/nphys3010 (cited on page 32).

REFERENCES
[76]

114

G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S.
Zherebtsov, I. Znakovskaya, A. L’Huillier, M. Y. Ivanov, M. Nisoli, F. Martı́n, and M. J.
J. Vrakking. Electron localization following attosecond molecular photoionization. Nature,
465 (7299), 2010, 763–766. doi: 10.1038/nature09084 (cited on page 32).

[77]

A. Gazibegović-Busuladžić, E. Hasović, M. Busuladžić, D. Milošević, F. Kelkensberg, W.
Siu, M. Vrakking, F. Lépine, G. Sansone, M. Nisoli, I. Znakovskaya, and M. Kling. Abovethreshold ionization of diatomic molecules by few-cycle laser pulses. Phys. Rev. A, 84 (4),2011, 1–8. doi: 10.1103/PhysRevA.84.043426 (cited on page 32).

[78]

W. Becker, A. Lohr, and M. Kleber. Effects of rescattering on above-threshold ionization. J.
Phys. B, 27, 1994, L325–L332. doi: 10.1088/0953-4075/27/14/005 (cited on page 32).

[79]

D. Milošević and F. Ehlotzky. Coulomb and rescattering effects in above-threshold ionization.
Phys. Rev. A, 58 (4), 1998, 3124. doi: 10.1103/PhysRevA.58.3124 (cited on page 32).

[80]

G. G. Paulus, F. Grasbon, H. Walther, R. Kopold, and W. Becker. Identification and Application of Quantum Trajectories in Above-Threshold Ionization. Laser Phys., 12 (2), 2002, 262–
267. url: http://www.maik.ru/full/lasphys\_archive/02/2/lasphys2\_02p262full.
pdf (cited on page 32).

[81]

P. Salières, B. Carré, L. Le Déroff, F. Grasbon, G. G. Paulus, H. Walther, R. Kopold, W.
Becker, D. B. Milosević, A. Sanpera, and M. Lewenstein. Feynman’s path-integral approach
for intense-laser-atom interactions. Science, 292, 2001, 902–5. doi: 10.1126/science.108836(cited on page 32).

[82]

G. Andriukaitis, T. Balciunas, S. Alisauskas, A. Pugzlys, A. Baltuska, T. Popmintchev, M.-C.
Chen, M. M. Murnane, and H. C. Kapteyn. 90 GW peak power few-cycle mid-infrared pulses
from an optical parametric amplifier. Opt. Lett., 36 (15), 2011, 2755–2757. doi: 10.1364/
OL.36.002755 (cited on page 32).

[83]

T. Morishita, A.-T. Le, Z. Chen, and C. D. Lin. Accurate Retrieval of Structural Informationfrom Laser-Induced Photoelectron and High-Order Harmonic Spectra by Few-Cycle Laser
Pulses. Phys. Rev. Lett., 100, 2008, 013903. doi: 10.1103/PhysRevLett.100.013903 (cited
on page 32).

[84]

Y. Wu, H. Ye, and J. Zhang. Extracting the information of scattering potential using angular
distributions of rescattered photoelectrons. Phys. Rev. A, 84 (4), 2011, 043418. doi: 10 .
1103/PhysRevA.84.043418 (cited on page 32).

[85]

Y. Huismans, A. Rouzée, A. Gijsbertsen, J. H. Jungmann, A. S. Smolkowska, P. S. W. M.
Logman, F. Lépine, C. Cauchy, S. Zamith, T. Marchenko, J. M. Bakker, G. Berden, B.
Redlich, A. F. G. van der Meer, H. G. Muller, W. Vermin, K. J. Schafer, M. Spanner, M. Y.
Ivanov, O. Smirnova, D. Bauer, S. V. Popruzhenko, and M. J. J. Vrakking. Time-resolved
holography with photoelectrons. Science, 331 (6013), 2011, 61. doi: 10 . 1126 / science .
1198450 (cited on pages 32, 35, 38, 73, 83).

REFERENCES
[86]

115

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F.
DiMauro. Strong-field photoionization revisited. Nature Phys., 5 (5), 2009, 335–338. doi:
10.1038/nphys1228 (cited on pages 33, 42, 73, 79).

[87]

F. H. M. Faisal. Strong-field physics: Ionization surprise. Nature Phys., 5 (5), 2009, 319–320.
doi: 10.1038/nphys1264 (cited on pages 33, 42).

[88]

C. Liu and K. Z. Hatsagortsyan. Origin of Unexpected Low Energy Structure in Photoelectron
Spectra Induced by Midinfrared Strong Laser Fields. Phys. Rev. Lett., 105, 2010, 113003.
doi: 10.1103/PhysRevLett.105.113003 (cited on page 33).

[89]

C. Liu and K. Z. Hatsagortsyan. Wavelength and intensity dependence of multiple forward
scattering of electrons at above-threshold ionization in mid-infrared strong laser fields. J.
Phys. B, 44, 2011, 095402. doi: 10.1088/0953-4075/44/9/095402 (cited on page 33).

[90]

T.-M. Yan, S. Popruzhenko, M. J. J. Vrakking, and D. Bauer. Low-Energy Structures inStrong Field Ionization Revealed by Quantum Orbits. Phys. Rev. Lett., 105, 2010, 253002.
doi: 10.1103/PhysRevLett.105.253002 (cited on page 33).

[91]

M. Y. Kuchiev. Atomic antenna. JETP Lett., 45 (7), 1987, 404–406. url: http : / / www .
jetpletters.ac.ru/ps/1240/article\_18763.pdf (cited on page 33).

[92]

K. C. Kulander, K. J. Schafer, and J. L. Krause. Super-intense laser-atom physics. In: Vol.
316 NATO Adv. Sci. Inst. Series. Ed. by J. Piraux, A. L’Huillier, and K. Rzazewski.
New York: Plenum Press, 1993, pp. 95–110 (cited on pages 33, 36).

[93]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum. Theory of highharmonic generation by low-frequency laser fields. Phys. Rev. A, 49 (3), 1994, 2117–2132.
doi: 10.1103/PhysRevA.49.2117 (cited on pages 33, 38).

[94]

D. G. Arbó, S. Yoshida, E. Persson, K. Dimitriou, and J. Burgdörfer. Interference Oscillationsin the Angular Distribution of Laser-Ionized Electrons near Ionization Threshold. Phys. Rev.
Lett., 96, 2006, 143003. doi: 10.1103/PhysRevLett.96.143003 (cited on page 35).

[95]

T Marchenko, H. G. Muller, K. J. Schafer, and M. J. J. Vrakking. Electron angular distributions in near-threshold atomic ionization. J. Phys. B, 43 (9), 2010, 095601. doi: 10.1088/
0953-4075/43/9/095601 (cited on page 35).

[96]

A. Rudenko, K. Zrost, C. D. Schröter, V. L. B. de Jesus, B. Feuerstein, R. Moshammer, and
J. Ullrich. Resonant structures in the low-energy electron continuum for single ionization of
atoms in the tunnelling regime. J. Phys. B, 37 (24), 2004, L407–L413. doi: 10.1088/09534075/37/24/L03 (cited on page 35).

[97]

Z. Chang, A. Rundquist, H. Wang, I. Christov, H. C. Kapteyn, and M. M. Murnane. Temporalphase control of soft-x-ray harmonic emission. Phys. Rev. A, 58 (1), 1998, R30–R33. doi:
10.1103/PhysRevA.58.R30 (cited on pages 36, 38).

[98]

G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther. Plateau in Above
Threshold Ionization Spectra. Phys. Rev. Lett., 72 (18), 1994, 2851–2855. doi: 10.1103/
PhysRevLett.72.2851 (cited on page 36).

REFERENCES
[99]

116

B. Yang, K. J. Schafer, B. Walker, K. C. Kulander, P. Agostini, and L. F. DiMauro. IntensityDependent Scattering Rings in High Order Above-Threshold Ionization. Phys. Rev. Lett.,
71 (23), 1993, 3370–4. doi: 10.1103/PhysRevLett.71.3770 (cited on page 36).

[100]

C. Lemell, K. Dimitriou, X.-M. Tong, S. Nagele, D. Kartashov, J. Burgdörfer, and S. Gräfe.
Low-energy peak structure in strong-field ionization by midinfrared laser pulses: Two-dimensional
focusing by the atomic potential. Phys. Rev. A, 85 (1), 2012, 011403(R). doi: 10.1103/
PhysRevA.85.011403 (cited on page 43).

[101]

P. P. Pronko, S. K. Dutta, J. Squier, and J. V. Rudd. Machining of sub-micron holes using
a femtosecond laser at 800 nm. Optics Comm., 114, 1995, 106–110. doi: 10.1016/00304018(94)00585-I (cited on page 46).

[102]

V. Amendola and M. Meneghetti. Laser ablation synthesis in solution and size manipulationof noble metal nanoparticles. Phys. Chem. Chem. Phys., 11 (20), 2009, 3805. doi: 10.1039/
b900654k (cited on page 47).

[103]

S. P. Hatchett, C. G. Brown, T. E. Cowan, E. A. Henry, J. S. Johnson, M. H. Key, J. A.
Koch, A. B. Langdon, B. F. Lasinski, R. W. Lee, A. J. Mackinnon, D. M. Pennington, M. D.
Perry, T. W. Phillips, M. Roth, T. C. Sangster, M. S. Singh, R. A. Snavely, M. A. Stoyer, S.
C. Wilks, and K. Yasuike. Electron, photon, and ion beams from the relativistic interactionof Petawatt laser pulses with solid targets. Phys. Plasmas, 7 (5), 2000, 2076–2082. doi:
10.1063/1.874030 (cited on page 47).

[104]

R. Lachaine, E. Boulais, and M. Meunier. From Thermo- to Plasma-Mediated Ultrafast LaserInduced Plasmonic Nanobubbles. ACS Phot., 1 (4), 2014, 331–336. doi: 10.1021/ph400018s(cited on page 47).

[105]

V. Pustovalov, A. Smetannikov, and V. Zharov. Photothermal and accompanied phenomenaof selective nanophotothermolysis with gold nanoparticles and laser pulses. Laser Phys. Lett.,
5 (11), 2008, 775–792. doi: 10.1002/lapl.200810072 (cited on page 47).

[106]

E. A. Peralta, K. Soong, R. J. England, E. R. Colby, Z. Wu, B. Montazeri, C. McGuinness,
J. McNeur, K. J. Leedle, D. Walz, E. B. Sozer, B. Cowan, B. Schwartz, G. Travish, and
R. L. Byer. Demonstration of electron acceleration in a laser-driven dielectric microstructure.
Nature, 503, 2013, 91–94. doi: 10.1038/nature12664 (cited on page 47).

[107]

C. B. Schaffer, A. Brodeur, J. F. Garcı́a, and E. Mazur. Micromachining bulk glass by useof femtosecond laser pulses with nanojoule energy. Opt. Lett., 26 (2), 2001, 93–5. doi: 10.
1364/OL.26.000093 (cited on page 47).

[108]

M. Durach, A. Rusina, M. F. Kling, and M. I. Stockman. Predicted Ultrafast Dynamic Metallization of Dielectric Nanofilms by Strong Single-Cycle Optical Fields. Phys. Rev. Lett.,
107 (8), 2011, 086602. doi: 10.1103/PhysRevLett.107.086602 (cited on pages 47, 51).

[109]

M. M. Murnane, H. C. Kapteyn, S. P. Gordon, J. Bokor, E. N. Glytsis, and R. W. Falcone.
Efficient coupling of high-intensity subpicosecond laser pulses into solids. Appl. Phys. Lett.,
62 (10), 1993, 1068–1070. doi: 10.1063/1.108797 (cited on page 48).

REFERENCES
[110]

117

K. R. Wilson, S. Zou, J. Shu, E. Ru, S. R. Leone, G. C. Schatz, and M. Ahmed. Size-Dependent
Angular Distributions of Low-Energy Photoelectrons Emitted from NaCl Nanoparticles. Nano
Lett., 7 (7), 2007, 2014–2019. doi: 10.1021/nl070834g (cited on page 50).

[111]

X. Zhang, K. A. Smith, D. R. Worsnop, J. L. Jimenez, J. T. Jayne, C. E. Kolb, J. Morris, and
P. Davidovits. Numerical Characterization of Particle Beam Collimation: Part II Integrated
Aerodynamic-LensNozzle System. Aerosol Sci. and Tech., 38 (6), 2004, 619–638. doi: 10.
1080/02786820490479833 (cited on pages 50, 90).

[112]

A. Zelenyuk, Y. Cai, and D. Imre. From Agglomerates of Spheres to Irregularly Shaped
Particles: Determination of Dynamic Shape Factors from Measurements of Mobility and Vacuum Aerodynamic Diameters. Aerosol Sci. and Tech., 40 (3), 2006, 197–217. doi: 10.1080/
02786820500529406 (cited on page 52).

[113]

T. M. Antonsen, T. Taguchi, A. Gupta, J. Palastro, and H. M. Milchberg. Resonant heatingof a cluster plasma by intense laser light. Phys. Plasmas, 12, 2005, 056703. doi: 10.1063/
1.1869500 (cited on pages 53, 65).

[114]

T. Döppner, J. P. Müller, A. Przystawik, S. Göde, J. Tiggesbäumker, K.-H. Meiwes-Broer,
C. Varin, L. Ramunno, T. Brabec, and T. Fennel. Steplike Intensity Threshold Behavior of
Extreme Ionization in Laser-Driven Xenon Clusters. Phys. Rev. Lett., 105, 2010, 053401.
doi: 10.1103/PhysRevLett.105.053401 (cited on pages 53, 64–66, 100, 105).

[115]

M. Lezius and S. Dobosz. Hot nanoplasmas from intense laser irradiation of argon clusters.
J. Phys. B, 30, 1997, L251–L258. doi: 10.1088/0953-4075/30/7/003 (cited on pages 53,
65).

[116]

W. L. Barnes, A. Dereux, and T. W. Ebbesen. Surface plasmon subwavelength optics. Nature,424, 2003, 824–830. doi: 10.1038/nature01937 (cited on pages 58, 59).

[117]

Z. Chen, A. Taflove, and V. Backman. Photonic nanojet enhancement of backscattering oflight by nanoparticles: a potential novel visible-light ultramicroscopy technique. Opt. Express,
12 (7), 2004, 1214–20. doi: 10.1364/OPEX.12.001214 (cited on page 58).

[118]

P. Ferrand, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, and H. Rigneault. Direct
imaging of photonic nanojets. Opt. Express, 16 (10), 2008, 209–215. doi: 10.1364/OE.16.
006930 (cited on page 58).

[119]

H. Guo, Y. Han, X. Weng, Y. Zhao, G. Sui, Y. Wang, and S. Zhuang. Near-field focusing of
the dielectric microsphere with wavelength scale radius. Opt. Express, 21 (2), 2013, 2434–43.
doi: 10.1364/OE.21.002434 (cited on page 58).

[120]

D. Ju, H. Pei, Y. Jiang, and X. Sun. Controllable and enhanced nanojet effects excited bysurface plasmon polariton. Appl. Phys. Lett., 102 (17), 2013, 171109. doi: 10 . 1063 / 1 .
4802958 (cited on page 58).

[121]

E. J. Blackie, E. C. Le Ru, and P. G. Etchegoin. Single-molecule surface-enhanced Raman
spectroscopy of nonresonant molecules. J. Am. Chem. Soc., 131 (40), 2009, 14466–14472.
doi: 10.1021/ja905319w (cited on page 59).

REFERENCES
[122]

118

P. Das, T. K. Chini, and J. Pond. Probing Higher Order Surface Plasmon Modes on Individual Truncated Tetrahedral Gold Nanoparticle Using Cathodoluminescence Imaging andSpectroscopy Combined with FDTD Simulations. J. Phys. Chem. C, 116 (29), 2012, 15610–
15619. doi: 10.1021/jp3047533 (cited on page 59).

[123]

A. Grubisic, E. Ringe, C. M. Cobley, Y. Xia, L. D. Marks, R. P. Van Duyne, and D. J.
Nesbitt. Plasmonic near-electric field enhancement effects in ultrafast photoelectron emission:correlated spatial and laser polarization microscopy studies of individual Ag nanocubes. Nano
Lett., 12 (9), 2012, 4823–4829. doi: 10.1021/nl302271u (cited on page 59).

[124]

B. Lahiri, G. Holland, V. Aksyuk, and A. Centrone. Nanoscale imaging of plasmonic hot
spots and dark modes with the photothermal-induced resonance technique. Nano Lett., 13 (7),2013, 3218–24. doi: 10.1021/nl401284m (cited on page 60).

[125]

F. Peano, J. L. Martins, R. A. Fonseca, L. O. Silva, G. Coppa, F. Peinetti, and R. Mulas.
Dynamics and control of the expansion of finite-size plasmas produced in ultraintense lasermatter interactions. Phys. Plasmas, 14 (5), 2007, 056704. doi: 10.1063/1.2436855 (cited
on pages 63, 105).

[126]

T. Ditmire, T. Donnelly, A. M. Rubenchik, R. W. Falcone, and M. D. Perry. Interactionof intense laser pulses with atomic clusters. Phys. Rev. A, 53 (5), 1996, 3379–3402. doi:
10.1103/PhysRevA.53.3379 (cited on pages 64, 65, 67, 68).

[127]

S. Zherebtsov, T. Fennel, J. Plenge, E. Antonsson, I. Znakovskaya, A. Wirth, O. Herrwerth,
F. Süß mann, C. Peltz, I. Ahmad, S. A. Trushin, V. Pervak, S. Karsch, M. J. J. Vrakking, B.
Langer, C. Graf, M. I. Stockman, F. Krausz, E. Rühl, and M. F. Kling. Controlled near-fieldenhanced electron acceleration from dielectric nanospheres with intense few-cycle laser fields.
Nature Phys., 7 (8), 2011, 656–662. doi: 10.1038/nphys1983 (cited on page 64).

[128]

T. Döppner, T. Fennel, T. Diederich, J. Tiggesbäumker, and K. H. Meiwes-Broer. Controlling
the Coulomb Explosion of Silver Clusters by Femtosecond Dual-Pulse Laser Excitation. Phys.
Rev. Lett., 94 (1), 2005, 013401. doi: 10.1103/PhysRevLett.94.013401 (cited on pages 64,
67, 105).

[129]

J. Dawson and C. Oberman. High-Frequency Conductivity and the Emission and Absorption
Coefficients of a Fully Ionized Plasma. Phys. Fluids, 5 (5), 1962, 517–524. doi: 10.1063/1.
1706652 (cited on page 66).

[130]

D. S. Gross, M. E. Gälli, P. J. Silva, and K. A. Prather. Relative sensitivity factors for alkali
metal and ammonium cations in single-particle aerosol time-of-flight mass spectra. Anal.
Chem., 72, 2000, 416–22. doi: 10.1021/ac990434g (cited on page 67).

[131]

T. Döppner, T. Fennel, P. Radcliffe, J. Tiggesbäumker, and K.-H. Meiwes-Broer. Ion andelectron emission from silver nanoparticles in intense laser fields. Phys. Rev. A, 73, 2006,
031202(R). doi: 10.1103/PhysRevA.73.031202 (cited on page 67).

[132]

A. Kawabata and R. Kubo. Electronic properties of fine metal particles II. Plasma resonanceabsorption. J. Phys. Soc. Jpn., 21 (9), 1966, 1765–1772. doi: 10.1143/JPSJ.21.1765 (cited
on page 68).

REFERENCES
[133]

119

M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich,and S. W. Haan. Three-dimensional HYDRA simulations of National Ignition Facility targets.
Phys. Plasmas, 8 (5), 2001, 2275. doi: 10.1063/1.1356740 (cited on pages 69, 70, 102, 103).

[134]

A. Heidenreich, J. Jortner, and I. Last. Cluster dynamics transcending chemical dynamics
toward nuclear fusion. Proc. Natl. Acad. Sci., 103 (28), 2006, 10589–10593. doi: 10.1073/
pnas.0508622103 (cited on pages 69, 71, 105).

[135]

E. Waxman and D. Shvarts. Second-type self-similar solutions to the strong explosion problem. Phys. Fluids A, 5 (4), 1993, 1035–1046. doi: 10.1063/1.858668 (cited on page 71).

[136]

Y. B. Zel’dovich and Y. P. Raizer. Physics of shock waves and high-temperaturehydrodynamic phenomena. Ed. by W. D. Hayes and R. F. Probstein. New York, NY,
USA: Dover, 2002 (cited on page 71).

[137]

R. Teyssier, D. Ryutov, and B. Remington. Accelerating shock waves in a laser-produced
density gradient. Astrophys. J., 127, 2000, 503–508. doi: 10.1086/313338 (cited on page 71).

[138]

Y. Huismans, A. Gijsbertsen, A. Smolkowska, J. Jungmann, A. Rouzée, P. Logman, F. Lépine,
C. Cauchy, S. Zamith, T. Marchenko, J. Bakker, G. Berden, B. Redlich, A. van der Meer, M.
Ivanov, T.-M. Yan, D. Bauer, O. Smirnova, and M. Vrakking. Scaling Laws for Photoelectron
Holography in the Midinfrared Wavelength Regime. Phys. Rev. Lett., 109 (1), 2012, 1–5.
doi: 10.1103/PhysRevLett.109.013002 (cited on page 73).

[139]

M. Gerrity, S. Brown, T. Popmintchev, M. M. Murnane, H. C. Kapteyn, and S. Backus. High
Repetition Rate, mJ-Level, mid-IR OPCPA System. CLEO: Science and Innovations, 2014,
STh4E.8. doi: 10.1364/CLEO\_SI.2014.STh4E.8 (cited on page 73).

[140]

A. Fleischer, O. Kfir, T. Diskin, P. Sidorenko, and O. Cohen. Spin angular momentum andtunable polarization in high-harmonic generation. Nature Phot., 8 (7), 2014, 543–549. doi:
10.1038/nphoton.2014.108 (cited on page 73).

[141]

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H.
Nembach, J. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen. Generation ofbright circularly-polarized extreme ultraviolet high harmonics for magnetic circular dichroism
spectroscopy. Arxiv preprint arXiv:1401.4101, 2014, 12. url: http://arxiv.org/abs/1401.
4101. arXiv: 1401.4101 (cited on page 73).

[142]

M. Ivanov and E. Pisanty. High-harmonic generation: Taking control of polarization. Nature
Phot., 8 (7), 2014, 501–503. doi: 10.1038/nphoton.2014.141 (cited on page 73).

[143]

W. Becker and D. B. Milos. Attosecond pulse trains with unusual nonlinear polarization.
Phys. Rev. A, 62, 2000, 011403(R). doi: 10.1103/PhysRevA.62.011403 (cited on page 73).

[144]

W. Becker, R. Kopold, and D. B. Milos. Generation of circularly polarized high-order harmonics by two-color coplanar field mixing. Phys. Rev. A, 61, 2000, 0. doi: 10.1103/PhysRevA.
61.063403 (cited on page 73).

REFERENCES
[145]

120

M. G. Pullen, J. Dura, B. Wolter, M. Baudisch, M. Hemmer, N. Camus, A. Senftleben, C. D.
Schroeter, R. Moshammer, J. Ullrich, and J. Biegert. Kinematically complete measurementsof strong field ionization with mid-IR pulses. J. Phys. B, 47 (20), 2014, 204010. doi: 10.
1088/0953-4075/47/20/204010 (cited on page 74).

[146]

W. Becker, S. P. Goreslavski, D. B. Milošević, and G. G. Paulus. Low-energy electron rescattering in laser-induced ionization. J. Phys. B, 47 (20), 2014, 204022. doi: 10.1088/09534075/47/20/204022 (cited on page 74).

[147]

Q. Li, X.-M. Tong, T. Morishita, C. Jin, H. Wei, and C. D. Lin. Rydberg states in the strong
field ionization of hydrogen by 800, 1200 and 1600 nm lasers. J. Phys. B, 47 (20), 2014,
204019. doi: 10.1088/0953-4075/47/20/204019 (cited on page 74).

[148]

N. G. Kling, D. Paul, A. Gura, G. Laurent, S. De, H. Li, Z. Wang, B. Ahn, C. H. Kim,
T. K. Kim, I. V. Litvinyuk, C. L. Cocke, I. Ben-Itzhak, D. Kim, and M. F. Kling. Thick-lensvelocity-map imaging spectrometer with high resolution for high-energy charged particles.
I. Inst., 9 (05), 2014, P05005–P05005. doi: 10.1088/1748- 0221/9/05/P05005 (cited on
page 75).

[149]

C. Peltz, C. Varin, T. Brabec, and T. Fennel. Time-Resolved X-Ray Imaging of Anisotropic
Nanoplasma Expansion. Phys. Rev. Lett., 113, 2014, 133401. doi: 10.1103/PhysRevLett.
113.133401 (cited on page 75).

[150]

H. Haberland. Thin films from energetic cluster impact: A feasibility study. J. Vac. Sci. andTech. A, 10 (5), 1992, 3266. doi: 10.1116/1.577853 (cited on page 77).

[151]

J. Kousal, O. Polonskyi, O. Kylián, A. Choukourov, A. Atremenko, J. Pesicka, D. Slavinska,
and H. Biederman. Characterization of nanoparticle flow produced by gas aggregation source.
Vacuum, 96, 2013, 32–38. url: http://www.sciencedirect.com/science/article/pii/
S0042207X13000675 (cited on page 77).

[152]

X.-B. Bian, Y. Huismans, O. Smirnova, K.-J. Yuan, M. J. J. Vrakking, and A. Bandrauk.
Subcycle interference dynamics of time-resolved photoelectron holography with midinfraredlaser pulses. Phys. Rev. A, 84, 2011, 043420. doi: 10.1103/PhysRevA.84.043420 (cited on
page 83).

[153] FDTD Solutions. Lumerical Solutions, Inc. url: http : / / www . lumerical . com / tcad products/fdtd/ (cited on page 91).
[154]

J. R. DeVore. Refractive Indices of Rutile and Sphalerite. J. Opt. Soc. Am., 42 (6), 1951,
416–419. doi: 10.1364/JOSA.41.000416 (cited on page 91).

[155] Handbook of Optics, Vol. 4. 3rd. McGraw-Hill, 2009 (cited on page 91).
[156]

A. Salabat and M. Alinoori. Viscosity, Density, and Refractive Index of Poly(vinylpyrrolidone)+ 1-Propanol and + 2-Propanol at 298.15 K. J. Chem. Eng. Data, 54 (3), 2009, 1073. doi:
10.1021/je800670w (cited on page 91).

[157]

E. D. Palik. Handbook of Optical Constants of Solids. Boston: Academic Press, 1985
(cited on page 91).

REFERENCES
[158]

121

B. Schütte, M. Arbeiter, T. Fennel, M. J. J. Vrakking, and A. Rouzée. Rare-Gas Clusters
in Intense Extreme-Ultraviolet Pulses from a High-Order Harmonic Source. Phys. Rev. Lett.,
112 (7), 2014, 073003. doi: 10.1103/PhysRevLett.112.073003 (cited on page 92).

[159]

C. T. L. Smeenk, L. Arissian, B. Zhou, A. Mysyrowicz, D. M. Villeneuve, A. Staudte, and P.
B. Corkum. Partitioning of the Linear Photon Momentum in Multiphoton Ionization. Phys.
Rev. Lett., 106, 2011, 193002. doi: 10.1103/PhysRevLett.106.193002 (cited on page 92).

[160]

A. D. McFarland and C. L. Haynes. Color my nanoworld. J. Chem. Edu., 81 (4), 2004,
544A–544B. doi: 10.1021/ed081p544A (cited on page 92).

[161]

J. A. Huffman, J. T. Jayne, F. Drewnick, A. C. Aiken, T. Onasch, D. R. Worsnop, and J. L.
Jimenez. Design, Modeling, Optimization, and Experimental Tests of a Particle Beam Width
Probe for the Aerodyne Aerosol Mass Spectrometer. Aerosol Sci. and Tech., 39, 2005, 1143–
1163. doi: 10.1080/02786820500423782 (cited on page 97).

[162]

S. G. Lias, E. J. Bartmess, J. F. Liebman, J. L. Holmes, R. D. Levin, and W. G. Mallard. Ion Energetics Data. In: NIST Chemistry WebBook, NIST Standard Reference
Database Number 69. Ed. by Linstrom P J and G. W. Mallard. National Institute of Standards and Technology, Gaithersburg MD, 20899. url: http://webbook.nist.gov (cited on
page 100).

[163]

G. P. Schurtz, P. D. Nicolai, and M. Busquet. A nonlocal electron conduction model for
multidimensional radiation hydrodynamics codes. Phys. Plasmas, 7, 2000, 4238. doi: 10.
1063/1.1289512 (cited on page 104).

[164]

J. D. Huba. NRL Plasma Formulary. Office of Naval Research, 2011, 1–71. url: http ://www.nrl.navy.mil/ppd/content/nrl-plasma-formulary (cited on page 104).