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EXPERIMENTAL STUDIES OF HARMONIC GENERATION FROM SOLID-DENSI'N PLASMAS PRODUCED BY PICBSECOND ULTRA-INTENSE LASER PULSES

Liang Zhao

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Physics University of Toronto

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Doctor of Philosophy, 1998, Liang Zhao, Department of Physics, University of Toronto

Abstract

In this thesis, an experimental investigation of harmonic generation from high- intensity laser-plasma interactions is presented. Harmonic experiments performed on the 1-terawatt FCM-CPA laser system at the University of Toronto, and on the 10-terawatt T3 laser system at the University of Michigan, are described. Using the FCM-CPA laser, various aspects of second harmonic generation were investigated systematicaily, with a focus on the effect of preformed plasma on harmonic generation. Experiments comparing hamonics generated by high-contrast pulses and by pulses containing weak prepulses show that the preformed plasma causes spatial and spectral breakup of harmonics and diffuses harmonic emission into large solid angles. On the T3 laser system, mid-order harmonic generation from various solid materials was studied and both odd and even harmonics up to the 7th were observed. Important features of harmonic generation, Le., the laser-polarization dependence and the angular distribution of harmonic emission, were characterized. Purnp-probe expetiments were carried out as well on both laser systems by adding a controlled prepulse, which demonstrated a strong dependence of harmonic production efficiency on the gradient of preformed plasma. We also describe what we believe to be the first observation of regular satellite features accompanying the mid-order harmonics. Their dependence on target materials and on laser intensity was measured, and possible pbysical explanations are discussed. Besides, the development of the Toronto FCM-CPA laser system is summarized. Its original design and unique features are described in detail. Acknowledgments

First, 1 would iike to thank my thesis supervisor, Professor Robin Marjoribanks, for his guidance and support during the course of this research. 1 thank him for introducing me to this fast developing, yet challenging research field and for providing me the opportunity of working in his lab. His advice and careful reading of various drafts of the manuscript have significantly improved the quality of this thesis. The members of rny Ph.D. supe~isorycommittee, Professor John Sipe and Professor Henry van Driel, have provided me a great amount of help in the past years. 1 am very grateful for the advice and assistance they have given to me. I would also like to thank Professor Paul Drake, Professor Aephrairn Steinberg, and Professor Peter Smith for their critical reading of my thesis and for their valuable suggestions. Constant help in many aspects provided by Mrs. Marianne IUiwana was also greatly appreciated. This work could not possibly have been completed without the support, help, and encouragement from my fellow graduate students, Fred Budnik and Gabor Kulcsh. During the past several years, it was their enthusiasm, Wendship, and optirnism that kept my spirit up, helped me to overcome the difficulties, and made this lab a much pleasant place to work and to study. 1 am also grateful to Professor Peter Heman, who kindly let me share most of his lab tools, and suggested many good ideas for my experiments. The assistance of other members in the group was also greatly appreciated. Among them are: Michel Stanier, James Mihaychuk, Hideo Yamakoshi, Sherry Crossly, Bin Xiao,

Hiroyuki Higaki, Estelle Rouillon, and Adrian Vitcu. I would like to thank the Center for Ultrafast Optical Science at the University of Michigan for providing me the opportunity of working on their excellent facilities. In particular, 1 would like to thank Dr. Anatoly Maksimchuk and Robert Wagner for assisting the expeririients in many ways and for staying so many late nights running the laser system. Thanks also go to Dr. Jonathan Workman for providing his target materials to me, to Dr. Paul Le Blanc and Professor Michael Downer for allowing me to use their prepulse setup, and to Professor Donald Umstadter and Professor Gérard Mourou for their encouragement and generosity with laser time. My thanks aIso go to the staff in this department and at Photonic Research Ontario who constantly provided both excellent technicai support and necessary equipment whenever 1 needed either. Financial support frorn the University of Toronto Open Fellowship, from the Burton Scholarship at the Department of Physics, and from the research funding provided by the Natural Science and Engineering Research Council of Canada and Photonic Research Ontario, is also gratefully acknowledged. 1 am especially grateful to my parents. Through out these years, it was their continuing support and encouragement that motivated me working towards this final goal. Without their support I could not have reached this far. Lastly, and most importantly, 1 am deeply h debt to my wife, Yuanyuan, who endured ail the late nights and lost weekends with remarkable patience and understanding. Table of Contents

Abstract

Acknowledgments

Table of Contents

Chapter 1 Introduction 1.1 A Brief Historical Review of Harmonic Generation in Solids 1.2 Scope of this Thesis

1.3 Outline of the Dissertation

1.4 Role of the Author

Chapter 2 Theoretid Background 2.1 Introduction to Laser-Plasma Interaction 2.1.1 Plasma Generated by Intense Laser Pulses on Solid Target

2.1.2 Waves in Plasma 2-1.3 Some Basic Processes in Laser-Plasma Interaction 2.2 Mechanisms of Harmonic Generation in an Overdense Laser- Produced Plasma Table of Contents

Simple Hmonic-Generation Phenomenology Second Harmonic Generation: a Perturbation Theory Particle-in-Cell Simulation Results The Linear Mode-Coupling Model The Oscillating-~irrorModel Model Predictions: Harmonic Generation with Varying Experimental Parameters 2.3 RoIe of Preformed PIasma 2.3.1 Laser Prepulses 2.3.2 Effects of Preplasma on Harmonic Generation 2.3.3 Modification of Plasma Density Profde by a Deliberate Prepulse 2.4 Conclusions

Chapter 3 Development of the Toronto FCM-CPA Laser System 3.1 Introduction to the CPA Technology 3.2 The Feedback-Controlled Mode-Locked (FCM) Oscillator 3.2.1 Purpose of Feedback Control in the Oscillator 3.2.2 Pulse Development in the FCM Oscillator 3.2.3 High-Contrast Characterization of Pulses from the FCM Osciliator 3 -3 The FCM-CPA Laser System 3.3.1 TheLaserSetup 3.3.2 Characterization of Beam Focus in the Target Chamber 3.3.3 Compressed Pulse Characterization Using High- Contrast Cross-cordation

3.3-4 Single-Shot Autocorrelation Table of Contents

3.4 A Novel Cross-correlation Technique 3 -4.1 Design of the WeiCross-correlator 3 -4.2 Experimental Results 3.5 Conclusions

Chapter 4 Experimental Results of Second Harmonie Generation

4.1 Experimental Setup

4.2 Laser Pulse Cleaning with Saturable Absorber 4.3 Second Harmonic Generation (SHG) and the Effect of Prepulse 4.3.1 Power Scaling of SHG 4.3.2 Anguiar Distribution of SHG 4.3.3 Imaging of the SHG Emission

4.4 SHG with Controiled Prepulses 4.4.1 Prepulse Setup 4.4.2 Experimental Results

4.5 Experiments Beyond SHG

4.6 Conclusions

Chapter 5 Experimental Results of Mid-Order Harmonic Generation

5.1 The T3 Laser System 5.2 Experimental Setup for the Hannonic Measurement 5.2.1 The Target Chamber 5.2.2 TheVUVSpectrometer 5.3 Results of Mid-Order Hannonic Generation 5.3.1 Observation of the Third to Seventh Harmonics 5.3.2 Dependence on Laser Polarization 5.3.3 Angular Distribution of the Harmonics

vii Table of Contents

5.4 Harmonic Generation with ControUed Prepulses 5.4.1 Prepulse Setup 5A.2 Experimental Results

5.5 Observation of Satellite Structure in the Mid-Harmonies 5.6 Conclusions

Chapter 6 Discussion and Conclusions 6.1 Summary of the Experimental Results Effects of Preplasma on Harmonic Generation Plasma Scale-length Dependence Mid-Order Warmonic Generation on Different Solid Targets Angular Distribution of Harmonic Emission Laser Polarization Dependence First Observations of Hannonic Satellite Structures High-Contrast CPA Laser 6.2 Suggestions for Future Experiments

References Chapter 1 Introduction

The development of the chirped-pulse-amplification (CPA) technique cl] in the last decade has enabled high power lasers to produce multi-terawatt femtosecond and picosecond laser pulses which cm be focused on target at intensities previously inaccessible in the laboratory. Many new interesting physical phenomena have been studied in this new regime [2-51. The generation of optical harmonies of very high order is one example of the new phenomena that occur when extremely intense ultrashort laser pulses interact with matter [6]. High odd-order harmonic generation has been studied extensively in noble gases [7], in molecular gases [8], in atomic clusters [9],and in ionized media [IO], and harmonic orders as high as 135 [Il] and wavelengths as shoa as 6.7 nm [12]have been reported. The observed hannonic spectra exhibit a characteristic non-perturbative behavior: with increasing harmonic order, the harrnonic intensity decreases initially, then remains approximately constant up to a rather sharp cutoff, beyond which no further emission is observed. The physical mechanism for this type of harmonic generation is now weli understood, thanks to a so-called two-step mode1 developed by Corkum [13] and Kulander [14]. In this quasi-classical interpretation, an electron first tunnels through the barrier formed by the Coulomb potential and the laser field. Once free, the electron moves in the laser field to gain a maximum energy of 3.2Up, where Upis the quiver energy of a free electron in an oscillating electromagnetic field, and then retums towards the nucleus as the laser field reverses direction. Harmonic photons with energies up to Chapter I Introduction

1, + 3.2UP, where Ip is the ionkation potential of the atom, can then be produced when the electron recombines with its parent ion. This predicted cutofT energy agrees very well with the experimentally observed value of Ip + 2Up, when taking into account the propagation effects 1151. Further development of this type of hannonic generation using higher laser intensities, however. has been limited by medium depletion through ionization, and by the resulting free electrons that induce phase mismatch between the pump pulse and the harmonic signal, degrading the harmonic conversion efficiency. High-order harmonic generation also occurs in intense laser interaction with solid media In fact, twenty years ago, long before the gas-interaction experiments, pXple had observed high-order harmonics from laser-produced plasmas on solid targets, using high-

intensity nanosecond COz lasers [16-191. Unlike the gas case, both odd and even orders of harmonics were observed in those experiments, indicating that the harmonic radiation was not from the ions in the laser-produced plasma, but generated under physical conditions lacking inversion symmetry-it is generally believed now that this type of harmonic generation originates from the strong anharmonicity of the collective electron motions across the vacuum-plasma boundary, where the restoring force is extremely non- uniform. Harmonies generated by this mechanism are not subject to the same saturation or phase-matching limitations that gas harmonics suffer, thereby offering a very promising and efficient means of producing intense short-wavelength coherent radiation. In some applications, such as deeply bored channels in fast-ignitor laser-fusion experiments [ZO], hmonic emission together with a clear means of interpretation may provide a valuable new diagnostic of the conditions of intense laser-matter interaction. Xn this thesis, we present an experimental investigation of harmonic generation from high-intensity laser-plasma interaction on solid targets. The general goals of this research are to gain insight bto the harmonic generation mechanism by testing various theoretical predictions, to provide new empirical information, and to find the optimum conditions for efficient harmonic production. 1.1 A Brief Elistorical Review of Harmonic Generation in Soiids

High-order harmonic generation in dense, laser-produced plasma was first reported two decades ago in a nanosecond CO2-laser-target expenment performed by Bunien et al. [16]at the National Research Council of Canada. Up to 1lth harmonic, with yields falling off approximately hearly with the harmonic order, were observed in the back-scattered beam direction for an incident laser intensity > 1014 Wlcm2. Similar results were produced later with a 75-ps N&glass laser at a intensity - 10'6 Wkm2 [17]. In the early 80's. in a series of experiments on CO2-laser-produced plasmas,

Carman et al. 118, 191 reported the observation of up to the 46th harrnonics at laser intensities greater tha. 1015 W/cm2. The harmonic spectra exhibited a nearly constant conversion efficiency over the observed harmonic orders before an apparent sharp high- frequency cutoff. Theoretical models developed by Beverides et al. [21] and Grebogi et al. [22] suggested that the high-harmonies onginated from the strong anhannonic electron motion dong a steep density gradient of the surface plasma produced by the laser pulse. By assurning a step-like discontinuity of the density arising from the ponderomotive force of the laser light, these models predicted a characteristic high- frequency cut-off in the harmonic spectra given by the plasma frequency corresponding to the upper level of the density profile, which seemed agree with Carman's experimental observations. In the go's, progress in the generation of extremely intense ultrashort laser pulses has led to renewed interest in the harmonic generation from overdense, laser-produced plasmas. Because of the limited time allowed for plasma to expand, the ultrafast laser- solid interaction naturaily provides a plasma with a steep density gradient, which is beiieved crucial for harmonic generation. Although efficient harmonic production from solid target using picosecond or sub-picosecond laser pulses has been predicted theoretically, experimental observation has been scarce, and has only corne recently. The Chapter I Introduction

explanation for this lies in the fact that, compared with the earlier CO2 work, there are disadvantages associated with the ultrafast lasers. One of the major differences is the laser wavelength. The current ultrafast lasers work mostly in the spectrai regions of W, visible or near IR, where the wavelength is at least ten times shorter than that of CO2 laser (A = 10.6 pm). This means that one needs rnuch higher laser intensities I to achieve the sarne value of IA*, a scaling factor associated directly with the oscillating current strength in a plasma and therefore the efficiency of harmonic generation. The shorter wavelength for the fundamental light also rneans that the harmonics generated will be in the UV region, where plasma recombination-emission background is strong; this makes the detection of the harmonics more mcult. Besides the wavelength factor, the ultrashort interaction time also means the ponderomotive steepening of the plasma density profile is less effective than with the nanosecond pulses of the CO2 laser. Therefore the intrinsichy foxmed plasma density profile, which is determined mostiy by the intensity contrast of the ultrashort laser pulse, becomes extremely important. The est experimental demonstration of high-order harmonic generation from sub-picosecond laser-solid interaction was made by Kohlweyer et al. [23]. Using a 150- fs terawatt Ti:sapphire laser, the authors detected up to the 7th harmonic of 794-nm light and up to the 4th harrnonic for 397-mlight from Al targets at intensities of 1017 Wlcmz. Time-resolved spectral measurement was used in this experiment to enhance the signal- to-noise ratio of the sub-picosecond harmonic signais by isolating them from the nanosecond plasma recombination background. This experiment also demonstrated, for the first time, the significant influence of laser prepulses on harmonic generation; the latter was shown only possible when the pulse-prepulse contrast was greater than 106.

Using a similar Ti:sapphUe laser, von der Linde et al. [24,25] observed up to the 18th harmonics at laser intensities of IOi7 - 1018 W/cm2. It was found that hannonic generation only occurred for p-polarized laser pulses with contrast better than 106. Both dielectric and metallic targets gave very similar harmonic spectra, which were Chapter I Introduction 5

characterized by a relatively smooth exponential roll-off at high frequencies. The conversion efficiencies were roughly estimated as leand 5 x 1û-8 for the lûth and 15th harmonics, respectively. Harmonie generation fiom a more extended plasma has recently been studied in a series of experiments [26-291 performed on the Nd:glass VüLCAN laser system, which produces 2.5-ps pulses with intensities up to 1019 Wkm2 and a contrast better than 106. Up to the 68th harmonics were observed with relatively high conversion efficiencies

estimated to be 10-4 (16th harmonic) to 1û-6 (68th hannonic). However, the observation of an isotropie harmonic emission over a 27~solid angle, and the insensitivity of harmonic efficiency to the laser polarization and to the introduction of Eurther prepulses, Iead the authors to conclude that they were observing harmonic production at a rippled critical density surface, rather than from a thin planar plasma at the solid surface. On the theoretical side, harmonic generation from thin, near-solid-density plasmas has also become a topic of keen interest in the last few years. Cornplementary to the theories developed by Bezzerides and Grebogi for the CO2 experiments, new harmonic generation mechanisms have been proposed. Among them are the oscillating-mirror mode1 [30-321 which interprets the harmonic generation as a phase modulation experienced by the light reflected from an oscillating critical surface; the vacuum heating mode1 [33, 341 which represents the harmonics as being produced by those electrons which undergo large-amplitude vacuum excursions; and the J xB mechunim [35] which emphasizes the AC-ponderomotive contributions to harmonic generation at relativistic laser intensities (> 10'8 WIcrn2).

1.2 Scope of this Thesis

Compared to the case of interaction with gas targets, experiments on harmonic generation using solid targets are much more difficult to perform and to analyze. Chapter 1 Introduction 6

Because of this, many fewer harmonic generation experiments have been carried out

using solid targets than using gas targets. One aspect of the complexity of high-harmonic generation from laser-plasma interaction is that nonlinear hydrodynamics is virtually always folded together with the nonlinear optical conversion process. In nanosecond CO2 experiments, the DC- ponderomotive force of the laser pulse steepens the plasma density profile significantly, and the process of harmonic production therefore folds together two types of nonlinearity: nonlinear optical conversion largely from the electron fluid, and hydrodynamic nonlinearities of grossly 'preparing' the plasma. This makes the interpretation of experimental results much more difficult. What makes things even more complicated is a preformed plasma. Plasma preformed by laser prepulses is a concem in ail experiments studying intense laser interaction with near-solid-density matter. It has particular impact in ultrafast laser-target experiments where ponderomotive density profile steepening is less effective. Although the effect of preformed plasma on harrnonic generation from solids had been widely discussed, its effect 011 harmonic generation had not been systematically tested until this work. These physics issues are of particular interest to us. To understand the physical mechanisms for harmonic generation in laser-plasma interaction, it would be useful to characterize the optical participation of electrons without at the same time grossly modifjring the plasma density gradients during irradiation. Because in sub-picosecond laser-plasma interactions, ponderomotive modification is less significant due to the short interaction time, studies of harmonic generation using very short pulse-durations offer the prospect of separating the nonlinear contributions. To avoid preformed plasma, a high contrast laser pulse is also needed. This wfi ensure a clean laser-soiid interaction. With this done, one can further study the dependence of harmonic generation on the plasma density gradient, which is of great theoretical and practical interest. Analytic models predict that there exists an optimum density gradient for which the electron motions responsible for hannonic generation can be driven most effectively by laser Light, and therefore can produce maximum harmonic efficiency and orders. This prediction has been demonstrated in cornputer simulations performed by Delettrez et al. 1361 and by Lichters et al. [37],and is ready to be tested experirnentally. In the experiments descnbed in this thesis, we have partly dissected the physical issues discussed above. We have used picosecond and subpicosecond laser pulses of contrast better than 101°-the highest puIse contrast to be used in such experiments-to study harmonic generation under the condition of minimized preplasma formation. Furthemore, by comparing harmonics generated with the ultra-clean pulse and with pulses containing a weak prepulse, we have systernatically investigated the effect of preformed plasma on harmonic conversion-efficiency and angular distribution, as well as on spatial and spectral brightness. Using a purnp/probe technique, we have also performed experiments in which the conversion efficiencies of the second and third harmonics were measured from different prepared plasma-gradients.

1.3 Outline of the Dissertation

In Chapter 2, the basic theory of laser-plasma interaction on a solid is provided. Various mechanisms of harmonic generation in overdense plasmas are discussed. The dependence of harmonic generation on several experimental parameters is also given. Chapter 3 is devoted to a description of the development of the FCM-CPA laser system constructed here at the University of Toronto. Unlike the original fiber-expansion and grating-compression scheme used in most of the CPA laser systems in the early go's, the FCM-CPA laser is an dl-Nd:glass system based on grating-only expansion and compression of high-contrast 1-ps seed pulses produced in a feedback-controlled Nd:glass oscillator. One of the unique features of this system is that, without using Chapter 1 Introduction 8 complicated pulse-cleaning techniques, it provides a 5 x 107 puise-to-pedestal contrast ratio. the highest arnong the systems built at the time of its construction. The original design and the characterization of this system are presented in detail. At the end of the chapter, a novel cross-correlation technique capable of measuring the true pulse shape of picosecond pulses is described. Chapter 4 describes the experiments perforrned on the FCM-CPA laser system to snidy the second harmonic generation from laser-plasma interaction. In this series of experiments, we focus on the effect of pre-formed plasma, produced by small prepulses, on the harmonic generation process. We present a systematic study of the influence of preplasma on harmonic yield, angular distribution, and spatial and spectral distributions. A pump-probe experiment using a deliberate and controlled prepulse is also described, and the relation between the harmonic generation efficiency and the plasma density scale- length is discussed. Experimental efforts on the FCM-CPA system searching for harmonics higher than the second are sumrnarized at the end of the chapter. in Chapter 5, the mid-harmonic experiments conducted on the T3 laser system at the University of Michigan are covered. We describe the experimental observation of up to 7th harrnonic from various solid targets and the results of their angular distribution and dependence on laser polarization. In addition, an improved pump-probe experiment together with a quantitative relation between the harmonic generation efficiency and the scaie-Iength of the plasma are presented. The chapter concludes with what we believe to be the first observation of a regular Stokes- and anti-Stokes-like satellite features accompanying the mid-order harmonics. Measurement of their dependence on target material and laser intensity are given, and possible physical explanations are discussed. The final conclusions are drawn in Chapter 6, together with suggestions for future directions of the work. Chapter 1 IntroductSon

1.4 Role of the Author

This thesis contains experimental work performed jointly by researchers from severai research groups. Due to the nature of this collaboration work, it is sometimes difficult to pull out single threads from individual researhers. The FCM-CPA laser system described in Chapter 3 represents a team effort with contributions from al1 the members in the Toronto group. The author's major contributions were: building of the hg-design regenerative amplifier, high-dynamic- range characterization of pulse contwst, meosvrement of pulse development in the FCM oscillator, and construction and calibration of the single-shot autocorrelator. The noveI cross-correlator described in 5 3.4 was originally built by Gabor Kulcsik, Michael Woodside, and James Mihaychuk. The author's involvement in this project was optirnizing the performance of the cross-correlator and using it to measure the real shape of pulses from the FCM oscillator. The second harrnonic experiments (Chapter 4) and mid-harmonic experiments (Chapter 5) were performed and analyzed mainiy by the author. But this work could not be compieted without the valuable suggestions and assistance from Fred Budnik, Ggbor KulcsAr, and my research supervisor Robin Marjoribanks, as well as the staff on the T3 system, AnatoIy Maksimchuk and Robert Wagner. Chapter 2 Theoretical Background

In this chapter, the theones of harmonic generation by the interaction of an ultra- intense laser pulse with a solid target are described. The harmonic generating mechanisms discussed here are diffèrent fiom those in relativistic harmonie-generation in underdense plasmas [38, 391, or in surface harmonie-generation at moderate-intensities [40,4 11. In order to understand the physics involved, a brief introduction is given fxst, in which the basic properties of plasmas produced by laser-solid interaction, and processes that are particularly important to the generation of harmonies, are discussed. As we will see, preformed plasmas produced by laser prepulses play important role in laser-solid interactions. Their influences on harmonic generation are discussed in the last section.

2.1 Introduction to Laser-Plasma Interaction

2.1.1 Plasma Generated by Intense Laser Puises on Solid Target When a terawatt laser pulse is tightly focused, extremely high intensities between 1017 - 1019 Wlcrn2 cm be achieved in the focal spot. The corresponding electric field amplitudes for such laser intensities are much higher than the magnitude of the atomic field. For example, the Coulomb field acting on an electron in the f~stBohr orbit of the hydrogen atom is E, = e/rb =5.1 x 109 V/cm. This high electric field amplitude can be achieved in a linearly poiarized laser beam with intensity 1, = c~z/8a= 3.4 x 1016 W/cm2. Chapter 2 Theoretical Background 11

When a solid target is exposed to such high intensities, its surface Iayer is immediately ionized and tninsformed into a hot expanding plasma. It is interesting to note that, under such high intensities, there is almost no difference in the behavior between dielectric and conducting targets, since in the dielectric case the fmt electrons are set free in a fraction of a laser cycle by field ionization. Plasmas produced in such a fashion exhibit many features different from those in conventional laboratory plasmas, such as very high electron density (near solid density) and temperature (a few keV, or

107 K), extreme non-uniformity, and ultrashort lifetime. In the case of a high-atomic number (2)target, free electron densities of at least one order of magnitude higher than in a metallic conductor cm be achieved. Thus, laser-produced plasma from solid targets provides an ideal object supporthg fundamental studies of matter in extreme conditions involving ultrahigh pressures, electric field, and temperatures. After creating the plasma, the same laser pulse will further interact with the plasma formed by its rising edge. The interaction between a laser pulse and plasma depends cntically on the ratio of the pulse carrier fiequency CO to the medium's electron plasma frequency a,,, (also called Langmuir frequency) defined as

where me is the electron mass and ne is the electron density in units of cm-3. The ratio w /apedefines two different regimes of laser-plasma interactions. In an underdense plasma, where w > ape,the plasma is transparent to the laser light. Physical processes such as inverse bremsstrahlung, stimulated Raman scattering, stimulated Brillouin scattering, and wake-field generation, etc., are generaIIy studied in this regime of laser- plasma interaction. On the other hand, the overdense region of the plasma, where o S wpe,acts much like a totally reflecting &or. Light incident at other than normal incidence is reflected before reaching the underdense-overdense plasma boundary called critical density sugace. The evanescent waves penetrating to the critical surface can be Chapter 2 Theoretical Background 12 coupled resonantly with the local plasma waves and produce resonance absorption. harmonic generation, etc. The critical density of a plasma is given by

where hp is the laser wavelength in microns. Obviously, the temis of underdense and overdense plasmas are relative, depending on the frequency of the incident laser. For example, a plasma with an electron density ne = 1019 cm-3 is underdense for a YAG laser

(Â= 1.053 un, n,= 1 x 1020~1~3).but is slightly overdense for a COz laser (A=10.6 p,nc= 9.8 x 1018 cm-3). Laser plasma produced from a solid is very non-unSom-the electron density drops from near-solid density to vacuum in a distance around the order of laser wavelength, As we will see in the following sections, much important physics in the laser interaction with overdense plasmas is govemed by the shape of the plasma density gradient in the coupling region. For example, plasmas with finite density gradients usually absorb laser energy much more efficiently than plasmas with sharp vacuum boundaries. The quantity which is often used to characterize the spatial extent of the underdense plasma at the vacuum-plasma boundary is the dense scale-le@ defmed as

Foliowing its creation by the laser pulse, the plasma will expand into vacuum clriven by the kinetic pressure of the hot electrons. As a result its density scaie-length will increase with time at a rate set by the ion-sound speed c, = (Figure 2.1). Here Z is the ionkation stage, Te is the electron temperature, and mi is the ion mas. Assuming the incident laser has a pulse-width Ar and contains no prepulse, the scale-length of the plasma which the laser will interact with cm be estimated as L = c,&. For a 300-eV silicon plasma, c,- 10' cds, or 0.1 Wps, which means that a 1-ps pulse wiil interact with a plasma of L - 0.1 p. Chpter 2 Theoretical Background

vacuum solid

Figure 2.1. A sketch illustrating the spatial profile of the electron density distribution. Scale-length L increctses as the plasma expmds.

Zn the discussion of ultra-intense laser-matter interactions, the laser field strength is usually expressed by the unitless laser-strenm* parameter

where 4 is the peak amplitude of the laser vector potentid, III is the laser intensity in units of 1018 W/crn2, and Ap is the laser wavelength in microns. The quantity 112 in Eq. (2.4) is associated with many phenornena in laser-plasma interactions, implying that the interaction depends not only on the laser intensity, but on the laser wavelength as well. The value of a. describes how quickiy an electron oscillates in a laser field, i.e., oo,& = ao/dG, where vox is the quiver velocity of the electron. From Eq. (2.4) we can see that for a laser with 1a2 abovel.4 x 1018 W~rn-~pmz, a. becomes greater than one, sipiQing the quiver motion of the electron becomes highly relativistic and

2.1.2 Waves in Plasma A characteristic feature of a plasma is its ability to support waves, or collective modes of interaction [42,43]. These waves correspond to charge-density fluctuations at a characteristic frequency determined by the electrons and/or the ions. In a plasma with no Chapter 2 Theoretical Background 24 large imposed magnetic fields (the electrostatic approximation), there are two such densiîy waves: a high-frequency electron plasma wave and a low-frequency ion-plasma wave. In addition, the propagation of electromagnetic waves in a plasma cm also be modified by the response of electrons.

EZectron plasma waves Electron plasma waves (also called Langmuir waves) are longitudinal electrostatic waves associated with the high-fiequency density fluctuations of electrons, for which the ions are practically immobile. They obey the following dispersion relation: where vtk = ,/ksT,/m,= 4 x 107 cm/s is the electron thermal velocity at electron temperatwe Te- One can see that the frequency of electron plasma waves is essentially mpe,the electron plasma frequency (Eq. 2.1), with a srnall thermal coirection depending on the wavenumber k . The dispersion relation (2.6) is actually an approximation for long-wavelength waves and has a limited range of validity. It is based on the assumption of adiabatic compression [42], which is valid when vtk «o/k - wpe/k, or kjl, CC 1. Here A, m vIhe/mpeis called the electron Debye length, a quantity we will discuss shortly. Taking this approximation into account, Eq. (2.5) can be written in another useful form:

Ion plasma waves In addition to the high-frequency electron plasma oscillations, a plasma also supports ion oscillations, typically at a much lower frequency. These oscillations, which generally involve longitudinal motions of both electrons and ions, are cailed ion plasma waves. The general dispersion relation for ion plasma waves is given by Chapter 2 Theoretical Background 15

where AD, = 4- is the electron Debye length which we have just seen, vthi=dm is the ion themai velocity at ion temperature Ti, and spi is the ion- plasma frequency defined as

Here Z and A are the ionization state and atomic weight of the ions, mi is the ion mas, and m, is the mass of a proton. Eq. (2.6) is valid when the second term on the right is much less than the first. In the foliowing, we will consider the case when the second term in Eq. (2.6) is ignored, Le., the hnit of Ti = 0. The electron Debye length is the scde-length over which the eiectrons can shield out the field of a test charge. In the long-wavelength bit, where A = 2 n/k >> AD,, or

kaDe

where c, = 4zkB~,/rni is the ion-sound speed which we discussed before. In this case, the single-fluid oscillations of electrons and ions together are driven by the restoring force of pressure gradients provided by changes in electron density, with the electrons closely tied to the ions by their Debye shielding. The quasi-neutrality assumption holds only for Long-wavelength waves. In the short-wavelength limit, where kAD, >> 1, the electrons are no longer able to screen the excess charge of ion density fluctuations, so quasi-neutraiity is no longer achieved and the restoring force is augmented by charge differences. In this case, the ion plasma wave becomes purely electrostatic, i.e., ions osciliate in a locally uniform background of negative charge, in a fashion sirnilar to the electron plasma wave in which electrons osciliate about a uniform ion background. An interesthg feature of this nonquasineutrd Chapter 2 Theoretical Background 16 mode of oscillations is that the wave kquency approaches an asymptotic value which depends only on the plasma parameters. In this case, the electrostatic ion plasma wave (often simply cded an ion plasma wave. in analogy to the electron plasma wave) simply oscillates at the ion plasma frequency, Le.,

Uniike the ion-acoustic wave, which has been thoroughly investigated, much less has been observed for the ion plasma wave, even though it was predicted 70 years ago

[44]. In fact, it was oniy recently that this wave was experimentdy observed for the fit tirne [45,46].

Electromagnetic waves Besides the electrostatic density waves described above, the only other waves in unmagnetized homogeneous plasma are electromagnetic waves, which have the foilowing dispersion relation

where a,, is the electron plasma frequency, and c is the speed of light in vacuum. Letting the plasma density approach zero we regain the free space light waves with o = ck . Note that the dispersion relation for the electromagnetic waves is very similar to that for the electron plasma waves (Eq. 2.5), where c2 is replaced by 3vk. In optical theory, the propagation of light in a medium is usually described by the medium's refractive index, nmf = ck/o. From Eq. 2.8 we can see that in a plasma the refractive index is

According to Eq. 2.9, the refractive index of a plasma becomes imaginary when w c mpe. This is why there is a minimum frequency for a propagating electromagnetic wave in the plasma. Chapter 2 Theoretical Background 17

We have discussed very bnefly the properties of the electron plasma wave, the ion-plasma wave (including the ion-acoustic wave), and the electromagnetic wave. They represent the three possible linear modes of plasma oscillations in an unifonn unmagnetized plasma. As a summary, the dispersion relations for these three waves are shown qualitatively in Figure 2.2. The number of linear modes in a plasma wili be greatiy increased with the addition of inhomogeneity or an extenid magnetic field [42].

e -1. ,,, , ,<, ,, ,, - ,, ,, ,-,z:-- .------, - - .- - --- 4 0 Z 0 4 1 / C =-, Ion plasma waves

Figure 2.2. Dispersion diagrams for electromagnetic waves, electron plasma waves and ion plasma waves in a homogenous unmagnetized plasma (Ti=O). The correspondhg asymptotic slopes are shown as the dashed Lines.

2.1.3 Some Basic Processes in Laser-Plasma Interaction The interaction between laser and plasma involves many physical processes. A full description of these processes is obviously out of the scope of this section. Here we will discuss some basic processes in laser-plasma interaction, which are most closely related to the generation of harmonics. Chapter 2 Theoretical Background

In an inhomogeneous plasma, the electromagnetic and the electron plasma waves are coupled. For instance, electromagnetic radiation will be emitted if electron-plasma waves are present in a plasma. Similady, an electromagnetic wave incident on a plasma cm excite electron-plasma waves. As we will see, these wave-coupling phenomena play a crucial role in the generation of harmonies. One of the wave coupling mechanisms is resonance absorption. When a electromagnetic wave is incident on a plasma gradient at an oblique incident angle 8, it will be reflected at a X position called classical turning point, t1 2 II where electron density ne = n, cos 0 (b) ewave t~Il Il II [47]. The subsequent evanescent wave Il II I beyond this point behaves quite differently depending on its polarization I' *X 1' II (Figure 2.3). The s-polarized wave (c) pwave simply decays exponentially as it propagates further into the plasma; the p- polarized wave, on the other hand, when )X reaching the critical density surface x = x,, will become resonant with the Figure 2.3. A sketch of the plasma local electron plasma wave, and wiii act density profile and the qualitative field as a resoaant driver for the electron distributions. (a) plasma density profile. The light is refiected at the classical turning plasma oscillations. Consequently, part point. (b) Amplitude of the parailel of the energy of the p-polarized incident component of the E-field. (c) Amplitude of laser is converted into the form of the normal component of the E-field. Chapter 2 Theoretical Background 19 electrostatic oscillations, which eventually become thermalized through various wave- dumping mechanisms. The absorption by this mode-conversion process is termed resonance absorption [48]. Resonance absorption is characterized by its strong sensitivity to the polarization and incident angie of the incident light. It only occurs with p-polarized light at an intermediate angle of incidence. At normal incidence, or with s-polarized light, there is no electric field component dong the plasma gradient; while at grazing incidence, the turning point is so far from the cntical surface that no evanescent field reaches it. For a p-polarized plane wave of wavelength A incident into a plasma with a linear density profile (scale-length of L), the optimum incident angle for maximum resonance absorption has been shown to be [49]

O,, = sin-' [o. 44(~/a )-'/3].

Resonance absorption is one of the most important collisionless mechanisms for laser-plasma coupling. It is associated with many physical phenomena in laser-plasma interaction, such as the steepening of plasma density profile near n, and the generation of supra-thermal electrons. As we will see later, one of the most important mechanisms of harmonic generation in plasma is through currents driven in resonance absorption.

Nonlinear excitation of plasma waves through inslabilities As discussed above, an electron plasma wave (aep,kep) can be resonantly excited at the critical surface by the incident laser light (a,k) through resonance absorption. This Iinear mode-conversion process involves two waves and occurs when w = mep, k = kp- As a laser of sufficientiy high intensity passes through a plasma, plasma waves cm also be excited through a family of three-wave interactions in which the incoming laser Light decays into two daughter-waves. The daughter wave can be the high-fiequency electron- plasma waves (EP), the low-frequency ion-acoustic waves (IA), or the scattered Chapter 2 Theoretical Background 20

electromagnetic waves. Since the beating between one of the daughter waves and the incident laser can normally enhance the other daughter wave, these three-wave processes are unstable and cm cause exponentid plasma-wave growth (instabilities) [SOI. Some of the welI known instabilities in plasma and their corresponding coupling conditions are listed in Table 2.1.

Table 2.1. Laser induced instabilities in plasma. Instability Couphg condition Coupling density

Stirnulated Raman scattering a = + mep9 k = kcat + kp < 1/4 n,

Stimulated BRLlo~inscattering = oxat+ Qa9 k = kat+ kia IQ,

Two-plasmon decay 63 = me, + sep, k = kep + kep - 1/4 n, -Ion-acoustic decay o=co~~+o~~,k=kia+bp -&

We note that many of the instabilities occur at densities significantly less than the critical density. Aiso, the thresholds and efficiencies of these instabilities depend mainly on the spatial inhomogeneity of the underdense plasma. It has ken shown [43] that the instabiiity thresholds IIh generally scale as Ith = L-l, where L is the density scale-length of the plasma. Therefore. most of the instabilities are not important in Our current discussion of the harmonic generation in short-scaie-length plasmas, aithough they can be effective and hence are of particular concem in long-scale-length plasmas. However, these processes can be important if the incident laser contains a substantial amount of energy in prepulse; in this case the peak of the laser pulse will interact with a large volume of underdense plasma before arriving at the overdense region. The ion-acoustic decay (also called parametric decay) instability is of special interest to us, since, Like resonance absorption, it ahoccurs at the critical surface and excites an electron plasma wave. Its relation with harmonic generation will be discussed in several places in this thesis. Chapter 2 Theoretical Background

Ponderomotive force and density profüe rnodifiatiun by a berpulse When a laser beam is incident on a plasma, the momentum it carries can be transferred directly to the plasma by means of the ponderomotive force. In contrast to the rapidly changing oscillating force of an electric wave which causes the quiver motion of the electrons, the ponderomotive force is a secular force, i.e., a force which acts in the same direction over the whole duration of the laser puise. The ponderomotive force has been recognized as an entity of centrai importance in many phenornena in laser-produced plasmas, including the harmonic generation process. The ponderomotive force oiiginates from the nonlinearity of the momentum equation of a charged particle in an electromagnetic field (48, 511, To see this, we consider an electron in an electromagnetic wave whose amplitude is spatially dependent, i.e., E = E, (r) cos ut. The force exerted on the electron is given by the Lorentz equation:

Using perturbation analysis, to first order in an expansion in IEl, the electron only responds to the electric field (the effect of the magnetic field is O(v/c)), and simply oscillates about its rest position at v = v,,,sinmt, where vos, = eEo/mp is the oscillation velocity (or quiver velocity) of an electron in an electromagnetic wave. To this order, the electron is not subject to a tirne-averaged force. It is oniy to second order that wave inhomogeneity and the magnetic field enter the problem, where Eq. (2.11)has a form e 2 F = -el&-, (r)cos wt - 2 VIE,(r )f (1 + COS 2~t). (2.1 1-1) 4m,w

We can see that besides the first-order oscillating force -eEo cosot, the electron also experiences an additional force which effectively pushes it away from regions of high field pressure. This second force is proportional to the gradient of IE 1 and is called the ponderomotive force. Notice that the ponderomotive force contains two parts, a tirne- Chupter 2 nieoretical Background 22 averaged DC-component Fp = -(e2/4meo2)~(~012and an oscillating AC-component

FF= Fpcos2mt. Conventionally, the term 'ponderomotive force' only refers to the DC-component Fp,because it is this force that actuaLiy transfers net momentum from the laser pulse to electrons. In an equivalent form, the ponderomotive force can also be written as F, = -VUp, where LIp is the ponderomotive potential which equals to the averaged kinetic energy of the electron in the electromagnetic field, 1/2 rn,~?~~. One of the ponderomotive effects in laser-plasma interactions is density-profile steepening. As a laser pulse reflects at the critical surface, twice its momentum is taken up by the plasma near the reflecting point. This local momentum deposition retards the plasma expansion [52] and steepens the density profile near the cntical surface [53]. With obliquely incident p-polarized light. the density-profile steepening can be further enhanced by resonance absorption because of the pressure from the resonantly-generated electrostatic field near the cntical surface [54]. At relativistic intensities, the pondero- motive force becomes so strong that it can even bore a hole into solid matter [55,56]. Besides causing density-profile steepening near the critical surface, the ponderomotive force can also give rise to oscillation of the critical surface at twice the laser fiequency. This is done through the AC-component FF,which drives electrons in and out across the plasma-vacuum boundary and effectively causes the cntical surface to oscillate at 201. As we will see in the next section, both the density-profile steepening and the critical-surface oscillation play crucial roles in the generation of harmonies from laser-plasma interactions.

2.2 Mechanisms of Harmonic Generation in an Overdense Laser-Produced Plasma

A laser-produced plasma is a very complex and extremely nonlinear medium. One of the nonlinear responses of such a medium to incident laser light is the generation of very high order harmonics of the fundamentai light. Generally speaking, there are numerous mechanisms and processes involved in the generation of hannonics of different types, under different conditions, but it seems likely that the host of mid- and high-order harmonics are al1 generated by the same basic mechanism, under any particular irradiation. To date, no analytical theory of mid- and high-order hmonic generation gives satisfactory quantitative agreement with expiment. PIC code simulation has been quite successfûl in descnbing general characteristics, although it is clear that few, if any, suitable experimental series, producing well-defined conditions, have been conducted before this work. Although satisfactory a prion anaiytical theory does not really exist, some physical models of harmonic generation have been suggested to create simple physicai pictures of possible mechanisms. In this chapter, we describe some of these models and their predictions. We will limit our discussion to a 1-D problem by assuming a plane laser wave and a Bat plasma density surface.

23.1 Simple Harmonie-GenerrUun Phenomenology At their sirnplest, free electrons driven by a harmonic forcing-term respond harmonically themselves, and radiate at the same frequency but with a phase delay associated with their back-reaction. Electrons in quadratic (harmonic) potentiais will also respond harmonically, and at the driving frequency, but with a power resonance and with relative phase which depends on the relation between their natural (resonant) frequency, as a simple harmonic oscillator, and the frequency of the driving force. The simplest mode1 of nonlinear response then follows when this potential is not quite harmonic. An electron in any non-quadratic potential will respond to a harmonic forcing term in a more cornplex way; for a non-pathological potential (e.g., with positive curvature) the response will typicaily be periodic, but it may be Fourier-analyzed to show anharmonic content at sub-multiples of the period. Thus, fairly generally, if plasma electrons reside in an anharmonic potential, strong laser fields wiil lead to currents with Chapter 2 Theoretical Background sub-multiple periods, and harmonic radiation via Larmor radiation [57]. In another simple example, very strong optical fields may lead to relativistic quiver velocities. In this case, the force equation qE = ma for a charge in a strong optical field is nonlinear because the mass is itself velocity dependent. This aiso leads to harmonic content in the radiation field of the accelerating charge. Much of the general nature of harmonics from laser-produced plasmas cm be reproduced simply fiom this mode1 of a harmonicaliy forced anharmonic oscillator; this includes the broad spectrum of odd- and even-order harmonics, and much of their character, including a monotonie drop of conversion efficiency with order, and aspects of their dependence on laser intensity. However, other aspects of harrnonic spectra are dependent on plasma characteristics, and more detailed physical modelling is necessary.

2.2.2 Second Harmonic Generation: a Perturbation Theory Second harmonic (SH) generation in a plasma cm be interpreted as a two-step process. In the first step, electron density oscillations (electron plasma waves) at a frequency equal or very close to the laser frequency o are produced. In the second step, the incident laser is nonlinearly scattered from the electron plasma waves, or two electron plasma waves interact to produce light around 20. As discussed in the last section, electron plasina waves can be excited by the incident laser through two main processes: resonance absorption (a linear process) and the parametric decay instabiiity (a nonlinear process), each occumng near the critical surface of the plasma. SH generation involving parametric processes is typically characterized by the existence of a certain threshold value and some non-specular distributions of the SH emission [58]. In fact, the non-specular SH emission is often used in experiments to detect and to identiQ parametric plasma processes. By contrast. a distinctive feature of the resonance absorption mechanism is the generation of SH in the specular direction. In the following, we will concentrate on this mechanism of SH Chapter 2 Theoretical Background 25 generation, since, as we will show in Chapter 4, it agrees with our expenmental observations. Like other nonlinear optical phenomena, SH generation in plasma cmbe treated by solving Maxwell's equations using the current density Jand charge density p = -en, as the source tems [59]. If J and ne induced by the applied electromagnetic fields are small, the response of the plasma may be obtained using a perturbation approach. We assume this is the case and expand the electron density and velocity as ne = n(O) + dL)t- - and v = v(') + d2)+--,where n(*) is the initia! electron density without perturbation and n(') is the fust order electron density perturbation. The current density can be expanded as:

J=-en,v=J (1) +J(2) +-. (2.12) where the linear cument density J(') = -en(o)~(')is responsible for the fust-order optical properties such as propagation, reflection and absorption of the incident light, while the second order current density f2) = -e(n(0)~(2)+n")dL)) gives rise to second-order nonlinear optical effects, in particular, second harmonic generation. Now we consider the case of an incident electrornagnetic wave of frequency o. The SH is generated through the Zu>-component of the second-order current density ~$0, which can be readily related to the a-component of the local electrk field E, [57]:

To find the SH emission field E20rone needs to fust find the local electric field E,, calculate ~$2using Eq. (2.13), and then solve the SH wave equation with ~$2as the source term. However, as discussed by von der Linde in Ref. [59], important characteristics of the SH emission can already be inferred sirnply by examining Eq. (2.13). For convenience in the following discussion, the fust and second ternis in Eq. (2.1 3) wiil be referred to ~$2and ~$2'. respectively . Chupter 2 Theoretical Background 26

(1) Angular dependence: SHG is rnost efficient at intermediate incident angles. This is because at normal incidence, no SH is generated since ~$2'vanishes (E-~n(*) = 0) and ~$2is normal to the surface and thus unable to radiate; for large angles of incidence, the SHG also decreases because of decreasing penetration of the fiindamental Iight to the critical surface. (2) Pola~zation:In the absence of a transverse gradient of the electric field, JI? always leads to current density polarized in the plane of incidence, thus p-polarized SH, no matter what the polarization of the incident light. On the other hand, SH due to Ji?' always has the same polarization as that of the fundamental. Since ~$2'vanishes for s- polarized incidence, only p-polarized SH is produced by this tem. Based on these discussions, the following can be concluded: (a) oniy p-polarized SH is generated when the incident light is purely s- or p-polarized; (b)p-polarized laser is more efficient in generating SH because in this case both tems in Eq. (2.13) contribute; (c) s-polarized SH can be generated in the following situations: fundamental beam with mixed polarization, existence of a transverse E-field gradient (due either to fdte spot size or to intensity nonuniformities in the focal spot), or electron density perturbations caused by other than resonance absorption. (3) Resonont enhancernenr: ~4:' demonstrates explicitly the dependence of the SH generation on plasma density gradient. It also shows that when vn(O) #O, SH generation is greatly enhanced at the resonant frequency o = w,,. In fact, this resonant effect occurs in both terms of the current density (2.13). In the limit of vanishing density scale-length (step profile), SH generation from a plasma is very much like that from metal surfaces [60, 611, where the resonmt effect disappears [62]. The resonant effect also becornes less significant in plasmas of large scale-lengths because of the increasing distance between the classical turning point and the cntical surface. Therefore, one expects the existence of an optimum scale-length for maximum resonant enhancernent of SH generation. Chapter 2 Theoretical Background 27

Finally we notice that ~$2'is proportional to (V - E,)E, a nz)~~[59], where ng) is the electron density perturbation associated with an electron plasma wave at frequency o. It follows that in certain configurations electron plasma waves can be detected by measuring the SH signal. This idea was indeed demonstrated by von der Linde, in an experiment where SH generation was used to detect eIectron density oscillations produced by a strong pump pulse [63]. The perturbation theory discussed above requires that the charge density fluctuation n(') induced by the extemal field rnust be srnail compared to the critical density n,. The ratio of n(') and n, can be estimated using the following expression [43]:

where x,,, is the oscillation amplitude of electrons, L is the density scale-length, and % is the nomalized laser field strength defined by Eq. (2.4). For a plasma gradient of

L/n = O. 1, ratio (2.13) becornes greater than one when 1~~> 1.4 x 1016 Wcm2 p2, indicating that this perturbation theory is no longer valid. One of the non-perturbation effects in SH generation is the depletion of the harmonic conversion eficiency at strong resonance due to wave-breaking of the excited electron plasma waves [64].

2.2.3 Particle-in-Ceil Simulation ResuIts The perturbation approach discussed above becomes very tedious and inconvenient when used to explain higher-order harmonic generation in plasma. It dso fails at high laser intensities, where the induced charge- and current-densities become too large. In this case, one has to rely on computer simulations in order to get reasonable quantitative solutions. In laser-plasma studies, two commonly used types of computer simulation codes are particle-in-ce11 (PIC) modelling, which treats plasma as a large collection of charged particles, and hydrodynamic modeliing, which treats plasma as fluids. Chapter 2 Theoretical Background 28

PIC simulations performed recently by severai authors have concluded that efficient high-order hannonic generation is possible fiom the interactions of sufficiently- intense laser pulses at solid surfaces. For a normal incidence laser beam with m? > 1018 Wcm-2 p*(% > l), Wilks predicted odd-order harmonics in both 1 -D and 2-D PIC simulations, and weaker even-order harmonics when 2-D effects were taken into account [35]. For oblique incidence, highly-resolved simulations of harmonic generation (restricted to specular emission) also become possible by carrying out 1-D calculations in the Lorentz-boosted be,in which the electromagnetic wave appears to be normaily incident [30]. Using this technique, Gibbon [34] and Lichters et al. [31] investigated harmonic generation over a large parameter space with varying laser intensity, angle of incidence, polarization, and plasma density. Their simulation results show that the high- harmonic yield increases significantly when approaching the relativistic laser intensities

(q, 2 1). The harmonic output also increases with decreasing plasma density and is particularly large for o, = 20, when the AC-ponderomotive force FF (5 2.1.3) is at resonance with the local pIasma frequency. For s-polarized incidence, the harmonic output decreases monotonically with increasing incident angle; for p-polarized incidence, the harmonic yield peaks at an optimal incident angle which depends on laser intensity and plasma density. Based on the simulation results, a phenomenological expression for the conversion efficiency of the nth-order harmonic (assuming p-polarized laser with a large incident angle) was given by Gibbon [34]:

This shows that, for example, a conversion eficiency of 9 x 10-5 can be achieved for the

10th harmonic with an incident laser of IA~= 1018 Wcm-2 gm2 (LQ = 0.85). The dependence of harmonic conversion-efficiency on plasma density scale- length was also studied theoretically using PIC-simulations, which showed the existence of an optimum scale-length near L - A for maximum harmonic generation [36,37]. Chapter 2 Theoretical Background 29

AIthough cornputer simulation is a very powerful tool and can usuaily deiiver valuable quantitative information, it provides Little physical insight of the high-order harmonic generation mechanism. In the efforts of presenting a physical picture of the harmonic generation process, several models have been developed. In the following sections, we will discuss two of these physical models which describe harmonic generation in two different physical regimes.

2.2.4 The Linear Mode-Coupling Model The mechanism of SH generation via resonance absorption can also be extended to explain the multiple-harmonic generation process 161. As discussed before, resonance absorption provides an efficient means of converting an electromagnetic wave (61)into a localized electron plasma wave (upe).At the critical surface where o = mpe,these two waves can mix to produce a second harmonic ( o2= CO + wp,= 20)via the current ~$2. This wave is mainly reflected, but part of it can propagate up to the density profile to 4nc where it excites an electron plasma wave at 20. This in tum couples with CU to generate a third hamonic, which is resonant at 9nc, and so on (see Figure 2.4). Shce only hannonics with frequencies up to the bulk plasma frequency find their respective resonance layers, a spectral cutoff at the bulk plasma frequency is predicted. Therefore, the highest order of harmonies which can be generated is m,, = ,/=, where n, is the upper plasma density (buik density). This simple mode-coupling pichue was suggested by a number of early harmonic experiments using nanosecond CO2 lasers

[18, 191 for which a spectral cutoff was indeed claimed. (This cutoff was interpreted from unreduced film densitometry; subsequent independent interpretation of this raw data by Zepf [29] including plausible spectrograph resolution, strongly suggests that this data does not in fact support the interpretation of a cutoff.) More-quantitative theories based on this model were further developed by Bezzerides et al. 1213 and Grebogi et al. WI- Chapter 2 Theoretical Background

Figure 2.4. Schematic picture of harmonic generation via linear mode- coupling in a plasma density gradient.

As discussed in the SH generation (5 2.2.2), the linear mode-coupling picture breaks down at high laser intensities or in very steep density gradients, where the electron oscillation amplitude becomes comparable to the density scale-length, Le., x,,/L 2 1. For a plasma of LIA. = 0.1, this breakdown condition is satisfied when ZA? is above

1.4 x 1016 Wcm-2 pm? In this regime, the oscillating-mirror mode1 discussed below becomes a good picture for harmonic generation.

2.2.5 The OsciUating-Mirror Mode1 As discussed previously, an electromagnetic wave incident on a plasma density profile couples strongly with the electron motions near the critical surface, where the electromagnetic forces push and pull electrons back and forth across the plasma-vacuum boundary. These collective motions of electrons represent strong oscillations of the cntical surface. With normally incident, or s-polarized obliquely incident light, the cntical surface is driven solely by the AC-ponderomotive force Fr,which osciliates at Chapter 2 Theoretical Background 3 1 twice the laser frequency o. The purely Coulomb force -eE, in this case, has no component dong the plasma gradient, and therefore is less effective in driving the cntical surface. For obliquely incident p-polarized light, since both Coulomb force (a)and the AC-ponderomotive force (20) contribute to the driving force, the cntical surface is expected to move as a superposition of two oscillation modes with frequencies w and 20. These collective motions of electrons were demonstrated ciearly by Lichters et al. in their

PIC simulations 13 11. Based on this analysis and the fact that hannonics are generated in a region very close to the cntical surface, Bulanov 1301 suggested an oscillating-mirror model which interprets the high-order hannonic generation from a plasma-vacuum interface as a phase modulation expenenced by the light reflected from an oscillating boundary (Figure 2.5). This mode1 was further developed by Lichters et al. [3 11 and von der Linde et al. [32]. The basic approximation made by this model is to neglect the details of the changes of the electron density profile and to represent the collective electronic motion by the periodic motion of the critical surface. Obviously, this picture of harmonic generation ceases to be true when the plasma-vacuum boundary is spread out over a distance comparable with the electron excursion ( x, / L < 1).

Figure 2.5. Schematic plot of electron-density surface (dashed line) oscillating relative to the fixed ion density (shade) . Chapter 2 Theoretical Backgrod 32

Let's consider a monochromatic plane-wave E = & eq(-iot) incident at angle 0 ont0 a mirror which oscillates sinusoidally at frequency a, dong the x-direction,

~(t)= s0 sin a>,t. The phase-shift of the reflected wave from this oscillating mirror is

@(t)= pino,t , (2.16) where x = (2~0s~cos 0)lc is the phase-modulation amplitude. Using the well-known

Jacobi expansion: exp(-i~sin ~,t)= J, (X)exp(-inm,,$), one can easily see that the reflected wave Er = Eo exp(-iot + i@(t))contains a senes of sidebands at frequencies on= o + no, with amplitudes given by J&), where Jn(x) is the Bessel function of order n. The normalized strength of the nth sideband in the reflected wave can be calculated as

Using this simple geometric model, and assuming o, = 2w, spectra consisting of odd-order harmonies are calculated for different values of x (Figure 2.6). The simple mode1 (2.17) is actually valid ody when the rnirror oscillates much slower than the oscillating fiequency of the incident wave (a, «a). When a, is close to optical frequencies, relativistic retardation effects corne into play which lead to important modification of the simple O 5 10 15 20 harrnonic order model presented above. When the relativis- tic retardation effects are taken into account, Figure 2.6. Harmonic spectra calculated (Eq. the harmonic conversion effkiencies are based on the simple- model - (2.17)). Chupter 2 Theoretical Background 33

found to be significantly enhanced. The detailed derivations are given in Ref. [3 1, 321. Here we only summarize the main results. For normal-incidence or s-polarized oblique-incidence light, we have w, = 20, and the reflected light is cornposed of s-polarized odd harmonics whose intensity distribution is given by

For p-polarized incident light, the mirror is driven with two frequencies. o and 2w. The spectrum of the reflected Iight contains p-polarized odd and even harmonics. The harmonic spectm produced by the CO mode done can be written as

I V . - O 5 1 O 15 20 O 5 10 15 20 harmonic order harrnonic order

Figure 2.7. Harmonie spectra generated by (a) s-polarized light and @) p-polarized light for different values of x (Eq. (18) and (19)). Chapter 2 Theoretical Background 34

The normalized harmonic spectra generated by s-polarized and p-polarized light with different phase-modulation amplitudes x are plotted in Figure 2.7. It shows that the efficiency of high-order harmonic generation increases strongly with X. Cornparison of Figures 2.7(a) and 2.7(b) also indicates that, for a given value of X, the harmonic conversion efficiency for s-polarized incident Light is higher than that for p-polarized light. This apparent disadvantage for p-polarized light in generating harmonies is somewhat artificial: it is overwhelmed by the fact that, with the same laser intensity on target, p-polarized light cm drive the osciiIating &or with much larger amplitude (therefore a higher value of X) than s-polarized light. Using the oscillation amplitude as the only free parameter, Lichters et al. demonstrated that the oscillating-rnirror model was able to quantitatively reproduce harmonic spectra calculated with PIC simulations uader a large range of experimental conditions [3 11. The model also works satisfactorily at relativistic intensities, where a. io 1, by adding a few high-order oscillation modes (30 and 40) to take into account the anharmonic mirror oscillations. In principle, if the plasma restoring force f&) on the electron surface is known, we should be able to calculate the motion of the critical surface s(t), hence the oscillation amplitude of the reflecting mirror. But f&) is very complicated and is strongly asymmetric across the plasma-vacuum boundary. So, to describe the situation satisfactorily, one has to rely on PIC simulations. Physically, the plasma restoring-force is supplied by charge-separation in the medium, which cm be approximated as f, = under the low driving fkequency limit ( rn << mpe) Here mpe is the electron plasma fkequency. Under this approximation, the oscillation amplitude for normal laser incidence is approximately given by [32]

-=-a a:[ -)l =-dl(%)"' A x ope nt? which shows the oscillation amplitude so decreases with plasma density ne. Chapter 2 Theoretical Background 35

Finally, the oscillating-mirror model cm also be used to explain another mechanism of harmonic generation. PIC simulation shows that s-polarized Light at obLique incidence is expected to produce not only s-polarized odd harmonics, but p- polarized even harmonics as weU. The latter, however, cannot be interpreted in tems of a phase-rnodulated reflected wave, because there is no incident light with p-polarization. This harmonic emission cm be considered in the following way. Since the ions are considered immobile, the forward and backward motion of the reflecting surface will induce an oscillating electric-dipole sheet at the plasma-vacuum boundary. For obliquely incident light, there is a penodic variation of the electric dipole moment dong the direction parallel to the target surface, with a spatial frequency given by the parallel component of the wave vector of the incident light. This dipole sheet oscillates at the same frequency as the oscillating rnirror. It cm be shown that this osciilating dipole sheet radiates a p-polarized wave composed of even harmonics [32]. Obviously, this harmonic generation mechanism also exists with p-polarized incident light. It is hard, however, to distinguish it from the phase-modulation mechanism because both mechanisms produce p-polarized odd and even hamonics in this case.

2.2.6 Mode1 Predictions: Harmonie Generation with Varying Experimental Parameters Using the oscillating-rnirror model, the dependence of harmonic generation efficiency on several experimental parameters can be discussed. These parameters include the laser intensity, polarization and incident angle, target matenal (i.e., the initial electron density) as wel1 as the initial plasma scale-length. In the following, we will discuss how harmonic generation will be Ïnfluenced by these factors.

Laser intensiîy Assume the reflecting surface oscillates with ampLitude so and frequency o. Since Chapter 2 Theoretical Background 36

the maximum surface velocity os0 must not exceed the speed of light, so is limited by

s,, < c/o= A / 27r = 0.16A. Similarly, the maximum amplitude of the 2w mode is 0.08 A,. At low incident intensity, the reflecting surface oscillates harmonically with

small amplitude so << 0.12, and the hannonic intensity falls off rapidly with increasing

order. At relativistic intensities ( a. 2 l), the surface starts to move very anharmonically with speeds close to the speed of iight, and higher order surface modes (at 3~~40,etc.) are induced by relativistic effects in addition to the w and 20 modes driven by the electric

and the ponderomotive forces. Harmonic emissions, particularly of the higher-order harmonics, are significantly enhanceci by these higher surface modes, which are of genuinely relativistic origin. Meanwhile, the oscillation amplitudes of the low-order surface modes (lm and 20) reach their limits at relativistic laser intensities, which result in saturation of the low order hannonic emissions. So with increasing laser intensity, the harmonic spectnim is expected to show both a slower growing (Le., saturation) of the low harmonies and a slower frequency roll-off of the high harmonics.

Laser polarization Harmonic generation depends strongly on the laser polarization because of the different driving rnechanisms associated with s-polarized and p-polarized waves. This has been discussed in the last section. The conclusion can be summarized in the following polarization selection rules: at normal incidence, Linearly polarized light generates only odd harmonics of the same polarization as the incident light; at oblique incidence, s-polarized light generates s-polarized odd harmonics and p-polarized even harmonics, while p-polarized light produces only p-polarized harmonics of both odd and even orders (Table 2.2). It is woah to note that the selection rules denved for SHG

(8 2.2.2) using perturbation theory are consistent with these generalized des. In practice, these selection rules may be violated by 2-D effects, e.g. nonuniformities due to preformed plasma (see the following section), finite size of the Chpter 2 Theoretical Background focal spot, hole bdng and surface rippling due to the Rayleigh-Taylor instability.

Table 2.2. Polarization selection des Fundamental Odd harrnonics Even harmonies Oblique incidence S S P P P P Normal incidence linear linear

Angle of incidence For s-polarized Light, the surface is driven only by the AC-ponderomotive force, which falls off monotonicaily with angle of incidence 8. For p-polarized Iight, the normal component of the electric field ( Ex = Eo sin O), which increases with 0, acts on the surface in addition to the decreasing ponderomotive force. So we expect to see the odd harmonics generated by a s-polarized laser fall off monotonically with 0, while harmonics generated by a p-polarized laser increase with 0 first, and then vanish at grazing incidence (8 = 90') because of the decreasing penetration of the electnc field, as for resonance absorption. The even harmonics generated by s-polarized light should have similar angle dependence as for p-polarized drive, but with much lower intensity. This dependence on incident angle is shown schematically in Figure 2.8.

Plasma density and scale-length

The frequency factor w / mp, (or equivalently, n, /ne)in Eq. (2.20) signifies the resistance of the medium to the perturbation of the electron density. It indicates that to obtain large so and therefore high output of harmonics one should use a plasma with relatively low density (Le., slightly overdense ne 2 n,). Furthemore, a considerable enhancement of the oscillation amplitude is expected to occur for resonant excitations, when the driving frequencies (w or 20) equals the electron plasma fiequency ope. Chapter 2 Theoretical Background 38

O 15 30 45 60 75 90 angle of incidence (degree)

Figure 2.8. Qualitative dependence of mid-order harmonic generation on angle of incidence for s-polarized (dashed-lines) and p-polarized laser (solid-lines).

The harmonic emission depends also strongly on the plasma scale-length L. Generally, the harmonic intensities increase with L, since then the laser pulse interacts essentiaily with plasmas of lower density and drives larger surface oscillations due to the weaker plasma restoring force. This trend eventually will stop at appreciably larger scale-lengths (typically L - Â ), above which the harmonic efficiency decreases again. This is because the distance between the classical tuming point and the critical surface increases with L, so that the light amplitude driving oscillations at the critical density decreases. This dependence has been verified by the PIC simulations perfomed by Delettrez, et al. [36], and by Lichters, et al. [37j. Chapter 2 ï7ieoretical Background

2.3 Role of Preformed Plasma

In discussions above, we have assumed an ideai physical picture in which short laser pulses interact directly with solid targets. From an expenmental point of view, a serious problem that can prevent this from happening may arisr from a laser prepulse. If

the prepulse intensity on target is higher than the threshold intensity for plasma formation, a preformed plasma (preplasma) is formed which prevents the main pulse from interacting directiy with the soiid. hdeed, the preplasma is a key issue in al1 experiments üsirig short-pulse intense lasers incident on solids [65].

2.3.1 Laser Prepulses Laser prepulse refers to any laser energy deposit on target prior to the main laser pulse. There are three kind of laser prepulses [65]. The first kind of prepulse is any laser light which reaches the target at a time independent of the main pulse. It could be the amplified spontaneous emission (ASE) from the laser amplifiers or the leak-through pulses from imperfect optical gates in the system. This kind of prepulse normally extends

several nanoseconds or longer. As the intensiv of this prepulse exceeds 108 Wkm*, it will evaporate the target surface, producing a cloud of vapor which expands at - 3 nm/ps. Thus, a prepulse that occurs more than 1 ns before the main pulse will produce a gas cloud of thickness > 3 pm in front of the target, which when ionized will fom a plasma that alters the interaction of the main laser pulse with the target. The second kind of prepulse is the pedestal under the main laser pulse. For a CPA laser, this pedestal is usuaily caused by uncompensated group velocity dispersion in the laser system (see 5 3.3.4). Comparing to the fnst kind of prepulse, the duration of the pedestal is usuaLly much shorter, and is typicaUy several times of the main pulse width. The intensity levels of these two kind of prepulses are usuaily characterized by the laser pulse contrast defined as b/lP, where Io and IF are the maximum laser and Chupter 2 Theoretical Background 40

prepulse intensities. Typically, preplasmas start to be produced by laser prepulses of intensities greater than 1012 W/cm2. So in a laser-target experiment where peak laser intensity Io = 1018 W/cm2, one needs a pulse contrast better than 1010 to avoid preplasma production. Two commonly used pulse-cleaning tools are saturable absorbers and frequency-doubling crystals. Both are effective in suppressing the fust kind of prepulse. For pedestai suppression, only the doubling crystal will work because of the short duration of the pedestal. In the harmonic experiments descnbed below, both pulse- cleaning methods were enployed (see Chapters 4 and 5). The thkd kind of prepulse refers to the laser energy on the leading edge of an ideal main Iaser-pulse itself, which dependents very much on the pulse-width and shape.

To illustrate this, the iime distributions of two Gaussian pulses used in Our experiments, together with a sech2 pulse, ail having the same peak intensity of 1018 W/cm2, are shown in Figure 2.9. Obviously, shorter pulses tend to produce less plasma by this mechanism,

time (ps) Figure 2.9. Intensity distributions of three pulses of different shapes and durations, with a peak intensity of 1018 Wkm? Chapter 2 Theoretical Background 41

so long as they retain smalI pedestals. We can see from Figure 2.9 that the 1.2-ps

Gaussian pulse reaches the plasma-forming intensity of 1012 ~lcrn2more than 2.5 ps before the peak reaches the target. If the plasma could expand freely at the typical ion- sound speed of - 0.1 Wps, it would approach 0.25 pn in extent by tirne the peak of the laser pulse arrives. Sirnilarly, a clean 350-fs Gaussian pulse and sech2 pulse would produce preplasmas of 0.08-p and 0.15-pm thick, respectively. Here we have ignored the ponderomotive steepening by the laser pulse. If this effect is taken into account, the actual preplasma might be thinner than we have estimated.

2.3.2 Effects of Preplasrna on Harmonic Generation Preformed plasmas have been proven useful for the purpose of maximizing the production of hot eiectrons [66] or x-rays [67,68],but they are hamiful if one's goal is to obtain very clear evidence regarding laser interactions with overdense and soiid-density plasmas. As we saw in the last section, harmonic emission generated from a flat cntical surface should be dong the direction of specular reflection. This will no longer be true, however, if a large extent of preplasma is present, because in this case the cntical surface is not flat any more, the incident angle is no longer well defmed, and therefore harmonies are expected to be emitted in a much broader solid angle. The polarization selection rule for harmonic generation is wother powerful criterion to test the validity of harmonic generation models. This selection rule may also be violated by the 2-D effects associated with the preformed plasma, making it more diffIcult to interpret the experimental result. Both of these effects (wide harmonic emission-angle and the polarization-insensitivity) were noticed in a recent experirnent performed at the Rutherford Appleton Laboratory where himnonics were generated by a laser containing of a substantial prepulse [26]. Hannonic conversion-efficiency can dso be strongly affected by a preplasma. Because of their long expansion time, preplasmas generdly have much longer scale- lengths, which make harmonic generation inefficient. The existence of a long scale- Chapter 2 Theoretical Background 42

length preplasma also means that the laser has to interact with a large amount of underdense plasma before reaching the overdense region. By this, beam quality at critical density is significantly altered through self-phase modulation and fdamentation in the underdense region. This will also innuence the harmonic conversion-eff~ciency. For the same reason, the spectral brightness of harmonic emission will also be reduced by the preplasma. The reduced harmonic efficiency by preplasma has been reported in an experiment in which harmonic emission was only observed when the prepulse was removed [23]. The preplasma effect on harmonic generation cm be studied experimentally if one can control the experimental conditions so that harmonies generated by a high-contrast clean pulse and by a pulse containing known amount of prepulse can be directiy compared. This idea is demonstrated experimentally in Chapter 4, in which preplasrna effects on SHG are studied in a systematic fashion.

2.3.3 Modification of Plasma Density Profile by a Deliberate Prepulse A laser prepulse is often an unwanted artifact in the study of laser-solid interactions. Under certain conditions, however, it can be a useful expenmental parameter, providing its intensity and timing are controllable. As discussed in § 2.2.6, harmonic generation depends also on the plasma density scale-length. This dependence can be studied experimentally in an expanding plasma produced by a prepulse deliberately added at a controiled time in advance of the main pulse. The scale-length of a ffeely evolving plasma, following a weak prepulse, can be reasonably estimated by hydrodynarnic modeling. We used the one-dimensional hydrocode MEDUSA [69,701 to calculate the electron density distribution in a plasma dong the direction of expansion, at various time derthe Iaser shot. Figure 2.10 shows two typical electron density profiles calculated for a 1-pthick silicon target and a laser pulse of I= 2.5 x 1016 Wkm2 and Â. = 0.526 p. The solid line represents the profile just Chaprer 2 Theoretical Backgrd 43

before the laser pulse arrives (solid density) and the dashed line is the profile 3 ps after the laser shot, Using Eq. (2.3), we caiculated the plasma scale-length for each electron density profile at different time delays. Based on the assumption that the laser-plasma interaction occurs mainly at the cntical surface, the scale-length was calculated at the critical density n,= 4.0 x 1021 cm3(for A = 526 nm). The result is plotted in Figure 2.1 1, which shows that the plasma scde-length increases with the time delay after the deiiberate prepulse, roughly at a speed of 0.06 pxdps. Based on this modeling, we perfomed an expenment in which the third-harmonic emission was measured at different delays of a controllable prepulse (see Chapter 5).

II - 3 - 11 solid : ', boundary 2 - - ,"t ,"t + 1' 1 L *- \ - \ \ - O-""'"'' b, O 0.5 1 1.5 x (crm) t (PSI Figure 2.10. Modification of electron Figure 2.11. Plasma scale-length caicu- density profile by a prepulse of intensity lated at different time-delays after the 2.5 x 1016 W/cm2. The solid line is the prepulse. The solid line is for visual profile just before the prepulse arrives; guidance ody. the dashed line is the profde 3 ps after the prepulse. Chapter 2 Theoretical Background

2.4 Conclusions

We have briefly discussed the important physical issues involved in the harmonie generation from intense laser interaction with solid targets. Cornputer simulations demonstrate that efficient high-order harmonies (of both odd and even orders) can be generated from soiid targets at Iaser intensities above 10'6 W/cm2. To get some insight of this harmonic generating mechanism, two physical models were introduced: at iow intensity and long scale-length plasma (x,,, /Le1). the linear mode-coupling mechanism presents a good picture for harmonic generation; at high intensity and short scale-Iength plasma ( xosc /L2 l), the oscillating-mirror mode1 provides satisfactory explanations. Based on the physical understandings from these models, the dependence of harmonic generation on several experimental parameters was given. Finally, the importance of the laser prepulse issue for expenmental studies of harmonic generation from solid targets was emphasized. Based on hydrodynamic modeling, an idea of using a controllable prepulse to study the scale-length dependence of harmonic generation was also developed. Chapter 3 Development of the Toronto FCM-CPA Laser Sys tem

In this chapter, the FCM-CPA laser systern developed at the University of Toronto is described. A systematic characterization of this system as well as a novel cross-correlation technique are presented.

3.1 Introduction to the CPA Technology

Since the invention of the pulsed laser, peak laser power has increased by nearly 12 orders of magnitude in 37 years. After a relatively quick development in the 1960s,

thanks to the invention of Q-switching and mode-locking techniques, for more than 20 yem the peak power of compact solid-state laser systems had stagnated near the gigawatt level. This was because in almost al1 gain media nonlinear optical effects that could break up the laser beam irnposed a severe limit on the power one could get from a laser of given aperture. So to obtain higher peak power, one had to increase the sizes of the amplifiers, as well as the cost. This situation changed dramaticaily in the mid-80s after the introduction of a new type of amplification, die chirped-pulse amplification (CPA) technique [Il. The basic scheme of this novel technique is Uustrated in Figure 3.1. Fist, picosecoii.: laser pulses are generated from an oscillator. Instead of being amplified directly, these seed pulses are sent to an optical expander where the pulse durations are stretched by, Say, 1000 Chapter 3 Development of the Toronto FCM-CPA Laser System

Figure 3.1. The chirped-pulse amplification concept. times. The chirped and temporaily stretched pulses, having their peak powers reduced by 1000 times, can then be amplified safely in the amplifiers. Afier ampiifïcation, the pulses are compressed back to their original picosecond durations in a cornpressor. In this way, one cm produce laser pulses which are 1000 times more powemil without darnaging the optical elernents, and without having to increase the sizes of the amplifiers. Nowadays, the CPA technique has become a standard solid-state-laser tool used to produce terawatt-class optical pulses [71]. This technique has been applied to many laser media which can be broadly divided into two groups: sub-100-fs systems based on the broad-band laser materials, such as Ti:sapphire [72-751, Cr:LiSAF [76, 771 and alexandrite [78], and roughly 1-ps systems based on the traditional high-power laser material Nd:glass [79-821. The first group approaches high peak power by producing pulses with extremely short pulse widths but of relatively low energies; terawatî-lasers producing pulses as short as 54s at 1-kHz repetition rate have been demonstrated recently [83,84]. In laser-produced plasma studies, one often needs not only high peak irradiance, but also substantial energy per pulse. For these kinds of applications, Nd:glass systems are still preferred; based on the best-developed, large-size, high-energy-storage Laser medium, they currently produce the greatest energy per pulse [82]. Chapter 3 Development of the Toronto FCM-CPA Laser System 47

The major disadvantage of using the CPA technique in Nd:glass systems was the lack of stable short-pulse oscillators. The onginal approach used puises from Nd:YLF or Nd:YAG osciliators. Because of their narrow bandwidths, a combination of fiber and grating expansion scheme had to be used, which led to a mismatch between the expansion and compression stages and resulted in a pedestal on the recompressed pulses. The intnnsic pulse contrast ratio obtained was limited to - 103. At terawatt power-levels this pedestal can form a substantial prepulse which will pre-ionize the target matenals. Much work had been done in an effort to solve this contrast issue by re-shaping the pulse spectmm [85], by fast temporal-windowing [86], or by applying additional pulse cleaning using saturable absorbers [87],plasma-shutters [88] or nonlinear birefringent fibers [89, 901. Contrast ratios of 105-107 had been achieved using these rnethods. In the last few years, with the matunng of the Tksapphire technology, hybnd systems combining a Ti:sapphire oscillator and regenerative amplifier with the well-developed Nd:glass power amplifier chain have become more common configurations among the multi-terawatt Nd:glass lasers [80-821 . Using direct grating expansion and compression, a contrast ratio of 106 is nomally achieved in these hybrid systems. At the University of Toronto, we have developed an improved dl-Nd:glass terawatt laser system [91, 921 which employs high-contrast (109,pJ-level, 1-2-ps pulses produced frorn a feedback-controlled mode-locked oscillator as seed pulses. These transform-limited seed puises are suitable for direct grating expansion and compression, and because of their relatively high energy, require less subsequent amplification. The system produces 14, 1.2-ps pulses with contrast better than 5 x 107 without additional pulse cleaning measures. This compact, relatively simple terawatt laser system has become a routine tool for the ongoing picosecond laser-plasma experiments in Our laboratory [93]. Chaprer 3 Development of the Toronto FCM-CPA Loser System

3.2 The Feedback-ControUed Mode-Locked (FCM) Oscillator

The FCM Nd:glass oscillator [94,953 is the key element in the Toronto CPA laser

system. Compared to other mode-locked oscillators, it has two unique features: high

output level (- pJ) and high pulse-contrast (108). The design and charactenzation of this oscillator are described in this section.

3.2.1 Purpose of Feedback Control in the Oscillator Figure 3.2(a) shows a schematic diagram of the FCM oscillator. It is a hybrid mode-locked Nd:gIass oscillator (Kigre 498 athermal phosphate glass, 6-mm @,21.2-nm gain-bandwidth). An acousto-optic modulator driven at 66.7 MHz provides active mode- locking. For passive mde-locking, a tramlatable thin dye ce11 is placed inside an intracavity telescope at Brewster's angle, in which Kodak Q-switch II (dye 9860) in 1,2- dichioroethane is used as the saturable absorber [96]. The dye concentration is adjusted such that the saturable absorber provides a round-trip transmission of - 65% for smdl signals. A photodiode, a fast high-voltage amplifier (- 500 V), a Pockels ceil and a thin- film polarizer together provide a negative feedback control of the intracavity laser pulse energy. The purpose of the feedback control is twofold. First, it maintains pulse energy at the optimum level for effective pulse shortening in the saturable absorber, preventing it from bleaching the dye and causing passive Q-switching. Second, it iimits the shot-to- shot variation intrinsic to passive mode-locking, and stabilizes the laser output. The feedback signal is provided by Fresnel reflection from one uncoated face of the laser rod; the circulating power in the cavity cm be continuously adjusted by attenuation of the optical feedback signal. Voltage pulses of up to 500 V can be generated from the negative-feedback control circuit and applied to the Pockels ce11 which is electrically biased at 1200 V, increasing the cavity coupling loss and Iowering the circulating pulse Chapter 3 Development of the Toronto FCM-CPA Laser System 49

-- -- - 1-4 1-4 1 ps (133 round trips)

Figure 3.2. (a) Schernatic diagram of the FCM oscillator. Ml (r = 5 m), M2

(r = .a), high reflectivity mirrors; LI, L2, lenses, f = IO cm; AOM, acousto-optic modulator; SA, saturable absorber; LR, laser rod; TFP, thin-film polarizer; PC, Pockels cell; FC, electronic feedback controller. @) Oscilloscope trace of the output pulse train. Label A identifes round-trip zero as used in Figure 3.3. energy. The thin-film polarizer also functions as the output coupler. Figure 3.2@) shows a typical feedback-controlled pulse train generated from the FCM oscillator, which consists of 256550 pulses depending on the adjustment of the control level.

3.2.2 Pulse Development in the FCM Osciliator Using a tunnel-diode discriminator and an external Pockels cell, we selected single pulses at different positions in the FCM pulse train, and measured their temporal width, spectral width and contrast ratio. The pulse duration and contrast measurements were made with a conventional rnulti-shot autocorrelator (the same as that used in Chapter 3 Development of the Toronto FCM-CPA Laser System 50

Ref. [87]), using non-collinear second harmonic generation in a thin (1-mm) LiIO3 crystal. The spectmm was measured by a single-shot spectrograph (Amencan Holographic). Figure 3.3 illustrates the results of these pulse-development measurements. Due to instrumental intemal delays (-100 ns), we could not select the very early pulses from the pulse train. The zero round-trip in Figure 3.3 corresponds to the position marked by the arrow in Figure 3.2@). In Figure 3.3(a), the measured pulse duration (filled circles) and spectral bandwidth (open circles) are plotted against round-trip nuber. We can see that, starting at about 8 ps early in the train, the pulse width continuously decreases and reaches a minimum value of 1.5 ps at about 80 round-trips in this non-optimized operation. With fresh dye, a shorter pulse width of 1.2 ps cm be routinely obtained in this FCM oscilIator. Accompanying this pulse shortenhg process, the conjugate spectral width increased from 0.25 nm to a final bandwidth of 1.35 nm at about 150 round-trips. It is interesting to note that at late times, after the pulse duration reaches its optimized value, its spectral width

continues to increase, presumably due to the effects of self-phase modulation inside the laser cavity, accumulating more bandwidth than the Fourier-transform-limitedsituation. The evolving tirne-bandwidth product of the pulse is shown in Figure 3.3(b) (filled circles). Mer a quick decreasing from 0.6 to 0.44 (transform limit for Gaussian pulse shape) in the early pulse train, it remains at this value for about 80 round-trips and then increases again to about 0.7 late in the pulse train. By positioning the glas dye ce11 near the focus of the intracavity telescope or altering the peak circulating intensity, the final bandwidth of pulse can be made as large as 6 nm, while leaving the pulse duration development unchanged. An example of this extra-bandwidth case is included in Figure 3.3(b) (open circles), where the pulse train has a fmd bandwidth of 3.6 m. If this non-transform-limited pulse were recompressed, it is anticipated that the nonlinear partial chirp of the puise would add to the pedestal of the recompressed pulse. Chapter 3 Development of the Toronto FCM-CPA Laser System

round-trip number Figure 3.3. Pulse development inside the FCM oscillator. (a) Pulse width (fïiied circles) and spectral bandwidth (open circles). (b) Time-bandwidth product (filled circles) and extra-bandwidth case described in text (open circles). (c) Contrast ratio. In al1 these three plots, the lines are for visual guidance O*. Chapter 3 Development of the Toronto FCM-CPA Laser Sysîem 52

Another aspect of the pulse development is the dramatic improvement of the pulse contrast as the round-trip number increases. Figure 3.3(c) shows the developrnent of nominal contrast as measured from the ratio of pulse intensity at the peak to that at the pedestal (10 ps away fiom the peak). It increases exponentially from a value of 2 to

5 x 105 der about 100 round-trips. This contrast ratio improvement is mainly due to reduction of the extended pulse background because of the saturable dye, which provides different transmissions for the peak of the pulse and the for the background. Assuming the dye ce11 has a round-trip transmission of T,for the peak of the pulse and T2 for the pedestal, after n round-trips, the pulse contrast is expected to increase from an initial contrast Co to a value given by

Cn = CO (T,IW (3.1)

Using Eq. 3.1 and the measured contrast, we obtain T~/T* = (5 x 10'/2)'~'~~ = 1.9 13 which means the small signal transmission T2 was about 88% of the large signal transmission Tl . It should be noticed that the pulse-width shortening ds:, reduces the intensity of the pulse wing (see Figure 2.12), therefore improves the nominai contrast. It can be shown, however, that this effect is negligibie comparing to above mechanism (Eq. 3.1) at the selected pedestal position (+IO ps).

3.2.3 Aigh-Contrast Characterization of Pulses from the FCM Oscillator The upper limit of the rneasurement shown in Figure 3.3(c) is about 5 x 105, which is instrumental and results from residual scattering light inside the autocorrelator. To produce a high-contrast autocorrelation, we searched the Li103 crystal for low- scattering sites, and carefuIly constructed grouped apertures to minimize the scattered single-beam harmonic Iight going to the detector-a high-sensitivity, low dark-current photomultiplier (Hamamatsu R2 12UH). Caïibrated neutral density fdters were used to attenuate the second harmonic signal to prevent saturation of the photomultiplier. Chapter 3 Development of the Toronto FCM-CPA Laser System 53

time delay (ps) 1 .O

Ah= 1.24 nrn 0.8 - (Gaussian fit) - - - 0.6 - - - - 0.4 - - - 0.2 - - 0.0 1050 1051 1052 1053 1054 1055 1 056 wavelength (nm)

Figure 3.4. Typical characterization of selected single pulse from the FCM oscillator. (a) Autocorrelation trace with Gaussian fit. Apparent satellites are actuaily trading pulses produced by residuai reflections in the wave plates. @) Spectrum wiîh Gaussian fit. The smd npple indicates the existence of an etalon, with an optical thickness of about 0.66 mm, in the laser cavity. Chapter 3 Development of the Toronto FCM-CPA Laser Sym 54

The improved autocorrelation measurement for a pulse selected after about 200 round-trips is shown in Figure 3.4(a). It can be seen that the 1.2-ps pulse is clean over nearly 8 orders of magnitude and very well fits a Gaussian curve throughout this range; its background is lower than Our detection limit. The apparent satellites proved to be trading pulses produced by residual reflections in the wave plates dong the optical path, since one could alter their ampli~deand delay by substituting different wave plates. Figure 3.4@) shows a typical pulse spectnim, which exhibits a Gaussian shape as well. This FCM oscillator can also be configured to produce subpicosecond pulses; pulse durations of 50-600 fs have been demonstrated in similar systems with different saturabie dyes 1971. Dye 9860 is used routinely in our system because of its relatively long Iifetime and because it produces stable operation of the oscillator, requiring only minor attention between dye changes. Elsewhere, by integrating feedback-controlled and additive-pulse mode-locking, pulse durations as short as 460 fs have been demonstrated from a Nd:glsss osciLlator [98]. The single-pulse energy from the oscillator can be adjusted between 1-5 pl Pulse-stability measurement shows a typical shot-to-shot amplitude fluctuation of AEE - 5%, where E and AE are the average and the standard deviation of the output energy per pulse. These high-contrast, high-energy and stable pulses from the FCM osciliator serve as ideal seed pulses for our CPA laser system.

3.3 The FCM-CPA Laser System

3.3.1 The Laser Setup The Toronto FCM-CPA laser system is shown schematically in Figure 3.5. Since we start from high-contrast, transfom-limited 1-ps pulses, the traditional hybnd fiber- grating expansion technique typically used with Nd:glass systems is no longer necessary, and a gratings-only expansionlcompression scheme can be used. The pulse train from the kinematic c, / 2

FIG. 3.5. Schematic diagram of the FCMÇPA laser system. FR, Faraday rotator; PC, Pockels cell; SBE, spatial beamexpander; VSF's, vacuum spatial filters; PA'S, power amplifiers; CR, corner reflector. Chpter 3 Development of the Toronto FCM-CPA Laer System 56

FCM osciliator is directed to a diffraction-grating expander [99],which consists of two anti-parallel 1740-line/mm gold-coated holographie diffraction gratings (Jobin-Yvon) separated by approximately 160 cm, and a pair of asphencal lenses with focal lengih f = 60 cm separated by 2f (120 cm). The incident and diffracted angles for the fist grating are 60.75' and 74-05' respectiveïy. This expander ha an effective length of 82 cm and exhibits a positive group velocity dispersion. After double-passing the expander, al1 pulses in the pulse train are stretched to about 410 ps as measured by a cross-correlation method described later; a single puise is selected from the train by a pulse selector on the rempass. The selected stretched pulse (0.5 pJ, 1 Hz) is then coupled into a ring regenerative amplifier [100] via mode-matching optics. The ring regenerative amplifier is a stable TEMw cavity, which contains a 2-m focal length lem, a Nd:glass laser head (Kigre 498 athermal phosphate glass) and a double-crystd Pockels ce11 (Medox). The intracavity Pockels ce11 is optically biased, yielding a stationary half-wave retardation. Mer the injected pulse enters the cavity, a half-wave voltage (4 kV) is applied to the Pockels cel1, trapping the pulse inside the cavity for amplification. The pulse is ejected from the cavity after about 40-80 round-trips by switching the voltage applied on the Pockels ce11 to the full-wave voltage (8 kV). Because of the microjoule injected pulse, a net gain of only 103-104 is required to bring the input pulse to millijoule level. Considering the cavity losses, the whole gain is estimated to be about 105-106, which is relatively low compared to other systems in which 100-pJ or 1-nJ seed pulses are injected. This results in relatively little gain-bandwidth narrowing in the regenerative amplifier. Experimentally, we found the input pulse bandwidth of 1.3 nm to be preserved in the amplified output pulse. The relatively low amplification by the regenerative amplifier also means that greater contrast between the amplified pulse and the amplified spontaneous ernission (ASE) background is expected. The regenerative amplifier output (2 mJ, 1 Hz) is beam-expanded by 3 x, then Chapter 3 Development of the Toronto FCM-CPALaser System 57

injected into a coliinear four-pass amplifier PA1 (IO-mm x 165 mm, phosphate glass) through a Pockels celI pulse selector (10-ns window) which provides additional contrast against pulse leakage and ASE background from the regenerative ampiifîer. The 100-mJ output pulse (at 4 pulses/min) fkom PA1 next passes a vacuum spatial filter VSFl (f/30, M = 2.5), and then is amplified by a double-pass amplifier PA2 (20-mm@x 200 mm, phosphate glass), producing 1.5-J pulses at 1 pulse/min. An additional pulse selector with a 30-1s temporal window is placed between PA1 and PA2, to prevent feedback damage from pulses reflected back into the early amplification stages. Mer PA2, the bearn is again spatialiy fdtered in a vacuum spatial filter VSF2 and expanded to 50 mm in diameter before entering the grating pulse compressor. The compressor gratings are identical to the expander gratings except for their sizes. The larger one has a ruled area of 21.5 cm x 16 cm. The gratings are parailel to each other, set with the same incident and diffracted angles as those in the expander. At a 74-cm center-to-center grating spacing, the amplified pulse is recompressed back to 1.2 ps. The compressor efficiency is rneasured to be 65%, corresponding to a single-pass diffraction efficiency of 90%. The final recompressed energy is 1 J. This 1-J. 1.2-ps TW laser has become a routine tool for the ongoing picosecond laser-produced plasma studies in Our laboratory. Longer-pulse and higher-energy experirnents (such as the XW laser experiment 1671) are accommodated by an additional two-pass amplifier PA3 (Quantel 64-mm + x 100 mm, borosilicate glass), which can deliver up to 5-J, 410-ps pulses.

3.3.2 Characterization of Beam Focus in the Target Chamber The recompressed 14pulse is directed to a U3.5 fmal focusing lens at the target chamber for the picosecond-laser-produced plasma studies. In most of the experiments the most important parameter is the laser intensity on target, which in tum depends to a large degree on the focusabiiity of the beam. So it is crucial to characterize the spot size Chupter 3 Development of the Toronto FCM-CPA Laser System 58

at the focus in order to determine the acnial intensity on target. The confocal parameter of the focused beam also determines the accuracy required for the target positioning system in order to keep the target at best-focus nom shot to shot. To measure the laser intensity distribution near the focus, the focal spot was imaged with 15-times magnification ont0 a CCD camera (Hitachi) using a 10 x microscope objective. The measured results are shown in Figure 3.6. By translating the objective lens along the optical axis (Az > O corresponded to moving the objective lens away from the focusing lens), a series of beam images were obtained at different positions around the focus (Figure 3.6(a)). This measurement was performed with the properly attenuated regeneratively-amplified and recompressed pulses. In Figure 3.6@), beam sizes W (w)dong horizontal (x) and vertical (y) axes are plotted, together with the best fits to the Gaussian beam equation. It cm be seen that the beam is slightly astigmatic, and the confocal parameter along the horizontal direction (20,= 1 13 pm) is about 61% of that dong the vertical direction (Gy= 185 p).The beam profile at the best focal position (z = O, where W, = Wy) is plotted in Figure 3.6(c), which shows a smooth Gaussian distribution with a spot size of L 1.6 pm FWHM. This corresponds to 1.4 times the diffraction lirnit .

Thermal distortions introduced by the power amplifiers were dso studied, These were done through Mng PA1 andor PA2 at full powers, while keeping the regen amplification at low level. When PA1 was fired, no obvious effect on the final beam focusability was observed. When the 20-mm diameter PA2 head was fired, however, both thermal-birefringence and a negative thermal-lensing were produced, which peaked at about one minute after the finng. The tirne-dependent thermal lens in PA2 effectively causes a shift of the best focal position in the target chamber; the amount of shift depends on the rate at which PA2 is fired. When PA2 was fied at a rate of one shot per two minutes, for example, we found the best focus shifted to z = 140 p,as compared with z = 0 when PA2 was not fired. This focal shift becarne unnoticeable when PA2 was fd Chapter 3 Developrnen? of the Toronto FCM-CPA Laser System Chapter 3 Development of the Toronto FCM-CPA Laer System 60

at one shot per 3 minutes. Based on this measurement, the FCM-CPA laser is normalIy operated at a rate not faster than one shot per 3 minutes whenever PA2 is needed.

3.3.3 Compressed Pulse Characterization Using High-Contrast Cross-correlation As discussed in 5 2.3, for a TW-laser system, the pulse contrast is a very important parameter. To characterize the contrast of the FCM-CPA laser, a cross- correlation method was used. Since we have very high contrast 1.2-ps oscillator pulses left over in the osciilator train, we can use them as 'probe' pulses to cross-correlate against pulses farther down in the CPA chah and analyze their shape, contrast and possible satellites. Because both probe pulse and unlmown pulse are initiated from the same oscillator pulse train, thei. relative time jitters are negligible. This cross-correlation technique has proved to be very useful in our laboratory. Using another Pockels ceIl (not shown in Figure 3.9, a single unstretched pulse is selected from the same osciiIator pulse train and sent to the cross-correlator together with the unknown pdse. The cross-

correlator is identical to the autocorrelator described in § 3.2.3, except one delay-arm of the autocorrelator carries the probe pulse. With the help of a fast photodiode and osciiloscope, the relative timing between the probe pulse and the unknown pulse can be adjusted to within 200 ps. Then by translating one delay-arm of the correlator, a cross- correlation signal between these two pulses cm be found. Figure 3.7 shows the result of two typical cross-correlation measurements. In Figure 3.7(a), we cross-co~elatedthe temporaily stretched regenerative amplifier output against the 1.2-ps probe pulse. A 410-ps Gaussian shaped pulse is detedned, which well agrees with Our calculation based on the input pulse bandwidth and the expander geometry. In Figure 3.7@), we cross-correlated the regeneratively amplified and recompressed 1.2-ps pulse with the high-contrast probe pulse. It shows that the leading edge of the recompressed pulse is clean to the 2 x level, which corresponds to a contrast of 5 x 107. It also clearly identifies postpulses resulting from residual Fresnel Chapter 3 Development of the Toronto FCM-CPA Laser System

time delay (ps)

time delay (ps)

Figure 3.7. Cross-correlation of the clean oscillator pulse with (a) the temporally stretched pulse and @) the recompressed pulse. The negative time delay represent the front edge of the pulse being studied. Chapter 3 Development of the Toronto FCM-CPA Luser System 62

reflections in the CPA system. Small pulses on the leading edge of the main pulse appear to be intemal reflectims of the clean probe pulse within the cross-correlation crystal. The above measurements demonstrate that the cross-correlation chamcterization is a significant improvement over what we could have provided by conventional second- order or third-order autocorrelation. The very high contrast and the relatively high encra of the oscillator pulse are important factors for the success of the high-dynamic-range measurement described in this section.

3.3.4 Single-Shot Autocorrelation The multi-shot correlation techniques described in the previous sections becorne tedious and impractical when used to study the fully amplified pulses because of the relatively low repetition rate of our laser system (one shot per 3 minutes). The multi-shot measurernent may also average out possible laser pulse-width fluctuations during the operation. In order to monitor the laser parameters for a given shot, it is necessary to build an autocorrelator which can measure the pulse width on one-shot basis. The single-shot autocorrelator built in our lab is similar to the multi-shot one explained in 5 3.2.3, but two cylindrical lenses (instead of the two spherical lenses) are used to produce horizontal line-focuses on the LiI03 crystal. The photomultiplier is replaced here by a CCD linear array (Thompson). To minirnize the effect of pulse spatial distribution on the temporal measurernent, expansion of the incident beam size is sometimes necessary. Calibration of the autocomlator is done by translating one of its arms by a known amount and recording the corresponding shift of the autocorrelation peak on the detector. By lirniting the room light and by carefully subtracting the CCD thermal background, rneasurernent with a dynamic range of 103 can be routinely achieved with this single-shot autocorrelator. Figure 3.8 shows the typicd sin@--shot autocorrelation traces of (a) a pulse from the FCM oscillator, and (b) a regeneratively amplified and recornpressed pulse. Both Chapter 3 Developmenf of the Toronto FCM-CPA Laser System

time delay (ps)

time delay (ps)

Figure 3.8. Single-shot autocorrelation of (a) an oscillator pulse (At = 1.03 ps) and (b) a recompressed regen pulse (At = 0.94 ps). The dashed-lines are the Gaussian fi&. The broad wings in both plots are believed to be an artifact from the autocorrelator. Chapter 3 Development of the Toronto FCM-CPA Lacer System 64 plots show a broad wing at the 10" level. Since the oscillator pulse is known to be clean down to the lelevel (see Figure 3.4(a)), we believe this broad wing is an artifact of the autocorrelator. The osciiIator pulse shows a perfect Gaussian pulse shape with a pulse width of 1.03 ps. The recompressed regen pulse exhibits a slightly narrower width of

0.94 ps, and shows a clear shoulder at the 10-2 level. This shoulder is indeed associated with the compressed pulse, as it also appears on the leading edge of the pulse in the cross- correlation measurement (Figure 3.7(b)). One possible explanation for this shoulder is the high-order phase errors in the CPA system. In practice, a perfectly rnatched expander-compressor system, where the total phase shift introduced equals to zero to ail orders, is very difficult to obtain [101]. Even if this is done, there are still phase shifts produced by the optical materials in the rest of the CPA system. The latter cannot be completely compensated by a simple change in the compressor length, because the phase function of the material does not match that of the compressor. Consequentiy, some high-order (cubic and/or quartic) phase errors cm be lefi over in the compressed pulse, producing a weak shoulder [ 1021. The single-shot autocorrelation of a fully amplified and recompressed pulse was also measured with suitable attenuation of the pulse going into the autocorrelator. The measurement gave a very similar result to that shown in Figure 3.8(b). In some experiments, the duration of the compressed pulse must be continuously adjustable. This cm be done by changing the length of the compressor by translating one of its gratings. Using the single-shot autocorrelator, the duration of the compressed pulse was measured at different grating positions (Figure 3.9). The linear part of this measurement agrees very well with the pulse width obtained from Our ray-tracing calculation for a spectral bandwidth of 1.2 nm. The departure from linear at - 5 ps shows the upper lirnit of this measurement, above which the spatial inhomogeneity 02 the incident pulse to the autocorrelator starts to affect the tempord measurement. Chapter 3 Developrnent of the Toronto FCM-CPA Laser System 65

grating position x (inch)

Figure 3.9. Compressed pulse width (At) measured at different positions (x) of the translatable grating in the cornpressor. The solid lines are linear fits to data with At c 5 ps. The departure from linear dependence, indicated by the dashed line, shows the upper limit of the measurement, above which the spatial inhomogeneity of the incident pulse starts to affect the temporal measurement.

3.4 A Novel Cross-correlation Technique

In rnany applications of picosecond light pulses, knowledge of the pulse shape is of great interest. The commonly used intensity autocorrelation techniques are effective in measuring the temporal width of optical pulses of picosecond to subpicosecond duration. However, the intensity autocorrelation function

d2)(7) = r-- I(t)Z(r - r)dt (3-2) carries ody partial information about the temporal profile of the pulse, and therefore cannot be used to determine the acnial pulse shape I(t). Higher order correlation Chapter 3 Developrnent of the Toronto FCM-CPA Luser System 66 methods have been developed, which can give more detailed information on the pulse shape. An even better approach is the cross-correlation (or optical sampling) technique, in which the intensity profie of the pulse to be studied is temporally mapped by a much shorter sarnpling pulse. In 8 3.3.3, we have shown an example of this technique, where the clean 1.2-ps oscillator puise was used to sample the chirped 400-ps pulse (Figure 3.7(a)). Limited by the 1-ps temporal resolution, however, that method cannot be used to anaiyze picosecond or subpicosecond pulse shape. In this section we wili describe an improved crosstorrelation technique in which 100-fs temporal resolution has been achieved.

3.4.1 Design of the Novel Cross-correlator The experimental arrangement is iliustrated in Figure 3.10. The 1054-nm,1.2-ps pulse from the FCM oscillator fist passes through a frequency doubler (KD*P crystal, type 1) where about 10% of its energy is converted into the second harmonic (527 nm). The 1054-nm and 527-nm beams are then separated by a hannonic beamsplitter. The 527-nm pulse is first coupled into a 67-cm long, 1.5-pm core diameter single-mode polarization-preserving optical fiber where it experiences self-phase modulation (SPM) and group-velocity dispersion (GVD), augrnenting its bandwidth and stretching its pulse width. The output pulse is then compressed by a double-pass grating compressor, yielding a - 100-fs, 527-nm probe pulse for crosscorrelation in a tripler crystal. The compressed 527-nm probe pulse and the orthogonally polarized 1054-nm pulse are then recombined by another hamonic beawplitter, and sent to a frequency- mixing non-linear crystal (KD*P, type II). The sum-frequency signal at 351 nm is isolated from the fundamental and the second harmonic by a pair of UV bandpass fdters (Schott UG1 and UG11) and detected by a photomultiplier. By varying the relative delay between the two pulses, a background-free cross-correlation can be recorded with a temporal resolution detemiined by the pulse width of the green probe pulse (- 100 fs). Chapter 3 Development of the Toronto FCM-CPA Laser Syste?n 67

nu-r doubler single mode fiber

Figure 3.10. Setup of the fiber-compressed subpicosecond cross-correlator. HBS, harmonic beamsplitter; G1, G2, diffraction gratings.

This experirnental configuration can also be seen as an improved version of the standard third-order autocorrelation technique [103] in which the SHG signal is directly mixed with the fundamental.

3.4.2 Experimental Results The spechum of the frequency-chirped green pulse at the output of the fiber was measured, exhibiting the characteristic structure of SPM and a bandwidth of about 3.0 nm

(Fm). High-dynarnic-range autocorrelation of the recompressed 527-nm pulse was done by non-collinear frequency doubling in a KDP crystal and measuring the 264-nrn SHG signal. By varying the grating separation in the cornpressor, an optimized autocorrelation width of 168 fs (F"wKM) was obtained for the recompressed green pulse. This corresponds to a pulse width of 84 fs if a Lorentzian pulse shape is assumed (Figure 3.1 l(a)). Chapter 3 Development of the Toronto FCM-CPA Laer System 68

time delay (ps)

-4 -2 O 2 4 6 time delay (ps)

Figure 3.11. (a) Autocorrelation of the fiber-sîretched and grating-compressed 527-nm probe pulse. Puise width At = Ar/2 = 84 fs, assuming a Lorentzian pulse shape. (b) Cross-correlation of the compressed 527-nm pulse with an IR pulse from the FCM oscillator. Negative time delay corresponds to the leading edge of the pulse. Chapter 3 Development of the Toronto FCM-CPA Laser System 69

Detailed pulse-shape analysis of Our FCM oscillator is one interest for this scheme. The 84-fs probe pulse was sent collinearly with the 1-ps pulse from the FCM oscillator to a KDP crystal where the cross-correlation was measured. Figure 3.1 1(b) shows the measured actual pulse shape of the oscillator pulse together with a Gaussian fit. The leading edge of the pulse, shown with negative time delays in the figure, appears to be more steep than that of the falling edge. This weakly asyrnmetric pulse shape is. in fact, expected as a consequence of the passive mode locking employed in the oscillator. Since the recovery time of the saturable absorber (4.2 ps in this case) is shorter than the round-trip time of the cavity but much longer than the pulse duration, for each round trip the leading edge of the pulse interacts with a recovered dye, while the falling edge interacts with a dye which is partidy bleached. As a result, more light is absorbed from the front of the pulse, leading to a pulse shape with sharper front edge than the trailing edge (1041.

3.5 Conclusions

In this chapter, an dl-Nd:glass CPA terawatt laser system built at the University of Toronto has been described. Using very high-contrast, high-energy 1-2-ps pulses from the FCM oscillator as seed pulses, and employing a gratings-only temporal stretching and cornpressing scheme, we have obtained an output pulse of 1 J, 1.2 ps with a prepulse contrast greater than 5 x 107 without the help of additional pulse cleaning techniques.

Focusing this TW pulse in the vacuum chamber, an intensity greater than 1017 W/cm2 can be achieved. Alternatively, the system can also be configused to generate 410-ps uncompressed pulses of up to 5-J energy. Finally a novel cross-correlation technique is descnbed, which can provide 100-fs resolution and map asymmetrical pulse shapes from subpicosecond flashlarnp-pumped lasers. Chapter 4 Experimental Results of Second Harmonic Generation

This chapter describes the experimental work of second harmonic generation from laser-solid target interaction. This work was done at the University Toronto using the FCM-CPA laser system. As pointed out in 5 2.3, laser pulse contrast is of crucial importance in the interaction of intense ultrashort laser pulses with solid surfaces. Preplasma produced by smail prepulses alters the interaction pichue and cm significantly degrade the quality of harmonic emission. The focus of the work descnbed in this chapter is to investigate this hypothesis systematically and to study the effect of preplasma on harmonic conversion efficiency, angular distribution, as well as spatial and spectral characteristics. At the end of the chapter, experimental attempts on observing hannonic higher than the second order using the FCM-CPA laser are also discussed.

The experimental layout is shown schematically in Figure 4.1. The 1.2-ps, 1 .OS nm laser pulses from the FCM-CPA system were delivered to the evacuated target chamber, and were focused by a f73.5, 16-cm focal-length multi-element lem onto the target at an incident angle of 35' to the target normal. This angle was chosen because it allowed the spectrometer to be conveniently positioned at the specula. reflection angle of the incident laser. Chapter 4 Eiperimenral Resulrs of Second Hamonic Generation

vacuum chamber

incident laser beam A

7filter set spectrograph /spectrometer

Figure 4.1. Schematic diagram of experimental setup for the harmonic measurement.

In the middle of the target charnber was the target positioning system built by three Linear translation stages and one rotational stage, ail driven by Encoder Mike motors

(Oriel). It held up to seven Bat targets each tune, and aliowed each target to be moved in the three orthogonal directions with a precision of 10 p. The positioning system was remotely controlied by a cornputer, and a LabVIEW program was written to automate the target positioning procedures. After each laser shot, the target was translated within its plane by a certain amount so that a fresh surface would be available for the next shot. Polished silicon wafers were used as the primary target for this study, because of their high-quality surface f~sh.During the experirnent, the target chamber was pumped down to a pressure of 2 x 10d Torr by an oil diffusion pump with liquid nitrogen cold trap. The specularly reflected Iight from the target was collected by a lens and was sent to the spectrometer (Jarrell-Ash) where the harmonic spectrum was analyzed. A group of optical band-pass filters (Schott glass) were used to prevent the strong fundamental light Chapter 4 Ehperimental Resu2t.s of Second Hannonic Generation 72

from entering the spectromeer and interferhg the measurement of the relatively weak 20 signal. At the output of the spectrometer, either a CCD camera (Hitachi) or a photomultiplier (PMT) (Hamamatsu R212UH) could be attached as the detector. The CCD camera was used for the second harmonic measurement; in this case, the monochromating output slit was removed so that a one-shot spectrum could be recorded. We also tried to measure the third or higher harmonies using the same experimental setup. In these experiments, the PMT was used because of its much higher detection efficiency and wider spectral response. The lack of spatial resolution for the PMT, however, meant that these experiments had to be done on a multi-shot basis. The wavelength readout of the spectrometer was calibrated to an accuracy of - 1 A using the atomic lines fkom a Hg lamp. To measure the laser energy on target, the light leakage through the fmt mirror of the penscope (used to lift the laser beam to the height of the target charnber) was detected with a large area photodiode (UDT), which had been calibrated using a pyroelectnc energy meter (Molectron).

4.2 Laser Pulse Cleaning with Saturable Absorber

As discussed in Chapter 3, one of the important features of the Toronto FCM- CPA laser system is the high pulse-contrast it produces: its intrinsic pulse-to-pedestal contrast is better than 5 x 107, as shown by the high-dynamic range cross-correlation measurernent. However, when using a fast oscilloscope to examine this intrinsic- configuration pulse in a larger tirne range, we observed a prepulse at 1Wenergy level and 1.5-ns ahead of the main peak. The prepulse, which we believe resulted from Pockels-cell leakage in the system, appeared to be as short as the main peak, although no detailed measurement was made because of the limited temporal resolution of the osciIloscope. Chapter 4 Ejrperimental Results of Second Harrnonic Generation 73

In order to clean up the inainsic pulses, a saturable-absorber dye ce11 [87] was used. The dye cell was 2-cm thick, and contained the same saturable absorber as that used in the FCM oscillator (5 3.2.1), i-e., Kodak Q-switch II (dye 9860) with 1,2- dichioroethane as the solvent. The relaxation tirne of this dye is 4.2 ps, which is much shorter than the tirne delay between the prepulse and the main peak. Uniike in the oscillator, where the dye ce11 has a single-pass small-signal-transmission of about 80%, the dye concentration here is much higher. the low-intensity transmission is < 10-5. The dye ce11 was placed directly in the fmal output line of the system, without using any focusing lens in front of it. It provided an attenuation of about 10-5 for the low-intensity pulses, while allowing a 30% transmission for the high-intensity main peak, increasing the intrinsic pulse contrast by a factor of at least 104. Mer a certain number of laser shots, the dye usually deteriorates and becomes more transparent for the Iow- intensity Iight. So a routine check on the dye-ce11 transmission was performed before each experiment, and new dye would be added if the transmission was too high.. To extend the lifetime of the saturable absorber, the dye ce11 was normally kept in a dark room and was used only when high-contrast pulse was required. With the dye cell in the beam line, the final pulse contrast was estimated to be greater than 10lO.

4.3 Second Harmonic Generation (SHG) and the Effect of Prepulse

With the dye-cell in and out of the beam he, two different laser conditions could be created: the dye-cell-cleaned pulse with a contrast greater than 10Io and the intrinsic configuration pulse which contains a fixed-fraction (104) prepulse at 1.5 ns ahead of the main peak. By comparing the harmonies generated under these two laser conditions, we did a series of experiments to study the effect of preplasma on harmonic generation. To be bnef, these two laser conditions are referred in the following as the 'clean pulse' and the 'intrinsic pulse', respectively. Chupter 4 Experimental Results of Seconà Hannonic Generation

43.1 Power Scaling of SHG

We fitmeasured the 20 yields generated with the clean pulse and the intrinsic pulse at different laser intensities. Since the CCD-carnera had a dynamic range of - 102, calibrated neutrai density fdten (Schott glas) were used in fiont of the spectrometer when the signal was too strong. The laser intensity was controlled maidy by varying the amplification of the regenerative amplifier. For the low-energy shots the PA2 amplifier was turned off. Figure 4.2 shows the dependence of the spectraily integrated 20 energies measured with the clean pulse (faed circle) and with the intrinsic pulse (open circle) on laser intensity.

When the clean pulse was used, the 20 yield, which was collected dong the specular direction, was found to increase with the fundamental laser intensity 1, following a power dependence of b2e4. This observed power dependence is slightly faster than the conventional square-law observed for SHG in other nonlinear media at lower laser intensities. This, however, is not surprising if one considers that in this experiment both the plasma and the SHG from the plasma were generated by the very same Iaser pulse. This result is also consistent with the observation made in an earlier expenment by von der Linde's group [los] in which a power of 2.6 was reported. As the target was irradiated by the intrinsic pulse, we found that the harmonic yield was identical to that generated by the clean pulse when the laser intensity was below 1 x 1015 W/cmZ. As the laser intensity increased above 1 x 1015 Wfcm*, the collected 20 energy with the intrinsic pulses fxst began to show a saturation and then started to pick up the same power dependence (dashed line) as that of the clean-pulse harmonic (soiid line) when the laser intensity was higher than 1 x 1016 W/cm2. Chapter 4 Experimental Results of Second Harmonie Generation

fit: E = 1 2-4 20 O

laser intensity (w/cm2)

Figure 4.2. Measured SH yield per steradian with clean pulses (solid circles) and intrinsic pulses (open circles), scaled with laser intensity. The solid Iine is a power fit for the clean-pulse harmonic. The dashed line illustrates that, after a period of 'saturation', the intrïnsic-pulse harmonic eventually picks up the same power dependence as that of the dean-pulse harmonic. Chapter 4 Ejcperirnental Results of Second Hannonic Generation 76

Since the intrinsic puise contained a fixed-fraction (IV) prepulse, as we increased the laser intensity the intensity of the prepulse was also increased. So the result shown in Figure 4.2 (open circle) can be also seen as the 20 yield measured with increasing level of prepulse intensities. At the laser intensity of 1015 W/cm2, where SHG started to saturate, the corresponding prepulse intensity was - 10" W/cm2, which was about the intensity threshold for plasma production. Therefore we can conclude that the observed initial saturation of SHG with intnnsic pulses was actually a result of beginning to make preplasma by the smail prepulses. It should be emphasized that the 20energies plotted in Figure 4.2 are only those energies collected by the spectrometer, which was positioned at the specular reflection angle of the incident laser and intercepted a total solid angle of i&= 3.1 x 102 sr. If the harmonics actually spread out in a solid angle greater than Ro,then the 20 yields we measured above would represent only partial yields. The angular distribution of SH emission has to be known in order for us to compare the total harmonic yields generated by the clean pulse and by the intrinsic pulse.

4.3.2 Angular Distribution of SHG When a laser pulse interacts with a flat cntical density surface of plasma, the hannonics generated are expected to have a narrow angular distribution dong the specular direction. If prepulses are present, however, the laser pulse will interact with a

observation

target Figure 43. Schematic diagram of measuring the non-specular harmonics. Chapter 4 Ejcperimental Results of Second Hannonic Generation 77 expanding non-fiat preplasma, and the consequently generated harmonics might emit in a larger solid angle. In measuring the harmonic angular distribution, we used the same experimental arrangement described in 4.1 to observe hannonics in the non-specular direction (see Figure 4.3). Ideally, this should be done by changing the observation angle eobswhile keeping the incident angle ei constant. But this was impracticable as the direction of the incident laser beam and that of the observation were fxed in our target chamber. So instead of rotating both the target and the incident Iaser direction (in order to keep Oi constant), ody the target was rotated in this experiment. This simple method ailowed us to measure the non-specular harmonics at different observation angles Bab, = 2(ei - 357, without making major modifications in the experimental setup; it had a tradeoff, though, in such that the effect of laser incident angle on harmonic generation was also integrated in our measured results.

\ 1O-' : \: - \ - - - - 20 profile ------laser profile (1O* FWHM) IO"? - - specular - -

8 (degrees) obs

Figure 4.4. Angu1a.r distribution of SH generated with clean pulses (solid-line). The dashed-line represents a laser profile with an angular width of 10' ïWHbi. Chapter 4 Experirnental Results of Second Hamonic Generation

8 (degrees) obs

8 (degrees) O bs

Figure 4.5. (a) Angular distribution of SH generated with intrinsic pulses at various laser intensities. (b) Cornparison of SH angular distributions measured with clean pulses (solid-line) and with intrinsic pulses (dashed-line) at the same laser intensity. Chapter 4 Fxperimental Results of Second Harmonic Generaîion 79

We fmt measured the angular distribution of SH produced by the clean pulses.

Using four targets mounted with different incident angles, Le., Oi = 33.4', 35.1 O, 36.7', and 37.2', SH emission was measured at observation angles from -3.5' to 8' relative to the center of the reflected laser beam (the specular direction). The result is shown in Figure 4.4. For comparison, the profile of the reflected laser beam-a cone with a. angular width of 10' I3vI-i~-is also plotted. We can see that, for a laser intensity of 1.8 x 1016 W/crn2, the SH emission was centered at the specular direction, with a cone angle smaller than that of the incident laser. Considering that the change of the incident angle was small, Le., a total of 3.8', we could assume that its effect on SHG efficiency was negligible in this measurement. Therefore the result shown here represents the actual angular distribÿtion of the SH generated with the clean pulses. Using a similar method, the angular distribution of SH generated by the intrinsic puises was also studied. Figure 4.5(a) shows the angular distributions of the intrinsic- pulse-produced SH measured at various laser intensities. We found that as the laser intensity (and concurrently the prepulse intensity) increased, notonly did the inz::y;'y collected SH energy increase, but the 2w by intrinsic harmonic emission also spread out into an pulse increasing solid angle.

A direct comparison of the angular distributions of SH emission using clean and intrinsic pulses is presented in Figure 4.5(b). 20 by At a laser intensity of 1.5 x 10'6 W/cm2, a clean pulse very sharp specular distribution was observed for the clean-pulse harmonic Figure 4.6. Illustration of SH cone- (solid-line), while a muc h broader angular emissions generated by a clean pulse and distribution was recorded for the htrinsic- by a intrinsic pulse. Chapfer4 EXperimental Results of Second Hannonic Generation 80 pulse harmonic (dashed-line). The corresponding SHG cone-angles (m)were found to be al = 6' for the clean pulse and a2 = 60' for the intrinsic pulse, respectively (see Figure 4.6). Assuming the two harmonic cone-emissions had cylindrical symmetry, the ratio of their corresponding solid angles can be calculated as:

Integrating the harmonic energies within the respective cone envelopes of each, it is significantly found that the overd total yields are almost identical. This indicates that the apparent saturation of the collected harmonic yield using intrinsic pulse in Figure 4.2 is alrnost entirely due to the spread of harmonic production into larger solid angles, under the effect of preplasma.

4.3.3 Imaging of the SHG Emission The spatial and spectral structures of the harmonic source also provide useful information for the hmonic generation process. In an ideal situation, one would expect a hannonic to have a sirnilar intensity distribution to that of the fundamental, both in space and in frequency. Any deviation from the ideal situation can be used as a diagnostic for the conditions of the laser-plasma interaction. From the application point of view, the intensity distributions of a hannonic in space and in frequency also characterize the quality of the harmonic source-a small smooth source with narrow spectral distribution means the radiation it generates will have good spatial and temporal coherence and high spectral brightness. A modified experimental setup, as shown in Figure 4.7, was used to image the SHG source with both spatial and spectral resolution. A pair of achrornats (Meiles Griot, f = 200 mm, 6 = 40 mm) used in an unitconjugate-ratio configuration [106]replaced the Chapter 4 Experimental Results of Second Hamonic Generntion

vacuum chamber

incident / laser beam , target

filter set Q CCD camera 2 H +I +I filter set

spectrogimagingrap h I

Figure 4.7. Modified expeiimental setup with imaging system. harmonic collecting lens in the previous setup (Figure 44, and relayed a nearly aberration-free real image of the harmonic source to a point outside the target chamber. This image was subsequently re-imaged and magnified by 23 times through a 10 x microscope objective, split, and recorded by two CCD cameras: Camera 2 was used to measure the spatial distribution of the harmonic source, whereas Camera 1 recorded a two-dimensional image of the SH source with both spatial and spectral resolution through an imaging spectrograph. Figure 4.8(a) shows a clean-pulse-generated 20 emission image superimposed on image of a damage crater. Horizontal and vertical lineouts taken through the center of the 2w source are plotted in Figures 4.8(b) and 4.8(c), respectively. The results show that the harmonic source has a smooth spatial distribution and is contained in an area of 7.4 px

7.9 pm at FWHM. Chapter 4 Evpeninental Results of Second Hannonic Generation 82

Figure4.8. (a) 20 emission image superimposed on image of darnage Crater. (b) Horizontal and (c) vertical lineouts through the image of the 2w source.

Spatially-resolved SH spectra measured with clean and with intrinsic pulses are shown in Figures 4.9(a) and 4.9(b), respectively. In each, the figure at left shows a spectrum (resolved horizontally) for a vertical slit-image of the plasma, taken at the center of the laser focus. The figure at right shows the lineout spectrum of SH generated around the center of focus. The clean-pulse-generated SH spectrum shows an instrument- ümited spectral iine that is red-shifted by about 10 A from k0/2 (5265A). This red-shift of the 20 spectmm has ken reported in a previous experùnent, and a detailed discussion about its origin has been presented [107]. Here we will concentrate on the differences in the 20 spectra generated by the clean pulse and by the intrinsic pulse. Cornparhg Figures 4.9(a) and 4.9@), we can see that the presence of preplasrna radically changes both the spatial and the spectral charactenstics of the harmonic generated. The intrinsic-pulse-generated harmonic source showed a structure consisting many 'hot spots' in both space and frequency dimensions. Chapter 4 Experimental Results of Second Harmonic Generation

(a)clean pulse, I = 2.0~1016W/cm2.

50 A spectrum I I

(b) intrinsic pulse, I = 4.5~1O1

spectrum I I

Figure 4.9. Spatially resolved 20 spectmm measured with (a) clean pulse, (b) intrinsic pulse. The figure at Iefi is a spectrum (resolved horizontally) for a vertical slit-image of the plasma taken at the center of the laser focus, and the figure at right is a spectral iineout cut across narrow spatial region. The spectra intensities were norrnalized for best cornparison. Chapter 4 Expen'mental Results of Second Harmonie Generation 84

For the spectral broadening and breakup of the harmonic source, we believe they are due to self-phase modulation experienced by the laser pulse when traveling through the extended underdense part of the plasma [108]. As for the spatial hot spots, one possible explanation is that they too are the result of beam breakup and filamentation as the laser propagates through the underdense region before interacting with the critical density surface of the plasma [log, 1101. This, though, is not necessarily the only explanation. For example, they may also be caused by interference in light refiecting from a non-homogeneous plasma formed by the prepulses, just as in the case of a mirage or when light passes through a rippled glass. This interference interpretation, however, may have the following limitation. If weU focused, the harmonic image we recorded is a near-field image, which should exhibit less intensity modulation than from an equivaient far-field image. This same issue is the reason why &am-relay optics are used to improve spatial uniformity in intense laser amplification, since the beam has zero effective path- length to diffkact. The argument is not definitive, but seems to favour filamentation in the plasma preformed nanoseconds in advance as the cause of the distortions recorded. Similar resdts on the spatial and the spectral breakup of the harmonies were also reported in the VULCAN experiments 128, 291. Our experimental results clearly demonstrated that this breakup was directly associated with the underdense plasma created by the small prepulse, rather than caused during the generation of the hamionics at the cntical density surface of the plasma.

4.4 SHG with Controlied Prepulses

To further study the effect of preplasma on SHG, we performed a pump/probe- like experiment in which a weak prepulse was added deliberately at a controllable time relative to the high-contrast main pulse. Since the preplasma will expand into the vacuum once it is created, depending on the time-delay after the prepulse, the following Chapter 4 Experimental Resulfs of Second Hannonic Generation 85 main pulse wiU interact with a plasma of varying scale-length. In this way, the relation between SHG efficiency and the scale-length of the source plasma cm be studied.

4.4.1 Prepulse Setup The setup used to generate a controllable prepulse is shown in Figure 4.10. At the output of the Toronto FCM-CPA system, the dye-cell-cleaned high-contrast I-ps pulse was amplitude-split by an adjustable half-waveplate and a thin-film polarizer, then sent to two delay annç where the am-length for the prepulse could be continuously adjusted. The two beams, separated by 3.8 cm (center-to-center) sideways, were then made to propagate in parallel to the target chamber. Before entering the target chamber, the polarkation of the two pulses was rotated 90' by the periscope so that the main pulse and the prepulse were p- and s-polarized, respectively, relative to the target. The energy ratio of the two pulses was controiled by rotation of the half-piate.

I compressed 1-ps pulse

adjustable U2 plate

Figure 4-10. Expenmental setup for generating controllable prepulse. The SH detection scheme inside the target chamber is shown in the inset. Chapter 4 Fxperïrnentul Results of Second Hannonic Generation 86

Inside the target chamber, a scheme like that in Ref. [IO71 was used. The two pdelbeams were focused by the same focusing lens onto the same surface area of the targets at different angles of incidence (see the inset in Figure 4.10). SH signal generated by the main pulse was colIected dong its specular direction, while the refîected prepulse beam was stopped by a beam-dump. The reiative timing between the two pulses was measured to an accuracy of +3 ps using a x-ray streak camera mounted on the target chamber. The spatial overlap of the two pulses at the focus was checked before each experiment using the SH imaging system (Camera 2 in Figure 4.7).

4.4.2 Experimental Results In this experiment, the main pulse/prepulse energy ratio was set to 10: 1, and the main pulse intensity was kept at 1.8 x 10'6 W/cm2. Control shots taken by blocking the main pulse confirmed that no 20 signal generated by the prepulse was collected by our detection scheme. This ensured that the measured harmonic yield was generated only by the interaction between the main pulse and the plasma. The 20 yield was measured at various prepuise delays. Because of the shot-to-shot fluctuation of the incident laser energies, approximately five shots were made for each time delay. The averaged 20 yield as a fùnction of prepulse delay is plotted in Figure 4.11. The overall features of the result can be described in the following: (1) When the prepulse was behind the main pulse (t < O), the 20 yield was independent of the time- delay between the two pulses, and stayed at the level as if no prepulse was present;

(2) When the two pulses were temporally overlapped (t = O), a near three-fold enhancernent of the 20 yield was observed; (3) When the prepulse came ahead of the main pulse (t > O), the 20 yield decreased monotonically as the tirne-delay between the two pulses was increased. Chapter 4 Erperirnental Results of Second Humonic Generation 87

time delay (ps)

Figure 4.11. Averaged 20 yield measured at different prepulse delays. Error bars represent the standard errors of the average. The soiid line is a guide for view only.

The responses of SHG in regions (1) and (3) are easy to explain. Obviously, no effect will be made by the prepulse when it lags the main pulse, as the main pulse will interact directly with the solid surface. On the other hand, when the prepulse leads the main pulse in tirne, preplasma will be made, and the main pulse will interact with an expanding plasma whose scale-length increases with the delay of the main pulse. Since longer scaie-length means less laser light will tunnel through the plasma and reaches the critical surface, we expect to see a trend of a decreasing 20 yieid with the increasing of plasma scale-length.

The observation of the 2w yield enhancement near t =O demonstrated that hannonic generation could indeed be enhanced by a weak prepulse, presumabiy through the resonant eKect discussed in 1 2.2.2. We noticed that the sarne phenomenon had also been observed in an early experiment performed by von der Linde et al. [107], in which a Chapter 4 Experimental Results of Second Harmonie Grneration 88 sharp peak of the 20 yield, comparable in duration with the laser puise width (65 fs), was recorded at t,, = 170 fs after the prepulse. They atvibuted the observed 20 peak to the expansion of the plasma to a state of maximum resonance enhancement of the fundamental opticd fields, which, according to their numerical calculation, was expected to occur for scale-lengths of 0.05Â < L < 0. la. Based on this interpretation, a plasma expansion velocity of oq = L/t- = 2 x 107 cmls was suggested by the author. On the other hand, if one knows the actual plasma expansion velocity, the optimum plasma scde-length can be inferred from the time delay t,, of the observed 20 peak. Unfortunately, this cannot be done for our measured resdt because of the large experimental error (B ps) in determinhg 'time zero' in Figure 4.1 1. Besides, considering the laser intensity used in this experiment was 10-times higher than that in Ref. [107], the ponderornotive modifications of the plasma profde [22, 11 11 might dso need to be taken into account in order to interpret the observed 20enhancement.

4.5 Experiments Beyond SHG

Experiments searching for harmonies above the second order were dso carried out on the Toronto FCM-CPA laser system. Third-harmonic generation fiom solid targets was studied using the experlmentd setup shown in Figure 4.1. Since Our silicon CCD camera was not sensitive at the wavelength of 30 (35 10 A), a photomuItipIier tube, together with a monochromating output dit, was used as the detector. To reduce the signal background caused by scattering of the relatively strong fundamental and second harmonic light, Schott glas fdters (UG1, UG5 and KG3) were used at the entrance of the spectrometer- A 30 spectrum measured with the dye-cell cteaned pulses at a laser intensity of 2.3 x 1016 Wkm2 is show in Figure 4.12, in which each data point represents an average of four measurements. Despite the relatively Iow signal-to-noise ratio, a peak structure at Chupter 4 Experimental Results of Second Hamonic Genemtioa

2.0, I 1 I t 1 I 1 I I I I I 1. 30 - piiii-1 I = 2.3 x 1016 w/cm2

n u, 1.5 - J, C, 9-I= 3 - 42 w 1.0-

,-a typical cn - c e rro r- bar a> -c.r 0.5 - -

Wavelength (A)

Figure 4.12. Third harmonic from a silicon target measured with clean pulses. Each data point represents an average of four measurements with the standard error shown as the error-bar. the wavelength of 30 can still be clearly identified in the spectrum. To compare the relative intensities of the 30 and 20 signals, a spectrurn of 2w emission was also measured using the same experimental scheme. After correcting for factors of filter transmission and the spectral response of the PMT, a ratio of - lewas found between the intensity of 3c~and that of 2w at our experimental conditions.

In the experiments searching for higher ( n > 3) order harmonies, a 20-cm VUV- spectrometer (Minuteman) equipped with a Micro-Channel-Plate (MCP) detector (Galiieo) was used. The use of the MCP detector, which combined the advantages of the high sensitivity of a PMT and the imaging capability of a CCD,enabled us to measure the hannonic spectra in the VUV region with great sensitivity on a single laser shot. To allow for detection of VUV light, the glass harmonie-coilecting lens and fdters shown in Figure 4.1 were removed. This detection scherne was sensitive in the spectral region Chapter 4 FJcpenhental Results of Second Hannonic Generation 90 from 600 A to 1800 A, which covered the 6th to 17th harmonies of the 1.053-nm fundamental lighî. Using the dye-ce11 cleaned pulses, experiments were done on several solid targets. In addition to silicon and aluminum, solid plastic and carbon (graphite) targets were also used because of their low recombination background and simple Iine structure. With laser intensities as high as 5 x 1016 W/cm2, we observed strong plasma line-emissions fiom all these targets. but could not identiQ any harmonic signal in the entire spectral region fiom 600 A to 1800 A. Based on the results of these experiments, we concluded that, under the experimental configuration we used and with laser intensities up to

5 x 1016 W/cd, the detection of the higher harmonic (n > 3) emission was limited by the plasma recombination background. There are two obvious solutions to this problem: (1) further increasing the Iaser intensity, because it is believed that harmonic emissions grow faster with laser intensity than the recombination background does; (2) using tirne- resolved spectroscopy to distinguish the fast harmonic emission from the relatively slow plasma recornbination background [23, 1121. Following the f~stsolution, we performed another series of experiments at laser intensities up to 1 x 1018 Wkm? Results of this series of experiments are discussed in the next chapter.

4.6 Conclusions

Using the FCM-CPA laser system at the University of Toronto, second harmonic generation from laser-plasma interaction was studied. Through experiments using very high contrast pulses and pulses with fixed-fraction prepulses, we systematically investigated the impact of preformed plasma on harmonic generation and characterized its effect in the spatial and spectral breakup of the harrnonics and in spreading harmonic emission into large soIid angles. By adding a deliberate and controlled prepulse, we also measured the second harmonic yield in a pump/probe-like experiment in which the Chaprer 4 Experimental Resulrs of Second Hamonic Generation 91 relation between the SHG efficiency and the scale-length of source plasma was studied. Experiments to search for harmonics above the second order were also canied out. At a laser intensity of 3 x 1016W/cm2, third-hamionic signal fkom an silicon target was recorded just above our detection bit. Detection of higher order harmonic was found to be limited by the plasma recombination background. which implied that even higher laser intensities (> 5 x 10'6 W/cm2) were necessary for the observation of higher (n > 3) harmonics. Chapter 5 Experimental Results of Mid-Order Harmonic Generation

To extend our effort of searching for higher order (n > 3) harmonies from laser- solid target interaction, a series of experiments were conducted on the T3 (Table-Top- Terawatt) laser system at Center for Ultrafast Optical Science at the University of Michigan. The experimental details and results are described in this chapter.

5.1 The ï? Laser System

Unlike our Toronto dl-glas CPA system descnbed in Chapter 3, the T3 CPA system is a hybnd one that inciudes a Ti:Sapphire osciliator (Coherent Mira-900) and regenerative amplifier, followed by three single-pass Nd:glass power amplifiers. The pulse expansion and compression scheme is similar to the Toronto system-no fiber is needed because of the broad bdwidth of TkSapphire. The laser system operates at a center wavelength of 1.053 p,and, for these experiments, produces 400-fs pulses with an energy of up to 3 Joules, yielding a maximum power of 7.5 W.

The intrinsic contrast of the IR pulse from the T3 system is around 5 x 105. In order to achieve higher contrast to avoid the production of preplasrna, the IR pulse was converted to its second harmonic (h= 526 nm) using a 4-mm thick type4 potassium dihydrogen phosphate (KD'P) crystal [113]. The nonlinear frequency-doubiing process, with its yield being proportional to intensity squared at low laser intensities, significantly Chapter 5 Experhental Results of Mid-Order Hamonic Genemtion 93 eliminated the wings and pedestals in the converted green pulses, leading to much higher pulse contrast. Figure 5.1 shows the optics setup used for the harmonic experiment. The 1053- nm pulses from the T3 laser were &st frequency doubled by passing through the KD'P crystal. In order to filter out the IR component in the 526-nm laser beam, four dielectric- coated green &ors (Ml to M4) were used in series after the doubling crystal. Each of these morshad a reflectivity of > 95% for the 526-nm pulse and about 3% for the IR fundamentai. This provided an attenuation of about (0.03)4 = 8 x le7for the relatively low contrast IR light. A 2-mm thick green band-pass filter (Schott glas BG39) was used before the parabolic &or to provide merdiscrimination against the IFt residual in the green laser beam. With these mesures, the contrast for the green pulse was estimated to be better than 1011, which was large enough to avoid the production of preformed plasmas for al1 intensities up to 1019 Wfcm? Confirmation that the T3 system produces negligible prepulses was provided by a previous study of solid-density laser-produced plasmas using x-ray spectroscopy [114]. The frequency-doubling of the 400-fs fundamental pulse should yield a Gaussian-shaped green pulse with a FWHM of 400/& = 280 fs. Because the frequency conversion was saturated, however, the actual w of the green pulse was around 350 fs. To monitor the energy of the 526-nm pulse on target, the 3% transmission of the green pulse through mirror Ml was picked up, fitered by other two green mirrors (M5 and M6) and a BG39 filter, and rneasured by a photodiode. To calibrate the photodiode, a green mirror was temporally installed iaside the vacuum chamber (between the BG39 filter and the parabolic rnirror), which redirected the green pulse onto a calorimeter located outside the vacuum chamber. The reading of the photodiode was then calibrated against the calorirneter which measured the actual laser energy on target. The conversion efficiency into a green pulse was found to be around 50% at moderate laser energies

(- 800 mJ of IR) and could reach as high as 70% at higher laser power (2 Joule of IR). Chapter 5 Eipeninental Results of Mid-Order Hannonic Generation 94

CCD A

Rowland Circle

\ l 1 1 beam di for IR pi

parabola zooming axis for focal scan IR pulse from the T3 laser

Figure 5.1. Experimental setup for mid-order harmonic generation from solid targets using the T3 laser system. PM is the parabolic mirmr; Ml to M6 are the green mirrors discussed in the text. Chapter 5 Expehental Results of Mid-Order Hamonic Generation 95

The frequency-doubled green pulse was originally s-polax-ized relative to Our target setup. However, for most parts of the harmonic experiment, a p-polarized Laser pulse was required. To rotate the laser polarization, a quartz half-wave plate was introduced after Ml. In the case when s-polarization was required, the wave-plate was taken out the beam, For laser pulses of terawatt ievel, the nonlinear ef5ects (Le., self-focusing and self-

phase-modulation) in air and in optical elements in the beam path become non-negligible. These eflects would not ody broaden the laser pulse width, but also cause severe beam distortion and breakup, producing hot spots within the laser beam which can seriously damage the optical components in the laser system [Ils]. A conventionally used critenon for these nonlinear effects is the B integral, which is defmed as

where 31is the optical Kerr coefficient, and I is the iaser intensity in the media. Generally speaking, a value of B S 3 - 5 is required to avoid serious nonlinear damage

and distortion effects in a conventional high-power system; in a CPA system the condition is more stringent-B S 1- 2. In order to reduce the B integral in the T3

system, the cornpressor and the following optical path are aii operated under vacuum. In addition, we found in our expenment that the transmissive media, such as the doubling crystal, quartz wave-plate, and the BG39 glass filter, produced large enough B integrai that significant beam breakup was observed at full laser power. For this reason, the laser energy was limited to below 500 mJ for the green pulse (or 1 J for the IR pulse) in most parts of the experiment.

5.2 Experimental Setup for the Harmonic Measmement

Figure 5.1 also shows a schematic diagram of the expenmental setup for Chapter 5 &verintenta2 Results of Mid-Order Hannonic Generation 96

measuring the harmonic spectra. The apparatus consists of a 75-cm diameter cylindrical target chamber and a 1-m focal length VUV spectrometer.

5.2.1 The Target Chamber Inside the target chamber, a f73.0 off-axis (15') parabolic rnirror of 23-cm focal length was used to focus the 43-mm diameter laser beam ont0 the solid target at an incident angle of 60" to the target normal. Ray-tracing simulation Cl161 showed that the size of the focal spot produced by a parabola was very sensitive to misalignment of the incident bearn. Before the target was moved into place, the focusing properties of the off- axis parabola were investigated using the IO-Hz repn-ampmed and frequency-doubled green beam. The spatial intensity distribution in the focal plane was measured by a 10x microscope objective and a CCD camera. By carefully adjusting the direction of the

incident beam into the parabola, a Gaussian-shaped focal spot of @ = 9 pm (FWHM) was obtained. Taking into account the effect of incident angle Bi (60'). the actual area of the spot on target cmbe caiculated as A = 1r@~/(4cosei) = 127 @ at m. The laser beam was tightly focused and the confocal parameter was estimated to be around 200 p at the focus. When the power amplifiers were fired, it was found that the best focal position determined using the regen beam would shift, presumably due to thermal lensing effect in the power amplifier chah. In order to compensate this focus shift and to optimize the laser intensity at the interaction region, a focal scan was needed before each series of hmonic experiment For this purpose, a x-ray PIN-diode was installed inside the target chamber to monitor the x-ray radiation from the laser-produced plasma. To prevent hot electrons generated in the plasma source from reaching and thereby saturating the diode, a pair of magnets were used in the path between the radiation source and the PIN-diode. By shooting the target, and at the same time scanning the parabolic rnirror dong the focal axis (see Figure 5.1). a focal position correspondhg to maximum x-ray generation could be conveniently located. This method Chapter 5 Experimental Resulfs of Mid-Order Hamonic Generution 97

proved to be very effective in b~gingthe target to a position close to the best focus; harmonic generation could then be easily optimized by scanning the target near this position. The typical focal range in which hannonic could be observed was - 1 mm, which was about 5 times of the confocal parameter of the laser focus. As in the SHG experiment described in Chapter 4, the fiat solid targets were mounted on a remotely controlled 3-axis transIation stage. After each laser shot, the target was translated by a certain amount dong the target plane so that a fresh surface would be avaiIabIe for the next shot. A telescope and a TV camera located outside the vacuum chamber (not shown in Figure 5.1) were employed to monitor the target condition and to guide the motion of the target positioner.

5.2.2 The VUV Spectrometer

The radiation from the plasma source was collected dong the specuiar direction of the incident laser light by a VWspectrometer in which the harmonic spectra were

analyzed. The spectrometer used in this experiment was a l -m Seya-Namioka type VUV spectrometer [117] (McPherson, Mode1 23 1), which was connected directly to the target chamber. The spectrometer was slit-less-its entrance slit was served by the laser focal spot on target (see Figure 5.1). Owing to the Iack of an entrance slit, this spectrometer could collect light from a large solid angle and therefore had good detection efficiency. To obtain the best spectral resolution, the laser focal spot was carefuliy positioned on the Rowland circle of the spectrometer. At the exit image plane of the spectrometer, a microchamel-plate (MCP) intensifier (Galileo) was used to ampli@ and convert the VUV radiation into a visible signal. Outside the vacuum chamber, the visible output of the MCP intensifier was coupled by a commercial SLR-camera lens to a 12-bits CCD camera (Photometncs), and the spectral images were coiiected and analyzed by a personal computer. The VWspectrometer was equipped with a curved (R = 1 m) 1200-lines/rnm Chapter 5 Experimental Results of Mid-Order Hannonic Generation 98 gold-coated grating, which was blazed at 800 A. The first-order spectnim was used for this experiment. In the spectral region of interest (300 A - 2000 A), this grating yields a plate factor, defmed as the reciprocal of the linear dispersion, of F = 7.2 A/mm at the exit image plane of the spectrometer. This results in an effective spectral window of D x F = 300 A for each single-shot measurement, where D = 40 mm is the diameter of the MCP detector. To cover different parts of the harmonic spectmm, this spectral window cm be centered at different wavelengths, A,, by rotating the grating. It should be noted that the plate factor is not a constant, but varies as a slow function of A, [117]:

This rneans that the linear dispersion will change slightly when the grating is rotated to cover a different spectral region. So, in the final data analysis, when to convert the spectral scale from pixels to A, different conversion factors (calculated using Eq. 5.1) were used for the spectra rneasured at different center wavelengths Ac. The overall spectral response of the system (the spectrometer grating and the MCP detector) is sensitive in the spectral region of 300 A to 2000 A, which covers the 3rd to 17th harmonic of the 526-nm input laser. The VUV spectrometer and the target chamber were pumped independently by two turbo-molecular pumps. A horizontally positioned differential-pumping slit (- 1-cm wide and 1-mm high) was used to isolate the spectrometer vacuum from the target chamber vacuum. The target chamber, which was ais0 connected directly to the evacuated beam iine, had a base pressure of about 1 x 10-5 Torr, whiie the pressure inside the spectrometer was maintained below 2 x lwTorr-safe for the operation of the MCP intensifier. Chnpter 5 Ekperimental Results of Mid-Order Harmonic Generation

53 Rdtsof Mid-Order Harmonic Generation

5.3.1 Observation of the Third to Seventh Harmonies When we irradiated flat solid targets with p-polarized high-contrast green laser pulses and increased the laser intensity to above 5 x 1016 W/cm*, we started to observe third and higher order hannonics. The recorded spectra were the-integrated, which

plasma background detector \ i background ,

pixel number Figure 5.2. (a) An example of raw data recorded by the CCD- camera showing the third harmonic generated when solid Ni target was irradiated with the 526-nm laser light. (b) Lineout of the spectnim by averaging over box L indicated in (a). Chapter 5 Qen'mental Results of Mid-Order Hannonie Generution 100 meant we could not distinguish the picosecond harrnonic emission from the nanosecond plasma line emission. As a result, the harmonic spectra were accompanied by a broad plasma background, presurnably due to recombination. Figure 5.2(a) illustrates an example of raw data recorded by the CCD camera, showing the third harmonic spectnim from a nickel target. The narrow 30 feature can be observed sining on top of the broad plasma background (Figure 5.2(b)). The off-spectnim detector-background was due to the thermal noise in the CCD camera, and was removed in the post-experirnent data analysis. Due to the limited spectrai range of the spectrometer, severai shots viewing different parts of the spectnim were needed in order to cover the spectral range between 600 A and 2000 A, and compose a complete harmonic spectra in this range. Figure 5.3 shows a typicai time-integrated harmonic composite-spectrum recorded from a silicon target (polished silicon wafer) irradiated in p-polarization at a laser intensity of 3.2 x 1OI7 W/cm2. Hannonics from 3rd to 7th, of both odd and even orden, can be easily identified sitting on top of the broad plasma recombination background. Besides the silicon target, several other solid targets of various atomic-numbers were also snidied in this experiment. The targets included beryilium, nickel, CH plastic (Parylene-N) coating on glass substrates, and silicon wafers covered with vacuum- evaporated duminum and gold coatings. Spectra measured from al1 these targets exhibited similar features to spectra from the siiicon target, and harmonies from 30 to 60 were observed in each case except for the gold target, fiom which the highest harmonic recorded was 50 (Figure 5.4). In addition, the broad plasma recombination background was found to be more pronounced with high-Z targets, which was expected. Chapter 5 Ekperimental Results of Mid-Order Hannonic Generation

wavelength (A)

Figure 5.3. Typical harmonic spectrum from a Si target at a laser intensity of 3.2 x 1017 W/cm2. The spectrum is composed of four separate laser shots with spectrometer set at different central wavelengths. The spectral lines at 8 13 A and 980 A are from plasma line emissions. Chapter 5 Experimental Results of Mid-Order Hamonic Generation

(b) berylIium, 1= 1.3 x 10" w/cm2

700,I~lI,I,I 30

400

300

200-

(c) nickel, 1 = 3.4 x 1017 w/cmZ (d) gold, I = 3.3 x 10" w/cm2 500-1 11 11 1111 t, I - 60 50 40 30 -

Figure 5.4. Harmonic spectra produced from materials of different atomic- numbers (Z). The broad background underneath the harmonic lines is due to fluorescence foliowing plasma recornbination. Note that the laser intensity in (b) is three-times higher than that in other plots. Chupter 5 Experimental Results of Mid-Order Hamonic Generation

5-32 Dependence on Laser Polarization Using s- and p-polarized laser bearns, experiments were also carrïed out to study the laser-polarization dependence of the harmonic generation process. The polarization of the laser beam was changed by rotating the half-wave plate located after the doubling crystal. A solid 100-pthick berylliurn target was used for this experiment. At a laser intensity of 1 x 10'8 W/cd, we measured the third-harmonic generation with s- and p- polarized incident laser pulses. The result, as shown in Figure 5.5, exhibits clear differences for these two cases: for p-polarized irradiation, strong 30signal was observed with SN(signal-to-noise ratio) near 30; for s-polarized irradiation, no 30 signal was observed at di. It should be noted that in our current experimental setup, the harmonic output was not polarization-analyzed, except by the intrinsic difference in reflectivity of the

" 1650 1700 1750 1800 1850 1900 wavelength (A)

Figure 55. 30 spectra from beryllium target produced by p-polarized (solid iine) and s-polarized (dashed line) incident laser pulses at an intensity of 1 x 1018 W/cm2. No 30signal was observed when the incident laser was s-polarized. Chapter 5 Experintental Results of Mid-Order Hannonic Grnerurion 104

spectrometer grating for s- and p-polarized light (the grating efficiency q is normally lower for s-polarization than for p-polarization). Therefore we cannot draw defmitive conclusions about the polarization of the hannonics generated and make a complete cornparison between our experimental results and the theoretical polarization selection dediscussed in 5 2.2-6. However, we can constmct a qualitative analysis of the data based on some reasonable assumptions. By assurning that a p-polaïzed pump laser aiways produces p- polarized harmonies (8 2.2.6), and that the grating effkiency of the spectrometer is 3- times greater for p-polarization than for s-polarization, the following cm be concluded fiom our measured result: the p-polarized 30 yield due to s-polarized pump ( s + p) is no more than 3% (1/30) of that produced with p-polarized pump (p + p); the s- polarized 30yield with s-polarized pump (s + s) is less than 10% (3/30) of p-polarized harmonic from p-polarized irradiation ( p + p). This experimentally observed polarization selection rule for the third harmonic is summarized in Table 5.1.

Table 5.1. Measured polarization selection rule for the third-harmonic generation in plasma.

3w polarization

* Assurning grating efficiency qp> 3r7, . Chapter 5 Experimental Results of Mid-Order Hamonic Genernrion

53.3 Anguiar Distribution of the Harmonies

The same method described in 5 4.3.2 was used here to measure the angular distribution of the mid-order harmonic emission (see Figure 4.3). By changing the incident angle from 60' to 63', the angular distributions of the third and fourth hannonics from the aluminum target were inferred, at an intensity of 1 x 10" W/cmZ. Again, we assumed the effect of incident angle on harmonic generation was negligible because of the smail angle change (maximum 3' in this measurement). Figure 5.6 shows the relative intensities of 30and 40as a hinction of the observation angle. For comparîson, the laser profile (assumed a Gaussian far-field shape with 10' FWHM) is also plotted. It shows that the harmonies are distributed well within the laser cone-angle, in the specular direction, with the 40 distribution slightly narrower than that of the 30, Le., es, = 5.3' f OS", and 04" = 3.8' f 0.5".

8 (degree) obs

Figure 5.6. Angular distribution of the third (solid line) and fourth (dashed line) harmonic signals measured from an Al target under laser irradiame of 1 x 1017 W/cm2. The laser profde is also plotted (dot-dash line). Chapter 5 Experiimental Results of Mid-Order Harmonic Generarion 106

According to the perturbation theory of harmonic generation, one expects the angular width of the n th harmonic to decrease as l/&, which means that the ratio of the 40 angular width to that of 30 should be J3/4 = 0.87. Comparing to this, Our measurement resuits yield a ratio of 04m/03a>= 0.7 f 0.1, which is slightly lower than the perturbation mediction. We also noticed that the experimentd error in this measurement was too large that a refined experiment would be necessary to allow a quantitative cornparison with the theoretical models.

5.4 Harmonic Generation with Controlled Prepulses

In 5 2.3.3, we discussed the possibility of using a deliberate prepulse to study harmonic generation from plasmas of varying density scale-lengths. It is generally believed that the effïciency of harmonic generation depends strongly on the gradient of the plasma density profüe. Qualitative analysis, as well as recent PIC simulations, show that there should be a optimum plasma scale-length around A (laser wavelength) where harmonic generation is most efficient. Keeping this in mind, we performed an expenment on third hamionic generation by adding a smaU prepulse at a controllable time. This experiment is similar to the one performed on SHG (5 4.4), except with improved control of the prepulse.

5.4.1 Prepulse Setup

After the cornpressor, a smali portion (20%) of the infrared laser pulse was split off, frequency-doubled in a siniilar KD*P crystal to the one descnbed in Q 5.1, and then made to CO-propagatewith the infrared pulse. The relative timing between the IR pulse and the orthogondly polarized green pulse could be continuously adjusted with an accuracy of il00 fs. as detemiined in another pump-probe experiment Cl181 in which frequency-domain interferometry was used. The dual pulses then propagated dong the Chupter 5 Eiperimentnl Results of Mid-Order Humonic Generatiun 107

beam-line into the harrnonic setup. Passing through the KD*P crystal shown in Figure 5.1, the resulting two green pulses (the main pulse and the weak prepulse) were sent to the target charnber and focused ont0 the target. The intensity of the prepulse was controiied by an adjustable iris which, by limiting the beam diameter, not only cut dom the prepulse energy but also produced a larger focal spot in the far-field distribution on target. The latter ensured that the expanding preplasma would have a large aspect ratio and so would stay in one- dimensional; it also made the spatial overlapping of the two pulses at focus easier. In this experiment, the main pulse intensity was 5 x 1017 W/cm2, and the prepulse intensity was set to be around 2.5 x 1016 W/cm2, which is about 5% of that of the main pulse.

5.4.2 Experimental Results Figure 5.7 shows 3w yield collected in the specular direction from a silicon target, as the delay between the main pulse and the smali prepulse was increased. It can be seen that the harrnonic efficiency starts to decrease once the prepulse moves ahead of the main pulse, and it drops quickly by two orders of magnitude as the prepulse arrives 3 ps ahead of the main pulse. There is an apparent 1.5-ps difference between time zero and the time when the 30 yield starts to decrease-the prepulse seerns to arrive 1.5 ps earlier. One possible explanation for this is that the leaûing edge of the 350-fs main pulse srarts to produce pre-plasma before t = O. This, however, is not enough to explain the observed 1.5-ps time difference, given the fact that 1.5 ps before its peak the Gaussian-shaped main pulse intensity is merely at 1û-22 of the peak level. The dispersion of the green and IR puises in the KD*P crystal cannot explain this apparent time difference either. The 'zero time' in Figure 5.7 represents the nominal position where the two pulses coincide. It was adopted from the measurement done in Ref. 11 181, on the assumption that the timing between the two green pulses used in Our experiment remained the same. We notice that the 1.5-ps time different corresponds to a spatial Chapter 5 Experimental Results of Mid-Order Harmonic Grneration

--- silicon, 30 z =35Ofs laser

Figure 5.7. 30 yield from silicon target as a function of prepulse timing. The harmonic conversion efficiency drops dramatically when the weak prepulse anives ahead of the main pulse (t> O). The solid line is drawn for visual guidance. The dashed line at t = O represents the 'nominal position' where the two pulses are temporally coincident (see discussion in the text). Chupter 5 Experimental Results of Mid-Order Harmonic Generation 109 difference of ody 0.45 mm. Considering the long optical path lengths (over - 10 m) of which the two green pulses had to travel before meeting on the target, it is conceivable that a 0.45-mm error could be introduced by non-collinearity in the actual beam-path. Based on this discussion, we speculate that the observed time mismatch was due to experimental error, and a 1.5-ps correction is added to the nominal the delay in our later data anaiysis. Combining this experimental result with the hydrodynamic rnodeling of plasma expansion discussed in $2.3.3, a sense of the dependence of third-harmonic efficiency on the scale-length initially seen by a generating pulse can be inferred. For each delay-time in Figure 5.7 (adjusted based on the new zero-tirne), the scale-length of the evolving plasma was calculated based on the result of MEDUSA calculations (Figure 2.1 1). The new correspondence is plotted in Figure 5.8, which shows that the harmonic eEciency

Figure 5.8. Efficiency of third-harmonic generation vs. normalized plasma scale-length, f = LIA, which is calculated by MEDUSA-modeling. The solid Iuie represents an exponential fit, which gives fo = 0.14. Chapter 5 Experimental Results of Mid-Order Hannonic Generatiun 110

decreases exponentially with the plasma scaie-length. As the scale-length changes from

about 0.1 A to about 0.6 Â ,the third-hannonic efficiency drops by almost two orders of magnitude. Surprisingly, no harmonic enhancement by the prepulse was observed in this experiment. Possible expianations for this wiil be discussed in $ 6.1.2.

5.5 Observation of Satellite Stwcture in the Mid-Harmonies

In resoiving the structure of hmonic lines at higher irradiances, we observed the appearance of satellite Lines, both red- and blue-shifted, which appea. to have a regular Stokes- and anti-Stokes-like structure. These lines appeared around each of the 3rd - 6th hannonics, apparently simultaneously across harmonic orders, but appreciably after the appearance of the hamonics themseIves. The threshold intensity of these satellites was around mid-10'7 Wkm? The satellites were repeatable and spectraliy narrow; in a few cases, the red-shifted satellite line was as intense as the harmonic heitself (Figure 5.9).

Figure 5.9. Detailed spectrum of 30 fiom CH target. A red-shifted satellite appears beside the hannonic line. I = 3 x 1017 W/cm2, Aa = 7.6 x 1013 rads. Chapfer 5 Experimental Results of MWrder Hannonic Generation 11 1

As the irradiance was increased to 7 x IOi7W/cm2, we observed the sequential appearance of three such peaks: fmt a red-shifted peak, then a blue-shifted peak, then an additional red-shifted peak, each stepped in frequency by the same increment Aw. Figure 5.10 shows this evolution of satellite structure from a CH target as the laser

intensity was varied from 4.5 x 1016 to 6.8 x 1017 Wkm? The spectrum of forward- scattered fundamental light was also measured, which showed sudden line-center depletion and large broadening exactly upon the appearance of the satellite features in the

harmonies (Figure 5.1 1). We further tried to measured the backscattered fundamental spectrum. However, to a sensitivity of 10-4 of incident intensity, no backscattered light was detected in our experimental geometry.

We also observed that the satellite structure depended on the target position, relative to the position for maximum harmonic yield. Figure 5.12 shows a typical focal scan for 30 generation from a CH target irradiated at a laser intensity - 5 x 1017 W/cm2. We cm see that the satellite structure was most apparent not at the best focus (x = O), but instead at a position where the laser focus was 300 pm behind the target surface. These satellite structures were observed for all the lower-Z materials that we used-Be, CH, and Si-but were not seen, under any of our conditions, for the higher-Z elements, Ni and Au. Initial analysis suggests that the frequency step Am between the satellite lines may be weakly Z-dependent, with a possible 10% difference between Be and Si. For CH targets (Z = 3S), this shift was found to be Am = 7.6 x 1013 rads, which is much lower comparing to the electron plasma frequency opeat critical density, i.e., op = 2m/A = 3.6 x 1015 rad/s, where A = 526 nm is the incident laser wavelength. On the other hand, Am is very close to the ion plasma frequency mpi for a Myionized CH plasma at critical density. Using Eq. 2.7 and the CH-plasma parameters Z = Z = 3.5 and

A = 6.5, we fmd 61, = 6.1 x 1013 rads. This shows that the observed frequency shift for the satellite iine is about 1.2 times of the ion plasma frequency, Le., Aw = L 2mPi. Chapter 5 Eiperimental Results of Mid-Order Hamonic Generation

Figure 5.10. Satellite structures Erom CH target recorded at different laser intensities. Chapter 5 Experimentul Results of Mid-Order Harmonie Generation

wavelength (A)

5175 5200 5225 5250 5275 5300 5325 5350 Wavelength (A)

Figure 5.11. Comparison of spectral changes for forward-scattered fundamental spectra from a CH target recorded at different laser intensities. (a) Spectra in actual intensity scaie; (b) Spectra plotted at the same peak intensity (normalized) to emphasize spectral features. Eqethental Results of Mid-Order Hamonic Generation 114

1650 1700 1750 1800 1850 1900 wavelength (A) Figure 5.12. 30spectra from a CH target measured at different focal positions. x = O represents the best focus. x i O corresponds to the case where laser-focus is beyond the target surface. Same intensity scale is used for each speccnim.

To Our knowledge, these satellite features have not been observed in previous harmonies experiments. Their exact physical ongin is still not clear for us. We notice, however, that the frequency shifts for the satellites are very close to the ion plasma frequency, which rnight suggest that the satellites are resulted from the participation of the ion plasma wave, a non-quasineutrd mode of ion oscillation, excited near the critical surface. In pursuing this interpretation, we will discuss several mechanisms in the following chapter ($6.1.6). which. under our experimental conditions of ultraintense laser interacting with a steep-gradient plasma, might result in non-quasineutrd plasmas in the interaction region. Chapter 5 Experhental Results of Mid-Order Hannonic Generation

5.6 Conclusions

In this chapter, an experimental snidy of mid-order harmonic generation from laser and solid target interaction is described. Tirne-integrated forward spectra were measured from various solid targets of different atomic numbers. Harmonies of both odd and even order, and up to 7th were found. The harmonics featured strong laser- polarization dependence, and narrow angular distribution around specuiar. Experiments using controllable prepulses demonstrated a strong dependence of harmonic yield on the scale-length of the preformed plasma, through the expected resonant enhancement of harmonic generation by the prepulse was not observed. FinaUy, we observed, apparently for the first time, a reguIar Stokes-like and anti-Stokes-Iike satellite features accompany ing the mid- harmonics . and measured their dependence on target materials as welI as on laser intensity. Chapter 6 Discussion and Conclusions

6.1 Sumrnary of the Experimental Results

We have presented an experimental study of harmonic generation from solid targets illuminated by picosecond ultra-intense laser pulses. The experiments were performed on two laser systems: the 1-TW FCM-CPA laser at the University of Toronto and the 10-TW T3 laser at the University of Michigan, where high contrast (> 1010) 1-ps, 1.053-pm. and 0.35-ps, 0.526-pm laser pulses were used. Important features of harmonic generation, Le., the anguiar distribution of hamionic ernission, dependences on Laser polarization and on plasma scale-length, and the effects of preformed plasmas were characterized [119, 1201. The main experirnental observations are summarized in the following sections.

6.1.1 Effects of Preplasrna on Harmonic Generation By comparing the second harmonic generated by a high contrast pulse and by a pulse containing a fixed-fraction (IO4) prepulse, the effects of preformed plasma on harmonic generation were investigated systematicdy . One of the preplasma effects we observed was the spreading of harmonic emission over increasing soLid angles as the prepulse intensity was increased. When the prepulse intensity reached 3 x 1012 WIcm2, we observed a nearly unifom angular Chapter 6 Discussion and Conclusions 117

distribution of harmonic emission, in contrast to a sharp distribution dong the specular direction when the prepulse was not present. We attnbute this effect to a non-fiat critical surface induced by the pre-formed plasma. We also found the observed temporary saturation of the hannonic yield coiiected in the specular direction could be explained almost entirely by this effect of increasing harmonic emission angle. Spatidly resolved spectra of the second harrnonic emission were measured with clean pulses and with pulses containhg prepulses. In the clean-pulse case, second harmonic was emitted from a source with small and smooth spatial and spectral distributions; in the prepulse case, however, severe breakup of the fiarmonic source, both spectraliy and spatidy, was observed. This breakup of the harmonic source was possibly due to modifications to the incident laser pulse via self-phase modulation (frequency modification) and filamentation (spatial modification) in the underdense part of the pre- fonned plasmas. Both of the wide (near 27c) harmonic emission angle and the breakup of hmonic spectra have been noted previously in numbers of experiments [26,28]. The significance of our experimental results is that it clearly demonstrated, for the fist tirne in a systematic manner, that these effects were directly associated with the underdense preplasma rather than caused during the generation of the hamonics at the critical surface.

6.1.2 Plasma Scale-length Dependence In using very high contrast pulses to which we have added controlled prepulses, we largely separated the contributions of nonlinear hydrodynamics and nonlinear optics in the generation of laser-plasma harmonies, and systematicdy quantified the sensitivity of harmonic generation efficiency to the gradient of preformed plasma. Two separate experiments were camied out: the 20 experiment on the FCM-CPA laser, and the 30 experiment on the T3 laser, both using identical silicon targets. Although both experiments demonstrated a strong dependence of harmonic conversion efficiency on the Chapter 6 Discussion and Conclusions scde-length of the plasma, different dependences were observed. In the 20 experiment, a near 3-fold enhancement of harmonic conversion efficiency was recorded around t = O, where the main pulse and the prepulse were temporally overlapped. This observation agreed with one mode1 prediction that there exists an optimum scale-length for maximum harmonic generation [37]. Since the position of the resonant peak could not be determined precisely, due to a relatively large experimental error in the temporal measurement (f3 ps), only a rough estimation could be made- By assuming that the prepulse-created plasma expands at the typical ion-sound speed of 0.1 pdps, the optimum plasma scale-length for harmonic generation was estimated as LIA 5 1. In the 30 experiment, the harmonie-generation efficiency was found simply to decrease exponentially with the plasma scale-length-no resonant enhancement was observed. There are several differences between these two experiments, including: the prepulse intensity and focal-spot size, wavelength and duration of the high-intensity pulse, and differences in collinearity of the two pulses (the 2w experiment used two different pulse-lines). Each might have an effect on the relation of prepulse and main pulse, and affect the enhancement feature. An obvious distinction between the two cases is that the prepulse intensity used in the 30 experiment was 2.5 x 1016 W/cm2, which was more than one order of magnitude higher then that used in the 20 experiment (1.8 x 1015 Wkm*). A faster expansion speed as the result of greater plasma temperature, may make it more difficult to resolve the enhancement if, Say, it results from the production of a special scale-length. An interesting prospect, too, is that in the 20 case, where enhancement was seen, the prepulse was delivered with the polarization onhogonul to the main pulse. In this case, the prepulse does not simply add its intensity to the pulse, but produces some elliptically polarized pulse during the time the two overlap; this polarization distinction Chupter 6 Discussion and Conclusions 119 was also present in a similar experiment performed by von der Linde et al. [107]. At times far from overlap, the prepulse might simply deposit energy into the plasma, without a significant coherent relationship to the main pulse. In the 30case, for which harmonic enhancement was not observed, the prepulse was deiivered with vimially identical polarization as the main pulse. For gas-interaction harmonics, eilipticaliy polarized light leads to great reduction in harmonic efficiency, but the reasons there do not apply in our case. The most clear-cut distinction is that there are well-recognized qualitative differences in 20 and 30production. More than one process, from both underdense and critical regions, can lead to 20 harmonic generation, whereas 3w production more clearly belongs in the same camp as mid- and high-order harmonics (for this reason, harmonic experiments examining 30are more significant in the study of the production of rnid- and high-harmonies in laser-plasmas). Thus, it may be that the enhancement results fiom the production of 20 from a distinct mechanism driven only as the two pulses ovedap in time and space. This may, in fact, tie together with the different polarizations of prepulse and fundamental, if it should happen that elliptically polarized light preferentially drives a different second-harmonic generation mechanism.

6.1.3 Mid-Order Harmonic Generation on DEerent Solid Targets Mid-order harmonic generation was studied using high-contrast pulses from the

T3 laser at intensities between 1017 and 1018 Wcm2. We observed up to the 7th harmonic, both odd and even orders, in the time-integrated forward spectra for various solid rnaterials, from beryllium to gold. Similar harmonic spectra were obtained from these targets, showing harmonic line emission sitting on a broad plasma recombination background. For targets of increasing atomic number 2,the hmonic yield appeared to decrease slowly with 2, while the plasma recombination background increased with Z as expected. Among the six target materials used in our experiment, the CH target (2= 3.5) Chapter 6 Discussion and Conclusions

produced the cleanest harmonic spectnim with best signal-to-background ratio.

6.1.4 Angular Distribution of Harmonic Emission The angular distributions of the second and mid-order harmonics were measured. At laser intensities up to 1 x 1017 W/cm2, we found the harmonics were distributed well within the laser cone-angle, dong the direction of specular reflection. These results agreed with the theoretical predictions of a harmonic generated from a flat critical surface, indicating that neither 2-D effects associated with preformed plasmas nor nppled critical surfaces due to Rayleigh-Taylor instability [56]-both assumed in the analysis of a previous Iaser-solid harmonic experiment [26]-occurred under our experimental conditions.

6.1.5 Laser Polarization Dependence The laser-polarkation dependence in the 30generation was studied at an oblique incidence (0 = 60') and a laser intensity of 1 x 1018 W/cm2. We observed strong 30 signal (SIN = 30) with p-polarized laser, but no indication of 30 at all with s-polarized laser. The interpretation of this result became compiicated because of the absence of a polarization analyzer in our expenmental setup and the uncertain polarization response of the spectrometer we used. However, a partial conclusion cm still be made based on some reasonable assumptions. By assuming that the grating efficiency for p-polarkation in our setup was

3-times that of s-polarization, we could conclude that the 30 yield generated by s- polarized irradiation was no more than 10% of that produced by p-polarized pump, if it were s-polarized, and would be even weaker (< 3%) if it was p-polarized. Chapter 6 Discrcssion and Conclusions

6.1.6 First Observations of Harmonic Satellite Structures Finaily, we reported what we befieved the first observations of regular Stokes-like and anti-Stokes-like satellite features accompanying the mid-order hamonics. These satellites were seen ody in low-Z materials (Be, CH, Si), and their frequency shifts were found to be weakly 2-dependent. The measured laser-intensity dependence of the structure showed a threshold intensity of - 3 x 1017 Wfcrn2 for the appearance of the satellites. The physical explanation for the satellites is still not quite clear for us, but several useful observations cm be offered: The frequency shift do of the satellite was noted to be approximately the ion plasma frequency oPi,which begins to suggest a Langmuir wave of ions, Le., an ion electrostatic plasma wave (5 2.1.2). This raises the prospect that the satellites are due to scattenng from ion plasma waves, which are excited near the critical surface in the density gradient and oscillate at frequency opi. An obvious difficulty with this notion is that typicdy one assumes the Debye shielding of ion density fluctuations, at this density and temperature, will result only in ion-acoustic oscillations, and not 'naked' ion electrostatic waves for which UDe>> 1 (see 5 2.1.2). Assuming the harmonic conversion and satellite generation processes take place together around the cntical surface, we can estimate the value of kADe for a homogeneous plasma of cntical density. Since ilDe= uDlhe/mpeand at critical density o, = o = ck, we have kaD, = ut&, the ratio of the electron thermal speed to the speed of light. For a typical laser-plasma of Te= 300 eV, we have v,h= 7x 108 cm/s, and so kaDe= 0.02 cc 1, which is in the ion-acoustic regime, rather than the ion plasma regime (see Figure 2.2). Two considerations might account for this difierence. First, within steep gradients, under intense irradiation, the plasma may not be quasi-neutral, as the electrons may possibly be 'pushed off their ion background due to Chaprer 6 Discussion and Conclusiom 122 the relativistic ponderomotive force, which becomes significant at laser intensities > mid

1017 Wlcmz. This displacernent cm effectively reduce the local electron density, increasing the Debye length and therefore reducing the shielding of the ions by the electrons. If the electrons are pushed into the gradient, then the ion plasma wave excited near the new critical surface would be at somewhat larger density than in a quasi-neutral plasma. and so mpi would be increased by the square root of the density increase factor. This picture would represent the non-steady equivalent of hydrodynarnic steepening of the cntical density surface by the ponderomotive force, fust quantified in CO2 laser- plasma interaction [Il 11. In this case, the density change might be grossly estimated from the scaie-length of the density profile together with the distance 6x by which the electrons might be pushed off the ions, roughly as:

The distance 6x might be found by equating the restoring force in a capacitor mode1 of plasma charge-separation and the ponderomotive force from the incident light. From the whole light-pressure at 1018 Wfcm2, a rough calculation suggests that a displacement 6' on the order of 0.1 pm is possible-a value which is appreciable in cornparison with ou anticipated scale-lengths (0.01 - 0.1 p).A displacement of a distance comparable to the scale-length or greater cm produce very substantial modification of the local electron density. Secondly, the Debye length AD, found above is calcdated for a homogeneous plasma, which may not be an appropriate mode1 in a steep gradient and with Te z> Ti. For that matter, if the excursion distance of the oscillating electrons is suffkiently far, longer than a Debye length and an ion-plasma wavelength, it may be that the shielding effect of the electrons is reduced by averaging quickly over the ion density fluctuations. The electron plasma frequency is characteristic of the electron-density Chapter 6 Discussion and Conctusions 223

response time following charge redistribution, and Debye shielding cornes from the electron response to imposed electric fields (e.g., test charge). But in Our case a new electric field (laser) is competing with this and should be able to make the electrons see only the ion density averaged over an electron cycle, which could reduce the shielding of ion oscillations if the electron oscillation amplitude is Iarge enough. In this case again, it may arise that kAD, >> 1.

6.1.7 High-Contrast CPA Laser Prior to these laser-plasma studies, a Iarge amount of the experimentai effort in this research was spent on building and developing of the FCM-CPA laser system at the University of Toronto [91,92], which was a significant technical challenge at the time of its construction. This work, particularly the high-dynamic range characterization of CPA laser pulses using the cross-correlation technique, was an important contribution in highlighting the issue of laser contrast, which was not widely emphasized among groups working on high-intensity laser-solid experiments in the early 1990's. Many people had thought the ponderomotive force would 'repair' the plasma density gradient in the interaction with solid, so contrast would not much matter. Between that laser-contrast work and these prepulse harrnonic experiments, we have shown that this assertion was not true-sontrast is an essential issue in laser-solid interactions.

6.2 Suggestions for Future Experiments

The experiments presented in this thesis cover many aspects of harmonic generation in laser-plasma interaction. It will be seen that they represent the fmt step in a new trend to quanw the interaction, to dissect it into parts, and to separately identiQ the nonlinear optics of harmonic conversion as distinct from nonlinear hydrodynamics. They are, however, far from complete, and some results were quite preliminary. Chupter 6 Discwsion and Conclusions 124

There is still much to be explored in this new field, and certain steps in these directions will help: Harmonic ernissions are usually accompanied by a strong plasma recombination background. This is especially the case when a high-Z target is used. In order to increase the sensitivity for harmonir- detection, this background has to be removed. The-resolved measurements (using a streak camera, for example) [23, 1121 should be used, to yield cleaner hannonic specua and therefore lower hannonic detection thresholds. The pump-probe experiment cm be improved in the following aspects. To completely isolate the nonlinear hydrodynamics from the noniinear optics in the overall production of harmonies, a different color probe pulse could be used. In addition, rather than relying on hydrocode simulations, direct measurement of the plasma density profile is feasible using methods such as frequency-domain interferometry [12 11. This method has been demonstrated in a recent experiment where laser light absorption was measured in plasmas of varying scale-lengths [122]. - In analyzing the pump-probe results, we have assumed that the harmonic angular distribution rernains unchanged. It is, however, possible that the spreading of the harmonic emission gets steadily worse with increasing prepulse delay. If this were bue, the harmonic yield we measured was not the total yield, just as in the case of SHG by uncontrotled prepulses. This open question could be answered by an experiment measuring the angular spread of the hamonics for different prepulse delays. We have observed different scale-length dependences for the generation of 20 and 30; the biggest difference is that no resonance enhancement was observed for 30. We have discussed in the last section that this might be for several different reasons. Experimentaily, this could be clarified by repeating these measurements under identical experimental conditions, Le., prepulse intensity and polarkation, fundamental laser wavelength, etc. Along the same line, enhancement of 20 could be compared using two Chapter 6 Discussion and Conclusions 125 different prepulse polarizations. This would determine whether the relative prepulse polarization is physically signifkant. Harmonic generation in plasma is seen to exhibit strong dependence on laser polarization. A polarization selection dehas been suggested, based on theoretical models (5 2.2.6), which is ready to be verifed through experiment. By studying this selection de, one may obtain valuable information about the rnechanism by which the harmonics are produced. The laser-polarization dependence of an odd-order hannonic (3w)has been partially tested in this work. The same experiment could be extended to study even harmonics, which, according to theoretical models, have a different dependence on laser-polarization than odd harmonics. To have an unarnbiguous test, a polarization analyzer should be added at the entrance of the spectrometer, and the polarization response of the spectrometer should be weU characterized. The effect cf incident angle on harmonic generation (also discussed in 12.2.6) is another issue not examined by the work presented here, but it wouid be interesting to study. Since, for a specular harmonie emission, the reflection direction changes with the incident angle, a different harmonic-collecting scheme would have to be used, in which the direction of at Ieast one of the incident or reflected beams could be freely rotated about the laser focus. In our current setup, both of these directions are fixed. Finally, the physical origins of the first observed harmonic satellites are still not clear. Obviously this is a very interesting subject deserving further studies. References

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