High-resolution Interferometric Diagnostics for Ultrashort Pulses

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7. LATERAL SHEARING INTERFEROMETRY FOR HIGH-HARMONIC GENERATIONturning the intensity Ĩ (ω,x ,y ) 1 . The aim of a spectrally resolved wavefront measurement is tocause the phase φ(ω,x,y ), up to an unknown function of frequency C (ω), to be imparted onto themeasured intensity. In the remainder of this section I will discuss some reasons for acquiring thisinformation.The first reason is exposing the physics of HHG itself. In the comparison of theory with experiment,phase information is particularly important in the context of HHG because the radiation isusually measured in the far-field, after significant diffraction from the generation region. However,the single-atom response applies directly in the spatial domain in the near-field, and its predictionsof the amplitude and phase are largely decoupled. The amplitude depends on the ionizationrate, electron diffraction in the continuum, and the recombination element, whilst the phase isdominated by the action integral in the continuum, with the laser phase also making a contribution.The near-field amplitude and phase is therefore the best basis for comparison of experimentwith single-atom theories; using the far-field intensity distribution for this purpose is both indirectand incomplete. Although macroscopic effects may complicate this picture, they often act as trajectory“filters”, favouring certain electron trajectories whilst suppressing others. The single-atomresponse, appropriately modified, is still a good description in such a situation.Despite two decades of study, much remains unknown about HHG. The physics of HHG consistsof three distinct conceptual units: the propagation of the driving laser field, the single-atomresponse at each point in the interaction region, and the macroscopic summation of the singleatomresponses. Only of the third, which involves linear propagation in a tenuous dielectric, canthere said to be a complete understanding. In both the laser pulse propagation and the singleatomresponse there is significant uncertainty in both the physical theory and in the practicaldetermination of experimental parameters, especially when moving to more exotic regimes suchas few-cycle pulses or molecular targets. For example, in many regimes, HHG is exquisitely sen-1The limited spatial dimensionality of current detectors must intrude here: whilst a three-dimensional XUV spectrometermay be technically feasible using techniques borrowed from integrated-field spectroscopy in astronomy, suchdevices have not yet been developed. A single image from the spectrometer therefore returns I (ω,y ), the field intensityat a distance y along a direction parallel to the entrance slit. The beam is either sampled or averaged in the directionperpendicular to the entrance slit. Three-dimensionality may be achieved by scanning the position of the entrance slit,but usually one renders this unnecessary by assuming cylindrical symmetry.156
7.1 Motivationssitive to the spatio-temporal profile of the laser pulse, which is currently challenging to controland characterize. At higher powers, nonlinear propagation effects such as the ionization-inducedplasma and possibly the Kerr effect play a role. However, significant uncertainty exists in bothionization rates and nonlinear scattering cross-sections.Much remains to be understood of the single-atom response itself. Within the strong fieldapproximation (SFA), the properties of the target that affect the result are the ionization rate andrecombination dipole element. Even in the simplest possible system, a hydrogen atom, there havebeen recent theoretical developments in this regard [415, 416], and for molecules the topic is underactive research [417]. Extensions of the SFA towards multi-electron systems, molecular systems,and more accurate incorporation of the ionic potential are also currently undergoing intensiveresearch, and have been the subject of controversy [356].The emerging role of HHG as a next-generation light source means that resolving the aforementioneduncertainties is of interest beyond strong-field physics. Section 2.1.2 outlined the symbioticdevelopment of ultrafast sources and ultrafast metrology; there are no indications this trendwill cease. For example, in applications of attosecond pulses, tight focusing may be desirable inorder to obtain high spatial resolution and also to increase the peak intensity so as to access nonlinearities,which have been limited thus far [398, 399]. A tight spatio-temporal focus requires thefocal planes of the harmonics to coincide; however as the experiments and calculations of thischapter show, this will not generally be the case. Characterization and ideally control will be requiredto overcome this problem.Ultraviolet and soft x-ray pulses from high harmonic generation have been proposed as aseed for the next-generation of ultrashort free-electron lasers [418, 419], although the term freeelectronamplifiers is more apt in this context. Since the amplified pulse inherits the phase ofthe seed, and harmonics are generated in the amplifier itself due to nonlinearities, it is likely thatwavefront characterization of the seed will assist in controlling and optimizing the output.157
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High-resolution InterferometricDiag
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AcknowledgementsMy supervisor Ian W
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6 High-harmonic generation 1256.1 D
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List of acronymsADK Ammosov, Delone
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Definitions and symbolsAll Fourier
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1. INTRODUCTIONprofile in space as
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2 BackgroundThis dissertation prese
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2.1 Metrology, ultrashort pulses, a
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2.1 Metrology, ultrashort pulses, a
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2.2 Formal introduction to ultrasho
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2.3 Introduction to ultrashort puls
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2.4 Extending ultrashort metrology
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3 Phase reconstruction algorithm fo
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3.1 Motivationration of information
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3.2 Quantitative noise analysis for
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3.3 Nature of the input datato give
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3.4 Sampling and uniqueness of solu
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3.5 Main algorithmfrom all the shea
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3.5 Main algorithmsituation, Γ k ,
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3.5 Main algorithmfor j = 1,2,...,k
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3.6 Implications for the relative p
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3.7 Signal-to-noise ratio cost of a
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3.8 Signal-to-noise ratio benefit o
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3.9 Numerical comparison of single-
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3.10 Summary, critical evaluation,
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4 Experimental implementations of m
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4.1 Sequential acquisition of shear
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4.1 Sequential acquisition of shear
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4.2 Simultaneous acquisition of she
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Page 117 and 118: 5 Compact Space-time SPIDERIn this
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8. QUANTUM-PATH INTERFEROMETRY IN H
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9 Summary and outlookThis chapter s
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the vacuum chamber on the laser pul
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A. NOISE AND UNCERTAINTYdomain, so
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A. NOISE AND UNCERTAINTYUsing the i
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B. SIMULATION CODES FOR HIGH-HARMON
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References[1] Rakov, V. & Uman, M.
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REFERENCES247 (1999). 11[63] Stiben
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REFERENCES[127] Gyuzalian, R., Sogo
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REFERENCES[189] Kornelis, W., Biege
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REFERENCES[254] Geindre, J. P., Aud
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REFERENCES[313] L’Huillier, A. &
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REFERENCESPhys. Rev. Lett. 91, 1630
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REFERENCESMarangos, J. In Conferenc
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High-resolution Interferometric Diagnostics for Ultrashort Pulses

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