High-resolution Interferometric Diagnostics for Ultrashort Pulses

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8. QUANTUM-PATH INTERFEROMETRY IN HIGH-HARMONIC GENERATION100(a) 0.0, 0.0(b) 0.0, 0.1(c) 0.1, 0.00-1Order50-2-3log 10B-40−2 0 2t (opt. cycles)−2 0 2t (opt. cycles)−2 0 2t (opt. cycles)-5Figure 8.9: Spectrogram of dipole emission with 5 fs, 5 × 10 14 Wcm −2 , 800 nm pulse with variousmonochromatic control fields (θ Q ,θ I ) with relative frequency ω C /ω D = 0.45.where one chooses the largest nonlinear coefficient as it is most likely to cause a problem.For the examples of section 8.5.1.2, the largest eigenvalues of the action nonlinearity are about1000 across most of the spectrum. The application of (8.25) suggests that a window width of w =0.03 is therefore appropriate. However, D(ω; ¯θ ) must be known over a window several times largerto eliminate artifacts from truncation.8.6 Simulated experimentHaving used a perturbative extension to the quantum orbits model to make predictions of theeffect of applying control fields, I now test these predictions against simulations of the single-atomresponse using the 1D TDSE.The drive and control fields were those of section 8.4.2. The control field amplitudes werescanned over θ I ,θ Q ∈ [−0.1,0.1] in 0.01 increments, and at each step, the dipole response wascalculated using a one-dimensional TDSE code. I denote the results (ω;θ Q ,θ I ). Figure 8.9 showsa sample of the resulting dipole responses for different control field combinations, representedusing spectrograms. In subfigures (b) and (c), the control fields are at the extremes of the scanrange, and the cutoffs have been modified significantly from the zero control field case. However,the window function introduced in section 8.5.2 will suppress these extreme cases.Figure 8.10 shows the amplitude and phase of the entire results set for the 45 th harmonic.204
8.6 Simulated experiment20.1(a)50.1(b)0.0540.05θ Q3000−0.0521−0.05-2−0.1−0.1−0.1 −0.05 0 0.05 0.1−0.1 −0.05 0 0.05 0.1θI|D|θIθ QargDFigure 8.10: (a) Amplitude and (b) phase of the computed dipole response (ω;θ Q ,θ I ) at the 49 thharmonic.Whilst the eye can discern some regular patterns in both, a normal fringe pattern is not observedbecause there are many Fourier components present. Around (θ Q ,θ I )=(−0.1,0), an enhancementof the amplitude over many periods of the pattern shows that control field is starting to distort theamplitude of the quantum paths, rather than just their phases.The results are best interpreted in control-field sensitivity space, found by taking discreteFourier transforms along both control field amplitude co-ordinates yielding ˜(ω;ᾱ). This is plottedfor four harmonics in Fig. 8.11, along with the control-field sensitivities ¯S (j )ω,Cexpected fromthe perturbative analysis. The αβm labelling system for the orbits has been extended slightly:above cutoff, α = C refers to “coalesced” long and short trajectories. For the 30 th harmonic, thereare many peaks and it is difficult to assign the orbits. However, for the higher harmonics, almostall of the strong peaks can be assigned to an orbit, showing that the quantum-path analysis hassucceeded.The next section addresses some technical issues which arise during the discrete Fourier transformto control-field sensitivity space. These do not affect the physics and it is possible to skip tosection 8.8 without losing much understanding.205
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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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5 Compact Space-time SPIDERIn this
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5.2 Role of the measurement planetr
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5.3 Analysis of ST-SPIDERof design
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5.4 A common-path re-imaging ST-SPI
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5.5 Experimental exampleRomero [295
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5.6 Effect of miscalibrationy (pix)
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5.7 Summary and outlooknow perform
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6. HIGH-HARMONIC GENERATIONcurrent
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6. HIGH-HARMONIC GENERATIONcomponen
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6. HIGH-HARMONIC GENERATION00−I p
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6. HIGH-HARMONIC GENERATION (t ) (E
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6. HIGH-HARMONIC GENERATIONstationa
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6. HIGH-HARMONIC GENERATION10080log
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6. HIGH-HARMONIC GENERATIONwhere re
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6. HIGH-HARMONIC GENERATION• Sadd
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6. HIGH-HARMONIC GENERATIONgiven in
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6. HIGH-HARMONIC GENERATIONderivati
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6. HIGH-HARMONIC GENERATIONPhase ma
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6. HIGH-HARMONIC GENERATION30(S31)2
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6. HIGH-HARMONIC GENERATIONwhere W
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6. HIGH-HARMONIC GENERATIONtheir re
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Page 241 and 242: References[1] Rakov, V. & Uman, M.
Page 243 and 244: REFERENCES247 (1999). 11[63] Stiben
Page 245 and 246: REFERENCES[127] Gyuzalian, R., Sogo
Page 247 and 248: REFERENCES[189] Kornelis, W., Biege
Page 249 and 250: REFERENCES[254] Geindre, J. P., Aud
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Page 253 and 254: REFERENCESPhys. Rev. Lett. 91, 1630
Page 255 and 256: REFERENCESMarangos, J. In Conferenc
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High-resolution Interferometric Diagnostics for Ultrashort Pulses

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