High-resolution Interferometric Diagnostics for Ultrashort Pulses

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8. QUANTUM-PATH INTERFEROMETRY IN HIGH-HARMONIC GENERATIONSω,I4002000−200−400−600(a) 0.841055↑55↑30↑55↑30↑213245↑1155↑30↑22 3330↑45↑45↑45↑(b) 0.741055↑55↑30↑55↑2130↑1145↑55↑30↑45↑3230↑45↑223345↑Sω,I4002000−200−400(c) 0.501055↑45↑55↑55↑30↑3345↑3245↑30↑2145↑1130↑55↑2230↑45↑(d) 0.36103255↑1155↑45↑55↑30↑30↑45↑30↑212255↑30↑45↑33−600−200 0 200 400S ω,Q−200 0 200 400S ω,QFigure 8.1: Action sensitivities of the quantum orbits of a monochromatic drive field of intensity5 × 10 14 W/cm 2 in Argon subject to in-phase and quadrature monochromatic control fields. Thelong/short orbit pairs are identified by their βm labels (boxed) as well as a color code identical tothat in Fig. 6.6. Within each pair, thin (thick) lines represent short (long) orbits. For each orbit, theposition of one harmonic is indicated; the arrow indicates the direction of increasing harmonicnumber. Each subfigure has fractional control frequency ω C /ω D indicated at the top left.half-cycles. For a pulsed drive field the orbits are not identical for each half-cycle. Nonetheless,even for a few-cycle pulse the similarity between the half-cycles is sufficient for a similar rotationprinciple to apply.8.4.2 Pulsed drive fieldHaving established some basic properties of the orbits in action-sensitivity space, I now considera few-cycle pulsed drive field, with 5.0 fs duration, 800 nm centre wavelength and peak intensity194
8.4 Example (t ) (a.u.)0.20−0.2(a)8060(b)1-1103011Order40201-22-12031211232220−1 −0.5 0 0.5 1 1.5t (opt. cycles)Figure 8.2: (a) Pulsed drive field, zoomed in on central region. (b) Harmonic order versus recombinationtime of the quantum orbits of a 5.0 fs, 800 nm, 5 × 10 14 Wcm −2 drive field in Argon. Theorbits are labelled by excursion length and recombination event βm, and short (long) orbits aresolid (dashed).5 × 10 14 Wcm −2 , in Argon. Mathematically, the drive field is 2cos D (t )=E 0 cos 2 −1 (2 1/4 )t cos(ω D t ) (8.14)T FWHMwhere I use a cosine-squared pulse for analytical tractability. The quantum path analysis is shownin Fig. 8.2.For these orbits, I evaluated the action-sensitivities to the in-phase and quadrature controlfields using (8.5). A sample of the results are shown in Fig. 8.3. For subfigures (a) and (b), thecontrol-to-drive phase advance per half-cycle ∆φ CD is small enough so that over the five halfcyclesthe net rotation is less than 2π. The first-order trajectories therefore do not overlap. Also,for these values of ω C /ω D the higher-order trajectories have larger action-sensitivity and do notoverlap the first-order trajectories. In particular, for ω C /ω D = 0.6 one has ∆φ CD = 2π/5, so the 5trajectories are equally spread around the circle. However, for ω C /ω D = 0.5 (not shown) ∆φ CD =−π/2 so that orbits separated by 4 half-cycles coincide azimuthally. For Fig. 8.3(c), the control-195
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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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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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