High-resolution Interferometric Diagnostics for Ultrashort Pulses

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6 High-harmonic generation 1256.1 Development and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1266.2 Theory of the single-atom response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.3 Theory of the macroscopic response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1446.4 Temporal metrology of high-harmonic generation . . . . . . . . . . . . . . . . . . . . . . . . . 1496.5 Spatial metrology of high-harmonic generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1536.6 Outline of this dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1547 Lateral shearing interferometry for high-harmonic generation 1557.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1557.2 Theory of the method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1587.3 Experiment: longitudinal gas jet scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1657.4 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1677.5 Comparison of results with simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717.6 Physical interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1747.7 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1838 Quantum-path interferometry in high-harmonic generation 1858.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1858.2 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1878.3 Action-shift induced by a weak control-field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1888.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1928.5 Limitation of the perturbative quantum path analysis . . . . . . . . . . . . . . . . . . . . . . 1968.6 Simulated experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2048.7 Fourier transform issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2068.8 Extraction of orbit amplitudes using filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2088.9 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2129 Summary and outlook 217A Noise and uncertainty 221A.1 Correlations of filtered additive white noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221A.2 Estimation of the filtered noise amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223A.3 Amplitude of the phase fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223A.4 Minimizing root-mean-square variation in a set of fields in the presence of trivialambiguities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224B Simulation codes for high-harmonic generation 225B.1 Time-dependent Schrödinger equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225B.2 Classical recollision solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226B.3 Quantum-orbits model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226B.4 Propagation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227References 244
PublicationsThe following publications arose out of work connected to this dissertation:D. R. Austin, T. Witting, C. A. Arrell, F. Frank, A. S. Wyatt, J. P. Marangos, J. W. G. Tischand I. A. Walmsley, “Lateral shearing interferometry of high-harmonic wavefronts,”submitted to Opt. Lett. 3 February 2011.D. J. McCabe, D. R. Austin, A. Tajalli, S. Weber, I. A. Walmsley and B. Chatel, “Space–time coupling of shaped ultrafast ultraviolet pulses from an acousto-optic programmabledispersive filter,” J. Opt. Soc. Am. B. 28, 58–64 (2011).D. R. Austin, T. Witting, and I. A. Walmsley, “Resolution of the relative phase ambiguityin spectral shearing interferometry of ultrashort pulses,” Opt. Lett. 35, 1971–1973(2010).D. R. Austin, T. Witting, A. S. Wyatt, and I. A. Walmsley, “Measuring sub-Planck structuralanalogues in chronocyclic phase space,” Opt. Commun. 283, 855–859 (2010).Quo vadis Quantum Optics?T. Witting, D. R. Austin, and I. A. Walmsley, “Ultrashort pulse characterization by spectralshearing interferometry with spatially chirped ancillae,” Opt. Express 17, 18983–18994 (2009).D. R. Austin, T. Witting, and I. A. Walmsley, “High precision self-referenced phase retrievalof complex pulses with multiple-shearing spectral interferometry,” J. Opt. Soc.Am. B 26, 1818–1830 (2009).D. R. Austin, T. Witting, and I. A. Walmsley, “Broadband astigmatism-free Czerny-Turner imaging spectrometer using spherical mirrors,” Appl. Opt. 48, 3846–3853(2009).T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectralshearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34,881–883 (2009).
Page 1 and 2: High-resolution InterferometricDiag
Page 5 and 6: AcknowledgementsMy supervisor Ian W
Page 10 and 11: List of acronymsADK Ammosov, Delone
Page 12 and 13: Definitions and symbolsAll Fourier
Page 14 and 15: 1. INTRODUCTIONprofile in space as
Page 17 and 18: 2 BackgroundThis dissertation prese
Page 19 and 20: 2.1 Metrology, ultrashort pulses, a
Page 21 and 22: 2.1 Metrology, ultrashort pulses, a
Page 23 and 24: 2.2 Formal introduction to ultrasho
Page 33 and 34: 2.3 Introduction to ultrashort puls
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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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6. HIGH-HARMONIC GENERATIONsmall pi
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7. LATERAL SHEARING INTERFEROMETRY
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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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