Phase retrieval of complex ultrashort pulses using multipleshearing spectral interferometry

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Phase retrieval of complex ultrashort pulses
using multiple-shearing spectral interferometry

• Dane. R. Austin, Tobias Witting, and Ian A.
  Walmsley
• Clarendon Laboratory, University of Oxford, UK

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Outline

• Complexity in ultrashort pulse characterization
• Applications of complex ultrashort pulses
• Spectral shearing interferometry
• Theory
• Scaling with pulse complexity
• Introduction to multiple shear reconstruction
• Experiment
• Summary
• Outlook

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Complexity in ultrashort pulse characterization
(Sampling theorem)
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Applications of complex ultrashort pulses
Dudley et al. Opt. Express, 2008, 16, 3644-3651
Brixner et al. Phys. Rev. Lett., 2004, 92, 208301
Hauri et al. Appl. Phys. B, 2004, 79, 673-677
Stibenz and Steinmeyer Rev. Sci. Instrum., 2006,
77, 073105
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Externally referenced methods

• Spectral interferometry

O(N) samples required
Fittinghoff et al. Opt. Lett., 1996, 21, 884-886

• XFROG

O(N2) samples required
O(N2 log N) reconstruction time
Gu et al. Opt. Lett., 2002, 27, 1174-1176
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Self-referenced methods

• FROG

Simulation
O(N2) samples required
O(N2 log N) reconstruction time
Xu et al. J. Opt. Soc. Am. B, 2008, 25, A70-A80

• Spectral shearing interferometry

O(N) samples required
O(N) reconstruction time
SPIDER, ZAP-SPIDER, SEA-SPIDER,
CAR-SPIDER, SPIRIT, Gold-SPIDER, HOT-SPIDER,
M-SPIDER, Micro-SPIDER, Self-diffraction
SPIDER 2DSI, SPIRIT
Iaconis and Walmsley Opt. Lett., 1998, 23,
792-794
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Spectral shearing interferometry
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Noise sensitivity
Anderson et al. Appl. Phys. B, 2000, 70, 85-93
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Spectral nulls relative phase ambiguity
Keusters et al. J. Opt. Soc. Am. B, 2003, 20,
2226-2237
take complex argument
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Multiple shear reconstruction
Preprocessing O(N)
Solution of banded linear equations O(N)
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Numerical example
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Experiment
Spectral range 375 425 nm Minimum shear 0.24
nm ? T 2.24 ps N 215, 36 x transform limit
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Results
RMS TBP 11.9, 24 x transform limit
RMS field variation 0.02 (double shear) vs 0.12
(single shear)
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Summary

• Spectral shearing precision scales inversely with
  TBP
• Advantages of multi-shear
• small shear to track fine features
• large shear to correct accumulated error
• large shear to cross spectral nulls
• Implementation
• efficient, direct, linear least squares
• requires additional preprocessing
• Experiment
• Spatially encoded SPIDER with external ancilla
• Six-fold precision improvement

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Outlook
Nonlinear pulse compression (HCF, filaments)
pushed to the limit
Electro-optic SPIDER easily adjustable shear
Bromage et al. Opt. Lett., 2006, 31, 3523-3525
Simultaneous acquisition of many shears
Bohman et al. Opt. Express, 2008, 16, 10684-10689
Gorza et al. Opt. Express, 2007, 15, 15168-15174

• Details submitted to JOSA B

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Appendices
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Implementation - preprocessing
Preprocess for self-consistency
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Implementation least squares solution
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Experiment
Chirped-pulse amplifier
TiSaphhire oscillator
Test pulse synthesis
Test pulse
Stretcher
Amplifier
Compressor
Multiple shear SPIDER
Chirped ancilla
Spectral range 375 425 nm Minimum shear 0.24
nm -gt T 2.24 ps N 215, 36 x transform limit
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Raw data
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Processing
SNR ¼ 50
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Numerical example