# Ultrashort pulse characterization

Much of my research has concerned the characterization of ultrashort pulses of light. I pioneered multiple spectral shearing interferometry, performed the first spatio-temporal reconstructions of few-cycle long wavelength pulses, and have been part of a range of other developments.

## Introduction to ultrashort pulse characterization

The phase of electromagnetic radiation defines both its direction and temporal structure, and is therefore essential information in characterizing ultrashort pulses. As a general rule, electronic detectors for infrared and shorter wavelengths are not sensitive to the phase of incident radiation – only to the energy.

## Shearing interferometry

In general, interferometry provides the phase difference between two fields. When the two fields are duplicates of one another but with one being shifted along a certain dimension such as space, time or frequency, the phase difference is just the approximation to the derivative as seen in elementary calculus. In this context, the amount of shift is called the shear. Shearing in space is known as lateral shearing interferometry and is a common means of measuring optical wavefronts and testing optical surfaces. Shearing in frequency is the basis of the well-known SPIDER [1] technique.

### Multiple-spectral-shearing interferometry

If the unknown field has a region of zero intensity along the shearing axis which is larger than the shear, then shearing interferometry cannot determine the phase difference between the adjacent (nonzero) regions. Because the shear determines the resolution, it cannot in general be increased without a loss of fine details. This leads to a relative phase ambiguity [2] in shearing interferometry, as illustrated in the following figure:

With Dr Tobias Witting and Professor Ian Walmsley, I developed the first algorithm for reconstructing the phase of a field from a set of interferometry measurements with different shears [3]. We demonstrated the algorithm with data acquired experimentally using the SEA-SPIDER [4, 5] technique, and later with the SEA-CAR-SPIDER arrangement for acquiring the different shears simultaneously [6]. We also used the technique to study a classical analogues of sub-Planck structure [7] in a bichromatic double pulse.

## References

[1] C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. lett., vol. 23, iss. 10, pp. 792-794, 1998.
[Bibtex]
``````@Article{Iaconis-1998-Spectral,
Title = {Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses},
Author = {Iaconis, C. and Walmsley, I. A.},
Journal = {Opt. Lett.},
Year = {1998},
Number = {10},
Pages = {792-794},
Volume = {23},
Abstract = {We present a novel, self-referencing interferometric technique for measuring the amplitude and the phase of ultrashort optical pulses. {T}he apparatus uses a collinear geometry that requires no moving components. {T}he phase-retrieval procedure is noniterative and rapid and uses only two one-dimensional {F}ourier transforms. {W}e apply the technique to characterize ultrashort pulses from a mode-locked {T}i:sapphire oscillator.},
Doi = {10.1364/OL.23.000792},
File = {Iaconis-1998-Spectral.pdf:I/Iaconis-1998-Spectral.pdf:PDF},
Keywords = {spider},
Owner = {boz},
Timestamp = {2006.10.02},
Url = {http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-23-10-792}
}``````
[2] D. Keusters, H. S. Tan, P. O’Shea, E. Zeek, R. Trebino, and W. S. Warren, “Relative-phase ambiguities in measurements of ultrashort pulses with well-separated multiple frequency components,” J. opt. soc. am. b, vol. 20, iss. 10, pp. 2226-2237, 2003.
[Bibtex]
``````@Article{Keusters-2003-Relative-phase,
Title = {{Relative-phase ambiguities in measurements of ultrashort pulses with well-separated multiple frequency components}},
Author = {Keusters, D. and Tan, H.S. and O'Shea, P. and Zeek, E. and Trebino, R. and Warren, W.S.},
Journal = {J. Opt. Soc. Am. B},
Year = {2003},
Number = {10},
Pages = {2226--2237},
Volume = {20},
Abstract = {Ultrashort-pulse characterization techniques, such as the numerous variants of frequency-resolved optical gating (FROG) and spectral phase interferometry for direct electric-field reconstruction, fail to fully determine the relative phases of well-separated frequency components. If well-separated frequency components are also well separated in time, the cross-correlation variants (e.g., XFROG) succeed, but only if short, well-characterized gate pulses are used.},
Doi = {10.1364/JOSAB.20.002226},
File = {Keusters-2003-Relative-phase.pdf:K/Keusters-2003-Relative-phase.pdf:PDF},
Owner = {dane_austin},
Publisher = {OSA},
Timestamp = {2012.04.22},
Url = {http://www.opticsinfobase.org/josab/abstract.cfm?id=74424}
}``````
[3] D. R. Austin, T. Witting, and I. A. Walmsley, “High precision self-referenced phase retrieval of complex pulses with multiple-shearing spectral interferometry,” J. Opt. Soc. Am. B, vol. 26, iss. 9, pp. 1818-1830, 2009.
[Bibtex]
``````@Article{Austin-2009-High,
author = {Dane R. Austin and Tobias Witting and Ian A. Walmsley},
title = {High precision self-referenced phase retrieval of complex pulses with multiple-shearing spectral interferometry},
journal = {{J. Opt. Soc. Am. B}},
year = {2009},
volume = {26},
number = {9},
pages = {1818--1830},
abstract = {We show that using multiple shears in spectral shearing interferometry is a powerful technique for improving precision, thus enabling the measurement of more complex pulses and resolving phase ambiguities. We derive an efficient and robust optimal phase reconstruction algorithm for extracting the spectral phase from interferograms taken at an arbitrary number of different shears. We show that if the shear is easily adjustable then a multishear measurement always offers a superior precision, even when considering the loss of precision of the raw data necessitated by multiple acquisitions. We present numerical examples and demonstrate an experimental implementation of the measurement of a double pulse using two shears.},
doi = {10.1364/JOSAB.26.001818},
file = {Austin-2009-High.pdf:A/Austin-2009-High.pdf:PDF},
keywords = {Interferometry; Phase measurement; Ultrafast optics; Ultrafast measurements; Phase unwrapping},
owner = {dane_austin},
publisher = {OSA},
timestamp = {2012.03.30},
url = {http://josab.osa.org/abstract.cfm?URI=josab-26-9-1818},
}``````
[4] E. M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, “Interferometric technique for measuring broadband ultrashort pulses at the sampling limit,” Opt. lett., vol. 30, iss. 3, pp. 326-328, 2005.
[Bibtex]
``````@Article{Kosik-2005-Interferometric,
Title = {{Interferometric technique for measuring broadband ultrashort pulses at the sampling limit}},
Author = {Kosik, E.M. and Radunsky, A.S. and Walmsley, I.A. and Dorrer, C.},
Journal = {Opt. Lett.},
Year = {2005},
Number = {3},
Pages = {326--328},
Volume = {30},
Doi = {10.1364/OL.30.000326},
File = {Kosik-2005-Interferometric.pdf:K/Kosik-2005-Interferometric.pdf:PDF},
Owner = {dane_austin},
Publisher = {OSA},
Timestamp = {2012.04.22},
Url = {http://www.opticsinfobase.org/ol/abstract.cfm?id=82495}
}``````
[5] A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. lett., vol. 31, iss. 12, pp. 1914-1916, 2006.
[Bibtex]
``````@Article{Wyatt-2006-Sub-10,
Title = {{Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction}},
Author = {Wyatt, A.S. and Walmsley, I.A. and Stibenz, G. and Steinmeyer, G.},
Journal = {Opt. Lett.},
Year = {2006},
Number = {12},
Pages = {1914--1916},
Volume = {31},
Doi = {10.1364/OL.31.001914},
File = {Wyatt-2006-Sub-10.pdf:W/Wyatt-2006-Sub-10.pdf:PDF},
Owner = {dane_austin},
Publisher = {OSA},
Timestamp = {2012.04.22},
Url = {http://www.opticsinfobase.org/ol/abstract.cfm?id=90026}
}``````
[6] T. Witting, D. R. Austin, and I. A. Walmsley, “Ultrashort pulse characterization by spectral shearing interferometry with spatially chirped ancillae,” Opt. Express, vol. 17, iss. 21, pp. 18983-18994, 2009.
[Bibtex]
``````@Article{Witting-2009-Ultrashort,
author = {Tobias Witting and Dane R. Austin and Ian A. Walmsley},
title = {Ultrashort pulse characterization by spectral shearing interferometry with spatially chirped ancillae},
journal = {{Opt. Express}},
year = {2009},
volume = {17},
number = {21},
pages = {18983--18994},
abstract = {We report a new version of spectral phase interferometry for direct electric field reconstruction (SPIDER), in which two spatially chirped ancilla fields are used to generate a spatially encoded SPIDER interferogram. We dub this new technique Spatially Encoded Arrangement for Chirped ARrangement for SPIDER (SEA-CAR-SPIDER). The single shot interferogram contains multiple shears, the spectral amplitude of the test pulse, and the reference phase, which is accurate for broadband pulses. The technique enables consistency checking through the simultaneous acquisition of multiple shears and offers a simple and precise calibration method. All calibration parameters ? the shears, and the upconversionfrequency? can be accurately obtained from a single calibration trace.},
doi = {10.1364/OE.17.018983},
file = {Witting-2009-Ultrashort.pdf:W/Witting-2009-Ultrashort.pdf:PDF},
keywords = {Fringe analysis; Phase measurement; Ultrafast optics; Ultrafast measurements},
owner = {dane_austin},
publisher = {OSA},
timestamp = {2012.03.30},
url = {http://www.opticsexpress.org/abstract.cfm?URI=oe-17-21-18983},
}``````
[7] D. R. Austin, T. Witting, A. S. Wyatt, and I. A. Walmsley, “Measuring sub-Planck structural analogues in chronocyclic phase space,” Opt. Commun., vol. 283, iss. 5, pp. 855-859, 2010.
[Bibtex]