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118:. Spectral shearing interferometry is similar in concept to lateral shearing interferometry, except the shearing is performed in the frequency domain. The spectral shear is typically generated by sum-frequency mixing the test pulse with two different quasi-monochromatic frequencies (usually derived by
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The final exponential term, resulting from the delay between the two interfering fields, can be obtained and removed from a calibration trace, which is achieved by interfering two unsheared pulses with the same time delay (this is typically performed by measuring the interference pattern of the two
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at one frequency to be referenced to the spectral phase at a different frequency, separated by the spectral shear - the difference in frequency of the two monochromatic beams. In order to extract the phase information, a carrier fringe pattern is introduced, typically by delaying the two spectrally
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are two 'alternating current' (ac) sidebands resulting from the interference of the two fields. The dc term contains information about the spectral intensity only, whereas the ac sidebands contain information about the spectral intensity and phase of the pulse (since the ac sidebands are
Hermitian
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The spectral intensity can be found via a quadratic equation using the intensity of the dc and ac terms (filtered independently via a similar method above) or more commonly from an independent measurement (typically the intensity of the dc term from the calibration trace), since this provides the
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There are several methods to reconstruct the spectral phase from the SPIDER phase, the simplest, most intuitive and commonly used method is to note that the above equation looks similar to a finite difference of the spectral phase (for small shears) and thus can be integrated using the trapezium
2456:
Radunsky, Aleksander S.; Kosik
Williams, Ellen M.; Walmsley, Ian A.; Wasylczyk, Piotr; Wasilewski, Wojciech; U'Ren, Alfred B.; Anderson, Matthew E. (2006). "Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal".
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1983:{\displaystyle {\begin{aligned}\phi (\omega _{0}+N|\Omega |)&={\begin{cases}-\sum _{n=1}^{N}\theta (\omega _{0}+n\Omega )&{\text{if}}\,\Omega >0\\\sum _{n=0}^{N-1}\theta (\omega _{0}+n|\Omega |)&{\text{if}}\,\Omega <0\end{cases}}\end{aligned}}}
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839:{\displaystyle {\begin{aligned}{\widetilde {S}}({\widetilde {t}})&={\mathfrak {F}}\\&={\widetilde {E}}^{dc}({\widetilde {t}})+{\widetilde {E}}^{ac}({\widetilde {t}}-\tau )+{\widetilde {E}}^{-ac}({\widetilde {t}}+\tau )\end{aligned}}}
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The unknown spectral phase of the pulse can be extracted using a simple, direct algebraic algorithm first described by Takeda. The first step involves
Fourier transforming the interferogram into the pseudo time domain:
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a copy of the pulse itself), although it can also be achieved by spectral filtering or even with linear electro-optic modulators for picosecond pulses. The interference between the two upconverted pulses allows the
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This method is exact for reconstructing group delay dispersion (GDD) and third order dispersion (TOD); the accuracy for higher order dispersion depends on the shear: smaller shear results in higher accuracy.
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falls to a sufficiently low value at some point on the concatenation grid, then the extracted phase difference at that point is undefined and the relative phase between adjacent spectral points is lost.
601:; and any dispersion of the pulse results in minor deviations in the nominal fringe spacing. Effectively it is these deviations in the nominal phase spacing that yield the dispersion of the test pulse .
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387:{\displaystyle {\begin{aligned}S(\omega )&=|E(\omega )+E(\omega -\Omega )e^{i\omega \tau }|^{2}\\&=I(\omega )+I(\omega -\Omega )+2{\sqrt {I(\omega )I(\omega -\Omega )}}\cos\end{aligned}}}
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fundamental pulses which have the same time-delay as the upconverted pulses). This enables the SPIDER phase to be extracted simply by taking the argument of the calibrated interferometric term:
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Radunsky, Aleksander S.; Walmsley, Ian A.; Gorza, Simon-Pierre; Wasylczyk, Piotr (2006). "Compact spectral shearing interferometer for ultrashort pulse characterization".
2111:
425:
2129:(SEA-SPIDER) is a variant of SPIDER. The spectral phase of an ultrashort laser pulse is encoded into a spatial fringe pattern rather than a spectral fringe pattern.
445:
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Witting, T.; Austin, D.R.; Walmsley, I.A. (2009), "Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization.",
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is an implementation of SPIDER in which the spectral shear required for a SPIDER measurement is generated in a thick nonlinear crystal with a carefully engineered
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One of the ac sidebands is filtered out and inverse
Fourier transformed back into the frequency domain, where the interferometric spectral phase can be extracted:
2141:
2011:
1403:{\displaystyle {\begin{aligned}D(\omega ,\Omega )&={\mathfrak {F}}^{-1}\\&={\sqrt {I(\omega )I(\omega -\Omega )}}e^{i}e^{-i\omega \tau }\end{aligned}}}
2358:"Accuracy measurements and improvement for complete characterization of optical pulses from nonlinear processes via multiple spectral-shearing interferometry"
2183:
Takeda, Mitsuo; Ina, Hideki; Kobayashi, Seiji (1982). "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry".
1165:{\displaystyle {\widetilde {E}}^{\pm ac}({\widetilde {t}}\mp \tau )={\mathfrak {F}}\{{\sqrt {I(\omega )I(\omega -\Omega )}}e^{\pm i}e^{\pm i\omega \tau }\}}
2226:
Kosik, E.M.; Radunsky, A.; Walmsley, I.A.; Dorrer, C. (2005), "Interferometric technique for measuring broadband ultrashort pulses at the sampling limit",
2118:
best signal to noise and no distortion from the upconversion process (e.g. spectral filtering from the phase matching function of a 'thick' crystal).
2270:"Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction"
2084:. Note that in the absence of any noise, this would provide an exact reproduction of the spectral phase at the sampled frequencies. However, if
853:
2561:
Iaconis, C; Walmsley, I. A. (1998), "Spectral Phase
Interferometry for Direct Electric-Field Reconstruction of Ultrashort Optical Pulses",
2631:
2515:, Ian A. Walmsley & Chris Iaconis, "Pulse measurement using frequency shifting techniques", issued 2003-8-26
2133:
58:
2016:
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pulse duration), the interference of the two time-delayed fields results in a cosine modulation with a nominal spacing of
2525:
Iaconis, C; Walmsley, I. A. (1999), "Self-Referencing
Spectral Interferometry for Measuring Ultrashort Optical Pulses",
1551:{\displaystyle {\begin{aligned}\theta (\omega )&=\angle \\&=\phi (\omega -\Omega )-\phi (\omega )\end{aligned}}}
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1732:{\displaystyle \phi (\omega _{N}-\Omega /2)\approxeq -\sum _{n=0}^{N}{\frac {\omega _{n+1}-\omega _{n}}{2\Omega }}}
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Wyatt, Adam S.; Grün, Alexander; Bates, Philip K.; Chalus, Olivier; Biegert, Jens; Walmsley, Ian A. (2011).
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The intensity of the interference pattern from two time-delayed spectrally sheared pulses can be written as
112:
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Walmsley, I. A.; Wong, V. (1996), "Characterization of the
Electric Field of Ultrashort Optical Pulses",
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SPIDER is an interferometric ultrashort pulse measurement technique in the frequency domain based on
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is the analytic signal representing the unknown (upconverted) field being measured,
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2144:(MIIPS), a method to characterize and manipulate the ultrashort pulse.
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spectral phase interferometry for direct electric-field reconstruction
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with a width inversely proportional to the spectral bandwidth, and
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Wyatt, A.S.; Walmsley, I.A.; Stibenz, G.; Steinmeyer, G. (2006),
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An alternative method us via concatenation of the SPIDER phase:
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conjugates of each other, they contain the same information).
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Concept of experimental implementation of conventional SPIDER.
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Flow chart describing the SPIDER reconstruction algorithm
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may be too technical for most readers to understand
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2142:multiphoton intrapulse interference phase scan
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95:measurement technique originally developed by
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59:Learn how and when to remove this message
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2134:frequency-resolved optical gating
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2106:{\displaystyle D(\omega )}
420:{\displaystyle E(\omega )}
2527:IEEE J. Quantum Electron.
559:Fourier transform limited
2619:10.1364/JOSAB.13.002453
2013:and concatenation grid
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440:{\displaystyle \Omega }
2205:10.1364/JOSA.72.000156
2122:Alternative techniques
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2132:Other techniques are
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460:{\displaystyle \tau }
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2383:10.1364/OE.19.025355
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2374:2011OExpr..1925355W
2328:2009OptL...34..881W
2286:2006OptL...31.1914W
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2197:1982JOSA...72..156T
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2648:Interferometry
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2459:Optics Letters
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2415:Optics Letters
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2362:Optics Express
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2316:Optics Letters
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2228:Optics Letters
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125:spectral phase
116:interferometry
108:
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67:
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28:
26:
19:
13:
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6:
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3:
2:
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2663:Laser science
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2138:streak camera
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98:
97:Chris Iaconis
94:
90:
86:
82:
73:
63:
60:
52:
42:
38:
32:
29:This article
27:
18:
17:
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2421:(2): 181–3.
2418:
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2188:
2184:
2178:
2164:Spectroscopy
2148:Micro-SPIDER
2147:
2146:
2131:
2126:
2125:
2116:
1993:for integer
1992:
1746:
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101:Ian Walmsley
88:
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2642:Categories
2563:Opt. Lett.
2191:(1): 156.
2170:References
2154:function.
107:The basics
2487:0146-9592
2435:0146-9592
2392:1094-4087
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49:May 2017
2607:Bibcode
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