Revealing Carrier-Envelope Phase through Frequency Mixing and Interference in Frequency Resolved Optical Gating

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by  Edward W. Snedden

Revealing Carrier-Envelope Phase through Frequency Mixing and Interference in
Frequency Resolved Optical Gating
E.W. Snedden,1,∗ D.A. Walsh,1 and S.P. Jamison1,2
1Accelerator Science and Technology Center, STFC Daresbury National Laboratory, Warrington, WA4 4AD, United Kingdom
2Photon Science Institute, The University of Manchester, Manchester M13 9PL, United Kingdom
(Dated: January 21, 2015; Received; Accepted)
I. ABSTRACT ultrafast metrology full temporal characterisation typi-
callyrequiresaseparateandoftencomplexmeasurement
5 of CEP in addition to information such as that provided
We demonstrate that full temporal characterisation of
1 byFROG.Stereo-ATIhasbeenusedtomeasureCEPby
0 few-cycle electromagnetic pulses, including retrieval of measuringthedirectionofphotoelectronsemittedfollow-
2 the carrier envelope phase (CEP), can be directly ob- ingionisationinatime-of-flightspectrometer.9,13–15CEP
tainedfromFrequencyResolvedOpticalGating(FROG)
n measurementhasalsobeendemonstratedinso-calledat-
a techniques in which the interference between non-linear tosecond streaking,16,17 which utilises the spectral anal-
J frequency mixing processes is resolved. We derive a ysis of photoelectrons excited by sub-femtosecond high
0 framework for this scheme, defined Real Domain-FROG harmonic pulses. In this latter case the principles of
2 (ReD-FROG), as applied to the cases of interference be- FROG have been applied to the emitted photoelectrons
tween sum and difference frequency components and be-
(as opposed to the input electromagnetic pulse as per
s] tween fundamental and sum/difference frequency com- usual) in the FROG-CRAB algorithm.18
c ponents. A successful numerical demonstration of ReD-
i FROG as applied to the case of a self-referenced mea- TheCEPappearsasthezero-order(constant)termin
pt surement is provided. A proof-of-principle experiment is aTaylorexpansionofphase. IfφCE isdeterminedatone
o frequency it is therefore known uniquely. Recently, No-
performed in which the CEP of a single-cycle THz pulse
. mura10 and Shira11 have utilised this, determining φCE
s is accurately obtained and demonstrates the possibility
c at low frequencies through THz electro-optic sampling
for THz detection beyond the bandwidth limitations of
i (EOS) techniques, obtaining complete pulse information
s electro-optic sampling.
y when combined with traditional FROG techniques.
h
Here we show that self and cross-referenced FROG
p
techniques can be extended to be directly capable of
[
II. INTRODUCTION
full characterisation of the electric field temporal pro-

1 file of few-cycle electromagnetic pulses; similarly, we
v
show and experimentally demonstrate the complete re-
4 Few-cycle electromagnetic pulses offer a means of gen-
trieval of electric field can be obtained through cross-
6 erating and controlling physical processes on sub-
reference with higher frequency pulses, even when the
8 femtosecondtimescalesrelevantinatomicandcondensed
4 matterphysics. Thecharacterisationofsuchshortpulses higher-frequency probe is of similar duration and un-
0 remains a crucial aspect of the experimental process and known carrier-envelope phase. There is no requirement
1. has a rich history1–3. Of the many techniques available for the to-be-determined pulse to contain low-frequency
0 today, Frequency Resolved Optical Gating (FROG) has content accessible to δ-function like sampling, with re-
5 found widespread application due to its robustness and trieval possible directly from frequency-mixing spectro-
1 grams.
relatively simple experimental implementation. An ex-
:
v pansive array of related FROG techniques have been de-
i velopedin thelast two decades4–8; each offerspecific ad-
X
vantages in varying experimental conditions, yet share III. RED-FROG: THEORY AND RETRIEVAL
ar a common mathematical and physical basis: the mea- ALGORITHM
surement of an intensity spectrogram from a non-linear
combination of pulses. This is widely held to make de-
FROG of electromagnetic pulse characterisation consists
termination of the carrier-envelope phase (CEP, φCE)
ofaspectrallyresolvedauto-orcross-correlationofpulses
beyond FROG techniques2,9–12.
mediated by a non-linear mixing process. Herein the de-
Forelectromagneticpulseswithmanycyclesofthecar- tailed discussion assumes second-order mixing through
rier frequency the CEP approximates a simple time shift χ(2), although the approach and results can be readily
of the carrier oscillation and is often of limited physical modified to higher order mixing. For observable, real,
interest; for few-cycle pulses however, CEP qualitatively electric fields in the time domain, E1(t), E2(t) the com-
alters the temporal profile of the electric field and subse- plex spectra E˜ (ω), E˜ (ω) are defined from the Fourier
1 2
quently the interaction physics of the pulse. In current transform, introducing the mathematical construct of
2
negative frequencies. For the χ(2) interaction between
pulses the spectrogram, the spectrum of χ(2) generated (A)
field as a function of relative delay τ between input
pulses, can be given as:
(cid:12) (cid:90) ∞ (cid:12)2
I(ω;τ)=(cid:12)(cid:12)R˜(ω) dΩE˜1(ω−Ω)E˜2(Ω)exp(iΩτ)(cid:12)(cid:12) (,1)
(cid:12) (cid:12)
−∞
in which we take the common approximation that the
linear and non-linear material response functions can
be collected outside the integral in the response func-
tion R(ω).12,19 Techniques such as surface harmonic
generation20,21 or phase-match angle-dithering22 are ca- (B)
pable of very high bandwidth response, as would be nec-
essary for few cycle pulses. As the specific form of R(ω)
does not affect either analysis or conclusion it is omitted
from the following discussion.
The carrier envelope phase φCE is the phase contribu-
tion that is widely accepted to be unmeasurable through
FROG phase retrieval; to highlight conditions for obser-
vationandretrieval,φCE isexplicitlyseparatedoutfrom
the total spectral phase. All electric fields are explicitly
constrained to be real in the time domain, which gives
(cid:26)E˜(ω)exp(iφCE) ; ω >0
E˜ (ω)= (2)
total E˜∗(|ω|)exp(−iφCE) ; ω <0
FIG. 1. Schematic demonstrating bandwidth conditions for
carrier envelope phase observation, for the two examples dis-
The imposition of the physical constraint for all fields to
cussed in the text. A) Self referenced mixing of a few cy-
be purely real in the time domain and, in particular, the cle pulse. (top) spectrum for input pulse; (bottom) the sum
Heaviside functional form of φCE(ω), is what gives rise and difference spectra. DFG = DFG for this configura-
+ −
to the observability of the carrier-envelope phase. Intro- tion. (B)Cross-correlationofspectrallydistinctpulses. (top)
ducing the functional form of equation 2 for the electric input spectra; (bottom) frequency mixed output, for which
fields, the spectrogram can be expressed as DFG− ≡0.
I(ω;τ)=|SFG(ω;τ)|2+|DFG (ω;τ)|2+|DFG (ω;τ)|2
+ −
and difference frequency contributions spectrally overlap
(cid:110) (cid:111) non-zero the absolute carrier phase becomes observable.
+2(cid:60) SFG(ω;τ)DFG∗+(ω;τ) ei2φC2E In this work we address two specific cases; that of a
single broad-band pulse cross-referenced with itself, and,
(cid:110) (cid:111)
+2(cid:60) SFG(ω;τ)DFG∗−(ω;τ) ei2φC1E as part of a proof-of-concept demonstration, the cross-
correlation of two spectrally distinguishable pulses. The
(cid:110) (cid:111) firstcaseappliestothemeasurementoffew-cycleoptical
+2(cid:60) DFG+(ω;τ)DFG∗−(ω;τ) ei2φC1E−i2φC2E (3) pulses;thesecondcasedescribestheunambiguousdeter-
minationoftheelectricfieldofapulsethroughsampling
where with another (unknown) optical field, which may be of
(cid:90) ω similarorlongerdurationthanthelowerfrequencypulse.
SFG(ω;τ)≡ dΩE˜ (ω−Ω)E˜ (Ω;τ), Representativefieldamplitudespectraofthesetwocases
1 2
0 and the relative extent of the sum and difference fre-
(cid:90) ∞
DFG (ω;τ)≡ dΩE˜∗(Ω−ω)E˜ (Ω;τ) quency terms are shown schematically in Fig. 1. The
− 1 2 principlesdiscussedwiththeseexamplecanbereadilyex-
ω
(cid:90) +∞ tended to address other specific spectral considerations,
DFG (ω;τ)≡ dΩE˜ (ω+Ω)E˜∗(Ω;τ). (4) such as spectrally overlapping pulses.
+ 1 2
0
Todemonstratethecompleteelectricfieldretrievalfor
The contributions arising from sum-frequency (SFG) the self-referenced measurement of a single pulse, test
and difference frequency generation are represented by pulses with complex spectra differing only in carrier-
SFGand(DFG ,DFG )respectively. Whenbothsum envelope phase have been constructed, as shown in
+ −
3
φ CE = 0
φ CE = π/2
FIG. 2. Numerical demonstration of the self-referencing retrieval of a transform-limited single-cycle optical pulse (110 THz
bandwidth Gaussian with peak centred at 375 THz). A) Simulated experimental spectrogram with φCE = 0. B) Retrieved
spectrogram, in which the retrieval has been performed over a truncated spectral region (frequencies above 375 THz); C)
comparison of input and retrieved electric field profile. D-F) as above, with φCE =π/2 rad. All spectrograms are shown with
logarithmic intensity scale.
Fig. 2C, F. Simulated ’experimental’ spectrograms were andcomplexityofReD-FROG,butislimitedtomeasure-
constructed directly as the product of the time domain ments obeying equation 1. For more complex pulses, or
fields. Modified FROG retrieval algorithms, accounting instancesforwhichdispersionofthemixingmediumcan-
for the constraint of a strictly real time domain field, not be neglected, a more complex version of the decon-
arethenappliedtothe’experimental’spectrograms. Re- volution algorithm may be required.24 The spectral con-
trieval has been examined in presence of both measure- straintofrealtime-domainfieldscanbeachievedthrough
ment noise and spectral truncation. extendingthemeasuredspectrogrambymirrorreflection
ConventionalFROGalgorithmsfollowatwostageiter- about zero-frequency and applying the so-called ’numer-
ativeprocedure,thefirstbeingthecomparisonofthefield ical constraint’ minimisation procedure on the extended
amplitudes of the product spectrogram and the data. dataset. Througheffectiveinclusionofnegativefrequen-
Thesecond’numerical-constraint’drawsonthephysicsof cies, and the pinning of the spectrogram to have mirror
therelevantfrequencymixingprocesstoextracttheindi- symmetry, the input field retrieved is constrained to be
vidualtimedomainfieldsfromthefield-productspectro- real in the time domain. In this case the mirror symme-
gram. Thisconstraintisconventionallyundertakenfrom try constrains the retrieved fields to have the Hermitian
afunctionalminimisationbetweenintensityspectrogram propertynecessaryforthetimedomainfieldstobepurely
andtheexpectedspectrograminferredfromiteratedtest real.
fields and the physical process giving rise to frequency Theretrievalalgorithmwasappliedonaspectraltrun-
mixing. cation of the measurement data; such a spectral limited
We have modified the PCGPA FROG retrieval algo- data set is to be expected in any practicable implemen-
rithm23 to include the physical constraint of a real time- tation. To fully investigate the effect of truncation, re-
domain field, which together with the frequency-mixing trievalwasrepeatedforarangeofcut-offfrequenciesbe-
spectral overlap, we label as ReD-FROG (Real Domain- tween 325 and 375 THz.
FROG) retrieval for distinction from conventional algo- AsshowninFig.2C,F,thecorrectandfull(including
rithms. TheuseofthePCGPAinprovidingthenecessary CEP)electricfieldtemporalprofileisrecoveredfromthe
deconvolution step decreases both the processing time modified retrieval algorithm. All ReD-FROG retrievals
4
were based on a 512x512 grid. For Figs. 2C and 2F, throughinterferencebetweeneitherthefundamentalfield
FROG errors of 5×10−3 and 6×10−3 were respectively E˜ and the sum-frequency field, or between the funda-
1
obtained. In the given case the to-be-determined pulse mental and E˜ and difference frequency fields. The rela-
1
was centred at 375THz, and only the spectrogram data tive bandwidth requirements are shown schematically in
for frequencies > 375THz was included in the retrieval; Fig. 3A; the carrier envelope phase is observable for a
similar agreement in the retrieved profile was obtained bandwidth satisfying ∆≥ωL. This criterion is the same
across the full range of cut-off frequencies investigated. asthatutilisedinf-2fbeatingschemesfortheCEPstabil-
Foranunambiguouselectricfielddeterminationitissuf- isationofrepetitivepulsetrains;14,25–27suchstabilisation
ficient to include the sum-frequency region of the spec- schemeshowevercannotprovideapracticalmeasurement
trogram, in the presence of some overlapping difference- of CEP, requiring extremely accurate characterisation of
frequency mixing spectral content. Stable convergence the dispersion associated with the experimental appara-
was recorded with and without use of a spectral con- tus.3,14 Equation 6 demonstrates resolving this process
straint corresponding to a measurement of spectral in- as part of a FROG measurement provides the means to
tensity6 applied over the truncated frequency range, al- measure absolute phase without the need of a frequency
though the rate of convergence was improved with its comb.
implementation.
Figure3Bpresentsanexampleofthespectrogramaris-
Up to this point in our analysis in we have taken
ing from a self-referencing measurement of a transform-
the conventional form of the FROG spectrogram (Equa-
limited Gaussian pulse (75 THz bandwidth) in which
tion 1), in which the only the non-linear generated fields
overlapwiththeinputfieldoccurs. Theoverlapbetween
are included. In this arrangement the bandwidth (∆ ≡
sum and difference frequency generated fields is absent
ωU −ωL) necessary for carrier envelope observability is
in this case and the interference features arise from the
∆ ≥ 2ωL. By inclusion of the input field in the mea-
first three interference terms in equation 6.
surementprocess,additionalφCE dependentinterference
terms arise which allow the bandwidth requirements to
be relaxed. As a simplification, we assume that only one
of the input fields spectrally overlaps with the mixing
fields; undertheseconditionsthespectrogramcanbeex-
pressed as:
(cid:12) (cid:90) ∞ (cid:12)2
I(ω;τ)=(cid:12)(cid:12)E˜1(ω)+ dΩE˜1(ω−Ω)E˜2(Ω)exp(iΩτ)(cid:12)(cid:12)(5.)
(cid:12) (cid:12)
−∞
Explicit introduction of the CEP and expansion of the
integral (as performed for equation 3) yields
(cid:12) (cid:12)2
I(ω;τ)=(cid:12)E˜ (ω)(cid:12) +|SFG(ω;τ)|2+|DFG (ω;τ)|2+|DFG (ω;τ)|2 Time delay / fs
(cid:12) 1 (cid:12) + − -10 -5 0 5 1 0 -10 0 10
A B
1000 0.6
(cid:110) (cid:111)
+2(cid:60) E˜1(ω)SFG∗(ω;τ) e−iφC2E 0.2
0
500 -0.2
++22(cid:60)(cid:60)(cid:110)(cid:110)EE˜˜11((ωω))DDFFGG∗−∗+((ωω;;ττ)) eeiiφ2φC2C1EE(cid:111)−iφC2E(cid:111) zHT / ycneuqerF 10000 C 00..011 ytisnetnI D -000..26.6 )desilamron( dleif cirtcelE
0.001
+2(cid:60)(cid:110)SFG(ω;τ)DFG∗+(ω;τ) ei2φC2E(cid:111) 500 -0.2
-0.6
(cid:110) (cid:111) 0
+2(cid:60) SFG(ω;τ)DFG∗−(ω;τ) ei2φC1E -10 -5 Time d0e lay / fs 5 10 -10 Time d0e lay / fs 10
(cid:110) (cid:111)
+2(cid:60) DFG+(ω;τ)DFG∗−(ω;τ) ei2φC1E−i2φC2E FIG. 3.(6)Schematic of bandwidth requirements for carrier
phase observation through interference between fundamental
andsum(ordifference)frequencyfields. (B,C)Spectrograms
The additional interference terms in the above expres-
for a self-referencing measurement of a Gaussian transform-
sion allow for carrier envelope phase observation even
limited femtosecond pulse (375 THz carrier frequency, band-
when there is no spectral overlap between sum and dif- width75THz),φCE =0andφCE =π/2 radfor(B)and(C)
ference frequency mixing. The first two interference respectively.
termsinequation6yieldmeasurementofthephaseφCE
2
5
IV. EXPERIMENT: CHARACTERISATION OF
SINGLE-CYCLE THZ RADIATION
We now consider the ReD-FROG process applied to the
case of spectrally distinct pulses, as in Figure 1B. For
this configuration DFG (ω;τ) ≡ 0, and therefore φCE
− 1
and φCE −φCE are not observable. Conversely the car-
1 2
rierenvelopephaseφCE observableisindependentofthe
2
(unknown) CEP phase of the upper band pulse. To ob-
serve φCE we require ∆ ≡ωU −ωL >ωL.
2 1 1 1 2
In this case a benchmarked proof-of-concept experi- Experiment
ment is feasible; a quasi-single cycle THz pulse can serve ‘True’ field,
EO sampling, 45fs probe
as the lower frequency pulse to be determined, while
an optical pulse of similar bandwidth acts as the higher
frequency probe. For the benchmarking, a significantly
broader bandwidth δ-function like optical pulse can be
employed for electro-optic sampling (EOS),28,29 obtain-
inganindependentmeasureofthetrueelectricfieldpro- ϕ CE = 17o r-FROG retrieved field
500fs probe
file. ReD-FROG retrieval
Such an experimental demonstration has been per-
formed, with the experimental arrangement shown in
Fig. 4. An amplified femtosecond Ti:Sapphire laser sys- EO sampling,
500fs probe
tem (Coherent Micra/Legend, amplifier output: 45fs,
1mJ at 800nm) was used to drive a large-area semi-
insulating GaAs photo-conductive antenna, producing
quasi-single cycle sub-ps THz pulses. The pulses were
detected within the near-field region of the antenna, al-
lowingtheelectricfieldoscillationtohaveaunipolarap-
FIG. 4. A) Schematic of experimental arrangement for car-
pearance. The optical probe pulse was selected prior to rierphaseretrievalandbenchmarking. B)Measuredspectro-
the PCA using a beam-splitter and directed through a gramwitha1THzbandwidth,500fsduration,opticalprobe;
zero-dispersion4-ffilter,allowingthepulsebandwidthto C) ReD-FROG retrieved spectrogram D) comparison of true
beselectedasrequired. Thebenchmarkingmeasurement electric field as determined by electro-optic sampling with a
of the temporal profile of the THz pulse was performed 45fs probe, and that from the ReD-FROG retrieval. The
using a standard balanced detection EOS arrangement electro-optic sampling measurement for the spectrally nar-
using a 45fs optical probe.30 For the spectrogram re- rowed 500fs probe is also shown for comparison. Spectro-
grams are shown with logarithmic intensity scale.
trieval experiments the optical bandwidth was restricted
to 1THz, less than the full bandwidth of the THz pulse,
withcorrespondingincreaseindurationto500fs. Optical
the CEP of the single-cycle pulse is correctly identified.
probetemporalenvelopeswereconfirmedwithacustom-
Forcomparisonthefieldprofileinferredbydirectelectro-
built SHG-FROG setup with 100 µm thick BBO.
opticsamplingwiththe1THzbandwidthprobe,without
Both optical and THz beams were focused into a spectrally resolved phase retrieval, is also shown.
(cid:104)¯110(cid:105)orientatedZnTecrystal. Thefrequency-mixingsig-
Whilst this experiment confirms the validity of CEP
nal was isolated from residual input-probe light using
retrieval using ReD-FROG, the approach also finds im-
a Glan-Thompson calcite polariser and spectrally anal-
mediate application in surpassing probe-duration limi-
ysed as a function of the relative delay between the THz
tations present in high time-resolution EOS. Continuing
and optical probe beams using an imaging spectrometer
the notation of section II, these limitations can be ex-
(JobinYvon,iHR550)andintensifiedCCDcamera(PCO pressedinthefrequencydomainas∆(cid:29)ωH;forthesame
DiCamPRO). A ReD-FROG algorithm as described ear-
optical probe duration, we estimate that ReD-FROG
lier was applied to retrieve the field, using only the mea- (∆ ≥ ωL) is capable of measuring THz pulse durations
sured spectrogram as input.
×3-4shorterthanthataccessiblethroughEOS.Theonly
The measured and retrieved spectrograms are shown existing or proposed THz schemes with similar capabil-
inFigures4B,C,togetherwiththeReD-FROGretrieved ities, such as spectral upconversion31 or BMX-FROG,32
fieldtimeprofile. TheFROGerrorintheretrievedspec- rely on multi-stage detection in which the output of the
trogram was 0.01. Despite the complex form of the THz electro-optic effect is measured as part of a second, dis-
pulse, both main peak and oscillations over a period tinct non-linear process (such as an auto-correlation or
of several picoseconds (due to THz absorption by am- FROG). The use of consecutive non-linear stages for
bient water vapour) are recovered almost perfectly and pulseanalysislimitstheavailablesignaltonoiseratioand
6
thustherangeofTHzsourcesthatcanbemeasured; the carrierenvelopephase. Numericalsimulationshavebeen
application of the ReD-FROG method, being a single- used to demonstrate the capability for few-cycle optical
stage direct analysis of the EO effect, overcomes such pulses. A proof-of-concept benchmarked experiment us-
limitations and presents as a more robust and versatile ing single-cycle THz radiation was performed and con-
measurement technique. firmed the validity of the formalism. This method opens
upnewavenuesofpossibilityinthemeasurementoffew-
cycle electric fields and demonstrates that, contrary to
V. CONCLUSIONS previous expectations, FROG is directly capable of mea-
suring absolute phase. Potential applications for ReD-
FROGinhightime-resolutionelectro-opticsamplingare
We have demonstrated that a spectrally-resolved mea-
also envisaged as a means to exceed the bandwidth lim-
surement of the superposition of non-linear frequency
itations of standard electro-optic sampling techniques.
mixing processes is capable of unambiguous electric field
temporal characterisation, including the measurement of
∗ [email protected] 18 Mairesse, Y., Qu`er`e, F. Frequency-resolved optical gat-
1 Rulli`ere, C. Femtosecond Laser Pulses (Springer, 2003) ingforcompletereconstructionofattosecondbursts.Phys.
2 Trebino, R. et al. Simple devices for measuring complex Rev. A 71, 011401 (2005)
ultrashort pulses Laser Photon. Rev. 3 314 (2009) 19 Baltuˇska, A., Pshenichnikov, M.S., Wiersma, D.A. Am-
3 Walmsley, I.A., Dorrer, C. Characterisation of ultrashort plitude and phase characterization of 4.5-fs pulses by
electromagnetic pulses. Adv. Opt. Photon. 1, 308-437 frequency-resolvedopticalgating.Opt.Lett.23,1474-1476
(2009) (1998)
4 Kane,D.J.,TrebinoR.Single-shotmeasurementofthein- 20 Tsang, T, Krumbugel, M.A., DeLong, K.W., Fit-
tensityandphaseofanarbitraryultrashortpulsebyusing tinghoff, D.N., Trebino, R. Frequency-resolved optical-
frequencyresolvedopticalgating.Opt.Lett.18,3277-3295 gating measurements of ultrashort pulses using surface
(1993) third-harmonic generation Opt. Lett. 21 1381 (1996)
5 Trebino, R. et al. Measuring ultrashort laser pulses in the 21 Anderson, M.E., Witting, T. Walmsley, I.A. Gold-
time-frequency domain using frequency resolved optical SPIDER: spectral phase interferometry for direct elec-
gating. Rev. Sci. Instr. 68, 3277-3295 (1997) tric field reconstruction ultilizing sum-frequency genera-
6 Trebino, R. The Measurement of Ultrashort Laser Pulses tionfromagoldsurface.J.Opt.Soc.Am.B 25A13(2008)
(Kluwer Academic Publishers, 2002) 22 Gu, X. et al. Frequency-resolved optical gating and
7 O’Shea, P., Kimmel, M., Gu, X., Trebino, R. Highly sim- single-shot spectral measurements reveal fine structure in
plifieddeviceforultrashortpulsemeasurement.Opt. Lett. microstructure-fibrecontinuum.Opt. Lett.271174(2002)
26, 932-934 (2001) 23 Kane, D. Recent progress toward real-time measurement
8 Fittinghoff, D.N. et al. Measurement of the intensity and ofultrashortlaserpulses.IEEE J. Quantum Electron.35,
phase of ultraweak ultrashort laser pulses. Opt. Lett. 21, 421-431 (1999)
884-886 (1996) 24 DeLong, K.W., Ladera, C.L., Trebino, R., Kohler, B.,
9 Paasch-Colberg et al. Solid-state light-phase detector Na- Wilson, K.R. Ultrashort-pulse measurement using nonin-
ture Photonics 8 214 (2014) stantaneous nonlinearities: Raman effects in frequency-
10 Nomura, Y., Shirai, H., Fuji, T. Frequency resolved opti- resolved optical gating. Opt. Lett. 20, 486-488 (1995)
calgatingcapableofcarrier-envelopephasedetermination. 25 Telle, H.R. et al. Carrier-envelope offset phase control: a
Nat. Commun. 4, 3820-3831 (2013) novel concept for absolute optical frequency measurement
11 Shirai,Y,Nomura,Y.,Fuji.TReal-timewaveformcharac- andultrashortpulsegeneration.Appl.Phys.B 69,327-332
terizationbyusingfrequency-resolvedopticalgatingcapa- (1999)
bleofcarrier-envelopephasedetermination.IEEEPhoton. 26 Jones, D.J. et al. Carrier-envelope phase control of fem-
J. 6, 3300212 (2014) tosecond mode-locked lasers and direct optical frequency
12 Cheng, Z., Fu¨rbach, A., Sartania, S., Lenzner, M. Ampli- synthesis. Science 288, 635-639 (2000)
tude and chirp characterization of high-power laser pulses 27 Holzworth, R. Optical frequency synthesis for precision
in the 5 fs regime. Opt. Lett. 24, 247-249 (1999) spectroscopy. Phys. Rev. Lett. 85, 2264-2267 (2000)
13 Paulus,G.G.et al.Measurementofthephaseoffew-cycle 28 Gallot, G., Grischkowsky, D. Electro-optic detection of
laser pulses. Phys. Rev. Lett. 91, 253004 (2003) THz radiation. JOSAB 16, 1204-1212 (1999)
14 Paulus,G.G.Ameterofthe”absolute”phaseoffew-cycle 29 Jamison, S.P., MacLeod, A.M., Berden, G., Jaroszynski,
laser pulses. Laser Phys. 15, 843-854 (2005) D.A.,Gillespie,W.A.Temporally-resolvedelectro-opticef-
15 Wittmann, T. et al. Single-shot carrier-envelope phase fect. Opt. Lett. 31, 1753-1755 (2006)
measurementoffew-cyclelaserpulses.NaturePhys.5,357- 30 Walsh, D.A. et al. Role of misalignment-induced angular
362 (2009) chirpintheelectro-opticdetectionofTHzwaves.Opt.Ex-
16 Hentschel, M. et al. Attosecond metrology. Nature 414, press 22, 12028-12037 (2014)
509-513 (2001) 31 Jamison, S.P., Berden, G., Phillips, P.J., Gillespie, W.A.,
17 Kienberger, R. et al. Atomic transient recorder. Nature MacLeod, A.M. Upconversion of a relativistic coulomb
427, 817-821 (2004) fieldterahertzpulsetothenearinfrared.Appl.Phys.Lett.
7
96, 231114 (2010)
32 Helle, M.H., Gordon, D.F., Kaganovich, D., Ting, A.
Extending electro-optic detection to ultrashort electron
beams. Phys. Rev. Spec. Top. Accel. Beams 15, 052801
(2012)