Research Article Optica 1 Spectral phase interferometry for direct electric-ﬁeld reconstruction of synchrotron radiation

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Research Article Optica 1

Spectral phase interferometry for direct electric-ﬁeld

reconstruction of synchrotron radiation

TAKAO FUJI1,*, TATSUO KANEYASU2,3, MASAKI FUJIMOTO3, YASUAKI OKANO3, ELHAM SALEHI3,

MASAHITO HOSAKA4,5, YOSHIFUMI TAKASHIMA4, ATSUSHI MANO4, YASUMASA HIKOSAKA6, SHIN-ICHI

WADA7,AND MASAHIRO KATOH8,3,†

1Laser Science Laboratory, Toyota Technological Institute, Nagoya 468–8511, Japan

2SAGA Light Source, Tosu 841-0005, Japan

3Institute for Molecular Science, Okazaki 444-8585, Japan

4Synchrotron Radiation Research Center, Nagoya University, Nagoya, 464-0814, Japan

5National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China

6Institute of Liberal Arts and Sciences, University of Toyama, Toyama 930-0194, Japan

7Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

8Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima 739-0046, Japan

*Corresponding author: fuji@toyota-ti.ac.jp

†Corresponding author: mkatoh@hiroshima-u.ac.jp

Compiled October 14, 2022

Ultraviolet and extreme ultraviolet electric-ﬁelds produced by relativistic electrons in an undulator of a

synchrotron light source are characterized by using spectral phase interferometry for direct electric-ﬁeld

reconstruction (SPIDER). A tandem undulator with a phase shifter produces a pair of wavelength shifted

wave packets with some delay. The interferogram between the pair of the wave packets is analyzed with

a SPIDER algorithm, which is widely used for ultrashort pulse characterization. As a result, a 10-cycle

square shaped electric-ﬁeld is reconstructed. The waveform corresponds to the radiation from an electron

accelerated with the undulator which consists of 10 periods of permanent magnets. ©

2022 Optica Publishing

Group

http://dx.doi.org/10.1364/ao.XX.XXXXXX

1. INTRODUCTION

Synchrotron light sources have been developed for more than 70

years and currently ultrashort X-ray pulses are generated with

some free electron lasers (FELs) [

–

]. Characterization of the

pulses generated from such sources is very challenging due to

the short wavelength and the short pulse duration.

To characterize ultrashort pulses in the ultraviolet (UV) or

extreme ultraviolet (XUV) region, it is straightforward to mea-

sure the cross-correlation between the test and reference pulses.

However, it is very difﬁcult to prepare a reference pulse for

synchrotron light sources. Several synchronization systems be-

tween an ultrashort pulse laser and a synchrotron light source

have been realized and used for the estimation of the duration

of the pulses from some FELs [

–

], however, it is always chal-

lenging to synchronize such very different light sources within

femtosecond timing jitter.

The waveform of the electric-ﬁeld produced by an relativistic

electron in the undulator is basically deﬁned by the number of

magnets and the gap between the magnets in the undulator. The

number of permanent magnets and the gap between the magnets

deﬁne the number of oscillations and the carrier wavelength of

the waveform respectively. In the UVSOR-III synchrotron light

source, there is a tandem undulator which can produce two

wave packets. The wavelength can be scanned from XUV to

visible region. By changing the gap between the permanent

magnets of each undulator, it is possible to change the wave-

length of each wave packet individually. A phase shifter, which

consists of three pairs of electromagnets and forms a small chi-

cane for the electron beam, between the undulators can control

the delay between the wave packets in femtosecond regime with

an attosecond accuracy. The system was applied for coherent

control of atoms and molecules [

–

]. It is important to char-

acterize the electric-ﬁeld produced in the undulator for such

experiments.

We reported linear interferometric autocorrelation measure-

ments in the UV region for the spontaneous radiation from the

tandem undulator of UVSOR-III recently [

]. The shapes of the

measured autocorrelation traces were well reproduced by the

calculations assuming that the wave packet had the form of a

double-pulsed 10-cycle sinusoidal wave. However, the wave-

form of the wave packet cannot be directly reconstructed only

arXiv:2210.06652v1 [physics.optics] 13 Oct 2022

Research Article Optica 2

Fig. 1.

Schematic of the experiment. (a) Tandem undulator in the UVSOR-III synchrotron, consisting of two APPLE-II undulators

and each relativistic electron in the bunch emits a pair of 10-cycle light wave packets. The undulators were set to horizontal linear

polarization mode. The delay time between the wave packets is controlled by the phase shifter magnet between the two undulators.

The light wave packets are randomly distributed within the overall pulse length of 300 ps (FWHM), reﬂecting the length of an

electron bunch in the storage ring. (b) Setup for frequency-domain interferometry in the UV region. The UV spectrum of wave

packets was measured by using a grating spectrometer. (c) Setup for photoelectron spectroscopy in the XUV region. The XUV

spectra were derived from the photoelectron spectrum of helium. A hemispherical electron energy analyzer was used to measure

the photoelectron spectrum.

by the autocorrelation trace. Thus, for accurate measurement of

the waveform of the electric ﬁeld emitted by a single electron

passing through the undulator, it is essential to introduce a pulse

characterization method which allows for determining both the

spectral phase and amplitude of the light pulse.

In this paper, we report the characterization of the electric-

ﬁeld waveform generated in the undulator using an algorithm

of spectral phase interferometry for direct electric-ﬁeld recon-

struction (SPIDER) [

]. To our knowledge, it is the ﬁrst

time to characterize the UV and XUV electric-ﬁeld produced by

an accelerated electron in the undulator without assuming the

shape of the waveform.

2. SPIDER OF SYNCHROTRON RADIATION

SPIDER is a well-established femtosecond pulse characteriza-

tion method invented in 1998 [

]. The concept of the SPIDER

is the retrieval of the spectral phase by analyzing the fringes

of the interferogram between the test pulse and a spectrally

sheared replica. In order to obtain such a pair of pulses, a

strongly chirped pulse is prepared and sum frequency between

the chirped pulse and the test pulse at two different delay times

is taken. In this way, two delayed pulses with slightly different

center wavelengths, namely spectrally sheared replicas of the

original pulse, are obtained. The fringe deviation of the interfero-

gram from that of two delayed pulses with the same wavelength,

namely zero sheared replicas, corresponds to the derivative of

the spectral phase with the frequency, namely, the group delay.

By integrating the group delay with the frequency, the spectral

phase is obtained and by calculating the Fourier transform of it

together with the power spectrum it is possible to reconstruct

the time-domain picture of the electric-ﬁeld of the test pulse.

The twin tandem undulator generates a pair of wavelength

shifted wave packets with some delay. The interferogram be-

tween the pair of the wave packets can be considered as a “SPI-

DER” interferogram. Therefore, we can apply the same algo-

rithm as the SPIDER to the interferogram to reconstruct the

electric-ﬁeld generated from the undulator.

The important difference from the electric-ﬁeld reconstruc-

tion of ultrashort laser pulses is that the synchrotron radiation

is basically incoherent. In general, many electrons (

∼

the current case) compose an electron bunch with the duration

of a few hundred picoseconds, and are circulating together in

the storage ring. Each electron produces a wave packet of light

which does not interfere with each other. As a result, the gen-

erated light pulse consists of randomly superimposed

∼

wave packets within the duration of a few hundred picoseconds.

However, each wave packet is supposed to be identical with

each other. Thus, by using the SPIDER analysis, we obtain the

electric-ﬁeld of the wave packet generated from a single elec-

tron. For example, at BL1U of UVSOR-III a 10-cycle wave packet,

corresponding to

∼

1.2 fs pulse when it is operated at 35 eV, is

produced. We aim to characterize such a waveform.

3. EXPERIMENTAL

The experiment was carried out at the 750-MeV UVSOR-III stor-

age ring [

]. Figure 1(a) shows a schematic illustration of the

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ResearchArticleOptica1Spectralphaseinterferometryfordirectelectric-eldreconstructionofsynchrotronradiationTAKAOFUJI1,*,TATSUOKANEYASU2,3,MASAKIFUJIMOTO3,YASUAKIOKANO3,ELHAMSALEHI3,MASAHITOHOSAKA4,5,YOSHIFUMITAKASHIMA4,ATSUSHIMANO4,YASUMASAHIKOSAKA6,SHIN-ICHIWADA7,ANDMASAHIROKATOH8,3,1LaserScienceL...

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Research Article Optica 1 Spectral phase interferometry for direct electric-ﬁeld reconstruction of synchrotron radiation

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