Techniques for Electro-Optic Bunch Length
Measurement at the Femtosecond Level1^
P. Bolton, D. Dowell, P. Krejcik*, J. Rifkin
Stanford Linear Accelerator Center
2575 Sand Hill Rd, Menlo Park CA 94025
Abstract. Electro optic methods to modulate ultra-short laser pulses using the electric field of a
relativistic electron bunch have been demonstrated by several groups to obtain information about the
electron bunch length charge distribution. We discuss the merits of different approaches of transforming
the temporal coordinate of the electron bunch into either the spatial or frequency domains. The
requirements for achieving femtosecond resolution with this technique are discussed. These techniques
are being applied to the Linac Coherent Light Source (LCLS) and the Sub-Picosecond Photon Source
(SPPS) currently under construction at SLAC.
INTRODUCTION
New generations of accelerator-based x-ray laser sources will utilize extremely
short electron bunches. The bunches are considerably shorter than can be measured
with existing streak camera technology and will require new, innovative techniques to
diagnose and tune them. The Linac Coherent Light Source (LCLS) [1] to be built at
SLAC utilizes electron bunches as short as 80 femtoseconds rms to generate selfamplified stimulated emission (SASE) X-ray radiation in a PEL. The new SubPicosecond Photon Source (SPPS) [2] at SLAC offers a near term opportunity to test
and compare these different diagnostic techniques with bunches as short as 30 fs rms,
far shorter than anything so far produced in a high energy electron accelerator.
Conventional laser technology has succeeded in producing and characterizing
visible light pulses with the time structure that is well matched to these electron beam
requirements. The bridge between the two systems exists in the form of electro optic
(EO) crystals whose birefringence properties are modulated by the electric field of the
electron bunch to be measured. The transmission of polarized light through an EO
crystal is in turn modulated and the problem of measuring an electron bunch length is
thereby transformed into one of measuring the duration of a light pulse.
This paper discusses first the choices of configurations between laser and electron
beam geometry. For a given geometry the sensitivity and bandwidth requirements are
then presented. The light pulse detection techniques discussed show the evolution
from interferometric techniques to nonlinear autocorrelation methods and the
advantages they offer. Finally, the limits to resolution are discussed and the latest
developments towards pushing this limit.
* corresponding author, [email protected]
f
This work is supported under the DOE contract DE-AC03-76SF00515.
CP648, Beam Instrumentation Workshop 2002: Tenth Workshop, edited by G. A. Smith and T. Russo
© 2002 American Institute of Physics 0-7354-0103-9/02/$19.00
491
ELECTRO OPTIC
OPTIC PROBE
PROBE GEOMETRY
GEOMETRY
ELECTRO
configurations are
are possible.
possible. One
One isis where
where the
the probe
probe laser
laser pulse
pulse isis
Two basic configurations
the electron
electron beam
beam and
and the
the second
second where
where the
the two
two beams
beams are
are parallel
parallel and
and
transverse to the
co-propagating. Each
Each of
of these
these geometries
geometries has
has implications
implications for:
for: laser
laser power
power in
in the
the
co-propagating.
pulse sampling
sampling should
should be
be performed
performed in
in the
the spatial
spatial or
or frequency
frequency
crystal; whether the pulse
domain; and
and on
on the
the ultimate
ultimate resolution
resolution that
that could
could be
be achieved.
achieved. An
An illustration
illustration of
of the
the
domain;
is shown
shown in
in figure
figure 1,1, similar
similar to
to that
thatproposed
proposedininreference
reference[3].
[3].
transverse geometry is
In the transverse
transverse scheme
scheme aa cylindrical
cylindrical lens
lens brings
brings the
the polarized
polarized laser
laser beam
beam toto aa
ribbon focus
focus at
at the
the EO
EO crystal
crystal where
where itit overlaps
overlaps the
the electric
electric field
field of
of the
the electron
electron
bunch.
The
length
of
the
ribbon
focus
determines
the
duration
of
the
timing
gateinin
bunch. The length of the ribbon focus determines the duration of the timing gate
which the electron
electron bunch
bunch must
must be
be coincident.
coincident. A
A cross
cross polarizer
polarizer normally
normally extinguishes
extinguishes
reaching the CCD
CCD detector.
detector. However,
However, the
the light
light will
will be
be modulated
modulated in
in
the light reaching
proportion to
to the
the change
change in
in birefringence
birefringence induced
induced by
by the
the electric
electric field
field of
of the
the bunch.
bunch.
proportion
image recorded
recorded on
on the
the detector
detector is
is therefore
therefore aa convolution
convolution of
of the
the electron
electron bunch
bunch
The image
distribution and
and the
the temporal
temporal profile
profile of
ofthe
thelaser
laserpulse.
pulse.In
Inorder
orderto
toachieve
achievegood
good
charge distribution
resolution aa laser
laser pulse
pulse length
length much
much shorter
shorter than
than the
the electron
electron bunch
bunch length
length must
must be
be
resolution
example, aa Ti:sapphire
Tiisapphire laser
laser with
with 20
20 fsfs would
would resolve
resolve sub-picosecond
sub-picosecond
used. For example,
bunches.
electron bunches.
100 fs
fs electron
electron bunch
bunchisis30
30µm
jimininlength
lengthso
sosome
somemagnifying
magnifyingoptics
opticsmust
mustbe
beused
used
A 100
detector to
to overcome
overcome the
the pixel
pixel resolution
resolution limit
limit of
of approximately
approximately 99 µm
jim
in front of the detector
CCD camera.
camera. Furthermore,
Furthermore, the
the retardation
retardation in
in the
the crystal
crystal isis wavelength
wavelength dependant
dependant
in aa CCD
since aa short
short pulse
pulse laser
laser has
has by
by nature
natureaavery
very large
large bandwidth,
bandwidth,care
caremust
mustbe
begiven
given
and since
calibrating the system.
system. Wavelength
Wavelength calibration
calibration isis difficult
difficult in
in the
the transverse
transverse
to calibrating
where the
the extent
extent of
of the
the bunch
bunch isisto
tobe
bemeasured
measuredininthe
thespatial
spatialdomain.
domain.
geometry where
problem is
is partially
partially overcome
overcome in
in the
the second
second transverse
transverse geometry
geometry scheme
scheme
This problem
1. The laser pulse
pulse is
is chirped
chirped and
and the
the modulation
modulation of
of the
the electron
electronbunch
bunch
shown in figure 1.
now acts to gate a portion of the stretched
stretched laser
laser pulse.
pulse. A
A spectrometer
spectrometer detects
detects the
the
modulation
modulation in
in the
the frequency
frequency domain
domain thereby
thereby avoiding
avoiding limitations
limitations due
due to
to pixel
pixel
resolution
resolution and
and beam
beam size.
size. The
The wavelength
wavelength calibration
calibration of
of the
the optical
opticalelements
elementsisisreadily
readily
done
done with
with the
the electron
electron beam
beam off
off and
andusing
usingquarter-wave
quarter-waveplates.
plates.
Incoming
chirped laser
pulse
Grating
GratingSpectrometer
Spectromel
ωl
Analyzer
CCD
Detector
Analyzer
Electro-Optic
Crystal
Polarizer
Ribbon focus
laser pulse
Electro-Optic
Crystal
Polarizer
t
Detector
Ι
ω
FIGURE
FIGURE 1.
1. Transverse,
Transverse, line-focus
line-focus probe
probe geometry
geometry can
can produce
produceaaspatial
spatialimage
imageofofthe
thebunch[3]
bunch[3](left),
(left),
or
or gating
gating of
of aa chirped
chirped laser
laser pulse
pulse (right).
(right).
492
Beam
Beampipe
pipe
Electron bunch
Co-propagating
Laser pulse
Polarizer
Polarizer
j
EO
Crystal
EoVrystal
Spectrometer
Spectrometer
Analyzer
Analyzer
I
ωl
t
Initial
Initiallaser
laserchirp
chirp
t
ωs
Bunch
Bunchcharge
charge
Gated spectral
spectral signal
signal
Gated
FIGURE2.2.InInthe
thelongitudinal
longitudinalgeometry
geometrythe
theelectric
electric field
field from
from aa bunch
bunch modulates the polarization in
FIGURE
electrooptic
opticcrystal
crystaland
andgates
gatesthe
thetransmission
transmission of
of aa co-propagating,
co-propagating, chirped
chirped laser pulse.
ananelectro
ordertotoachieve
achievegood
good resolution
resolution the
the laser
laser must
must be
be focused
focused to a spot at the EO
InInorder
crystal
much
smaller
than
the
bunch
length.
Spot
sizes
of
few microns would be
crystal much smaller than the bunch length. Spot sizes of aa few
be
adequate
for
a
30
micron
(100
fs)
bunch
but
the
technique
now
suffers from
adequate for a 30 micron (100 fs) bunch but the technique
suffers
from excessive
excessive
powerdensity
densityininthe
theEO
EOcrystal.
crystal.
power
Transverse
probe
geometries
were used
used successfully
successfully in early experiments[4]
experiments [4] with
Transverse probe geometries were
picosecond
beams,
but
for
femtosecond
resolution
the
longitudinal
picosecond beams, but for femtosecond resolution the longitudinal probe
probe geometry
geometry
shown
in
figure
2
has
distinct
advantages.
In
the
longitudinal
geometry
shown in figure 2 has distinct advantages. In the longitudinal geometry the
the laser
laser pulse
pulse
co-propagateswith
withthe
theelectron
electron bunch.
bunch. The
The chirped
chirped laser
laser pulse
pulse is
is stretched
stretched to
co-propagates
to around
around
ensure timing
timing overlap
overlap with
with the
the electron
electron bunch.
bunch. The
The chirp
chirp provides
provides aa
1010psps toto ensure
correlation
between
the
time
domain
and
the
frequency
spread
of
the
pulse
correlation between the time domain and the frequency spread of the pulse which
which can
can
be
measured
with
great
precision[5]
with
a
spectrometer.
The
laser
pulse
need
be measured with great precision[5] with a spectrometer. The laser pulse need not
not be
be
focusedtotosmall
smalldimensions
dimensionsininthe
the EO
EO crystal
crystal so
so there
there is
is no
no limitation
limitation due
due to
focused
to laser
laser
powerdensity
densityininthe
thecrystal.
crystal.To
Tounderstand
understand the
the limiting
limiting resolution
resolution of
of this
power
this technique
technique we
we
firstlook
lookatatsome
someofofthe
theproperties
propertiesof
ofthe
theEO
EO interaction.
interaction.
first
ELECTRO OPTIC
OPTIC BASICS
BASICS
ELECTRO
Theelectric
electric field
field ofof the
the bunch
bunch alters
alters the
the optical
optical retardation
retardation of
of the
the birefringent
The
birefringent
crystal.
The
polarization,
F,
of
the
probe
laser
in
the
crystal
changes
with
the electric
crystal. The polarization, P, of the probe laser in the crystal changes with the
electric
field,
E,
in
proportion
to
the
susceptibility
according
to
field, E, in proportion to the susceptibility according to
2
3
P = e [x E+X E +X E +...~]
(1)
(1)
P = ε 00Xi1 E + X2 2 E 2 + 3X3 E 3 + K
The susceptibility, X , has the same symmetry as the crystal so that all crystals
The susceptibility, X , has the same symmetry as the crystal so that all crystals
except those with inversion symmetry exhibit some EO properties. The first term in
except those with inversion symmetry exhibit some EO properties. The first term in
the expansion in equation (1) is the linear, isotropic term. It is the second-order term
the expansion in equation (1) is the linear, isotropic term. It is the second-order term
that is exploited here, namely the linear EO effect, or Pockels effect, in which the
that is exploited here, namely the linear EO effect, or Pockels effect, in which the
polarization changes under the influence of the external, applied electric field of the
polarization
changes under
influence
the external,
applied
electric field
of the
bunch. A third-order
termthealso
exists of
which
drives the
second-order
EO effect,
bunch.
A
third-order
term
also
exists
which
drives
the
second-order
EO
effect,
referred to as the Kerr effect. Birefringence is the anisotropy of the crystal's refractive
referred to as the Kerr effect. Birefringence is the anisotropy of the crystal’s refractive
493
indices and results in differing propagation velocities along the different crystal axes.
Inindices
isotropic
of refraction,
n, velocities
is related along
to the the
susceptibility
by axes.
andmedia
resultsthe
inindex
differing
propagation
different crystal
2
In isotropic media the index of refraction,
n,
is
related
to
the
susceptibility
by
X^^ -!
(2)
2
n1 −through
1
(2) the
It is convenient to define the change Xin1 =
index
the EO crystal, following
methodology
of Yariv[6],
by the
defining
aninindex
principal
It is convenient
to define
change
indexellipsoid
through with
the EO
crystal,axes
following the
2
methodology of Yariv[6], by defining
with principal axes
x an index zellipsoid
2
2
2
(3)
nz2 = 1
nlx + y + —
(3)
2
2
nz2 given by the coefficients r// for a
The change in index with appliednxfieldn y is then
The crystal
change in index with applied field is then given by the coefficients rij for a
specific
specific crystal
3
 1
∆  2  = ∑ rij E j
(4)
 n ibunch
j =1
The electric field of an ultra-relativistic
of Ne electrons at a distance r, from
The electric
the crystal
is [7] field of an ultra-relativistic bunch of Ne electrons at a distance r, from
the crystal is [7]
s2
2N.e e −
in m.k.s units
E = 9x10' 9 2 N e e e 2σ
Er = 9 × 10
in m.k .s units
(5)
r
2π σ z
(5)
2N.e
1
and Er = 9x10 9 2 N e e 1
and Er = 9 × 10
r
2π σ z
measured at the center of a Gaussian bunch of length <7Z.
measured at the center of a Gaussian bunch of length σz.
The
opening angle, 1/y, of the electric field lines dictates that the crystal should be
The opening angle, 1/γ, of the electric field lines dictates that the crystal should be
within
for low
low energy
energy bunch
bunch length
length
within a a couple
couple ofof millimeters
millimeters of
of the
the bunch
bunch for
measurements
at
the
electron
gun.
At
GeV
energies
the
crystal
can
be
a
centimeter
measurements at the electron gun. At GeV energies the crystal can be a centimeter
away
awaywithout
withoutloss
lossofofresolution
resolution or
or sensitivity.
sensitivity.
The
retardation,
F,
of
the
light
crystal with
with trigonal
trigonalsymmetry
symmetrysuch
such
transmitted by
by aa crystal
The retardation, Γ, of the light transmitted
asasLiTaO
or
LiNbO
is
3
3
LiTaO3 or LiNbO3 is
2
z
max
d
1/γ
1/y
r
3
L
1
2
Ê
FIGURE 3. A relativistic bunch at a distance r from the crystal and laser pulse.
FIGURE 3. A relativistic bunch at a distance r from the crystal and laser pulse.
494
πL
Γ = 71'L E (/ne33r33 − no33r13 )\
= —-E(n
er33-n0rl3)
λ0
(6)
(6)
and is determined by the electric field strength, E, and the thickness of the crystal
and is determined by the electric field strength, E, and the thickness of the crystal
along
alongthe
thelight
lightpath,
path,L,
L,
/2 (when
the polarized
polarized light
light
The
electric
The electric field
field corresponding
corresponding to
to aa retardation
retardation of
of λA/2
(when the
changes
from
zero
to
100%
transmission)
is
therefore
changes from zero to 100% transmission) is therefore
λ0
1
EE=π =
3
L ( ne r33 − no3 r13 )
L (nlr^-ri.
(7)
(7)
N
e
2
9
e
==99x10'
×10 9 2N.e
r 2π σ z
from
fromwhich
whichthe
therequired
requiredthickness
thickness of
of the
the crystal
crystal can
can be
be determined.
determined.
AUTOCORRELATION
AUTOCORRELATION AND
AND DETECTION
DETECTION
The
by its
its amplitude
amplitude A,
A,
Thelight
light pulse
pulse transmitted
transmitted by
by the
the EO
EO crystal
crystal is
is characterized
characterized by
carrier
frequency
ω
,
carrier
phase
ϕ
and
chirp
ϕ
(t),
0 carrier phase (fa0 and chirp q> (t),
carrier frequency #b,
EE (( tt )) == A
(t ) +
(8)
( t ) cos (ω00tt ++ϕ(p(t)
A(t)cos(a
+ϕ(p00))
(8)
Its
means, shown
shown in
in figure
figure
Itstemporal
temporalprofile,
profile, C(t),
C(t), can
can be
be measured
measured by
by interferometric
interferometric means,
4a,
4a,which
whichisisan
anautocorrelation
autocorrelationtechnique
technique
∞
CC(0=
(t ) = ∫ E (τ )E ( t + τ ) dτ = E ( −t ) ⊗ E ( t )
(9)
(9)
∞
However,
to the
the Fourier
Fourier transform
transform of
of
However, by
by the
the Wiener-Khinchin
Wiener-Khinchin theorem
theorem this
this is
is equal
equal to
2
the
E  ,, and
not preserve
preserve phase
phase or
or
the magnitude
magnitude squared,
squared, FF \\E
and consequently
consequently does
does not
 νV 
asymmetry
asymmetryinformation
informationabout
aboutthe
thebunch.
bunch.
3rd harmonic
generation in
nonlinear crystal
M1
M1
N.L.
Xtal
M2
BS
time t
BS
grating
CCD
Detector
delay time t
FIGURE 4.4. Autocorrelation
Autocorrelation (left)
(left) with
with an
an interferometer,
interferometer, and
and aa nonlinear
nonlinear autocorrelator
autocorrelator (right)
FIGURE
(right) for
for
FrequencyResolved
ResolvedOptical
OpticalGating.
Gating.
Frequency
495
Alternatively, if the light rays cross at an angle inside a nonlinear crystal, as illustrated
in figure 4b, higher harmonics are generated and the unbalanced, third-order
correlation terms preserve pulse asymmetry information. Combining the nonlinear
autocorrelator with a grating spectrometer results in a powerful diagnostic to
Frequency Resolve the Optically Gated (FROG) pulses.
LIMITS TO RESOLUTION
The EO detection method is resolution limited by the phase slippage that occurs
from the slight difference in propagation velocity for the sub-millimeter radiation from
the bunch and the 800 nm laser radiation in the crystal arising from the difference in
refractive index, An,
Ar = -Arc
c
(10)
This effect is minimized by choosing a crystal with small An and small thickness, L.
For example, in LiTaOs An= 0.1 so that a 100 |Lim thick crystal has a slippage of 30 fs.
As an alternative we are investigating a new technique based on measuring the
wavelength shift that occurs at the entry and exit of the crystal where there is a timedependant change in refractive index
A/I
L dn
L 1/
3
3
-^=c--r
=--(^33A
dt c 2 ^
This effect has been observed in laser-plasma interactions[8] and is proposed as a
means to surpass the resolution limits set by phase slippage. For the crystal parameters
above, equation (11) predicts a 3% wavelength shift at the edges of the crystal.
In conclusion, it is expected that improvements in EO detection techniques will go
hand-in-hand with progress in the generation of ultra-short electron bunches over the
next few years.
REFERENCES
1. "LCLS CDR", SLAC-R-593, April 2002.
2. M. Cornacchia et al., "A Subpicosecond Photon Pulse Facility for SLAC", SLAC-PUB-8950, LCLSTN-01-7,Aug 2001. 28pp.
3. T. Srinivasan-Rao et al., "Novel Single Shot Scheme to Measure Submillimeter Electron Bunch
Lengths Using Electro-Optic Technique", Phys. Rev. ST Accel. Beams 5, 042801 (2002).
4. MJ. Fitch et al., "Electro-optic Measurement of the Wake Fields of a Relativistic Electron Beam", Phys. Rev.
Letters, Vol. 87, Num. 3, 034801(2001).
5 I. Wilke et al., "Single-shot Electron-beam Bunch Length Measurements", Physical Review. Letters 88, 124801,
2002.
6. A. Yariv, "Quantum Electronics", Springer-Verlag (1967).
7. A.W. Chao, "Physics of Collective Beam Instabilities", John Wiley & Sons, New York, 1993.
8. P. Bolton et al., "Propagation of Intense, Ultrashort Laser Pulses Through Metal Vapor", J.O.S.A. B, Volume
13, Issue 2, p. 336 (Feb. 1996).
496