OPTICAL PHASE LOCKING OF MODELOCKED LASERS FOR PARTICLE
ACCELERATORS*
T. Plettner, S. Sinha, J. Wisdom, Stanford University, Stanford, CA 94305
E. Colby, SLAC, Menlo Park , CA, 94025
Abstract
Particle accelerators require precise phase control of the
electric field through the entire accelerator structure. Thus
a future laser driven particle accelerator will require
optical synchronism between the high-peak power laser
sources that power the accelerator. The precise laser
architecture for a laser driven particle accelerator is not
determined yet, however it is clear that the ability to
phase-lock independent modelocked oscillators will be of
crucial importance. We report the present status on our
work to demonstrate long term phaselocking between two
modelocked lasers to within one dregee of optical phase
and describe the optical synchronization techniques that
we employ.
INTRODUCTION
Laser-driven acceleration of relativistic particles in
vacuum has been proposed and studied on a theoretical
basis for many years [1,2,3]. A strong motivation for this
effort has been the potential ~ 1 GeV/m sustained energy
gradient that laser-driven particle accelerators could
deliver [4]. Two elements that have allowed this particle
acceleration technology to become feasible are the
appearance of tabletop high peak power lasers [5] and the
maturing of micro fabrication technologies [6].
Furthermore, the physics principle for laser-driven
acceleration of relativistic electrons in a structure loaded
vacuum was recently demonstrated [7]. At present
extensive research and development is being carried out
on the architecture design of extended laser accelerator
structures [8,9] and on efficiency and luminosity
considerations [10,11]. On the other hand little thought
has been devoted on the still pending development of the
laser architecture that will drive an extended laser driven
particle accelerator. While it is true that laser-driven
particle acceleration profits from progress made in laser
power scaling, wallplug efficiency improvements [12],
newly developed laser frequency comb stabilization and
pulse synchronization techniques [13] there are still laser
requirements specific to particle acceleration that will
require dedicated research. One such aspect is the ability
to sustain optical stability between independent
modelocked oscillators to within 1 degree of phase for an
extended period of time.
The individual laser stabilization techniques required to
reach our objective already exist, and our task is to
combine and adapt them to reach our goal of long term
optical phase coherence between modelocked lasers.
DISCUSSION
Laser Frequency Stabilization Methods
Single mode continuous wave (CW) lasers require one
parameter (the length of the laser cavity) to control the
frequency of the laser beam. The frequency
n
ν
is
inversely proportional to the optical path length of the
laser cavity
l and is given by
repn
nf
l
c
n ≡=
2
ν
1
rep
f is the frequency spacing c is the speed of light and n
is a large integer representing the mode number. For a
typical 1 m cavity and a 1 µm wavelength n~106. Small
perturbations in
l can be used for active frequency
stabilization [14] and for control of the optical phase of
the laser beam.
A typical modelocked laser possesses on the order of
104 simultaneous modes
n
ν
. Since intra-cavity
dispersion affects the effective cavity length that each
mode observes a modelocked laser requires two
parameters to control its pulse structure. The cavity length
of the laser controls the pulse envelope repetition rate
rep
f
, and the dispersion in the cavity controls the carrier-
to-envelope optical phase relationship. In the frequency
domain the dispersion causes the modes to shift by a
uniform frequency comb offset
δ
[15]
δ
ν
+=
l
c
n
n
2
2
The consequence of the comb offset on the carrier-to-
envelope relationship is a pulse-to-pulse phase slip
φ
∆
rep
f
⋅
∆
=
φ
πδ
2 3
Thus, in order to phase lock two separate modelocked
lasers the pulse repetition rate
rep
f and the comb offset
δ
of the two lasers have to be matched. Comb offset
detection and control techniques [16,17,18] as well as
techniques for sub-femtosecond pulse stabilization [19]
___________________________________________
*Work supported by DOE grants DE-FG03-97ER41276 and DE-
AC02-76SF00515.
Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee
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2005 IEEE
have been developed and reported extensively in recent
years.
The Proposed Experimental Approach
Present frequency comb and pulse envelope
stabilization techniques alone are not going to be
sufficient to lock the optical phase of two modelocked
lasers to within 1degree of optical phase. While balanced
cross-correlation techniques can detect pulse envelope
timing to within ~1/10 of an optical cycle an additional
higher resolution timing monitor is required to detect
optical phase shifts to within 1 degree. This can be
accomplished by a simple interferometric detection
scheme that generates a optical phase dependent error
signal that actuates on a variable optical delay for one
laser beam. Figure 1 is a schematic of the proposed two-
laser optical phase locking scheme.
Figure 1
Each modelocked laser has its comb offset stabilized to
the same reference frequency offset
δ
, which does not
have to be zero but has to be the same for both lasers.
Laser 1 is the master laser and can be RF-locked to an
external reference
rep
f
. A balanced crosscorrelator
measures the timing difference of the pulse envelopes
between laser 1 and laser 2 and produces an error signal
that adjusts the cavity length of laser 2. An optical
interferometer placed downstream detects optical phase
drifts between laser beams 1 and 2 and produces an error
signal that controls a PZT driven variable delay arm for
laser beam 2. Optical phase stability of one degree of
optical phase will manifest as a stable fringe pattern
observable by a CCD between lasers beams 1 and 2 that
is stable to 1/360th of a fringe.
Comb Offset Detection and Control
Initial comb offset detection and control experiments
were carried out with a commercial 80 MHz, 1 W, 800
nm, 100 fsec pulse Ti:Sapphire laser. To broaden the
frequency comb width of the laser beam to a full octave a
white light continuum fiber was used. To detect the comb
offset the standard self-referencing technique was
employed [20]. A PMT followed by bandpass filters was
employed to isolate the comb offset frequency beat signal
which was converted by a frequency-to-voltage converter
to an error signal. Figure 2 shows the electronics
employed to extract the comb offset frequency.
Figure 2
The laser intra-cavity dispersion can be adjusted by
control of dispersion compensating prisms in the cavity or
more simply by small adjustments in the power of the
pump laser beam. For convenience the latter method was
employed. An acousto-optic modulator placed in the
pump laser beam allowed for electronic control the intra-
cavity dispersion of the modelocked laser. Figure 3 shows
the comb offset error signal when a 1 kHz square wave
and a 10 kHz triangle wave are applied through the AOM
to the laser dispersion.
Figure 3
Pulse Envelope Timing Monitor
A balanced crosscorrelator as described by Schible et al
[19] was constructed. In essence a balanced
crosscorrelator consists of two separate crosscorrelators
with optical path lengths set such that the crosscorrelators
give an optimum crosscorrelation signal at slightly
different relative beam timings. The difference of the two
signals gives a very steep error signal curve that allows
for the sought sub-fsec timing resolution. To test the
sensitivity of the device the laser beam from the
modelocked laser was split into a beam going through a
fixed delay and another beam going through a PZT
controlled delay arm. The two beams were sent into the
balanced crosscorrelator whose sensitivity was tested as a
Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee
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2005 IEEE 1390
function of delay changes caused by the PZT. Figure 4
illustrates the layout and the resulting error signal
observed from a 240 attosecond delay.
A
B
A-B
PZT
fixed
delay
laser
PZT delay
voltage
V
pp
= 60 mV
T = 240 attosec
Scope picture
delay
signal
A-B
A
B
A-B
PZT
fixed
delay
laser
PZT delay
voltage
V
pp
= 60 mV
T = 240 attosec
Scope picture
delay
signal
A-B
PZT delay
voltage
V
pp
= 60 mV
T = 240 attosec
PZT delay
voltage
V
pp
= 60 mV
T = 240 attosec
Scope picture
delay
signal
A-B
delay
signal
A-B
Figure 4
FUTURE WORK
We have successfully tested the individual techniques
for phase locking with a single commercial modelocked
Ti:Sapphire laser. For the next phase of experiments we
are switching to a home built Yb:glass modelocked fiber
laser that is more suitable for particle acceleration. We are
presently setting up the comb offset detection apparatus
and are preparing to build a second fiber modelocked
laser that will allow us to carry out the phase locking
experiment for modelocked lasers. Furthermore we plan
to develop and characterize amplifiers for modelocked
lasers.
Although aimed for optical phase locking, these
experiments provide an opportunity to test other important
aspects such as reliability, wallplug efficiency and
compactness that will ultimately help determine the future
laser architecture for an extended laser driven particle
accelerator.
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Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee
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2005 IEEE