MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 20 (2009) 055302 (5pp)
A versatile digital GHz phase lock for
external cavity diode lasers
J¨ urgen Appel1, Andrew MacRae2and A I Lvovsky2
1Niels Bohr Institute, Copenhagen University, 2100 København, Denmark
2Institute for Quantum Information Science, University of Calgary, AB T2N 1N4, Canada
E-mail: firstname.lastname@example.org, email@example.com and firstname.lastname@example.org
Received 18 September 2008, in final form 9 March 2009
Published 17 April 2009
Online at stacks.iop.org/MST/20/055302
We present a versatile, inexpensive and simple optical phase lock for applications in atomic
physics experiments. Thanks to all-digital phase detection and implementation of beat
frequency pre-scaling, the apparatus requires no microwave-range reference input and permits
phase locking at frequency differences ranging from sub-MHz to 7 GHz (and with minor
extension to 12 GHz). The locking range thus covers ground-state hyperfine splittings of all
alkali metals, which makes this system a universal tool for many experiments on coherent
interaction between light and atoms.
Keywords: laser, frequency stabilization, phase lock, GHz
(Some figures in this article are in colour only in the electronic version)
Many experiments on coherent interaction of light with matter
require two or more separate light fields whose frequency
difference is precisely maintained at a particular value. If the
required frequency difference is relatively small, the mutually
coherent fields can be produced by splitting the light from a
single source and shifting the frequency by acousto-optic or
fields differ by more than a few hundred MHz, frequency
modulation techniques become impractical and it is often
preferable to use two separate sources. In this case, long-
term phase coherence between these sources can be achieved
using an optical phase-locked loop (OPLL). In such an OPLL,
the rate at which the relative phase between a master laser and
a slave laser changes is locked to a fixed value fbeatcalled the
A number of OPLL designs have been implemented
[1–5]. However, most of the existing schemes are designed
with a specific setup in mind and require expertise in
require expensive equipment for the generation of stable
microwave-range reference signals.
of lockable beat frequencies is often restricted to less than an
In addition, the range
major modifications in the hardware.
In this work, we present a versatile OPLL for use
with external cavity diode lasers (ECDLs) which is simple
to construct and is made from inexpensive off-the-shelf
components. Recent advances in digital phase detection,
associated with the development of wireless communications,
allow us to develop a robust design which is insensitive to beat
signal amplitudes over a wide range and avoids the frequency
range limitations of passive microwave mixers. Since the beat
low-frequency reference may be used. The high-frequency
part of the printed circuit board layout is kept compact,
so constructing the device does not require high-frequency
electronic measuring equipment and expertise.
of the beat signal was measured around fbeat= 6.9 GHz and
the phase variance ?(?φ)2? is found to be less than 0.08 rad2.
Two lasers, each locked to the same source, were interfered
and steady fringes were observed.
2. Construction of the device
The basic setup for our OPLL is displayed in figure 1. Beams
from the master and slave lasers are mixed at a beam splitter,
© 2009 IOP Publishing LtdPrinted in the UK
Meas. Sci. Technol. 20 (2009) 055302J Appel et al
Figure 1. Experimental setup implementing our phase lock.
and a total optical power of 0.5–2 mW is focused onto a fast
photodetector. The generated beat signal is amplified up to
frequency between a spectrum analyzer and the OPLL
circuitry. Based on a reference signal received from a function
generator, the OPLL produces the error signal for the slave
laser, closing the feedback loop.
The coupler and the spectrum analyzer are not required
for daily operation but prove to be useful to monitor the lock
performance when initially setting up the system.
span as much as a few hundreds of kilohertz, the loop must
be made as fast as possible in order to correct for this noise.
The loop must as well be able to correct for the low-frequency
noise and drifts due to mechanical vibrations. To achieve
the required frequency range, dual feedback was employed:
by modulating the external cavity length with a piezo-electric
transducer and by direct modulation of the injection current.
Thebandwidth ofthepiezo modulation islimitedtoafewkHz
by mechanical resonances, but it allows significant correction
to the laser frequency. On the other hand, the current injection
modulation is fast (up to a few MHz), but the frequency
corrections are limited by modehops.
The electric schematic of our OPLL is shown in figure 2.
The reference and beat signals are sent to the digital phase-
frequency-discriminator chip (Analog Devices ADF4107).
signal by a factor N digitally and then compares the frequency
and phase of both divided signals with a dual flip-flop circuit.
ADF4107 is interfaced with a micro-controller that programs
change of these values. A similar circuit based on ADF4007
that does not require programming but is less versatile has
been constructed and shows similar performance.
The N counter can be programmed to any value between
24 and about 5×105; the range of permitted values of R
can take values between 1 and 16383. The phase lock can
thus be implemented for the beat signal of any frequency up
to the maximum permitted by ADF4107 (7 GHz), with the
reference produced by a generic MHz-range signal generator.
A −10 dB directional coupler splits the beat
When needed, the frequency range can be extended by
preceding the OPLL beat signal input with a pre-divider
(Hittite HMC364S8G). The lock stability generally improves
divided reference frequency significantly exceed the required
If the phase difference of the beat and reference signals
issmall, thisphase-frequency-discriminator circuitproduces a
feedback current proportional to this quantity. Otherwise the
error signal polarity corresponds to the sign of the frequency
differencebetweenthetwosignals. Inthisway, thecapture
range of the phase lock circuit is limited only by the modehop
free tuning range of the slave laser.
The feedback current enters a proportional-integral (PI)
filter formed by C1, R9 and is amplified in two stages. Since
ADF4107’s output voltage is restricted to a range of 0–5 V, a
gain-two preamplifier (IC1A) converts the voltage on the PI
is added so that the output of the second amplification stage
(IC2) with gain 300 is symmetric around zero when locked.
This bias voltage has been strongly low pass filtered to avoid
introducing noise to the error signal (using IC1B, not depicted
in figure 2). Finally, the output of IC2 is split into the fast and
slow feedback paths.
A characteristic challenge in constructing a feedback
circuit for a diode laser is due to the shape of its transfer
function’s phase. At low modulation frequencies, a change
in the diode injection current affects the lasing frequency
mainly because of the modulation of the recombination area’s
temperature.At high modulation frequencies, the lasing
frequency is affected due to current-induced charge density
modulations which affect the refractive index of the gain
medium. Unfortunately these two mechanisms oppose each
other, which leads to a phase shift of 180◦at modulation
frequencies typically between 1 and 10 MHz . In order to
partly compensate for this effect, a phase-advance loop filter
is used in the fast feedback path, followed by a buffer stage
(IC1D) with an adjustable gain to drive the laser diode current
The current feedback is implemented as depicted in the
inset in figure 2 and is based on the FET modulation circuit
Meas. Sci. Technol. 20 (2009) 055302J Appel et al
Figure 2. Circuit diagram of the OPLL controller. Inset: laser diode current modulator.
for Toptica DL100 lasers. The gate voltage of a N-junction
field effect transistor is clamped by protection diodes. C13
and the J-FET’s capacitance. The input voltage causes the J-
FET to bypass a fraction of the diode’s supply current. This
way the diode current never exceeds that provided by the
current controller, so the expensive laser diode is protected.
We now describe the slow feedback path. The signal part
is integrated by IC1C and R18, C8 to control the length of the
external cavity. The integrator ensures that under the locked
condition the output of stage IC2 is zero on average, so that
the current modulation is free of dc components which may
saturate the amplifier stages and drive the laser closer toward a
modehop. A bipolar LED conveniently displays the integrator
over-run, indicating the need for operator intervention.
The transfer function of the integrating arm controlling
the piezo is not critical to the lock performance. In fact, we
choose the gain in this path so high that, in the absence of the
current feedback loop, oscillations about the target frequency
occur. Once the fast current feedback is engaged, it easily
counters this effect and renders the loop stable as a whole.
Special care has been taken in order to obtain good
noise performance. Since digital switching noise can have
a detrimental effect on the operation, the analog and digital
sections of the circuit each have their own voltage regulators
and are located on separate ground planes.
This OPLL has been put into operation in a variety of
setups including locking a commercial Toptica DL-100 diode
laser to a coherent MBR Ti:sapphire laser, a self-made diode
laserwithan Eagleyard laserdiode totheTi:sapphire laserand
two self-made diode lasers with Sharp and SDL diodes to each
3. Characterization of the lock performance
An important parameter for measuring the performance of a
PLL is the mean-square phase error ??φ2?. This error can be
determined by measuring the power fraction of the carrier in
the electronic spectrum P(ν) of the beat signal :
To that end, we set up the lock circuit to operate at a frequency
around 6.9 GHz and recorded the RF power spectrum in a
10 MHz frequency span around this frequency with a Hewlett-
Packard E4405B spectrum analyzer. The spectrum analyzer
resolution bandwidth was set to 3 kHz, video bandwidth to
30 kHz and the detector type to average . During a 100 s
scan, the analyzer acquired a n = 8192 point data set. In this
way, the resolution bandwidth is significantly larger than the
frequency range associated with each data point (1.22 kHz).
The beat spectrum is shown in figure 3. Remarkably,
the width of the central peak, corresponding to the carrier
signal, could not be resolved even with the lowest resolution
bandwidth setting (10 Hz) of the spectrum analyzer.
The carrier power fraction is calculated from the acquired
data set Pi(where 1 ? i ? n) as follows. The power in the
carrier Pcarrieris the direct reading of the spectrum analyzer
at the beat signal frequency. The surrounding noise power
density P(ν) can be determined from Pi by applying the
following corrections .First, we add 2.51 dB to each
Pi to compensate the error associated with the logarithmic
10log10(3000) dB, we normalize the noise power density to
the 1 Hz bandwidth.
Meas. Sci. Technol. 20 (2009) 055302 J Appel et al
Table 1. Phase noise.
Agilent 33220A waveform generator at 18 MHz
Agilent 33250A waveform generator at 72 MHz
Mini-Circuits JTOS 400, phase locked to 216 MHz
Figure 3. Spectral noise density of the RF signal produced by
interference of two phase-locked lasers (resolution bandwidth =
3 kHz). Curve (a) is associated with a 18 MHz reference signal
produced by an Agilent 33220A reference generator and curve
(b) with a 216 MHz home-made generator. The inset shows a
blowup of the central portion of the plot.
We performed the experiment with three reference
oscillators, as summarized in table 1. The best results were
obtained with a home-made generator consisting of a Mini-
Circuits JTOS 400 voltage-controlled oscillator locked to
an Agilent 33220A waveform generator using an additional,
narrowband (∼1 kHz) phase-lock circuit. The noise reduction
associated with this generator is due to a low multiplication
factor N/R. Note that in spite of a lower N, the lock with the
Agilent 33250A reference generator (80 MHz) produces more
noise than Agilent 33220A (20 MHz). We believe this to be
due to the intrinsic phase noise of the reference signal, which
is about −115 dBcHz−1for 33220A and −90 dBcHz−1for
33250A. These results emphasize the need for a low phase-
phase detection frequency fbeat/N that is significantly bigger
Ultimately even with a high quality reference oscillator,
locking approach presented in this work will be limited by
circumventing the frequency division by multiplying up an
ultralow noise frequency reference into the microwave regime
To illustrate the capabilities of our circuit, we have
219?dBcHz−1. Significantly lower values can be obtained
0.0 0.2 0.4 0.6 0.81.0
Figure 4. 3.84 Hz beat signals between two slave lasers locked to
the same master lasers, each with its own OPLL. Curve
(a) represents a set of 1000000 data points and curve (b) the same
set, smoothened by computing averages of 100-element bins.
locked to the same master laser at 6.9 GHz and with a
relative frequency difference of 3.84 Hz. The interference
signal between the two slave lasers was measured with a fast
photodiode and recorded with a digital oscilloscope.
result of this measurement is displayed in figure 4 and exhibits
clearly discernible interference fringes.
Further insight into the noise behavior of the phase lock is
provided by the modified Allan variance, which quantifies the
average drift of the oscillator frequency over time τ [10, 11].
Using the 10 MHz output of a digital oscilloscope as a
reference, we phase locked two diode lasers to a common
master laser at fbeat = ν0= 4 GHz. To measure the Allan
variance, we recorded four data sets of the interference signal
between the slave lasers, with sampling rates ranging between
varied the optical path lengths so that the interference pattern
was held at 50% of its fringe. For acquisition times over 0.5 s,
the piezo-signal was disengaged and the measurement was
started manually after the pattern drifted to the 50% fringe
As depicted in the inset of figure 5, the modified Allan
deviation (root Allan variance) decreases approximately as
τ−3/2over a wide range of integration times between ∼300 ns
and ∼30 ms (region III, black dotted line), which corresponds
to frequencies outside the free-running linewidth of the diode
laser, so the Allan variance levels off (1/f frequency noise,
region II). At even shorter integration times (below ∼10 ns,
region I), the electronic noise of the photodetector comes
into play, leading, again, to behavior similar to white phase
Meas. Sci. Technol. 20 (2009) 055302J Appel et al Download full-text
5 10 20 kHz 50 100 200 kHz 0.5 1 2 MHz 5 10 20 MHz
Single sided noise power (dBc/Hz)
1 ms 1 s
Figure 5. Background: power spectrum of the interference signal of
two lasers phase locked to a common master. Inset: modified Allan
deviation based on the same signal. The Roman numerals indicate
regions of different dominating noise types; see text.
noise. At very large τ’s (region IV), the phase measurement
is disturbed by optical path length fluctuations (vibrations, air
flow), which show up as frequency and phase drifts.
The power spectrum of the interference signal of the
two slave lasers is shown in figure 5.
acoustic resonances are visible. At intermediate frequencies
50 kHz,..., 1 MHz, distinct narrow peaks corresponding
to various electronic noise sources in the laboratory can be
observed. At high frequencies, the 10 MHz reference and
a 4.7 MHz modulation which is used to modulate and lock
the master laser can be identified. Increased noise at ≈1 MHz
least one laser was chosen slightly too high. When sampling
the phase difference signal of the two slaves with a rate of
Phase and frequency stability is not the only important
characteristic of a laser. For most of today’s high precision
measurements, it is also important that the light intensity is
stable to a high degree. Many quantum optics experiments
rely on the property of diode lasers to emit light with intensity
noise levels that are essentially shot noise limited at sideband
of microwatt.Since the phase-lock circuit modulates the
diode’s injection current, there is a potential risk in producing
excess intensity noise when controlling the laser’s phase.
However, we found the added intensity noise to be less than
3dB mW−1with respect to the shot noise level in a 500 kHz
bandwidth. Since the laser diode current modulations mainly
affect the frequency, a phase lock even quietens noisy current
supplies to a certain degree.
Below 10 kHz,
In this paper, we have presented a simple yet versatile optical
phase lock operating in the frequency range from sub-MHz
to 7 GHz. All-digital phase frequency detection leads to
a wide capture range and renders the circuit robust against
amplitude fluctuations of the beat signal. A special feature of
this design is that the reference is provided by an affordable
MHz-range waveform generator. The unit contains virtually
little experience in high-frequency electronics.
Our circuit has been successfully tested in a number
of different configurations and is an integral component of
several experiments involving electromagnetically induced
transparency in atomic87Rb, where the control and signal
fields need to be phase locked to the ground-state hyperfine
splitting frequency (6.834 GHz) [12–16]. The high stability
of the circuit permits long-duration measurements in atomic
coherence experiments. Locking times of many days are
 Telle H R 1993 Spectrochim. Acta 15 201
 Prevedelli T H M and Freegarde T 1994 Appl. Phys. B 60 241
 Cacciapuoti L, de Angelis M, Fattori M, Lamporesi G,
Petelski T, Prevedelli M, Stuhler J and Tino G M 2005 Rev.
Sci. Instrum. 76 053111
 Marino A M and Stroud J C R 2008 Rev. Sci. Instrum.
 Gou¨ et J L, Mehlst¨ aubler T, Kim J, Merlet S, Clairon A,
Landragin A and Santos F P D 2008 Appl. Phys. B 92 133
 Curtin M and O’Brien P 1999 Phase-locked loops for
high-frequency receivers and transmitters: I–III Analog
Dialogue 33 9
 Kobayashi S, Yamamoto Y, Ito M and Kimura T 1982 IEEE J.
Quantum Electron. 18 582
 Agilent Technologies 2008 Spectrum Analyzer Basics
(Application Note 150) available at
 Agilent Technologies 2008 Spectrum Analyzer Measurements
and Noise (Application Note 1303) available at
 Allan D and Barnes J 1981 Proc. 35th Annual Frequency
Control Symp. (Washington, DC) vol 35 pp 470–5
 Rutman J and Walls F L 1991 Proc. IEEE 79 952–60
 Figueroa E, Vewinger F, Appel J and Lvovsky A I 2006 Opt.
Lett. 31 2625
 Vewinger F, Appel J, Figueroa E and Lvovsky A I 2007 Opt.
Lett. 32 2771
 Appel J, Figueroa E, Korystov D, Lobino M and Lvovsky A I
2008 Phys. Rev. Lett. 100 093602
 Figueroa E, Lobino M, Korystov D, Appel J and Lvovsky A I
 MacRae A, Campbell G and Lvovsky A I 2008 Opt. Lett.