Abstract
We present here two of the projects in progress in our lab. The
first one is the realization and the characterization of an optical frequency
standard based on a frequency doubled Nd:YAG
laser locked to a hyperfine transition of molecular iodine. A relative
frequency stability of 6.10-14.-1/2 has been
obtained and a reproducibility of 200 Hz is reached. The second one is the
development of a compact heterodyne refractometer at
633 nm based on the measurement of the frequency of a laser diode locked to a Fabry Perot cavity, by comparison with a He-Ne laser. An agreement with Edlen
formulas has been obtained at the level of 4.10-8, limited by the
accuracy of these formulas. The principle of this instrument is similar to the refractometer already developed in our laboratory and
working at 780 nm [1-2]. This apparatus may be also used as an air wavelength
reference as described in ref. [2].
Introduction
The BNM-INM is in
charge of the realization of the meter within the Bureau National de Métrologie (BNM). Since 1983, the meter is defined
as the length traveled by light in vacuum during a time of 1/299 792 458 of a
second. This definition implies the use of frequency-stabilized lasers for the
materialization of the meter. Our task is then to develop high frequency stable
and reproducible laser sources based on atomic or molecular reference
transitions. The frequency of these lasers is commonly reproducible at a level
of 10-11 in relative value, while measurements of length in air can
be made only at the scale of 5.10-8 in the best cases, due to the
difficulty in measuring the refractive index of air with such accuracy. One of
our activities is then to develop better systems for this kind of measurements.
The Nd:YAG frequency standard
Introduction
Diode pumped solid state lasers enable to obtain compact laser
sources with a high spectral quality. Associated to atomic or molecular
transitions spectrally sharp, they permit to realize very stable and
reproducible optical frequency standards. The frequency doubled Nd:YAG laser emitting around 532 nm,
locked to hyperfine transitions of molecular
iodine has already exhibited better achievements than every standards
locked to molecular iodine [3,4]. It is recommended for the « mise en pratique »
(practical realization) of the definition of the meter [5]. The emission
frequency of this laser, locked to a10 component of the R(56) 32-0
transition has been measured, using secondary frequency references as the 633
nm He-Ne laser or a two photon transition in
Rubidium. Recently, this transition has also been measured with femto second lasers, which permit to directly link the
microwave primary frequency standard to optical frequencies by generation of an
optical comb [6]. The most performing systems use the technique of modulation
transfer to detect the saturated absorption signal to which the laser is
locked. We have chosen a simpler method (the so-called « 3-f »
technique) that consists of the modulation of the laser frequency to a
frequency lower than the width of the transition and to detection to the third
harmonic of the modulation frequency. The results we have obtained with this
system are equivalent to those obtained with the modulation transfer technique.
The characterization of the stability and reproducibility of our laser have
been realized during a recent international comparison hold in BIPM [7].
Experimental
set up
We use a commercial laser, from Ligthwave
Company (model 140). A power of green radiation of 50 mW
is available. The length of the laser cavity may be changed via the crystal
temperature or the action of a piezo electric
ceramic. To realize the modulation frequency of the laser and its frequency
correction for the servo control we use the piezo
electric ceramic.
We excite the R(56) 32-0 rovibronic transition and the frequency of the laser is
locked to one of its hyperfine components. This hyperfine structure is resolved
by a saturated absorption experiment.
We have tested the reproducibility of two different
well-known configurations for the experiment of saturated absorption. The first
one consists of the separation of the saturated and probe beam (figure 1). This
kind of scheme is used for the modulation transfer technique, where only the
saturated beam is frequency modulated.
This scheme enables one to control independently the power
of the probe and saturating beams. Another configuration consists of the
retro-reflection of the saturating beam and to the detection of this reflected
beam. This is a simpler configuration and permits a better reproducibility of
the adjustment of the angle between the two beams and of their overlapping.
In both cases, a part of the beam is used to carry out
balanced detection of the signal to compensate the residual amplitude
modulation due to the modulation frequency applied to the laser. The modulation
frequency is made to a frequency of 5,5 kHz, with
peak-to-peak amplitude of 1 MHz. The signal is detected to the third harmonic
of the frequency of modulation. It is then integrated before being applied to
the piezo electric ceramic terminals.
Figure 1 : Saturated absorption experimental set-up for the servo
control of the laser frequency with a separation of the saturated and probe
beam.
The best frequency stability of the laser is obtained for pumping
beam power of 1 mW at the entrance of the cell and a
cold finger temperature of the iodine cell of -15 °C (which corresponds to
pressure vapor of 0.8 Pa in the cell). The 1/e2
diameter of the beam is 3 mm.
Results
Reproducibility
of the laser frequency
We have compared our system to the one realized at BIPM. We
have studied the influence of several parameters on the frequency of the laser : iodine pressure in the cell, modulation of the
frequency of the laser, the angle between the pump and probe beam and the power
of the laser beams. The frequency shift due to the temperature of the cold
finger of the cell (which control the pressure) is 550
Hz/°C around –15°C, that is the working temperature. The reproducibility of
this temperature is better than 0.05 °C and has a negligible contribution to
the global reproducibility of the laser frequency.
Figure 2 : frequency of the laser versus the angle between
saturating and probe beam.
The figure 2
shows the variation of the laser frequency with the angle between the pump and
probe beams.
The reproducibility of the angle adjustment between the two beams
has a contribution of around 300 Hz in the total reproducibility of the laser
frequency. Figure 3 displays the variation of the frequency of the laser with
the power density of the laser. The induced shift is roughly 18 kHz/(mW/mm2). The reproducibility of the power
adjustment induces an uncertainty of 100 Hz.
The amplitude of the modulation frequency has a weak
influence on the frequency of the laser. This evolution is depicted on figure
4.
The test of the reproducibility of the frequency of the
laser has been carried out at BIPM and has shown
Figure 3 : frequency of the laser versus the power density at the
entrance of the cell.
Figure 4 : evolution of the laser frequency with the amplitude of
the modulation.
Stability
of the laser frequency
We have realized beat frequency measurements with a laser of the
BIPM. The best stability we have obtained is 6.10-14.-1/2.
The figure shows the corresponding Allan standard deviation. The problem of the
frequency drift corresponding to the raising of the Allan standard deviation
after 10 s of integration has been overcame.
Figure 5 : Allan standard deviation of the frequency doubled Nd :YAG
laser locked to molecular iodine.
The
refractometer and air wavelength standard
The
refractive index of air is one of the limiting parameters for the accuracy of
length measurements in air by interferometry. A
practical approach to providing index of refraction information is to employ a
miniature “weather bureau” to determine the local pressure, temperature,
humidity and CO2 concentration.
The main part of the system is the Fabry
Perot cavity, realized in zerodur with gold mirrors
optically adhered. This 10 cm long interferometer is illuminated by a laser
diode emitting around 633 nm. This cavity is coupled to the diode by an optical
fiber, so that the bare captor (the FP cavity) may be
placed easily in a volume where the measurement of n is required. The laser diode is based on a Littmann
type extended cavity and may be frequency tuned by a piezo
electric ceramic over 5 GHz without mode hop. This scanning range is enough to
follow the fluctuations of the refractive index of air continuously with a
large variation of the atmospheric conditions (especially the pressure). A
schematic representation of the apparatus is depicted on figure 1.
In the “calibration” step
of the refractometer, the frequency of the laser
diode is locked onto a particular peak of transmission k’
of the Fabry Perot cavity under vacuum and its value k’,vide
is measured by a beat frequency measurement made against a standard iodine
stabilized He-Ne laser. After this calibration, the Fabry Perot cavity will always stay in ambient air. A
correction is applied to this value to take into account the compression of the
cavity when it will be in ambient air. This correction is calculated thank to
the value of the Poisson coefficient and the Young modulus. The uncertainty on
these parameters is the main contribution to the global uncertainty on the
measurement of the refractive index with our refractometer.
When the cavity is put back in air, the peak to which the laser
was locked in vacuum is shifted of approximately 125 GHz. For the measurement
of the refractive index, the beat frequency is made between the He-Ne laser and a peak k
of the FP cavity such that the beat frequency measured is below 1.5 GHz. The
difference k=k’-k is
determined without ambiguity by comparing the value of n given by our refractometer with an
arbitrary value of k to the
value given by a simple weather station with a 10-6 relative
accuracy (atmospheric pressure with 300 Pa of accuracy and temperature with 1°C
of accuracy). The frequency of the peak k
in vacuum is then deduced from the frequency of the peak k’ in vacuum and the free spectral range of the cavity, previously
measured with a relative uncertainty of 2.10-6 [2].
The
beat frequency between the He-Ne laser and the peak k of the cavity in air enables one to
deduce the refractive index of the ambient air in the FP cavity.
We
have compared the results obtained with our refractometer
to the value of the refractive index calculated by the Edlén
Formula, using our weather station, which the accuracy is 3.10-8.
The mean of the differences between the two measurements is 4.10-8,
which is limited by the accuracy of our weather station.
Figure 6 : Schematic representation of the refractometer.
ECDL : Extended Cavity Laser Diode- PD : Photodiode –
OF : Optical Fiber.