The frequency of a DFB quantum cascade laser (QCL) emitting at 4.3 μm has been long-term stabilized to the Lamb-dip center of a CO2 ro-vibrational transition by means of first-derivative locking to the saturated absorption signal. Thanks to the non-linear sum-frequency generation (SFG) process with a fiber-amplified Nd:YAG laser, the QCL mid-infrared (IR) radiation has been linked to an optical frequency-comb synthesizer (OFCS) and its absolute frequency counted with a kHz-level precision and an overall uncertainty of 75 kHz.
©2008 Optical Society of America
The most recent trace-gas sensing and frequency metrology applications are increasingly looking toward the mid-IR spectral region, also known as the molecular “fingerprint” region, pushed by the presence of the fundamental ro-vibrational transitions of many simple molecules like CO2 and CH4 that are particularly relevant for atmospheric implications (greenhouse effect, pollution monitoring).
Difference-frequency generation (DFG) of tunable light has proven to be a suitable technique for mid-IR trace-gas detection , high-resolution spectroscopy  and, after the introduction of OFCSs [3, 4], precise absolute frequency measurements [5, 6]. Depending on the visible or near-IR sources used, even assembled in quite compact designs , this non-linear process can provide narrow-linewidth and widely-tunable radiation . However, DFG-based spectrometers are limited to the mW power range  by relatively low conversion efficiencies and have an upper wavelength cut-off imposed by the transparency range of the non-linear material used (about 5 μm for LiNbO3) .
The recent availability of high-power single-mode QCLs has extended the high-sensitivity and high-precision spectroscopic applications to the mid-IR spectral region, ranging from 3.5 up to 100 μm wavelength. In the last decade the features of these innovative sources have been deeply studied and gradually improved: the working temperature has been raised up to 300 K or even more [10, 11], while the threshold current has been sensibly reduced [12, 13]. Moreover, QCLs have been assembled in external-cavity configurations  and have been frequency stabilized by electronic servo-locking [15, 16, 17] and phase-locking techniques . Applications of QCLs for both sensitive trace-gas detection [19, 20] and high-resolution sub-Doppler spectroscopy [21, 22] have been recently demonstrated.
In the last years, the high versatility of these sources has allowed us to perform both sensitive detection on N2O and CH4 by frequency-modulation spectroscopy  and Doppler-limited comb-assisted absolute frequency measurements of CO2 transitions . These experiments pointed out the benefits coming from a frequency stabilization of the QCL: in particular, a higher precision in frequency measurements can be achieved by locking the laser to a narrow reference and averaging the counts over long timescales.
In this paper we report on a long-term frequency stabilization of a 4.3 μm emitting QCL to the Lamb dip of a ro-vibrational CO2 transition. Frequency counting with respect to an OFCS takes to a relative precision of 5 parts in 1011. Saturated-absorption spectroscopy provides a narrow and stable reference, and the final result is a remarkable improvement (a factor 30) compared with the Doppler-limited frequency measurements reported in our previous work . Although not effective in narrowing the laser linewidth, the frequency lock to this reference allows to overcome the previous limitations due to the free-running low-frequency fluctuations of our QCL source, thus enabling long-time-averaging measurements of the frequency with the consequent statistical reduction of the uncertainty.
In Section 2 we describe our saturated-absorption experiment, based on an original set-up allowing the efficient exploitation of most of the QCL available power for both the spectroscopy and the non-linear frequency generation. In Section 3 the first-derivative locking scheme is briefly treated. Section 4 is finally dedicated to the analysis of the resulting beat note and its counting for the absolute frequency measurement of the molecular transition.
2. Sub-Doppler spectroscopy of CO2 with a QCL
In Fig. 1 a simplified schematic of the experimental set-up is shown, describing mainly the optical layout used for saturated-absorption spectroscopy. We have used a single-mode distributed-feedback (DFB) QCL emitting at 4.3 μm and operating at cryogenic temperatures. The QCL has a quite low threshold current (about 100mA at 86 K) and a frequency tunability with current of 400 MHz/mA; it is housed in a liquid-N2-cooled dewar and is connected to a low-noise current driver. Since the electrical isolation of the current driver is not sufficient to reject additional noise coming from the AC line, which induces a spurious modulation of the QCL frequency, we adopt an UPS battery supply for powering the current driver.
Before being sent to the cell, the laser beam is collimated and size-reduced by a telescope as previously described in . In order to perform sub-Doppler spectroscopy with two counter-propagating beams while avoiding undesired optical feedback to the laser, we have used two crossed wire-grid polarizers (P1 and P2 in the figure). The p-polarized QCL beam passes through a half-waveplate, which rotates its polarization by few degrees. The first polarizer (P1) transmits the p-polarized fraction of the beam (about 80% of the total power) while reflecting the s-polarized part. The former acts in the absorption cell as the “pump” beam for the CO2 transition, is totally reflected by the second polarizer (P2) and reused in the next section of the experiment (the SFG process). The latter beam, transmitted by P2, acts in the cell as the “probe” radiation and is totally reflected by P1 to be finally detected onto a liquid-N2-cooled HgCdTe biased photoconductive detector (1.5 MHz bandwidth). Despite the lack of mid-IR optical isolators, this solution allows us to have a full control on the counter-propagating beams overlap and focusing while avoiding optical feedback onto the laser. The absorption cell is 12 cm long and has AR-coated CaF2 windows. Thanks to the ability of independently focusing the two beams, we have adjusted the diameter of the probe beam in order to make it smaller than the pump beam along the whole cell, thus ensuring a high contrast of the saturation signal. The detector is connected to a home-made voltage preamplifier provided with DC/AC-coupled outputs: these two channels allow us to continuously monitor the absorption signal level (DC output) while using the AC signal for the feedback loop to the laser.
Due to the long open-air path of the laser beam before the cell (about 1.5 m), we suffer strong absorption from atmospheric CO2 molecules. In order to have a good compromise between a suitable ro-vibrational transition strength for saturation spectroscopy and low absorption in air, the hot-band (0111-0110) P(30) CO2 transition has been chosen. The transition center frequency and linestrength, as reported in the HITRAN database , are ν=2310.5062 cm-1 and S=6.6×10-20 cm respectively. The QCL working temperature is 86.00 K and the corresponding driving current is 170 mA. The pump beam power incident upon the CO2 sample is about 2 mW, leading to an intensity of 160 W/m2; this is a factor 2 greater than the saturation intensity of 80 W/m2, calculated for our gas pressure (20 mTorr) and the P(30) transition dipole moment (5.09×10-2 D) according to . We point out that, depending on the laser linewidth, this intensity may not lead to a strong saturation regime.
The saturation signal has been first observed in direct absorption, by continuously scanning the laser frequency with a slow (few Hz) saw-tooth modulation of the laser current. Figure 2(a) shows a trace recorded by a digital scope: the well contrasted Lamb dip (13% contrast factor) shows a HWHM of about 5 MHz. Wavelength modulation spectroscopy is then implemented at 40 kHz rate, with a modulation depth of about 3.5 MHz: this value has been chosen in order to have the largest first-derivative signal without broadening the dip. The AC channel of the detector preamplifier is sent to an analog lock-in amplifier for demodulation. Figure 2(b) shows a first-derivative saturated-absorption spectrum recorded in the same experimental conditions as in Fig. 2(a). The best fit of the experimental data has been obtained with a convolution between two Gaussian functions (accounting for both the Doppler profile and the Lamb dip). The Lamb-dip HWHM resulting from the fit is about 5.3 MHz.
From the HITRAN database the pressure-broadening coefficient is about 3.5 MHz/Torr. The expected contributions of both pressure and transit-time broadening to the Lamb-dip width (HWHM) are about 70 kHz and 100 kHz respectively : both are negligible with respect to the measured HWHM. For this reason the measured Lamb-dip width can be attributed to the free-running QCL frequency jitter (as confirmed by further measurements reported below: see figure 4).
3. Frequency locking to the Lamb dip
From preliminary measurements on the laser frequency noise (following the method used in Ref. ) it results that there is a 1/f type noise dominating for f<100 kHz that does not arise from the driver current noise: it thus can be corrected by a feedback loop on the current driver itself. Among the sources of this additional noise we mention temperature fluctuations, that are responsible for all the slow frequency drifts and that, if not compensated, strongly disturb the measurement, as we will see in the next section.
We used the first-derivative saturation dip as the error signal to lock the QCL frequency to the transition center. The lock-in output is processed by a home-made PID controller, and the feedback signal is sent to the modulation input of the current driver. During operation in locked mode, the stability of the optical alignment is monitored by checking the absorption signal from the DC channel of the detector preamplifier.
Figure 3(a) shows a comparison between the frequency noise power spectral density of the QCL in both locked and unlocked modes. A noise reduction exceeding 20 dB at frequencies lower than 30 Hz is obtained; it is also evident the cut-off introduced by the lock-in time constant, set to its minimum available value of 1 ms. The reduction of the slow frequency fluctuations is qualitatively presented in Fig. 3(b), where the lock-in output, in locked and unlocked conditions, is shown.
Because of the small bandwidth, the loop is unable to reduce the laser high-frequency jitter. However, the advantage brought on the precision of our frequency measurements, which mainly require a long-term stability, is evident (as shown later in Fig. 5(a)).
4. Absolute frequency measurements of the CO2 saturated transition
After interaction with the gas, the pump beam reflected by the polarizer P2 is available for the second stage of the experiment: it is superimposed to the beam of a fiber-amplified Nd:YAG laser by a diffraction grating and then sent to a non-linear crystal for the sum-frequency generation of light at 854 nm. The set-up is similar to that described in : the non-linear crystal is a 40-mm-long PPLN crystal with a poling period of 22.8 μm chosen to achieve phase matching at nearly room temperature. The crystal temperature is stabilized at 17°C within 1 mK by using a Peltier element controlled by PID electronics. Despite the fact that the pump beam contains 80% of the total power, the combination of several loss effects (absorption from air and in the cell, reflections from the uncoated surfaces of the polarizers and the half-waveplate), makes the QCL radiation available for the SFG process to be about 1/3 of the original power. The maximum generated near-IR power at the crystal output in working conditions (laser resonant with the CO2 transition and locked to the Lamb dip) is about 3 μW. After the PPLN crystal an interference filter centered at 850 nm filters out both residual QCL and Nd:YAG beams and transmits only the SFG radiation, which is then collimated and superimposed to the beam of an external-cavity diode laser emitting at a frequency 150 MHz apart. A fast avalanche photodiode finally detects the resulting beat note Δν, with a 40 dB signal-to-noise ratio (in a 400 kHz resolution bandwidth).
Both the Nd:YAG laser and the diode laser are referenced to an OFCS operating in the 500÷1100 nm region, with a repetition rate of about 1 GHz, based on a mode-locked femtosecond Ti:sapphire laser . The locking scheme is an upgrade of that already described in , and results in an actual phase lock between the two lasers, with the comb behaving as a transfer oscillator . This cancels out all the phase-noise contributions from the Nd:YAG, the diode laser and the comb in the detected beat-note, whose linewidth is due to the QCL only. The beatnote has been acquired with a real-time spectrum analyzer, and its spectral profile has been studied over different time scales, ranging from 40 μs to few tens of ms. As expected from the performances of our slow frequency-lock loop, we observe a few-MHz-broad fast jitter with a quite irregular profile, which fades into a regular Gaussian profile when averaged over longer time scales. As an example, Fig. 4 shows the comparison of the spectral profiles obtained by FFT of two data streams of different lengths, with the QCL locked to the Lamb dip.
The Gaussian fit superimposed to the experimental points shows a HWHM of 5.3 MHz, in very good agreement with the measured Lamb-dip width (see figure 2(b)). From this comparison we can conclude that the residual frequency jitter of the laser is the crucial issue that limits the resolution of our experiment. Moreover, the Gaussian profile of the frequency-noise distribution suggests that, on time scales longer than few tens of μs, a random noise source is still predominant and masks both the Lorentzian intrinsic linewidth of the QCL emission and the natural linewidth of the Lamb dip. At the same time, the random nature of the frequency fluctuations ensures that a statistical average of the frequency counts can lead to the determination of its “true” value.
In order to perform absolute frequency measurements, the beat-note signal is amplified up to 0 dBm level to be properly measured by a frequency counter. The CO 2 transition center frequency νC can be thus easily obtained by the following relation:
where νD and νY are the frequencies of the comb-referenced diode laser and Nd:YAG laser, respectively.
Each measurement session consisted in consecutive 1 s gate-time countings of the beat-note frequency. The data stream was acquired by a PC via a GPIB interface. Each session lasted several minutes, and was stopped only when some instabilities occurred in the locking of any of the lasers. Between two consecutive sessions, the optimization of the three lasers locking and, eventually, of the spectroscopy alignment was performed. Each data set yields the mean frequency value Δν with the associated uncertainty (standard deviation of the mean). Following this procedure, we have acquired 53 data sets over a period of 2 weeks. As an example, Fig. 5(b) shows a 20 minutes long data set. As we can see, the acquisition is affected by slow drifts and oscillations, which can be mainly ascribed to the presence of residual optical interference fringes that shift the locking point by adding a variable background to the derivative signal. Such unwanted effects are barely visible in the typical timescale of a single acquisition, but are much more evident when comparing two different data sets. They give the main contribution to the uncertainty budget of our measurements. Since, at present, it is not possible to fully control these effects, we have tried to convert the systematic error into a statistical one. This has been done by changing the optical alignment between a measurement session and the next one, thus randomly modifying the free-spectral range of the spurious etalon effects. A second systematic error contribution arises from the non-zero background of the derivative signal due to small asymmetries of the Doppler profile with respect to the Lamb dip. We have provided a precise offset regulation at the PID input in order to cancel out this effect, so that it can be neglected as compared to the statistical uncertainty.
The contribution of all these effects is clearly visible in Fig. 6, where the Δν values and uncertainties obtained from the complete set of measurement sessions are summarized. Although the error associated to a single mean value is of only few kHz, the final uncertainty in determining the transition absolute frequency is limited by the repeatability of the measurements, as the spread of the points clearly shows. For this reason we adopt the standard deviation as a safer estimate of the final frequency uncertainty. The 3.5 kHz average value of the errors associated to the measurements can be assumed as a reasonable estimate for the ultimate precision (5 parts in 1011) achievable in the absence of all the systematics.
The average of all the Δν points gives the best value of 149.538 MHz for the beat-note frequency, with a 75 kHz standard deviation. As both νD and νY can be measured with a precision well below the kHz level, by using Eq.(1) we can obtain the absolute measurement of the transition center frequency νC as
With 20 mTorr of CO2 in the cell the contribution to νC given by the pressure shift is about 2 kHz , well within the uncertainty. The obtained value agrees with the frequency reported by the HITRAN database (ν=69267233 MHz with a 3÷30 MHz error) improving the uncertainty by two orders of magnitude.
In conclusion, a liquid-N2-cooled cw DFB QCL emitting at 4.3 μm has been used for saturation spectroscopy of CO2. The Lamb dip has been recorded both in direct absorption (with a contrast of about 13%) and in first derivative (by using a lock-in amplifier). The measured dip width (5.3 MHz HWHM over tens of ms timescales) cannot be explained in terms of collisional and transit-time broadening but is ascribed to the QCL frequency jitter. The first-derivative dip signal has been used to stabilize the QCL frequency to the transition center. The locking loop allows a significant frequency-noise reduction below 1 kHz, which removes the slow fluctuations but is not suitable for a reduction of the QCL fast jitter. Thanks to a SFG process with a Nd:YAG laser in a PPLN crystal, the QCL stabilized frequency has been compared with that of a diode laser emitting at 854 nm. As both the Nd:YAG and diode lasers are phase-locked to an OFCS, the absolute frequency of the observed CO2 transition can be measured. Thanks to the locking-loop, several long-time measurements of the Lamb-dip frequency have been acquired over a period of 2 weeks, with a relative short-term precision of 5 parts in 1011(3.5 kHz) and an overall uncertainty of 75 kHz limited by systematics.
By improving the frequency-lock performances up to the levels already obtained by other groups , an ultimate precision only limited by the comb stability (parts in 1013 for our setup) is in principle achievable, assuming a complete control on all the systematic error sources. This requires a completely different servo electronics and a proper coupling of the correction signal to the laser chip.
The ability of measuring a transition frequency with such a precision can be of great importance, since it may allow to define, in the spectral region covered by QCLs, a set of molecular lines forming an inexpensive grid of secondary frequency standards, suitable for applications requiring relative accuracies in the 10-12÷10-13 range. Moreover, thanks to the drastic reduction of the uncertainty with respect to the HITRAN database, performing frequency measurements on a set of transitions of the same molecule will allow to determine the related set of molecular parameters with an improved accuracy.
This work was partially supported by Ente Cassa di Risparmio di Firenze and EU under the JRA Contract No. RII3-CT-2003-506350 (FOSCIL).
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