2.1

Optical link to a frequency COMB

The OFCS used in this experiment is a mode-locked femtosecond Ti:sapphire laser operating in the 500÷1100 nm range. In order to set a link between the OFCS and the QCL an up-conversion of its frequency is required. It has been achieved by a SFG process with a Nd:YAG laser into a non-linear periodically-poled LiNbO3 crystal. The starting wavelengths are those of the QCL (λ_QCL = 4.34μm) and of a Nd:YAG (λ_YAG = 1.064 μm), which is referenced to the OFCS. The obtained radiation, with a wavelength at about 854 nm, is superimposed to the beam of a laser diode working at a close wavelength and referenced to the OFCS too. A fast photodiode detects the radio-frequency beat-note, the signal is analyzed by a spectrum analyzer and its frequency measured by a counter. The details of the experimental setup and of the direct digital synthesis (DDS) method used for referencing the Nd:YAG and the laser diode to the OFCS are reported in [13,16,17,18]. The important point is that the locking scheme used makes the beat note spectrum to exactly reproduce the line-shape of the QCL emission spectrum, and from the counting of its frequency (ν_beat) it is possible to derive the absolute value of the QCL frequency by:

since ν_YAG e ν_diode are known with the OFCS precision and have few-kHz-linewidths, negligible in comparison with the QC laser linewidth.

2.2

Sub-Doppler FM Spectroscopy and frequency locking

Unlike other experimental works [19,20], where the QCL frequency has been locked even at very high levels, but without any absolute reference, our aim was to use, for frequency stabilization, the narrowest feature having also absolute reference and intrinsic stability characteristics. We opted for the Lamb-Dip of a molecular CO₂ line, obtained by a typical saturated absorption spectroscopy setup, described in details in [13]. Even considering the pressure and transit time broadening effects, determined by our experimental conditions, the total width of the Lamb-Dip feature is not larger that 200 kHz.

The dispersive signal centered on the line has been obtained by a conventional wavelength modulation of the laser and a lock-in first-derivative detection of the absorption signal. This feedback signal is processed by a PID and then sent to the laser, together with the dither, through the modulation input of the low-noise current driver.

In our case, the bandwidth of the feed-back signal is limited by the 1 ms time constant of the lock-in; in general, the critical point is the presence of the dither itself, since it occupies most of the available modulation bandwidth at the expense of the feed-back signal bandwidth, the only playing a role in frequency stabilization. Our current driver, for example, has a 150 kHz modulation bandwidth, and the feed-back signal bandwidth could not be anyway larger than few tens of kHz. This value is still not enough for a linewidth narrowing, as we will see in the following.

In principle it is possible to send the dither signal directly to the QCL bypassing the current driver and avoiding the limitations imposed by its bandwidth, but it is a dangerous choice, since the device is very sensitive to electrical shocks and the risk of breaking it was too high.

We do not report here the graphs with the saturated absorption signal and its first-derivative. They are shown in Sec.3 where a comparison with the polarization spectroscopy in presented.

A clear representation of the effectiveness of the locking loop is provided by the comparison between the frequency noise spectra in free-running and locking conditions, shown in Fig.2. Both spectra have been acquired by using the slope of the transmission peak of a germanium etalon as a frequency-to-amplitude-noise discriminator. The small loop bandwidth is determined, as already stated, by the lock-in 1 ms time constant; the noise suppression of up to 25 dBm is satisfying and ensures a good long-term stability of the frequency, as described in the following.

Fig.2.

Comparison between the laser frequency noise in free-running (red) and locking (blue) conditions. The bandwidth below 1 kHz is what we expected considering the 1 ms lock-in time constant.

2.3

QCL emission lineshape analysis and absolute frequency and stability measurement

From the analysis of the beat-note spectrum we can directly characterize the QCL frequency noise, obtaining informations that are complementary to those of Fig.2. The real-time FFT spectrum analyzer allows to follow the time evolution of the beat-note spectrum with a resolution of 40 μs, corresponding to the frame rate of the FFT spectra (25 kHz).

Fig.3(a) shows the time evolution of the beat-note during a 2 ms interval, with the free-running QCL; an acquisition over longer timescales was not possible because the fluctuations were larger than the maximum available frequency span of the analyzer (only 15 MHz in real-time mode). Such fluctuations, as well as the width of the fast jittering envelope, heavily depend on the current noise of the driver. This is clearly shown by a comparison with Fig.3(b), in which the same QCL is powered by an ultra low-noise home made driver: not only the peak is sharper, but also its fluctuations are smaller, and it is possible to follow the evolution for a longer time (10 ms). Unfortunately, the home made current driver is still not provided by a modulation input, and it is not yet suitable for frequency locking.

Fig.3.

The evolution of the beat note as detected by our real-time spectrum analyzer, with the QCL powered by a commercial low-noise driver (a) and by a home-made ultra low-noise driver (b). Different current noise levels determine different fluctuation amplitudes of the QCL frequency.

The effects of the locking loop can be analyzed by observing the beat-note spectrum with the loop on: in this condition the fluctuations are reduced, and lie well within the analyzer spectral window, so that longer acquisitions are possible. Fig.4 shows a comparison between two spectra corresponding to 70 ms and 40 ms acquisition lengths, both with the laser locked: the intrinsic linewidth appears very narrow but, even in locked condition, the non suppressed fast jitter determines a gaussian broadening of the line shape over long timescales.

Fig.4.

The blue profile is the FFT spectrum of a 40 μs-long acquisition of the beat-note, while the black one is the FFT of a 70 ms-long acquisition. The latter can be interpreted also as an average of 1750 spectra of the blue type. In background a 10 ms-long real-time acquisition during locking is shown. The maximum frequency span in single FFT mode is double than in real-time mode.

Anyway, the regular shape of this gaussian envelope, ensured by the locking, allows an affordable frequency counting. In fact, the frequency counter used has a 1 s gate time, thus averaging all the faster random jitter and achieving a short-term precision drastically better than the linewidth of the laser.

Fig.5 shows a comparison between two typical sets of frequency counts, with the QCL in free-running and locked operation. The stability achieved by the locking enables the acquisition of several hundreds of points, and allows to minimize the statistical error. In this way a standard deviation, on a single data set, of a few kHz can be achieved. This can be assumed as the intrinsic precision of our system. Unfortunately the presence of unwanted slow drifts ascribed, for example, to interference fringes shifting the locking point, limits the overall accuracy to the level of some tens of kHz. However, the final precision of the measurement of the molecular transition absolute frequency is about two orders of magnitude better than the error stated by the HITRAN database.

Fig. 5.

The frequency locking loop reduces the spread of the frequency counts by a factor comparable to its gain (>20 dB). An example of a 20 minutes-long data set is shown in the nght part of the graph.

The next step is an improvement of the loop bandwidth and gain, in order to achieve a narrowing of the laser emission, together with an enhancement of the stability of the error signal, in order to eliminate the spurious effects that limit the final precision.

3.1

Principle and advantages

Polarization spectroscopy is among the most sensitive spectroscopic techniques [21,22], even if it is still not widely used. It is a pump-probe technique like the saturation spectroscopy, and it is based on the detection of an optical anisotropy induced in a medium by the pump beam. It works for every ro-vibrational molecular transition, and thus it has a very wide range of applicabilty in the mid-infrared region, that is precisely known as the molecular fingerprint region, thanks to the presence of the most intense ro-vibrational bands of many common molecules.

Its principle is to induce a birefringence in a medium, with a circularly polarized pump beam, and to interrogate this with a linearly polarized counterpropagating probe beam, watching for the rotation of its polarization. It can be regarded as a form of saturation spectroscopy, with the change of the complex refractive index being proportional to the pump intensity.

To our knowledge, the results presented here are the first reporting the successful utilization of this technique in the mid-IR region and with a QC laser.

As we have already stated, it offers several chances of improving our experiment.

The key concept is the production of a dispersive signal suitable for frequency locking without any modulation (dither) on the driver current.

The absence of the dither offers a direct benefit from the point of view of spectral purity. Moreover it allows a complete exploitation of the modulation bandwidth available for the locking loop, and thus for frequency noise reduction. Moreover, it simplifies the electronics involved in the locking loop (the lock-in is no more required), and this is a valuable point in the perspective of a space-oriented experiment.

Also from the point of view of sensitivity, polarization spectroscopy is an important advance, and will enhance the loop gain by improving the signal-to-noise ratio. The limitations of this technique involve especially the single detection scheme, presented in the following. In fact it does not provide a zero background signal, the locking point can not be easily determined and is affected by offset variations, at the expense of the stability. As we will see, it is possible to overcome these restrictions by adopting a double detector differential acquisition setup, that we are going to implement soon.

3.2

Experimental Set-Up and test acquisitions

The changes made in the experimental set-up have involved only the manipulation of the beams polarizations, as shown in Fig.6. The tunable λ/2 waveplate, in combination with first wire grid polarizer (P1), splits the QCL beam into the pump and probe beams. The polarization of the former is set to circular by the tunable λ/4 waveplate. The polarization of the probe beam is already linear since it is determined by the first polarizer, but it is further cleaned by the P2 polarizer, just before the spectroscopy cell. After the cell the probe beam encounters the analysis polarizer (P3) and its transmitted component is detected.

Fig.6.

Schematic of the polarization spectroscopy setup. The polarizers P1 and P2 are parallel; P3, the analysis polarizer, is nearly crossed in respect to the others. The electronic apparatus required for locking is drastically simplified with respect to Fig.1.

In this first experiment the polarizers P2 and P3 are nearly crossed: this means that the detected signal is very weak, compared with the typical amplitude of a saturated absorption signal (Fig.7). For this reason a larger amplification has been applied to the detected signal.

Fig.7.

By tuning the orientation of the analysis polarizer it is possible to continuously move from the usual saturated absorption signal to the polarization spectroscopy signal. The polarization signal in intrinsically weaker since it is obtained for nearly crossed polarizers.

The dispersive profile appears in place of the Lamb-Dip, or better overlapped to it, since the background sub-Doppler profile is still present, and grows faster when moving far from the nearly crossed position. On the other hand, for perfectly crossed polarizers, no dispersion signal is present. Due to the residual background, the signal is not symmetric and suffers from offset fluctuations. A test of frequency locking performed with this signal did not lead to significant improvements in respect to the first-derivative locking loop, mainly because of amplitude fluctuations of the error signal itself.

However the improvements made in terms of sensitivity and bandwidth of the signal are noticeable. Fig.8(a) shows a comparison between a simple saturated absorption signal and the polarization signal: a S/N enhancement of more than a factor 5 is achieved without any effective bandwidth reduction. On the other hand, Fig.8(b) points out the improvement, in terms of bandwidth, in comparison with the first-derivative dither-locking technique. In fact it is evident how, in that case, a comparable signal-to-noise ratio is obtained at the expenses of a smaller signal bandwidth. The comparison between the slopes is a further evidence of this fact.

Fig.8.

(a) Comparison between the direct saturated-absorption signal and the polarization spectroscopy signal. Both are obtained without any dither on the driver current. (b) Comparison between the sub-Doppler feature acquired in first-derivative lock-in mode and in polarization spectroscopy mode. The signal bandwidth is larger in the second case, thanks to the absence of the dither.

It has to be pointed out that here the factor limiting the steepness of the slope is the laser emission linewidth: with a better current driver we plan to see even sharper features with the polarization spectroscopy, where with first-derivative spectroscopy the presence of the modulation and the lock-in time constant would have prevented a better resolution.