1 Introduction

The mid-infrared (3–20 μm) is a spectroscopically important region, containing the fundamental vibrational bands of many different molecules of both fundamental and applied interest. The theoretical development [1], and subsequent experimental realization of quantum cascade lasers (QCLs) [2], has allowed relatively simple access to this spectral region for high-resolution laser spectroscopy with a wide variety of applications such as in chemical physics [3], trace gas sensing [4], plasma characterization [5], breath analysis [6], and the investigation of supersonic expansions [7, 8].

The tuning range of readily available distributed feedback continuous wave (cw) QCLs is typically limited to a few cm−1. When broader spectral coverage is required, available options include monolithic devices composed of multiple gain media [9, 10], cascade structures coupled together [11] or parallel arrays of a few tens of DFB lasers [12]. These solutions extend tunability to hundreds of cm−1. External cavity based systems exploit the full gain profile of the QCL allowing comparable or greater tuning ranges without the need for such complex material engineering. Such devices, operating around room temperature and in cw mode are now commercially available [13] (at least for wavelengths greater than ca. 4 μm) and these attributes combined with high power, broad tunability and narrow linewidth mean that external cavity quantum cascade lasers (EC-QCLs) are set to transform mid-infrared spectroscopy. For more information on the developments and applications of EC-QCLs, we refer the reader to various review articles [14–17] and the references therein. Such devices, which often operate at room temperature, open up the possibility for trace gas detection of multiple species and/or species with unresolved rotational structure in their infrared spectra, and indeed condensed phase species [18–20]. The narrow linewidth and high power also make them excellent sources for combination with optical cavity techniques [21], both within resonant and non-resonant cavities, with a view to producing broadly tunable quantitative sensors based upon small sample volumes [22, 23]. Furthermore, these high fidelity sources allow detailed studies of non-linear optics and the interaction between light and matter. Another example of an area where wide tunability is advantageous is the study of the photodissociation and reaction dynamics of rovibrationally state-selected small gas phase molecules [24]. The output powers of cw QCLs are now such that significant saturation has been achieved in a number of studies [25–27], a fact which suggests that these devices may be suitable candidates for use as mid-IR pump sources in state preparation studies and the first step toward this has recently been published using an EC-QCL as a pump laser [28].

For many of these studies, it is important to know the laser linewidth: for example, phase fluctuations will limit the extent of coherent excitation that may be achieved. There are several ways of measuring or estimating the laser linewidth such as deducing the laser linewidth from spectroscopic measurements of Doppler broadened spectral transitions, (self-)heterodyning [29], or using the steep slope of a low pressure absorption line to convert the wavelength fluctuations into detector voltage fluctuations [30]. Perhaps the most commonly used is Lamb-dip spectroscopy which allows direct observation of the actual laser emission linewidth. For this technique, a strong pump beam saturates a transition in a low pressure gas and the sample is then probed by a counter-propagating weaker beam formed from the same laser; the probe beam signal then essentially consists of a Gaussian absorption signal which shows a depletion at line center where its absorption is diminished when it interacts with the maximally saturated sample [31]. For transitions in the mid-infrared, the spontaneous emission lifetimes are typically of the order of tens of ms or longer; therefore, at sufficiently low pressures, where the collision rate is also minimal, the width of the Lamb dip will directly reflect the linewidth of the pump and probe field. Recently, the linewidth of EC-QCLs as deduced from the width of the Lamb dips have been reported [25, 27]. Linewidths of ∼4 and 2.5 MHz were observed using NO2 and a custom-built EC-QCL at 6.3 μm, and using a commercial Daylight EC-QCL at 5.3 μm on NO, respectively. Other studies have, in general, found linewidths in the 4–50 MHz range for free running cw EC-QCLs for integration times typically greater than 1 s [15, 29, 33–37], while a recent work showed a linewidth of 480 kHz for microsecond-integration times for an EC-QCL through optical feedback from a partial reflector [29]. We also note that the linewidth can be reduced further using stabilisation electronics and note particularly the remarkable work of Bartalini et al. [36] in measuring QCL linewidths which are significantly below the Schawlow–Townes limit.

In this study, we extend our previous work on laser linewidth measurements on an EC-QCL by considering the laser linewidth as a function of injection current and interpreting this behavior using the three-level system developed by Yamanishi et al. [38] and values for both radiative and phonon-assisted relaxation rate constants reported in literature. We also report the occurrence of cross-over resonances, observable at the lowest rotational states where the hyperfine coupling is largest in NO, and further confirm our measurements of the laser linewidth using polarization spectroscopy.

2 Experimental setup

The laser used in this work is a water-cooled external cavity QCL (Daylight Solutions) tunable over the range 1,776–1,958 cm−1 including a modehop free area of 1,870–1,920 cm−1 at a chip temperature of 17 °C, with a maximum output power of 140 mW and a beam waist of 0.6 mm [36]. The majority of the output from the EC-QCL formed the pump beam and was passed through a 70-cm long cell bounded with BaF2 windows containing a low pressure of NO gas (10–100 mTorr) and overlapped with the weaker counter-propagating probe. The probe contained ∼5 % of the total laser power and was created using a CaF2 beam splitter placed immediately following the laser as is shown in Fig. 1.

Fig. 1
figure 1

Diagram of Lamb-dip experimental setup. A CaF2 flat was used to split ca. 5 % of the laser radiation from the main beam and this weak ‘probe’ beam then overlapped with the strong ‘pump’ beam in a counter-propagating manner

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After passing through the cell, the probe beam was focused using an off-axis paraboloid mirror onto a thermoelectrically cooled mercury cadmium telluride detector (VIGO PVI-2TE-6), the output of which is fed into an oscilloscope (LeCroy Wavesurfer 44MXs-A) and stored for further processing. Calibration of the relative frequency scale was achieved using a germanium etalon with a free spectral range (FSR) of 500 MHz. A typical Lamb-dip experiment would employ maximum overlap of the two beams, however, the frequency instabilities caused by optical feedback into the EC-QCL made this optimal mode of operation unfeasible and resulted in an experimental uncrossing angle of ∼0.2°; even under this alignment condition, frequency instabilities during the scan caused by mechanical jitter in the external cavity of the laser and low-frequency noise in the current controller meant that the narrow dips were unobservable following any oscilloscope-based averaging. A post-processing routine has been employed by which individual scans were recentered and then averaged using a routine in MATLAB. While the averaging process effectively lengthens the measurement time and thus would allow more laser jitter to affect the results, the measured Lamb-dip widths for both single shot and averaged data gave essentially identical values. Thus, averaged data, which has a lower uncertainty due to a higher signal-to-noise ratio was determined appropriate for use.

In the limit where the laser linewidth is negligible in comparison to the homogeneous linewidth of the transition, the Lamb dip should be well described by a Lorentzian function [31]. However, it was found that the laser linewidth is much larger than the homogeneous linewidth, and therefore, the Lamb dip provides a direct measurement of the laser linewidth. The dips are well described by a Gaussian lineshape and, therefore, the data were subsequently fit using the following equation [33],

$$ \alpha(\omega)=\alpha_0(\omega)\left\{\exp[-((\omega-\omega_0)/\delta_{\rm D})^2]-\frac{\sqrt{\pi}\gamma}{\delta_{\rm L}}\left[1-\frac{1}{\sqrt{1+G}}\right]\exp[-((\omega-\omega_0)/\delta_{\rm L})^2]\right\}, $$
(1)

where α 0(ω) is the unsaturated absorption coefficient, ω 0 is the frequency at resonance, G is the (on resonance) saturation parameter, γ is the power broadened homogeneous linewidth and δ D and δ L are the Doppler and laser linewidths, respectively. G is given by

$$ G = \frac{2I_{\rm p} \mu^2\tau^2}{\epsilon_0 c h^2}, $$
(2)

where μ is the transition dipole moment, I p(ω) is the pump laser intensity and τ is the relaxation time of the system, \(\epsilon_0\) is the permittivity of free space, c is the speed of light and h is Planck’s constant.

The experimental setup for polarization spectroscopy was very similar to that used in the Lamb-dip experiment (Fig. 1), except for the addition of a tunable λ/4 waveplate (Alphalas PO-TWP-L4-25-UVIR) after the probe beam is separated from the pump, and crossed MgF2 Rochon polarizers (Alphalas PO-RO-8-MGF) with an extinction coefficient of 10−5 placed both directly after the laser to clean-up the polarization state of the probe beam and immediately before the detector, which acts as the analysis polarizer. The polarization component of the beam rejected by the polarizer was emitted at a separation angle of 1.8° from the main beam and was removed with the use of irises placed after the polarizers. The rotation angle θ of the analysis polarizer is adjusted with respect to the other polarizer to obtain the desired polarization signals. The λ/4 waveplate required angle tuning for optimal operation at this wavelength, and this was performed by passing the beam through the waveplate and then returning it along the same path. A wire grid polarizer was then set to allow only the vertically polarized light to pass through, and the angle of the waveplate tuned such that maximum signal was observed. In this manner, as the horizontally polarized light first passes through the waveplate, it becomes circularly polarized. When the light is retroreflected, the direction of polarization rotation is reversed (σ + to σ − or vice versa), and the waveplate then further rotates the polarization into the vertical plane. Thus, by minimizing the signal incident upon the detector, the degree of circular polarization was optimized. This polarization was again checked and readjusted in the far field at the position of the cell to correct for any depolarization caused by the intervening mirrors.

3 Results and discussion

3.1 Linewidth measurements

Initial experiments were performed scanning the laser over both \(\Uplambda\) doublet components (e, f) of the \(v =1 \leftarrow v =0\) R(13.5)1/2 rovibrational transition of NO at 1,920.7 cm−1 at a rate of 40 Hz by applying a voltage to the piezoelectric transducer controlling the external cavity grating and at pressures of NO within the range 2–100 mTorr. A selection of data recentered and averaged for 100 scans is shown in Fig. 2, overlaid with a global fit performed using Eq. (1) and zoom upon the lower frequency transition at 1,920.705 cm−1 originating from the e \(\Uplambda\) doublet. At the lowest pressure shown (12 mTorr), a global fit of the data returns a saturation parameter of 615 corresponding to a transition dipole moment of 0.053 D and a dip width of 1.7 ± 0.5 MHz. This value correlates to a direct measurement of the laser linewidth and along with the transition dipole moment is in good agreement with previously measured values [25, 37, 39, 40]. Furthermore, we reiterate that the dip was found to be best fit with a Gaussian profile rather than a Lorentzian, again mirroring findings in the literature [25, 37, 40], and most likely due to injection current fluctuations. It is also noticeable that the dip in the R(13.5)1/2 f transition at 1,920.715 cm−1 is generally deeper than the e \(\Uplambda\) doublet, which is not reflected in the fit. This is due to the assumption made here, and in the literature [39] that each of the doublets is a single transition with equal intensity; they are in fact split by hyperfine interactions into three closely spaced transitions (<1 MHz) [41]. We further note that a rapidly scanned cw-QCL can induce a sufficiently large AC Stark effect to cause splitting of the hyperfine structure of NO as recently reported by Duxbury et al. [42] on similar IR transitions. Rapid passage effects within Lamb dips have also been observed using rapidly scanned DFB QCLs [43]. The splitting in transition frequencies is slightly different for the two doublets with the separation approximately three times larger for the e transition than for the f at 1,920.715 cm−1 (0.9 vs 0.27 MHz). In the work that follows detailing laser linewidths, we focus primarily on the f \(\Uplambda\) doublet component as it displays minimal hyperfine structure and simply treat it as a single transition and only utilize low laser scan rates such that rapid passage effects are negligible. It is also apparent from Fig. 2 that the magnitude of the Lamb dip (relative to the maximum absorbance) increases markedly as the sample pressure is reduced and this trend reflects the increasing value for G as the collisional relaxation rate decreases.

Fig. 2
figure 2

Lamb-dip spectra of the \(\Uplambda\) doublet components (e, f) of the \(v =1 \leftarrow v =0\) R(13.5)1/2 rovibrational transition of NO at 1,920.7 cm−1 for a pressure of 25 mTorr (top). A global fit and zoom upon the (e) component of the transition are also shown for data taken at 12, 25 and 67 mTorr, respectively. The Lamb-dip size relative to absorbance can clearly be seen to increase as pressure is decreased

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Subsequently, the effect of laser power upon the Lamb-dip linewidth was investigated for low pressure mixtures (5 mTorr), which provide the highest contrast by minimizing collisional relaxation. To reduce the laser power without affecting its linewidth, a wire grid polarizer was utilized immediately after the laser and measurements taken at both 5 and 10 mTorr of NO. Figure 3 summarizes the results of this study; Fig. 3a shows that as the saturating power increases so does the magnitude of the dip, as would be expected as the degree of saturation is proportional to the incident pump laser power. Figure 3b demonstrates that the linewidth is essentially invariant to the incident pump laser power within error. This latter observation is in good agreement with our expectations from Eq. (1).

Fig. 3
figure 3

The effect of changing the saturating power on a the dip height ratio given by (α 0 − α S )/α 0, where α S  = α in Eq. (1), and b on the dip width. It is apparent here that changing the saturating power increases the size of the dip

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Power was also altered by changing the injection current to the laser and, as shown in Fig. 4, injection current impacts upon the laser linewidth. Far from the threshold current, I th, the observed laser linewidth is constant at ca. 2 MHz, but that as the current is reduced, the observed linewidth significantly increases. This is a well-known effect and the one which is described thoroughly by Yamanishi et al. [38] in a paper discussing the intrinsic linewidth of QCLs. The following discussion briefly describes their work and investigates the linewidth of our laser in more depth.

Fig. 4
figure 4

Measured laser linewidth as a function of applied injection current

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The fundamental limit upon a diode laser’s linewidth, δ ω, is traditionally given by the modified Schawlow–Townes (ST) formula [44, 45],

$$ \delta\omega=\frac{v_{\rm g}^2 h \omega\alpha\alpha_{\rm m} n_{\rm sp}}{4\pi P_{\rm o}}(1+\alpha^2_{\rm e}), $$
(3)

where α e is the Henry linewidth enhancement factor, v g is the group velocity of the electrons, α the cavity losses, α m the mirror losses, n sp the spontaneous emission factor and P o the output power. α e accounts for refractive index variations caused by fluctuations in the electron density throughout the gain material, an effect which has typically broadened traditional diode laser linewidths beyond the ST limit but which in QCLs is close to zero, as refractive index variations are negligible at the peak of the gain spectrum [2, 46, 47]. Yamanishi et al. [38] have reformulated this equation in terms of the generic rate processes occurring within a three-level QCL (see Fig. 5a). Here N i corresponds to the electron population in each of the states, P corresponds to the rate of influx and outflow of photons from the laser system, η to the coupling into the level 3 and the τ’s correspond to the time constants for relaxation. It should be noted that only τ r corresponds to a radiative process and all other time constants τ ij refer to phonon-assisted relaxation between the levels i and j. By considering only the case above threshold, the linewidth then can be written as [38]

$$ \delta\omega=\frac{1}{4\pi}\frac{\beta_{\rm eff}\ \gamma_{\rm photon}n_{\rm sp}}{1-\epsilon}\left[\frac{1}{(I_{\rm o}/I_{\rm th}-1)}+\epsilon\right](1+\alpha_{\rm e}^2), $$
(4)

with

$$ \epsilon=\frac{\tau_{21}\tau_{31}}{\eta\tau_{\rm t}(\tau_{21}+\tau_{31})}, $$
(5)

where τ ij corresponds to the the reciprocal of γ ij , the relaxation rate between two levels i and j, η is the upper level injection efficiency, I o and I th are the operating and threshold currents, and β eff is the effective coupling of the spontaneous emission given by the ratio of the spontaneous emission rate coupled into the lasing mode, (β/τ r), to the total relaxation rate, (1/τ t), where β is the coupling efficiency of spontaneous emission into a single laser mode. For EC lasers, the losses involved within the system (and thus largely included within α and α m) are also tempered by the mirror and grating reflectivities as well as the coupling of light from the QC device into the cavity [48]. As there is no detailed information regarding the internal specifics of the external cavity in the Daylight system, these losses were subsumed into terms for those of a bare QC device.

Fig. 5
figure 5

a Three-level model and rate processes utilized in this linewidth model. The assumption is made that all three-level systems within the gain medium are equivalent (adapted from [38]). b Width of the Lamb dip as a function of injection current with a least-squares fit of the data (see text)

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In this manner, the laser linewidth can be related to the ratio of the operating current to the threshold current with all other parameters fixed and dependent only on laser design. Unfortunately, as the EC-QCL laser system is commercially produced, little information about the exact constants for the QCL chip are available, including the level of losses. However, a range of reasonable values for QCLs are given in the literature [37, 38] and using these as limiting values added in quadrature with a baseline noise level of ca. 2 MHz allows the performance of a least-squares fit as shown in Fig. 5b. The constants returned from this best fit are detailed in Table 1, and these imply an ‘inherent’ linewidth of 200 kHz. These values are consistent with literature where theoretical calculations and more recently experimental data [37] have shown that the inherent QCL linewidth can in fact be very narrow, and sub-kHz values have been reported at optimal conditions.

Table 1 The constants returned from the best fit shown in Fig. 5b alongside the ranges of these constant as reported in the literature and taken as the bounds for each parameter within the fitting routine
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Evidence that 2 MHz is related to random phase fluctuations induced by vibration and/or current noise is further shown in Fig. 6, where the laser was scanned using direct modulation of the injection current with a 15-mA sine wave at a range of frequencies. The QCL bias tee and the acquisition electronics limit the range of accessible scan rates between 5 and 2 MHz. It can be seen that increasing the scan frequency decreases the width of the observed dip. This shows that the observed laser bandwidth is decreased as a function of measurement time, down to 1.3 MHz at 30 kHz scan rate when the bandwidth of the detector became the limiting factor. This behavior implies a low-frequency noise source causing additional broadening at longer observation times. It should be noted that, in this case, the scanning range was limited such that our Ge etalon FSR was too large to provide useful frequency scale data, instead the frequency scan rate was calibrated using the width of one of the \(\Uplambda\)-doublet resolved transitions, explaining the larger error bars. Theory indicates that the linewidth should be inversely proportional to the square root of the scan frequency. In Fig. 6, the linewidth is plotted as a function of the root of the scan frequency and over the limited frequency range (5–30 kHz), a linear fit is shown. Extrapolating the linear fit to the y-axis yields a limiting linewidth of 3 MHz consistent with our ‘slow’ data obtained through external cavity mechanical modulation and reflects the increase in measured linewidth when the transition was scanned over a longer time period.

Fig. 6
figure 6

Width of Lamb dip as a function of scanning frequency for fast scan rates and for probing both e and f \(\Uplambda\) doublets. Extrapolation of the linear fit to the data returns a y-axis intercept of ca. 3 MHz, in reasonable agreement with our slow scan data

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3.2 Cross-over resonances

The narrow EC-QCL linewidth has also allowed the observation of cross-over resonances. These occur when two transitions that overlap within their Doppler widths share either a common upper or lower state, resulting in extra resonances in the Lamb-dip spectra. When two transitions are separated outside their Doppler widths, as the pump laser scans from low velocity to high velocity (with respect to beam propagation), the probe laser scans through the same transition in the other direction and dips are only seen at the central frequency. When the transitions overlap, however, an extra dip is observed in the probe spectrum at the average frequency, both velocity subsets are pumped simultaneously, while at the same time being probed on the opposing transition. Thus, an extra dip is seen in the observed spectra with an intensity equal to the square root of the individual transition probabilities [31]. In the case of a shared ground state, then a decreased population in this state means that an extra dip is seen; however, in the case of a shared upper state, then both fields contribute to an increase in that population and a peak should be observed at the central frequency. This effect was first observed by Uzgris et al. [49] and is fairly common in molecular spectra, largely due to the prevalence of hyperfine structure.

Figure 7 shows a spectrum of the R(1.5)1/2 transition of 8 mTorr of NO alongside the HITRAN positions and linestrengths (red) and the anticipated positions and linestrengths of cross-over transitions (cyan). It is apparent that, in this case, individual hyperfine components are easily observable as Lamb dips, all with a FWHM of approximately 2 MHz. Furthermore, extra cross-over resonances are clearly observable at the mid-points between transitions with shared upper or lower states as marked out by cyan lines. Figure 7b shows a Doppler subtracted spectrum of the R(1.5)1/2 e transition, again with the HITRAN line positions and predicted cross-over resonances. The composite feature at 1,884.2938 cm−1 is actually four cross-over resonances due to shared F = 1.5 and 2.5 components in either the ground or excited state.

Fig. 7
figure 7

Lamb-dip spectrum of R(1.5)1/2 transition of 8 mTorr of NO. a The entire transition and b a Doppler subtracted spectrum of the e peak at 1,884.293 cm−1. Also displayed are the HITRAN data for the positions and linestrengths of the hyperfine split transitions (red), and the positions of anticipated cross-over peaks (cyan) between the \(\Updelta F=+1\) transitions around 1,884.293 cm−1 and the weaker \(\Updelta F = 0\) transitions at 1,884.2942/3 cm−1

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3.3 Polarization spectroscopy

As further confirmation of the laser linewidth polarization spectroscopy was used to interrogate the low pressure NO samples. While Lamb-dip spectroscopy measures the change in absorption induced by a pump beam upon a probe beam, polarization spectroscopy detects a polarization change induced in the probe beam by an anisotropic sample itself generated by a high-power polarized pump beam. The principle of polarization spectroscopy can be understood as follows. When a beam of infrared radiation excites a rovibrational transition, then along with the change of J, there is also a change in the projection of J along the axis of beam propagation, M. For a linearly polarized beam, the selection rule is \(\Updelta M=0,\) while for circularly polarized light beams σ + and σ −, the specific selection rule is \(\Updelta M= +1\) and \(\Updelta M = -1, \) respectively. If a single circularly polarized pump beam is used, say σ +, then \(\Updelta M =+1\) and the spatial distribution of angular momentum will become anisotropic, as some M levels will not be populated [or not be depopulated depending upon the spectral branch (P, Q, or R) being interrogated]. When this sample is then interrogated by a second, linearly polarized beam, this spatial anisotropy is observed as a birefringence within the sample and causes the plane of polarization to rotate.

More quantitatively, when the linearly polarized probe beam passes through a sample within which anisotropy has been induced using a strong circularly polarized pump laser, then the two components of the probe, σ + and σ −, will experience different absorption coefficients α + and α −, and refractive index n + and n −. The difference \(\Updelta\alpha(\omega)=\alpha^+-\alpha^-\) represents the circular dichroism, while the difference \(\Updelta n(\omega)=n^+-n^-\) is the optical birefringence. As was the case for saturation spectroscopy, there will be an array of molecules that interact with the pump and probe beams simultaneously around ω 0, and this will result in a change in absorption and dispersion signals with a Lorentzian dependence on frequency, \(\Updelta\alpha(\omega)\) and \(\Updelta n(\omega), \) respectively. The observed transmitted signal I t can be described by the following equation which is a hybrid of Demtröder’s formalism [31] and the work presented by Bartalini et al. [26],

$$ I_t(\omega)=2I_0(\omega){\hbox{e}}^{-\alpha L}\left[\xi+|\sin\theta \cos\Upphi+\cos\theta \sin\Upphi|^2\right], $$
(6)

where ξ is equal to the transmission at θ = 0, and is a function of the polarizers used, and the factor I 0e−αL represents the saturated absorption spectrum with L, the path length of the sample. The phase factor \(\Upphi\) is given by

$$ \begin{aligned} \Upphi&=\frac{1}{2}\left[\left(\Updelta\alpha_0 L \frac{\frac{\gamma_s}{2}(\omega-\omega_0)}{\left(\frac{\gamma_s}{2}\right)^2+(\omega-\omega_0)^2} +\Updelta b_r'\right) \right. \\ &\quad\left. +i\left(\frac{\Updelta\alpha_0L}{2}\frac{\left(\frac{\gamma_s}{2}\right)^2}{\left(\frac{\gamma_s}{2}\right)^2+(\omega-\omega_0)^2} + \Updelta b_i\right)\right], \end{aligned} $$
(7)

with \(\Updelta b_r\) and \(\Updelta b_i\) being the contributions due to birefringence and dichroism within the cell windows.

Initially, experiments were performed analogous to the Lamb-dip spectroscopy with the addition of a λ/4 waveplate and polarizers uncrossed, such that θ = 90°. Once again, the R(13.5)1/2 transition was chosen, and Fig. 8 shows the effect of left and right circularly polarized probe beams with 12.5 mTorr of NO. The dispersion signal can be clearly seen to change sign as the selection rule for the transition is reversed and the system oriented with or against the direction of pump beam propagation. The polarizer angle was then adjusted as shown in Fig. 9a for polarization spectra of 15 mTorr of NO at a selection of crossing angles, with simulations overlaid in Fig. 9b. It should be noted that the data in Fig. 9b are offset in the y-direction for clarity. As this simulation is performed for qualitative rather than quantitative agreement, the laser linewidth was accounted for by replacing γ s with a value of 2 MHz [26]. The simulations are found to be in good agreement with the experimental data and consistent with measurements presented earlier in this paper.

Fig. 8
figure 8

Polarization spectrum of R(13.5)1/2 transition of NO at a pressure of 12.5 mTor with left and right circularly polarized pump beam detected by a linear probe with an uncrossing angle of 20°. σ + data are offset for clarity

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Fig. 9
figure 9

The polarization signals of NO as a function of uncrossing angle, θ. As θ is decreased, the dip becomes observably less symmetric as the dispersion signal becomes dominant

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It is apparent that the expected polarization spectroscopy behavior can be observed as the angle of the polarizer is changed toward crossing (θ = 0); the dispersive profile at line center becomes increasingly apparent, while the ‘normal’ absorption signal decreases. As with the Lamb-dip data, these data have once again been recentered and averaged for 100 scans. The dispersive signal apparent in the polarization signals should in fact completely disappear at θ = 0 [26] and a purely Lorentzian profile be returned. However, even realigning using the signal from the pump beam did not produce enough contrast for signal to be observed below θ = 10°.

4 Conclusions

Lamb-dip spectroscopy on a low pressure sample of NO has been performed to measure the linewidth of an external cavity QCL as a function of both injection current and laser scan rate. The measured linewidth of ca. 2.5 MHz is in good agreement with values found for DFB QCLs and in keeping with the intrinsic physical properties of the QCL architecture. Sub-Doppler polarization spectroscopy has also been performed, independently confirming the observed laser linewidth. Collectively, these experiments have demonstrated the high-power and low-bandwidth nature of EC-QCLs and their applicability to high-resolution spectroscopy, as well as hinting toward their use as an optical pumping source.