1 Introduction

Optical spectroscopy in the mid-infrared (mid-IR) spectral region based on tunable monochromatic sources has proven to be the method of reference for gas analysis and detection nowadays. Even though wavelength modulation spectroscopy (WMS) [1,2,3] is still the most widely employed detection approach, the emergence of new spectral interrogation techniques has pushed the limits of technology allowing optical gas analyzers to reach calibration-free operation [4,5,6] and astonishingly high performances. For instance, recent advances in photoacoustic spectroscopy led to limits of the detection in the level of parts-per-trillion on very small sampling volumes [7, 8]. Similarly, the development of molecular dispersion spectroscopy has made possible for optical instruments to provide both immunity to optical intensity changes and superb linearity in the measurement of concentration [9,10,11,12,13]. The mid-IR region is often the spectral range of choice to maximize the sensitivity of the previous methods, as it provides access to the strongest characteristic transitions of many important molecules.

For the previously introduced methods to operate flawlessly, reliable optical monochromatic sources with high optical power are required. In this respect, the advent of quantum cascade lasers (QCLs) has completely redefined optical sensor design [14,15,16]. Nevertheless, these sources present a narrow tuning range at a considerably high price-to-performance ratio. The limitations on tuning range are overcome by mechanically actuated external-cavity QCLs, but wavelength consistency and repeatability remain challenging [17]. There is, therefore, ample room for other optical sources to have an impact in mid-IR gas spectroscopy. A good example is difference frequency generation (DFG), which is generally used in spectroscopy for getting access to the characteristic molecular transitions of hydrocarbons in the mid-IR band around 3.4 µm [18,19,20,21]. This mid-IR light generation approach is based on nonlinear frequency conversion processes (to generate an optical signal whose frequency is equal to the difference in frequency between two input signals) that are particularly efficient when (for example) periodically poled lithium niobate (PPLN) crystals are used, as they offer quasi phase-matching operation. Fortunately, in DFG systems mature 1064 nm lasers can be employed in conjunction with semiconductor lasers and devices developed for optical telecommunications operating at 1.55 µm for the generation of optical radiation in the 3.4 µm band. This provides great flexibility and enables the implementation of robust and reliable optical sources, allowing for quickly accessible tuning ranges greater than 10 nm. Although the level of mid-IR power is well below the capabilities of QCLs, the tens (up to hundreds) of µW emitted by commercial DFG sources are more than sufficient for highly sensitive gas detection. Nevertheless, the nonlinear signal generation process makes the intensity of the mid-IR radiation extremely sensitive to parameters such as intensity, polarization or wavelength of the two source signals. These characteristics complicate the development of absorption-based gas spectrometers with DFG [22, 23], especially those based on derivative approaches as WMS [24]. Nevertheless, as previously introduced, one of the preeminent features of molecular dispersion spectroscopy is an inherent immunity to optical intensity changes; and this enables to straightforwardly use DFG systems as sources for optical gas detection in the mid-IR. In fact, the flexibility of DFG overcomes the complications associated with the generation of the particular spectral interrogation signals that are required for dispersion spectroscopy [25]. The only available possibility for a QCL laser to generate a multi-tone interrogation signal characteristic of a dispersion spectroscopic architecture is the direct modulation of the bias current of the laser. This produces both intensity and frequency modulation, distorting the output waveforms and making the performance of the instrument dependent on both the particular device employed and the operation point of the laser, impeding calibration-free operation. Instead, DFG permits the utilization of electro-optic intensity modulators to generate ideal intensity modulated signals at 1.5 µm that can be subsequently downshifted to the 3.4 µm band. This enables to combine all the benefits provided by dispersion spectroscopy in the near-IR alongside the distinctive high-sensitivity of mid-IR operation.

To date, only chirped laser dispersion spectroscopy (CLaDS) instruments [26, 27] have proved their suitability for operating with DFG optical sources. In this paper, we demonstrate that heterodyne phase sensitive dispersion spectroscopy (HPSDS) [11] is, by its very nature, equally capable of taking full advantage of the benefits of DFG sources.

2 Heterodyne phase sensitive dispersion spectroscopy based on difference frequency generation

2.1 Heterodyne phase sensitive dispersion spectroscopy

HPSDS is a recently developed spectroscopic approach that, as a dispersion spectroscopic technique, senses the characteristic change in refractive index that appears in the proximity of molecular transitions. Since this change is directly proportional to the number density of the target analyte in the sample, gas concentration can be directly retrieved. HPSDS sends a symmetric three-tone optical signal (generated by intensity modulating the light from a monochromatic source) through the sample using tone separations (modulation frequencies) that are in the order of the linewidth of the transition. As the signal propagates through the sample, the differences in the refractive index found by the three tones induce optical phase shifts between them that are transferred to the RF domain when the signal impinges on a fast photodetector. Any electronic phase detector can be employed to recover the optical phase shift that, at the center of the spectral feature, is directly proportional to the concentration of gas. Therefore, the trough of the HPSDS spectrum provides a direct measurement of gas concentration. The main benefit of HPSDS is its simplicity; in fact, its architecture is similar to that of WMS with the only exceptions of an increased modulation frequency, the application of intensity modulation and the output parameter of interest, which in this case is the phase of the detected signal instead of the amplitude. Similarly, there is no need for data processing for concentration retrieval and calibration-free operation can be directly achieved. HPSDS has already been demonstrated in the near-IR using conventional semiconductor diodes [11, 13] and widely tunable vertical-cavity surface-emitting lasers [28] and in the mid-IR with directly modulated QCLs [12, 29, 30]. To the authors’ knowledge, this manuscript presents the first demonstration of HPSDS in the mid-IR using a DFG source.

2.2 Architecture of the instrument

The architecture of the DFG system for HPSDS is presented in Fig. 1. The signal laser diode, emitting at a central wavelength of around 1538 nm, is directly connected to an electro-optic Mach–Zehnder intensity modulator (LN56S-FC, Thorlabs Inc., USA) that generates the three-tone HPSDS signal. The spacing between the central tone and the sidebands is equal to the frequency of the first signal generator (SG1 in Fig. 1). After optical amplification, the HPSDS signal is combined with a free-running pump laser (1064 nm) using a fiber-coupled wavelength division multiplexer and focused into a 40 mm MgO:PPLN crystal (MOPO1-0.5-40, Covesion Ltd., United Kingdom). The crystal was stabilized to a temperature of 415 K and the grating with a period of 29.98 µm was selected. The idler mid-IR radiation emitted by the crystal (with a wavelength of 3452 nm) was then collimated, filtered (to remove any remaining near-IR signal) and propagated through a methane gas cell (1% CH4 in N2 at a total pressure of 400 Torr, the path length is 50 mm and MgF2 optical windows were employed). The free-space light beam is finally detected by a thermoelectrically cooled MCT photodetector (PVI-4TE-8, Vigo Systems S.A, Poland). The RF beat note created on the detector is downshifted using a mixer and a second signal generator to a frequency within the input range of the lock-in amplifier (HF2LI, Zurich Instruments AG, Switzerland) that was used to extract the phase of the beat note. The phase reference for the locking is generated by an extra phase-locked signal generator.

Fig. 1
figure 1

Architecture of the difference frequency generation system for heterodyne phase sensitive dispersion spectroscopy. LD S signal laser diode, LD P pump laser diode, IM electro-optic intensity modulator, SG signal Generator, EDFA Erbium-doped fiber amplifier, FPC fiber polarization controller, FL focusing lens, PPLN periodically poled lithium niobate crystal, CL collimating lens, GW germanium window, PD photodetector, MIX RF mixer

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2.3 Characterization of performance

Prior to performing any experiments, the performance of the DFG system was thoroughly assessed. Foremost, for the characterization of the conversion efficiency the power of the pump laser was kept constant at 250 mW and the optical power of the HPSDS signal was swept between 30 and 770 mW by acting over the bias current of the EDFA. The results obtained are presented in Fig. 2, which illustrates both the linear dependence between the squared input power with the mid-IR idler power and the conversion efficiency. The maximum mid-IR idler power emitted by the crystal was found to be approximately 50 µW, a level that has proved to be more than adequate for sensitive gas spectroscopy. In the same way, the conversion efficiency of the system has demonstrated a remarkable stability with an average value of 73 µW/W2cm, which is similar to other values found in the literature for PPLN in single-crystal setups with loose overlap between signal and pump beams [31].

Fig. 2
figure 2

Idler output power as a function of the squared input power and the estimated conversion efficiency

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Even though the level of mid-IR optical power available is one of the parameters that have a greater impact on the performance of the gas analyzer, an accurate determination of the phase-matching bandwidth is equally important, as it ultimately defines the wavelength tuning range of the sensor (with some limitations, a greater wavelength emission range can be obtained by readjusting the temperature of the crystal). In this paper, the acceptance bandwidth was assessed by tuning the emission wavelength of the signal laser while the rest of parameters (input power, pump wavelength, the temperature of the crystal and the selected poling period) remained unchanged. As shown in Fig. 3, an experimental phase matching bandwidth with a full width at half maximum (FWHM) of roughly 270 GHz was measured, this corresponds to a wavelength tuning bandwidth of 10.7 nm (9 cm− 1) at 3452 nm.

Fig. 3
figure 3

Phase-matching acceptance bandwidth for the grating with a period of 29.98 µm (crystal length = 40 mm)

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Figures 2 and 3 clearly illustrate the limitations of DFG. First, the quadratic relationship between input and output power puts a huge amount of strain on the stability of the sources and the linearity of detectors, causing very often strong baselines to appear. Besides this, there is a highly non-linear intensity dependence on wavelength that includes prominent fringes which, in combination with the previous feature, extremely complicates concentration retrieval and system calibration on absorption-based systems. The output power is also highly sensitive to polarization changes, and this creates further difficulties. As presented in the Introduction, the immunity of properly designed molecular dispersion spectroscopic methods to changes in the optical power level inherently overcome the previous obstacles.

3 Experimental results: methane detection

After the initial characterization of the performance, the capabilities of the instrument for the sensitive detection of methane were evaluated. For that purpose, the wavelength of the source laser was biased at a central wavelength of around 1538 nm and modulated with a ramp signal generating a peak-to-peak wavelength sweep of 0.1 nm with a period of 2 s. Even though the modulation frequency that maximizes the HPSDS signal is 1 GHz, a separation between sidebands of 500 MHz was employed. In this way, the beat note lies within the bandwidth of the photodetector for maximum SNR (at the expense of a reduction in sensitivity of 22%). A RF power of − 3 dBm and a DC bias of 0.5 V were applied to the optical intensity modulator. At the entrance of the crystal, optical powers were adjusted to 250 mW for the pump laser and 500 mW for the source signal. The emitted mid-IR HPSDS signal has approximately 35 µW, which, after propagation through the gas cell, generates a 500 MHz beat note with an amplitude of around 200 mV. This signal is then downshifted to 5 MHz on the mixer and inputted to the lock-in amplifier.

A measurement of the HPSDS signal for a ro-vibrational line of methane at 3451.9 nm for a time constant of the lock-in amplifier of 23.4 ms (the spectral feature is swept at a frequency of 0.5 Hz) is represented in Fig. 4 together with a HITRAN simulation, demonstrating a high correspondence. The noteworthy smoothness of the measurements and the lack of apparent interference fringes demonstrate the high suitability of HPSDS as the selected method for DFG-based gas detectors. An SNR equal to 280 was calculated (ultimately restricted by etalon effects on the instrument), defined as the HPSDS negative peak value divided by the standard deviation of the baseline away from the spectral feature. This corresponds to a 1σ limit of detection of 250 ppb m Hz− 1/2 (that coincides with a noise-equivalent absorbance of ~ 3.5 × 10− 5/Hz− 1/2), a figure that enables accurate atmospheric methane concentration determination with short optical paths. Nonetheless, both the sensitivity and the limit of detection of the system could be greatly improved by targeting some of the stronger P branch absorption lines that, as shown in Fig. 5, are present in the vicinity of 3400 nm.

Fig. 4
figure 4

HPSDS signal (red dots) and simulation (blue line) for methane at 3451.9 nm. The inset shows a baseline measurement

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Fig. 5
figure 5

HITRAN simulation of the transmittance spectrum of methane around 3.4 µm (1% concentration, optical path 50 mm). The spectral feature analyzed in this manuscript is highlighted by a red arrow

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4 Conclusion

DFG sources can generate mid-IR radiation with sufficient power for highly sensitive gas spectroscopy. At the same time, this approach permits to take advantage of the whole set of devices developed for optical communications that are available in the 1.5 µm wavelength range for the generation of complex spectral interrogation signals that are later transferred to the mid-IR by means of nonlinear processes. The final product is a robust, reliable and highly flexible system in terms of both emission wavelength and spectral control. Accordingly, an ideal HPSDS three-tone signal with pure high-frequency intensity modulation can be achieved in the near-IR by means of an electro-optic intensity modulator and afterwards shifted to the 3.4 µm mid-IR band, where the fundamental resonances of the hydrocarbons lie. The result is a dispersion spectroscopic system that avoids the problems associated with directly modulated QCLs, ensures good sensitivity, immunity to fluctuation in optical power, superb linearity and true calibration-free operation.

In this paper, we have demonstrated HPSDS based on DFG nonlinear optical conversion. The straightforward architecture of the instrument is capable of generating several tens of µW of optical power in the mid-IR allowing for fast and accurate gas detection with integration times of a few milliseconds. Furthermore, the experimental limit of detection obtained confirms the ability of the architecture to detect methane in short optical paths. In the same way, a 3 dB tuning range of more than 10 nm (9 cm− 1 at 3.4 µm) paves the way for multi-species HPSDS gas detection in the mid-IR in the near future. Indeed, this feature would be greatly benefited by the use of a shorter crystal with a much wider phase-matching bandwidth (at the expense of a lower conversion efficiency, and therefore, lower mid-IR idler power).