A dual-comb spectroscopy (DCS) technique is a widely implemented [1] scheme for comb-based spectroscopic measurements. DCS instruments heterodyne two optical domain combs to produce down-converted radio frequency (RF) domain dual-comb spectra that may be measured with commercially available electronics [2] and without moving parts [3]. In the mid-infrared (MIR), DCSs have been demonstrated using a variety of comb sources, including difference frequency generation (DFG) of Ti:sapphire laser femtosecond pulses [3, 4], direct MIR emission in Cr2+:ZnSe femtosecond lasers [5], and DFG in periodically poled lithium niobate (PPLN) crystals [6], which has resulted in impressive MIR scaling (2.6–5.2 µm) [7] and in excess of 80 000 emitted comb lines [8]. DFG dual combs may also be implemented in MgO:PPLN [9, 10] or orientationally patterned gallium phosphide, the latter of which produces emissions spanning 4–12 µm [11].

Optical parametric oscillation (OPO) is another nonlinear process used to generate comb emission and has been extensively used in DCS platforms. DCS systems based on OPO sources have also utilized MgO:PPLN and PPLN [12, 13]. In practice, these sources have achieved sensing of methane [14] and acetylene [15] in the 3.2–3.5 m range, leading to real-time measurements [16, 17]. Additionally, MIR DCSs have been implemented with microresonators around 3 µm, either directly [18] or through interleaved DFG from near-infrared microresonator comb sources [19], silicon nitride supercontinuum sources around 3 µm [20], quantum-cascade laser frequency combs (QCL-FCs) around 8.5 µm [21, 22], and interband-cascade laser frequency combs (ICL-FCs) [23, 24]. QCL- and ICL-FCs offer the distinct advantage of MIR comb operation in a small-footprint semiconductor device with direct electrical pumping [23, 25].

The viability and utility of various MIR DCS systems have been confirmed by field campaigns conducted in operational environments including oil and gas industry facilities [26], agricultural land [27, 28], and urban areas [29]. DCSs have also demonstrated impressive measurements with an airborne reflector target [30] and over a 100 km range through air [31]. While some DCS systems are highly robust and can operate at [32, 33] or below the shot noise limit [34], free-running QCL-FCs operate with a relatively high level of intensity noise, which is nonideal for precision measurements. Given the attractive functional characteristics of DCS instruments based on free-running QCL-FC sources, here we focus on studies of balanced-detection techniques that can suppress intensity noise in dual-comb spectra in two common configurations of DCS, an assymetric DCS (aDCS) and a symmetric DCS (sDCS). Each DCS configuration has its uses—for example, sDCS benefits from relative simplicity, while aDCS provides local oscillator (LO) power revival and access to phase information. Reflecting these relative advantages, both configurations are widespread (sDCS: [2–4, 14, 16, 17, 19, 26, 28, 30, 34], aDCS: [5–10, 15, 18, 20–24, 29, 32]). This work seeks to examine the noise performance and noise mitigation of the two configurations, particularly in the context of noisy sources. Intuitively, we expect the balanced symmetric configuration to possess a greater degree of correlated intensity noise between the signal and the reference channels than the balanced asymmetric configuration, since both lasers have similar propagation paths in each channel. With the ability to suppress correlated noise through computational balancing, it follows that the spectroscopic signal in sDCS systems should have a higher level of intensity noise suppression than that in aDCS systems. While it is established and intuitive that a balanced DCS measurement provides noise suppression [35], to the best of our knowledge, the extent of this suppression has not been quantified for the two DCS configurations. In this paper, we experimentally characterize the extent of this noise suppression in both balanced-symmetric and balanced-asymmetric configurations with free-running QCL-FCs.

The two common configurations of the DCS, the aDCS and the sDCS [1], are schematically shown for our test system with a balancing channel in figure 1. In aDCS, one comb (the ‘sample comb,’ depicted as QCL1 in figure 1(B)) interrogates the gas sample in a multipass cell (MPC) and is subsequently combined with an LO comb (depicted as QCL2 in figure 1(B)) and heterodyned in a fast photodetector. In sDCS, the two combs, QCL1 and QCL2, are combined before interaction with the sample, followed by the heterodyne process on a photodetector. Both aDCS and sDCS can be implemented in a balanced configuration with a reference detector channel used for more effective intensity noise cancellation. An example multiheterodyne spectrum (MHS) obtained using the sDCS configuration is shown in figure 2.

Figure 1. Simplified schematics of (A) sDCS and (B) aDCS configurations. BS: non-polarizing beam splitter.

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Figure 2. MHS obtained from a single 100 acquisition in the sDCS configuration (top), with a magnified view (bottom). The modes extracted for intensity noise analysis (figure 6) are marked with red circles, and the mode analyzed in figure 3, figure 5, and figure 7 is indicated with a green arrow.

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Our system implements two free-running QCL-FCs operating at a central frequency of ∼1260 cm−1 and a repetition rate of ∼9.9 GHz, giving ∼ 4.7 MHz. These lasers can provide output power on the scale of 500 mW. They are configured as signal and LO combs in a setup that supports both aDCS and sDCS configurations, as indicated in figure 1. An MPC with a 76 m path length (Aerodyne AMAC-76-LW) is used as a typical gas sample cell commonly implemented in high-resolution laser spectrometers; this device enables long optical path lengths in a compact spatial footprint.

In laser spectroscopy, the Beer–Lambert Law is commonly leveraged to extract spectral transmission information from optical intensity measurements:

where is the laser frequency, is the signal channel intensity transmitted through the sample, is the intensity of light before it reaches the sample, is the absorption spectrum of the sample, and is the optical path length. The multiheterodyne process beats the optical frequencies down to radio frequencies , which are then analyzed using standard RF electronics. The reference channel is used to obtain I0 for normalization of the spectroscopic signal. Since our spectral quantities of interest are related to the quotient (or, in practice, ), where Isig represents the intensity measured by the signal detector and Iref represents the intensity measured by the reference detector, the noise (or uncertainty) of these quantities propagates into the noise observed in this normalized transmission signal. Therefore, a comparison of noise suppression in the spectroscopically relevant normalized signal (NS) with respect to the measured signal channel noise is an important indicator of the performance of any laser absorption spectrometer.

This work is focused on the characterization of a spectroscopic system’s general level of performance rather than focusing on a specific target gas species. Therefore, only zero-gas measurements have been performed for noise characterization. Two fast photodetectors (Vigo PVI-4TE-10.6) are used to measure the Isig and Iref signals. These signals are acquired by an FPGA (National Instruments PXIe-5575) with a sampling rate of 3.2 GHz and an acquisition duration of 100 , as described in [36]. The recorded signal and reference DCS interferograms are postprocessed using cross-correlation-based alignment in the time domain (TD) to compensate for any differences in optical path (i.e. the 76 m MPC) and electrical signal transmission delays between the two channels. Then, a computational coherent averaging algorithm [37] is applied, which corrects for carrier envelope offset and repetition rate fluctuations in the multiheterodyne RF spectrum ( and ) within a single 100 acquisition. Corrected spectra from subsequent acquisitions are then aligned in the frequency domain, also using a cross-correlation based method, to correct for shot-to-shot fluctuations and enable coherent averaging of consecutive acquisitions.

In addition to the corrected reference and signal channel data, an NS is obtained as the quotient . To evaluate the intensity noise, amplitudes of 29 selected modes with varying strengths in the center of these spectra (circled in red in figure 2) are extracted so that the time evolution of their intensities may be analyzed. These modes are selected in the region of the RF spectra where the mode with the highest intensity is found. This avoids the situation where photodetection noise dominates the weaker modes and provides a representative comparison of the two DCS configurations. As an example, the time evolution of these three signals (reference channel evolution, signal channel resolution, and NS) for one of the selected modes in each system is shown in figure 3. The relative intensity noise (), defined as the standard deviation of the intensity () over the mean light intensity (),

Figure 3. Intensity evolution (linear scale) of a single mode in the sDCS and aDCS multiheterodyne spectra measured in the signal channel (A) and in the reference channel (B). The evolution of the NS calculated as a quotient of the signal channel intensity/reference channel intensity is also presented for both configurations in (C).

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is measured for both the signal channel, , and the NS, . The level of suppression of the correlated noise can be clearly evaluated using an improvement factor (), defined as:

This is defined in such a way that a quotient >1 indicates a higher level of suppression of the relative intensity noise obtained via balanced detection as compared to the noise of the same mode observed in the signal channel alone. This formulation of noise analysis is somewhat atypical; commonly, figures of merit such as the common mode rejection ratio are utilized. However, DCS measurements are not differentially acquired in the TD (i.e. ) in practice, and the frequency domain/spectroscopic analysis fundamentally depends on the quotient . Therefore, the IF figure of merit can be considered to more directly analyze shared noise in the modes of the two DCS channels.

The nature of noise correlation in both MHS channels with free-running QCL-FCs can be highlighted by comparing the TD alignment statistics for both DCS configurations, plotted as a histogram in figure 4. First, we will make a critical clarification: this analysis considers the ‘fast’ TD alignment of signals in each interferogram acquisition. Each interferogram is processed to provide individual shots of the MHS. The evolution of modal intensity across these shots is the noise analyzed throughout this work.

Figure 4. Comparison of TD alignment statistics for sDCS and aDCS interferogram trains. The sDCS train shows one preferred alignment, where the signal channel is delayed relative to the reference channel by 254 ns, which corresponds well with the expected delay from the 76.2 m MPC. In the case of the aDCS train, a predominantly bimodal alignment distribution is observed. The relative separation of the preferred alignment (214 ns) corresponds closely with , indicating that alignment is shifting between adjacent bursts on the photodetected interferograms.

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In the case of sDCS, we find a very consistent alignment of the two channels, matching the expected optical path delay of 254 ns (corresponding to the ∼76 m optical path in the MPC). Notably, for this particular set of QCL-FCs, the difference in repetition rates, is ∼4.7 MHz, which corresponds to the ∼213 ns time separation of consecutive interferograms (calculated as ). The fact that we can align the sDCS interferogram bursts with the optical path delay with high confidence points to highly correlated amplitude noise. However, for aDCS, we observe a multimodal histogram of calculated delays separated by . This indicates that the correlation between the amplitude noise from the two lasers is low, and that the cross-correlation is dominated by consecutive interferogram bursts that yield several time delay options separated by ∼214 ns. This is caused by the asymmetric (76 m) delay of the signal laser field, E1, compared to a virtually zero delay for the LO comb field, E2, in the signal channel of the aDCS configuration. The preferred alignment of the aDCS interferograms is to align the nearest neighbor bursts in the two channels, and the aim of secondary alignment is to align the second nearest neighbor bursts (forward and backward). This asymmetry does not exist in sDCS. In both configurations, the E1 and E2 fields have virtually no delay in the reference channel. We can generally represent this by modeling the MHS signal in the reference channel as

and by introducing the time delay of the MPC, , into the signal channels of the two configurations, which for sDCS results in

For aDCS, we obtain

Therefore, in aDCS, the cross-correlation process is primarily sensitive to the alignment of MHS interferograms rather than amplitude noise that is no longer well correlated. For simplicity, we assume that exactly the same electric field amplitudes are present in both (reference/signal) channels and that all other optical and electrical signal propagation delays are negligible. In the case of sDCS equation (5), the signal channel interferogram is simply a time-delayed version of the reference channel interferogram. However, for aDCS equation (6), the relationship between the signal and reference channels is nontrivial, as the time delays of the amplitude noise of the signal and LO lasers are different and may not be easily accounted for in the multiheterodyne interferogram alignment process.

To understand how the shared noise from the laser source affects each interferogram, we first consider modal intensity noise observed over numerous subsequent shots. Correlation plots of the intensity fluctuations of the same mode in the reference and signal channels in both DCS configurations are shown in figure 5. Here, the linear correlation between the reference and signal channels is clearly superior for the sDCS case (with a coefficient of determination of R2 = 0.995) compared to aDCS (with R2 = 0.908), illustrating better intensity noise correlation in sDCS.

Figure 5. Correlation of intensities (linear scale) between the reference and signal channels, measured for the same single mode in the MHS for both DCS configurations.

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We can extend this by introducing correlated and uncorrelated noise terms contributing to the measured intensity of mode m. Let us assume the ‘true’ intensity is invariant, such that any TD fluctuations in are only caused by the sum of correlated () and uncorrelated () noise:

To formalize the nature of these signals, we will assume each noise contribution is zero-centered white noise. As a result, the mean value of the signal is simply . Each noise contribution is described by a standard deviation of that can be normalized to Io, resulting in . For each reference and signal channel mode, the normalized standard deviation of the measured intensity is:

The noise levels observed in the signal channel and the reference channel for the 29 extracted modes (indicated with red circles in figure 2) are presented in figures 6(A) and (B), respectively. We clearly observe that the scale of the total noise in each channel of both sDCS and aDCS is comparable. In fact, it is the aDCS modes that present slightly less noise overall, at on average. Signal channel and reference channel measurements of the sDCS configuration yield roughly in each mode.

Figure 6. Comparison of noise statistics in the reference and signal channels and in the NS for both DCS configurations. While the initial noise of both channels is comparable, sDCS clearly shows superior noise mitigation in terms of the noise of the NS that resulted in the IF shown in the bottom panel.

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Assuming a balanced detection system, we can expand the measured time-domain NS generally as

Applying this to the two configurations, we can then write

Owing to our ability to align noise in the TD through a computational balancing for sDCS, the signal channel delay is removed equation (5); however, this is not the case for aDCS equation (6), since both laser fields (E1 and E2) propagate over different optical paths. To approximate this, we consider that in the aDCS, the delay mismatch between in the numerator of and in the denominator signifies that the common-mode laser noise, which is easily suppressed in sDCS, becomes uncorrelated in the aDCS measurement, such that and . Indeed, when we analyze the noise levels of the NS in both sDCS and aDCS, a stark contrast emerges. Figure 6(C) clearly shows that the noise level of the sDCS NS is greatly reduced to the scale of 10−4, whereas the aDCS NS noise level remains on the order of 10−3.

The practical impact of sDCS versus aDCS noise suppression on spectroscopic measurements is further emphasized by examining the fractional Allan deviation [38] of the time evolution of an extracted mode’s amplitude (figure 7). Once again, the Allan deviations in the signal and reference channels of both sDCS and aDCS configurations are quite similar, which is expected for the analysis of raw signals. The Allan deviation of the aDCS NS shows modest improvement, while the strongest improvement is observed for the sDCS NS. The magnitudes of these improvements agree well with the IFs calculated for each configuration in figure 6.

Figure 7. Fractional Allan deviation in the signal channel, reference channel, and the corresponding NS of a single mode for both sDCS and aDCS configurations.

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Following our general description of in equation (9), we can now consider the relative scales of