1. Introduction

Rapid spectroscopic techniques for sensitive detection of transient species are powerful tools in both fundamental and applied scientific fields, including the elucidation of physical mechanisms, biological chemistry, atmospheric studies and combustion analysis [1–4]. With the advantages of broadband, high speed, and high resolution in spectroscopic measurements, frequency-comb spectroscopy has promoted the development of time-resolved spectroscopy [5–9]. As a state-of-the-art scheme of frequency-comb spectroscopy, dual-comb spectroscopy (DCS) inherits its strength of rapid and broadband detection and has been utilized to simultaneously monitor multiple time-dependent parameters with temporal resolutions on the scale of milliseconds or microseconds in some studies [10–14].

In general, frequency-comb sources with high repetition rates can contribute to high-speed DCS, mainly as an increase in the comb repetition rate can improve the acquisition time for a single full-resolution spectrum while retaining the same optical bandwidth in DCS [15]. Trocha et al. reported a soliton Kerr comb generation in integrated silicon nitride microresonators with a repetition frequency of ${f_r}$∼ 95.8 GHz to realize a dual-comb distance measurement with an accuracy down to 12 nm at 13 µs [16]. With a quantum-cascade-laser-based DCS with ${f_r}$ ∼ 10 GHz, Pinkowski et al. carried out a high-temperature kinetic study at a measurement rate of 4 µs with an uncertainty of 5% at a temperature of 1000 K [17]. High-sensitivity gas sensing at an integration time of 100 µs was demonstrated by a mid-infrared intraband-cascaded-laser-based DCS with ${f_r}$ ∼ 9.7 GHz [18]. Recently, Picqué et al. identified a path to broadband gas-phase spectroscopy on a chip at a repetition frequency of 1 GHz at times as short as 5 µs [19]. Furthermore, a mode-filtering technique where the multiple repetition rate of the transmitted comb reached 1 GHz was introduced into the DCS to realize a 11-µs time-resolved spectroscopy [20]. However, the increased repetition rate of the comb has an immediate impact on the spectral resolution. The spectral resolution above the GHz level in time-resolved spectroscopy would lead to difficulties in resolving the ro-vibrational absorption lines of gas-phase molecules and isotopic and hyperfine splittings of spectral lines [21]. In addition to the method where a high-repetition-rate DCS is used, rapid high-spectral-resolution spectroscopy at a time scale of microseconds can be realized at the expense of a broad optical bandwidth in DCS. Electro-optic-modulator-based (EOM-based) DCS, as a frequency-agile spectrometry, is increasingly used in high-speed measurements owing to its adjustable line spacing and high power per line over a spectral coverage of a few nm. Millot et al. recorded Doppler-limited spectra spanning 60 GHz in 12.7 µs by EOM-based DCS with ${f_r}$ ∼ 300 MHz [22]. A common and robust platform utilized in high-spectral-resolution DCS is based on fiber mode-locked combs with repetition rates on the order of 100 MHz. Baumann et al. measured accurate complex spectra of the methane ${v_3}$ band through a fiber mode-locked DCS at a measurement speed of 1.5 kHz with a spectral resolution of 100 MHz. However, a tunable 7-nm-wide bandpass filter is used for a high signal-to-noise ratio (SNR) [23]. Although the sacrificed optical bandwidth in these DCS can be beneficial for high-spectral-resolution time-resolved spectroscopy, it is inapplicable for a rapid sensing of multiple reaction intermediates in the investigation of kinetic reactions. There exists a trade-off between the optical bandwidth, spectral resolution and refresh rate for high-speed DCS measurements. In this case, for the related research on multi-species reaction kinetics, it is essential to address the trade-off among these characteristics in DCS.

In this letter, we present a solution to achieve a rapid multi-molecular sensing using a spectrum-encoded technique introduced into the DCS. The specific absorption lines of multiple gas molecules (C₂H₂, HCN, CO, CO₂) can be selectively encoded over a spectral coverage range of 1520 to 1580 nm by a programmable digital micro-mirror device (DMD). In such spectral coverage, the aliasing effect in DCS with ${f_r}$ ∼ 108 MHz is avoided by this spectrum-encoded technique and the measurement speed is increased from 778 Hz to 4.8 kHz. As a single-shot multi-molecular absorption spectrum is measured at 208 µs, the identification and concentrations of multiple molecules are carried out and sensed rapidly, respectively. The encoded spectra with four and two encoding bands realize 3.65 and 5.68 times higher short-term SNRs than that of conventional spectra, respectively. Furthermore, to obtain a narrower-band encoded spectrum with a higher SNR, an encoded DCS with two pairs of fiber Bragg gratings (FBGs) centered at two wavelengths is demonstrated. The average SNR of this FBG-based encoded dual-comb spectrum is 17.1 times that of the unencoded dual-comb spectrum. Multi-molecular sensing at a time scale of sub-microseconds can be realized when this spectrum-encoded technique is combined with a high-repetition-rate DCS.

2. Experiment schematic and setup

The rapid multi-molecular sensing requires a broadband spectral measurement capability with a time resolution on the scale of milliseconds, even microseconds. In the conventional DCS for multi-molecular sensing, a consecutive spectral measurement is performed to resolve extensive ro-vibrational absorption features over a broad spectral coverage even an octave. However, to one-to-one map these absorption features from the optical to the radio-frequency (RF) domain, the measurement speed of $\Delta {f_r}$ is limited, where the spectral bandwidth of $\Delta v$ should satisfy $\Delta v \le f_r^2/2\Delta {f_r}$. In addition, the broadband spectral measurement results in a low SNR for a resolved single-shot molecular spectrum, thus reducing the measurement speed [24]. For high-speed multi-molecular sensing, we introduce a spectrum-encoded technique into the DCS to improve the measurement speed. In this technique, the DCS with a broad spectral bandwidth is encoded spectrally and a group of ultra-narrow spectral regions is extracted. Each spectral region, defined as an encoding band, covers a selected absorption line to sense the corresponding molecule. Instead of a consecutive broadband measurement of massive absorption lines, quantitative determination of multiple molecules can be achieved when one or two specific absorption lines of each molecule are measured by these encoding bands. In this manner, the encoded DCS is capable of realizing multi-molecular sensing, while the measurement speed and single-shot SNR in DCS can be largely improved owing to the reduced spectral bandwidth. A schematic of the spectrum-encoded technique in DCS is shown in Fig. 1. A conventional DCS is used to detect multiple molecules whose species number is N, as shown in Fig. 1(a). A broad spectral measurement with a bandwidth of ∼ $\Delta v$ is required to cover the absorption lines of N molecules. However, the maximum measurement speed is limited to $\Delta {f_{r1}} = f_r^2/\Delta v$ because of the aliasing effect. In the spectrum-encoded technique, a single absorption line with a spectral bandwidth ∼ $\delta v$ is measured by an encoding band with the same bandwidth and only N encoding bands with a bandwidth ∼ $N\delta v$ remain for multi-molecular sensing. To identify the aliasing spectral regions in the encoded DCS at an improved measurement speed, the N encoding bands are arranged across the entire spectral coverage according to the aliasing law. As shown in Fig. 1(b), the ${i^{th}}$ aliasing encoding bands are marked with the same color in the spectral regions, which can be expressed as $[C \ast 2N\delta v \pm (i - 1) \ast \delta v,C \ast 2N\delta v \pm i \ast \delta v]$, where $i = 1,2,3,\ldots ,N$ and C is an integer. To avoid the aliasing effect and ensure a single-shot spectral measurement, N encoding bands from different orders are extracted and each band covers a specific absorption line of an individual molecule, as shown in Fig. 1(c). As a result, the measured spectral bandwidth decreases to $N\delta v$. The maximum measurement speed of $\Delta {f_{r2}}$, which is inversely proportional to the measured bandwidth, can be increased to

 

Fig. 1. Schematic of the spectrum-encoded technique in DCS. (a) As extensive absorption lines of multiple molecules are measured in the conventional DCS, multi-molecular sensing is achieved; however, the measurement speed is limited owing to the broadband spectral measurement. (b) Encoded spectrum with the aliasing law. The encoding bands marked with different colors represent the spectral regions for sensing different molecules. To ensure a single-shot spectral measurement, only one encoding band is preserved to measure the specific absorption line of one molecule, while other bands with the same color should be eliminated. (c) As a result of the reduced spectral bandwidth, a rapid multi-molecular sensing can be realized by the encoded DCS with improved measurement speed and single-shot SNR.

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Figure 2(a) shows the optical configuration of the spectrum-encoded DCS. The generation of the passive mutually coherent DCS is based on our previous study using the ultrafast optical modulation technique [25,26]. The two combs have similar output characteristics, such as an output power of 500 mW and center wavelength of 1550 nm. Their spectra have optical bandwidths of 15 nm as shown in Fig. 2(b). The homemade comb sources have repetition rates of ${f_r}$ ∼ 108 MHz, corresponding to a spectral resolution stabilized to the Rb atomic clock. The outputs of the two combs were coupled into two fiber collimators spliced by two highly nonlinear fibers (HNLFs) to broaden the optical bandwidth of the combs and the broadened spectra were presented in Fig. 2(c). An off-axis parabolic mirror was used to output the comb with a spectral coverage range of 1520 to 1580 nm and output power of 150 mW into the free space. A programmable DMD was then used as a spectrum-encoded tool. The combs were subjected to a DMD-based quasi-4-f setup to achieve an arbitrary spectrum-encoded technique in our DCS. The two encoded combs were amplified by an erbium-doped fiber amplifier to reach the power required by the detector and were transmitted through a sample cell. The gas sample cell was composed of a fiber-coupled hydrogen cyanide cell (HCN-13-H(16.5)-25-FCAPC, Wavelength References) and Herriott cell including acetylene, carbon monoxide, and carbon dioxide. Finally, the two combs with an input power level of 0.5 mW were guided to two ports of a 150-MHz commercial balanced detector (PDB450C, Thorlabs) for heterodyne detection. The detector signals were digitized by a 500-MS/s 12-bit data acquisition board (ATS9350, AlazarTech). The streams of recorded raw data were fast-Fourier-transformed to obtain an encoded dual-comb spectrum.

 

Fig. 2. (a) Experimental layout for the spectrum-encoded technique in DCS. A DMD-based quasi-4-f setup is introduced into the DCS to realize a spectrum-encoded technique. Col, collimator; PM, parabolic mirror; PBS, polarizing beam splitter; L, lens; LD, laser diode; EDF, erbium-doped fiber; BD, balanced detector. (b) Optical spectra of the comb sources. (c) Broadened spectra after HNLF.

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In this experiment, the DMD-based quasi-4-f arrangement was composed of a pair of gratings, pair of lenses with a focal length of 75 mm, and DMD (DLP4500NIR, Texas Instrument 0.45 Inch, 1140 × 912 pixels). The grating had a groove density of 940 lines/mm and efficiency of 95%. In the telecom band, the DMD had a maximum diffraction efficiency of 35% at its first diffraction order when the angle between the incident beam and micromirrors on the DMD was approximately 40°. The overall efficiency of the spectrum-encoded setup was approximately 27%.

The arbitrary spectrum-encoded technique was achieved by the use of a DMD, which was a programmable device for shaping light fields. A DMD consisted of several hundred thousand micromirrors (called as pixels), where each pixel served as a binary mirror with two reflection angles, i.e., ±12°, corresponding to the “on” and “off” states. A “black” stripe was displayed on the DMD when a group of pixels along the vertical direction of incident dispersive beams were all in the “off” states. Conversely, a “white” stripe was generated when the group of pixels were in the “on” states. For a broadband comb spectrum projected onto the DMD, multiple narrow spectral bands were reserved and encoded selectively by the “white” stripes along the horizontal direction of the DMD while the filtration of other comb lines was completed by the encoded “black” stripes. Furthermore, the pixels along the vertical direction on the DMD can be controlled to shape the spectral amplitude for a flat spectral distribution in the encoded spectrum [27]. Before the experiment, the relationship between the wavelength coordinate of the spectrum and pixel coordinate of the DMD should be calibrated using a spectrometer. The spectrum distribution $\lambda (pix)$ on the DMD is

The spectrum in the ranging of 1520 to 1605 nm was dispersed along the horizontal direction of the DMD. The required detection bands can be encoded selectively according to the pixel position transformed by the wavelength. In this experiment, each spectral band encoded by a “white” stripe had a minimum full width at half maximum of approximately 1 nm and minimum spectral coverage of approximately 2 nm.

3. Results and discussion

To evaluate the performance of the spectrum-encoded technique for improvements in measurement speed and SNR in our spectrum-encoded DCS, unencoded and encoded dual-comb spectra were measured. The un-encoded mode-resolved spectra within 1 s are presented in Fig. 3(a). The referenced 1550-nm continuous wave (CW) is at zero frequency in the RF domain of the dual-comb spectrum; thus, a short-wave spectrum covering 1520 to 1550 nm and long-wave spectrum covering 1550 to 1580 nm were measured, respectively. The repetition rate difference between the two combs was set to 4.8 kHz. In a measurement time of 1 s, the average SNR across the short-wave span of 3.2 THz is 49.1 and the average SNR across the long-wave span of 3.0 THz is 52.1. Their figures of merit (SNR × M) are 1.49 × 10⁶ and 1.45 × 10⁶, respectively, where M is the number of comb lines across the optical bandwidth. According to the Nyquist sampling constraint, the non-aliasing region has a spectral bandwidth of only 10 nm in DCS when the repetition rate is 108 MHz and the repetition rate difference is 4.8 kHz. In Fig. 3(a), the measured mode-resolved spectra with a spectral bandwidth of 30 nm are in the range of three times the nonaliasing bandwidth because a fast fluctuation still exists in the repetition rate ${f_r}$ [28]. The coherence of the RF beat signal ∼ $C{f_r}/2 + n\Delta {f_r}$ is degraded owing to the fluctuation when C is a nonzero integer. With a long measurement, the beat signal that would cause an aliasing effect gradually vanishes.

 

Fig. 3. Comb-mode-resolved unencoded and encoded dual-comb spectra in a measurement time of 1 s. The encoding stripes marked with four colors corresponding to four molecules follow the arrangement of the aliasing law. (a) Un-encoded spectra (log scale) spanning 1520 to 1580 nm. (b) Encoded spectrum with four encoding bands for sensing of four molecules, along with the recorded interferogram. The expanded insets present attenuation modes originating from multi-molecular absorption. (c) Two groups of encoded spectrum with two encoding bands for multi-molecular absorption lines, along with the recorded interferograms.

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After detector signals with encoded-DCS interferograms as shown in right panels of Figs. 3(b) and (c) were recorded by the high-speed data acquisition board, encoded dual-comb spectra were obtained by performing a fast Fourier transform of the raw data. Encoded spectra with multi-molecular absorption lines at a measurement time of 1 s are presented in Figs. 3(b) and (c). In this experiment, the gaseous mixture (0.22% C₂H₂, 34% CO, 65.78% CO₂) at a total pressure of 950 mbar in an 8.8-m-long cell and HCN at 33.3 mbar in a 16.5 cm-long fiber-coupled cell are detected in parallel. For these gaseous molecules, there are widely distributed absorption lines over the spectral coverage range of 1520 to 1580 nm. To perform single-shot multi-molecular sensing in such coverage, the measurement speed in the unencoded DCS is limited to 778 Hz to avoid the aliasing effect. In the encoded DCS, multiple discrete encoding bands were reserved and measured simultaneously, where each narrow encoding band only covering a spectral bandwidth of approximately 2 nm was used to sense an individual molecule. Figure 3(b) shows the encoded dual-comb spectrum with four encoding bands for sensing of four molecules. The insets show comb-tooth-resolved spectra with absorption lines of different molecules. Owing to the reduced measured bandwidth, the encoded spectrum with 5217 comb teeth has an improved SNR of 239.6 and the repetition rate difference is thereby increased to 4800 Hz. The temporal resolution of a single-shot spectral measurement is shortened to 208 µs, improved 6.15 times compared to that of the unencoded DCS. In addition, the encoded DCS with two encoding bands that had a fewer measured bandwidth was measured to demonstrate multi-molecular spectral measurements with a higher SNR. Figure 3(c) shows two groups of encoded spectra with two encoding bands, which are measured sequentially. The encoded spectra shown in yellow zones (2842 comb teeth) and purple zones (2551 comb teeth) have improved average SNRs of 436.2 and of 442.9 in 1 s, respectively. The insets of Fig. 3(c) show that the absorption lines of not only individual molecules but also multiple molecules are measured in one encoding band. A higher measurement speed in multi-molecular sensing can be achieved when fewer encoding bands are used to measure overlapping absorption lines of multiple molecules.

To demonstrate high-speed multi-molecular sensing in the encoded DCS with an improved SNR, unencoded and encoded absorption spectra at the same time scale of sub-milliseconds are presented in Fig. 4. In the following experiments for the short-term spectra, the apodization windows with a one-fifth interferogram width were applied in the post-processing to reduce the measurement noise and improve the short-term SNR. The spectral resolution after the apodization is 540 MHz, which is sufficient to resolve the experimental absorption feature with a spectral width of several GHz in atmospheric sensing. An unencoded DCS is used to sense four gaseous molecules under the above-mentioned conditions. To avoid the aliasing effect in single-shot unencoded spectra, the repetition rate difference of the unencoded DCS was set to 1.2 kHz and the single-shot measurement time was 833 µs. Through a polynomial fitting for the intensity distributions of the unencoded spectra, the reference spectra were extracted; baseline-corrected absorption spectra (gray curve) are shown in Fig. 4. The single-shot SNR of the unencoded absorption spectrum is 9.2, calculated by the standard deviation of the noise baseline, as shown in the green shadow in Fig. 4. An encoded DCS with four encoding bands is then used to sense the same molecules when the repetition rate difference is increased to 4.8 kHz. The single-shot measurement time is shortened to 208 µs. To compare the short-term SNR to that of the unencoded spectrum at the same measurement time, coherent averaging of four interferograms is used. An encoded absorption spectrum at 833 µs is obtained. The measured SNR of the encoded absorption spectrum is 33.6, 3.65 times that of the unencoded spectrum. To showcase the improvement in SNR, the encoded absorption spectrum (red curve) is overlaid on the unencoded spectrum for comparison, as shown in Fig. 4(a). Finally, an encoded DCS with two encoding bands was used to sense these molecules in the same measurement time. Two groups of encoded absorption spectra with higher SNRs at 833 µs are presented in Fig. 4(b). The encoded absorption spectra shown by the green and blue curves have short-term SNRs of 51.4 and 52.3, respectively. The measurement time for the un-encoded absorption spectrum should be extended to 11.1 and 26.9 ms to reach the same short-term SNR as that of the encoded spectra with four and two encoding bands, respectively. In this experiment, the $1 - \sigma$ sensitivity of concentration detection in DCS is estimated when the intensity of absorption line in the measurement spectral region equals the standard deviation of the noise baseline [29]. For the unencoded DCS in a measurement time of 833 µs that has a standard deviation of 11%, the $1 - \sigma$ sensitivity of C₂H₂ is calculated to be ∼100 ppm according to the simulation results in an 8.8-m-long cell. For the encoded DCS with four encoding bands in 833 µs that has a standard deviation of 3%, the $1 - \sigma$ sensitivity of C₂H₂ is improved to be ∼27 ppm in the same measurement condition.

 

Fig. 4. Multi-molecular sensing using un-encoded and encoded DCSs at 833 µs. Absorption lines of four molecules are extracted from the unencoded spectra (gray curve). The noise baselines in the green shadow are used to calculate the short-term SNR of the absorption spectra. (a) Multi-molecular absorption lines extracted from the encoded spectrum with four encoding bands (red curve). (b) Multi-molecular absorption lines extracted from two groups of encoded spectrum with two encoding bands (green and blue curves).

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Benefitting from the improved measurement speed and short-term SNR in the encoded DCS, single-shot multi-molecular sensing at a time scale of hundreds of microseconds can be realized. For the multi-molecular absorption lines in the range of 1520 to 1580 nm in a single-shot unencoded spectral measurement, the single-short measurement time was limited to 1.28 ms. In our encoded DCS, the single-short measurement time was shortened to 208 µs as the measurement speed was increased to 4.8 kHz. Figure 5(a) presents the encoded spectra with multi-molecular absorption lines at 208 µs. Each of four encoding bands was used to measure the specific absorption line of one molecule. For comparison, the fitted intensity distributions of the encoded spectra with theoretical multi-molecular absorption lines from the HITRAN2016 database were overlaid on the encoded spectra in Fig. 5(a) [30]. The standard deviations of the observed fitted residuals were 5.27%, 5.93%, 5.09%, and 7.74%, respectively. The average single-short SNR was calculated to be 16.6, according to the average residuals. In addition, single-shot multi-molecular spectral measurements with higher SNRs were performed by the encoded DCS with two encoding bands. The measured and fitted spectra along with the residuals are shown in Fig. 5(b). The standard deviations of the residuals were 3.75%, 2.97%, 2.53%, and 3.81%, respectively. The average single-shot SNRs were calculated to be 29.8 and 31.5, respectively. In addition to the shortened measurement time, the improved SNR enables a single-shot measurement with a time interval of hundreds of microseconds for a rapid multi-molecular sensing.

 

Fig. 5. Single-shot multi-molecular sensing using the encoded DCS at 208 µs. Fitted intensity distributions of encoded spectra with theoretical absorption lines from the HITRAN database (brown curve) are compared to measured encoded spectra along with the residuals. (a) Encoded spectrum with four encoding bands (red curve). (b) Two groups of encoded spectrum with two encoding bands (green and blue curves).

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For practical applications based on absorption spectroscopy with encoded DCS, the spectral region and bandwidth of an encoding band can be measured selectively, depending on the specific absorption line of the targeted molecules and the spectral width of the measured absorption feature. Especially in the concentration and temperature measurements of gaseous molecules, the concentration detection limit and the temperature sensitivity can be improved, benefitting from an increased SNR in encoded DCS owing to the reduced measured bandwidth. In principle, the SNR of the encoded dual-comb spectrometer can be increased up to the level of the tunable diode laser spectrometer when both spectrometers have same figure of merit and measured bandwidth [24]. In addition, instead of using an array of diode lasers, a single encoded DCS with multiple encoding bands has the ability to achieve multi-molecular sensing. Furthermore, the encoded DCS with supercontinuum combs can detect some transitions appearing in some sub-bands that are available inefficiently due to the gap in the spectral emission of diode lasers [31].

Limited by the filtering spectral bandwidth of 2 nm in the DMD, an FBG with an ultra-narrow spectral bandwidth can be used as a spectrum-encoded tool to obtain a narrower-band encoded spectrum with a higher SNR. In this experiment, an FBG-based encoded-spectrum technique in our DCS is demonstrated when the measurement speed is 4.8 kHz. A pair of FBGs centered at 1560.2 nm with a bandwidth of 0.23 nm and pair of FBGs centered at 1565 nm with a bandwidth of 0.15 nm are cascaded to filter two ultra-narrow encoding bands spectrally. In the measurement time of 1 s, the average SNR is 839 with 597 comb teeth, 17.1 times that of the conventional dual-comb spectrum. The figure of merit is 5 × 10⁵ below the typical range for fiber-laser-based DCS. This originates from the remaining power of tens of microwatts after filtering, considerably lower than the up-limit response power of the detector before saturation of ∼ 500 uW. In this case, the average SNR at low comb powers is dominated by detector noise or shot noise on the detector [24]. This problem can be overcome when combs with higher powers are incident on this FBG-based encoded-spectrum system. The single-shot dual-comb spectrum with a spectral resolution of 540 MHz at 208 µs is shown in Fig. 6. In principle, the maximum measurement speed can be set to 90 kHz, as the number of comb teeth in the FBG-based DCS has a frequency bandwidth of 65 GHz. At such a high measurement speed, the single-shot SNR at 11 µs with a proper apodization window can enable the FBG-based DCS to resolve absorption lines of multiple molecules. Furthermore, through the combination of the FBG-based technique and gigahertz-repetition-rate DCS, it is promising to achieve high-speed multi-molecular sensing at a time scale of sub-microseconds.

 

Fig. 6. Single-shot dual-comb spectrum at 208 µs with an FBG-based encoded DCS.

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4. Conclusion

We proposed and experimentally demonstrated a spectrum-encoded DCS capable of a rapid multi-molecular sensing. In the demonstration of our DMD-based encoded DCS, this spectrum-encoded technique enabled the DCS to improve the measurement speed and obtain multi-molecular encoding bands with a noticeable improvement in the SNR over a broad spectral coverage. Compared to the single-shot unencoded spectrum at 833 µs, the encoded spectra with four encoding bands and two encoding bands had improved short-term SNRs by factors of 3.65 and of 5.68 in the same measurement time, respectively. Furthermore, a single-shot multi-molecular sensing at a time scale of hundreds of microseconds was achieved when the single-shot measurement time was shortened from 1.28 ms to 208 µs. The improved single-shot SNR of 16.6 enabled to resolve absorption lines from the noise baseline. In the FBG-based encoded DCS, an encoded spectrum with a narrower spectral bandwidth was obtained, which reached a higher SNR. This indicates that the gigahertz-repetition-rate DCS with the FBG-based encoded-spectrum technique has a high potential to achieve a rapid multi-molecular sensing at a sub-microsecond time scale. Altogether, this technique provides a flexible and effective approach combined with DCS to implement high-speed broadband spectroscopic measurements in multi-species reaction systems.