# An Investigation of All Fiber Free-Running Dual-Comb Spectroscopy

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## Abstract

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## 1. Introduction

_{2}and H

_{2}O obtained from a high-resolution phase-locked DCS system by conducting an open-path experiment and retrieved the concentrations of 426.2 ± 3.7 ppm and 4441 ± 40 ppm, respectively [14].

^{3}, containing an f-2f locking, “bootstrapped” frequency referencing system. The fieldable DCS was capable of a spectral coverage of 44 THz in near-IR, with a precision of 2.8 ppm-km at 1 s, which did not deviate from the values measured using a laboratory-based system, being within 5.6 × 10

^{−4}. The volume of the DCS system described in [17] was 0.6 × 0.9 × 0.7 m, enabling f-2f locking, the phase locking of each comb to a narrow-bandwidth commercial CW diode laser, digitization and real-time averaging. This DCS is capable of a spectral coverage of 70 nm, operates in the field for up to 12 months, offers the ability to continuously operate and enables autonomous monitoring across multiple-square-kilometer regions, with emission rates as low as 1.6 g/min. Moreover, scientists from Spain and Ireland [18,19,20] realized two combs with mutual coherence through gain switching and optical injections. Three narrow-bandwidth commercial lasers were used. One served as the master laser, and the other two served as slave lasers. The use of a single master laser ensured a high degree of mutual coherence between the two gain-switched OFCs with different line spacings. The DCS realized by this scheme can cover regions ranging between the visible and mid-infrared, and has the advantages of a simple, compact and integrable structure, adjustable line spacing, a low cost and the potential to be applied outside of the research laboratory environment.

## 2. Principle

#### 2.1. Mathematical Model

_{r}= 1/$f$

_{r}is the time period. The DCS system uses two OFCs with slightly different PRFs as light sources, serving as the signal comb (SIG) and local oscillator comb (LO), respectively. Assuming that the SIG and LO combs have the same time domain envelope, after multi-heterodyne spectroscopy, the spectrum information is transferred from the OF domain to the RF domain through the detector. A series of RF combs are obtained, and Figure 1 [22] demonstrates the down-converting process in both the time and frequency domains. The optical sampling is realized by the PRF difference between the two combs, which is clearly shown in the time domain in Figure 1a,b. In this process, one comb appears to pass through the other comb. The multi-heterodyne interference process is clearly shown in the frequency domain in Figure 1c,d. According to [22], the one-to-one correspondence between the OF and RF combs can be guaranteed using a band-pass filter (BPF) and a low-pass filter (LPF) to prevent aliasing and confusion, respectively.

_{r}is the frequency difference of the two combs, ${f}_{c}^{RF}$ is the carrier frequency in the RF domain, ${\phi}_{0}^{RF}$ is the initial phase in the RF, and $\Delta {\phi}_{0}{}^{RF}$ is the carrier envelope phase in the RF. Supposing the comb frequencies of SIG and LO are ${f}_{1\mathrm{m}}$ and ${f}_{2n}$ respectively, they can be expressed as Equation (5). The RF combs can be expressed as Equation (6) [22]:

#### 2.2. DCS Principle

#### 2.3. SNR

_{d}is the low parallel acquisition stage. T is the sampling time. ${\sigma}_{\phi ,fast}^{}$ is the inter-pulse variance in the carrier phase white noise. The final SNR is determined by SNR

_{add}and SNR

_{mult}together.

#### 2.4. Signal Process

## 3. Simulation

_{r}/2, which equals approximately 13 MHz. Therefore, the corresponding maximum OF spectrum width must be approximately 4.6 nm to avoid aliasing. According to Figure 3, the 3 dB bandwidth of the laser source spectrum of the system is approximately 0.7 nm. Therefore, the BPF is not necessary in this system setup.

_{2}is approximately 4.5 GHz. The 3 dB bandwidths of the reflective spectra of the two narrowband FBGs are 9.27 G and 11.3 G, respectively. This means that the 3 dB bandwidth of the FBG reflective spectrum and the real gas absorption linewidth are of the same order of magnitude. Therefore, the two reflective spectra of the narrowband FBGs can be used to simulate the absorption effect of the measured gas.

## 4. Experiment

## 5. SNR Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Principle of dual-comb interference [22]. (

**a**) Time domain of the two combs’ periodic sequence; (

**b**) time domain of the interference envelope diagram in the RF; (

**c**) OF domains of the LO and SIG combs; (

**d**) RF spectrum of SIG.

**Figure 4.**Simulation of the DCS system’s RF spectra with jitters. (

**a**) Reference path spectrum, (

**b**) signal path spectrum.

**Figure 5.**Simulation of the reference path signal. (

**a**) Raw time domain signal; (

**b**) raw frequency domain signal; (

**c**) corrected time domain signal; (

**d**) corrected frequency domain signal; (

**e**) Magnified view of red rectangle shown in (

**b**); (

**f**) Magnified view of red rectangle shown in (

**d**).

**Figure 6.**Simulation of the signal path signal. (

**a**) Raw time domain signal; (

**b**) raw frequency domain signal; (

**c**) corrected time domain signal; (

**d**) corrected frequency domain signal; (

**e**) Magnified view of red rectangle shown in (

**b**); (

**f**) Magnified view of red rectangle shown in (

**d**).

**Figure 11.**Phase noise measurement of the large anomalous dispersion fiber comb used in this work and another typical dispersion-managed fiber comb [32].

**Figure 12.**Experiment of the reference path signal. (

**a**) Raw time domain signal; (

**b**) raw frequency domain signal; (

**c**) corrected time domain signal; (

**d**) corrected frequency domain signal; (

**e**) Magnified view of red rectangle shown in (

**b**); (

**f**) Magnified view of red rectangle shown in (

**d**).

**Figure 13.**Experiment of the signal path signal. (

**a**) Raw time domain signal; (

**b**) raw frequency domain signal; (

**c**) corrected time domain signal; (

**d**) corrected frequency domain signal; (

**e**) Magnified view of red rectangle shown in (

**b**); (

**f**) Magnified view of red rectangle shown in (

**d**).

**Figure 17.**Comb component after the signal process in the experiment: (

**a**): around the absorption peak, (

**b**): around the peak of the whole spectrum.

Devices | Parameters |
---|---|

Comb1 (SIG) | PRF: 26.64 MHz Output power: 71 mW Center wavelength: 1064.4 nm 3 dB width: 0.664 nm |

Comb2 (LO) | PRF: 26.64 MHz Output power: 71 mW Center wavelength: 1064.4 nm 3 dB width: 0.714 nm |

Δf_{rep} | Approximately 281 Hz |

LPF | 3 dB 10.7 MHz |

ADC sampling rate | 100 M |

Sampling time (simulation) | 100 ms (28 IGMs) |

FBG1 | Center: 1064.15 nm BW = 0.035 nm (9.27 GHz) R = 73.6% |

FBG2 | Center: 1064.39 nm BW = 0.042 nm(11.13 GHz) R = 70.5% |

Noise | $\delta {T}_{\mathrm{r}}^{RF}\left(N\right)$: average jitter of 0.1 μs $\delta {f}_{c}^{RF}\left(N\right)$: average jitter of 0.2 Hz $\delta {\phi}_{0}^{RF}\left(N\right)$: average jitter of 0.3 rad White noise: 0.15 (8.2 dB lower normalized) Pink noise: 0.025 (16 dB lower normalized) Quantization noise: 30 dB lower normalized |

Parameters | Symbol | Value |
---|---|---|

Sequential detection series | F | 1 |

Parallel detection series | N_{d} | 1 |

Spectral resolution | ${v}_{res}$ | 281 Hz |

PRF | f_{r} | 26.640992826 MHz |

Duty cycle | $\epsilon $ | 1 |

Number of RF combs | M | 14,223 |

Laser relative intensity noise | RIN | −130 dBc/Hz |

Valid digits of ADC | N | 10 |

Detector dynamic range | D | 1774 |

RF comb spectral bandwidth | $\Delta {v}_{RF}$ | Approximately 4 MHz |

OFC spectral bandwidth | $\Delta \upsilon $ | Approximately370 GHz |

Standard deviation of fast-change phase noise | ${\sigma}_{\phi ,fast}^{}$ | 1.45 × 10^{−5} rad |

Sampling time | T | 100 ms |

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**MDPI and ACS Style**

Yang, F.; Lu, Y.; Liu, G.; Huang, S.; Chen, D.; Ying, K.; Qi, W.; Zhou, J.
An Investigation of All Fiber Free-Running Dual-Comb Spectroscopy. *Sensors* **2023**, *23*, 1103.
https://doi.org/10.3390/s23031103

**AMA Style**

Yang F, Lu Y, Liu G, Huang S, Chen D, Ying K, Qi W, Zhou J.
An Investigation of All Fiber Free-Running Dual-Comb Spectroscopy. *Sensors*. 2023; 23(3):1103.
https://doi.org/10.3390/s23031103

**Chicago/Turabian Style**

Yang, Fu, Yanyu Lu, Guibin Liu, Shaowei Huang, Dijun Chen, Kang Ying, Weiao Qi, and Jiaqi Zhou.
2023. "An Investigation of All Fiber Free-Running Dual-Comb Spectroscopy" *Sensors* 23, no. 3: 1103.
https://doi.org/10.3390/s23031103