# Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Generation of Dual-Frequency Laser

## 3. Setup and Principle of DFDL System

_{1}and A

_{2}, respectively, $\u2206\varphi (t)={\varphi}_{2}(t)-{\varphi}_{1}(t)$. After passing A

_{1}and A

_{2}, two current signals are sent to a microwave mixer and outputting a signal ${P}_{mix}$, which is proportional to the product of ${I}_{r}(t)$ and ${I}_{t}(t)$. According to Equations (6) and (7), the product of ${I}_{r}(t)$ and ${I}_{t}(t)$ is shown below,

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Optical spectrum of the dual-frequency laser signals. (

**a**–

**h**) with different external cavity length.

**Figure 6.**Experimental setup of Dual-frequency Doppler LiDAR (DFDL) system. LD, single-mode laser diode; MFS, microwave frequency synthesizer; BS, beam splitter; VA, variable attenuator; BOF, bandpass optical filter; FC, fiber coupler; Circulator; Fiber and Fiber spool; ${\mathrm{PD}}_{1}$ and ${\mathrm{PD}}_{2}$, high-speed photodiodes; ${\mathrm{A}}_{1}$ and ${\mathrm{A}}_{2}$, microwave amplifiers; Mixer, microwave mixer; ${\mathrm{OSC}}_{1}$ and ${\mathrm{OSC}}_{2}$, digital oscilloscopes; OSA, optical spectrum analyzer; LF, lowpass filter; PC, computer.

**Figure 7.**(

**a**) LD operates at P1 state; (

**b**) Enlargement of boxed area in (

**a**); (

**c**) Optical spectrum of laser light with two frequency components.

**Table 1.**Physical meanings of symbols in Lang and Kobayashi (L-K) equations [33].

Symbol | Physical Meaning | Value | |
---|---|---|---|

LD Internal Parameters | ${G}_{N}$ | Model gain coefficient | $8.1\times {10}^{-13}\hspace{0.17em}{\mathrm{m}}^{3}{\mathrm{s}}^{-1}$ |

${N}_{0}$ | Carrier density at transparency | $1.1\times {10}^{24}\hspace{0.17em}{\mathrm{m}}^{-3}$ | |

$\epsilon $ | Nonlinear gain compression coefficient | $2.5\times {10}^{-23}\hspace{0.17em}{\mathrm{m}}^{3}$ | |

$\Gamma $ | Confinement factor | $0.3$ | |

${\tau}_{p}$ | Photon lifetime | $2.0\times {10}^{-12}\hspace{0.17em}\mathrm{s}$ | |

${\tau}_{s}$ | Carrier lifetime | $2.0\times {10}^{-9}\hspace{0.17em}\mathrm{s}$ | |

${\tau}_{in}$ | Internal cavity round-trip time | $8.0\times {10}^{-12}\hspace{0.17em}\mathrm{s}$ | |

$e$ | Elementary charge | $1.6\times {10}^{-19}\hspace{0.17em}\mathrm{C}$ | |

$V$ | Volume of the active region | $1\times {10}^{-16}\hspace{0.17em}{\mathrm{m}}^{3}$ | |

${\omega}_{0}$ | Unperturbed optical angular frequency of a laser diode, ${\omega}_{0}=2\pi c/{\lambda}_{0}$, where $c$ is the speed of light, ${\lambda}_{0}$ is the wavelength of the LD | ||

$\alpha $ | Line-width enhancement factor | ||

LD Controllable Parameters | $J$ | Injection current | |

$\kappa $ | Feedback strength | ||

$L$ | External cavity length | ||

$\tau $ | External cavity round trip time, $\tau =2L/c$ |

This Work | [35] | [14] | [36] | [37] | [16] | |
---|---|---|---|---|---|---|

Velocity measurement resolution | $4.8\text{}\mathsf{\mu}\mathrm{m}/\mathrm{s}$ | $26\text{}\mathsf{\mu}\mathrm{m}/\mathrm{s}$ | $310\text{}\mathsf{\mu}\mathrm{m}/\mathrm{s}$ | $327.9\text{}\mathsf{\mu}\mathrm{m}/\mathrm{s}$ | $7.5\times {10}^{4}\text{}\mathsf{\mu}\mathrm{m}/\mathrm{s}$ | $1.2\times {10}^{6}\text{}\mathsf{\mu}\mathrm{m}/\mathrm{s}$ |

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**MDPI and ACS Style**

Chen, Z.; Yu, Y.; Ruan, Y.; Nie, B.; Xi, J.; Guo, Q.; Tong, J.
Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser. *Sensors* **2020**, *20*, 6303.
https://doi.org/10.3390/s20216303

**AMA Style**

Chen Z, Yu Y, Ruan Y, Nie B, Xi J, Guo Q, Tong J.
Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser. *Sensors*. 2020; 20(21):6303.
https://doi.org/10.3390/s20216303

**Chicago/Turabian Style**

Chen, Zhuqiu, Yanguang Yu, Yuxi Ruan, Bairun Nie, Jiangtao Xi, Qinghua Guo, and Jun Tong.
2020. "Dual-Frequency Doppler LiDAR Based on External Optical Feedback Effect in a Laser" *Sensors* 20, no. 21: 6303.
https://doi.org/10.3390/s20216303