# A Tunable Mid-Infrared Solid-State Laser with a Compact Thermal Control System

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## Abstract

**:**

## 1. Introduction

## 2. Module Design

#### 2.1. Design of a Tunable Mid-Infrared Solid-State Laser

#### 2.2. Design of the Thermal Control System

#### 2.2.1. Constitution of the Thermal Control System

^{3}/s. There were 7 fans parallel connected in a line to increase airflow.

#### 2.2.2. Hardware Circuit Design of the Thermal Control System

_{t}is the resistance value (Ω) at temperature of t (°C). An 0.1 mA precise constant current source flows into the PT1000 resistor. The voltage on two sides of the resistor is amplified by an instrumentation amplifier INA128 before entering the analog-to-digital converter (ADC) interface on STM32. Then, the STM32 chip calculates the temperature value according to the conversion formula.

#### 2.2.3. Software Design of the Thermal Control System

- (1)
- $\left|\mathrm{e}\right|>{E}_{a1}:{K}_{p}={K}_{p1},{K}_{d}={K}_{d2},{K}_{i}=0;$
- (2)
- ${E}_{a2}>\left|\mathrm{e}\right|>{E}_{a1}:{K}_{p}={K}_{p2},{K}_{d}={K}_{d1},{K}_{i}={K}_{i2};$
- (3)
- $\left|\mathrm{e}\right|<{E}_{a2}:{K}_{p}={K}_{p1},{K}_{d}={K}_{d1},{K}_{i}={K}_{i1}.$

_{p}

_{1}> K

_{p}

_{2}>0, K

_{d}

_{1}> K

_{d}

_{2}> 0, K

_{i}

_{1}> K

_{i}

_{2}> 0, E

_{a}

_{1}>E

_{a}

_{2}>0. K

_{p}

_{1}, K

_{p}

_{2}, K

_{d}

_{1}, K

_{d}

_{2}, K

_{i}

_{1}, K

_{i}

_{2}, E

_{a}

_{1}and E

_{a}

_{2}are constants. When |e| is larger, we choose a larger K

_{p}and smaller K

_{d}to promote the tracking performance of the system, setting K

_{i}= 0 to avoid larger overshoot when the system responds. When |e| is of medium size, we set smaller K

_{p}and K

_{i}values to decrease the system response overshoot. When |e| is smaller, we set larger K

_{p}and K

_{i}values to decrease the steady error and a medium-sized K

_{d}to avoid system vibration near the set value.

## 3. Mathematical Model and Numerical Simulation

#### 3.1. Thermal Analysis of TEM

_{c}, heat absorption power on the cold side) of the TEM is

_{h}, on the hot side of the TEM is

_{m}is the Seebeck coefficient of TEM, T

_{c}is the temperature of the cold side of the TEM and T

_{h}is the temperature of the hot side of the TEM, I is the direct current through the module, R

_{m}is the electrical resistance of the TEM and K

_{m}is the thermal conductance of the TEM.

_{m}, R

_{m}and K

_{m}, can be figured out by the TEM parameters of I

_{max}, ΔT

_{max}, T

_{h}and V

_{max}given by the manufacturer through Equations (5)–(7) [19,20], of which I

_{max}is the direct current flowing through TEM that causes the maximum temperature difference, ΔT

_{max}. ΔT

_{max}is the maximum temperature difference between the cold and hot sides of the TEM at a certain temperature, T

_{h}. V

_{max}is the direct voltage that diverges the ΔT

_{max}.

#### 3.2. Mathematical Model of the Thermal Control System

_{1}is the thermal resistance of the thermally conductive grease between the substrate of the heat sink and the cold side of the TEMs. R

_{2}is the thermal resistance of the thermally conductive grease between the hot side of the TEMs and the bottom inside of the cabinet. R

_{1}is approximately equal to R

_{2}. R

_{3}is the thermal resistance from the bottom inside of the cabinet to the ambient environment. T

_{1}is the upper surface temperature of heat sink, since the 4 LD modules and fibers are closely fixed on the heat sink and they are the main heat sources. Thus, it is important to maintain T

_{1}at a suitable and stable temperature to ensure the pump laser module works reliably. T

_{c}is the cold side temperature of the TEMs, T

_{h}is the hot side temperature of TEMs and T

_{a}is the temperature of the ambient environment. Q

_{pump}is the heat generated by the pump laser module and Q

_{c}is the cooling capacity of the TEM, since there are 16 pieces of TECs used in the system, and assuming each TEC hasthe same Q

_{c}, it can be deduced that the equation at the steady heat transfer state is

_{1}, can be carried out by thermal analysis as shown below:

_{h}is the heat release output at the hot side of TEM. Thus, we can determine the one-dimensional steady heat transfer equation:

_{c}) can be written as the following expression:

_{c}mainly depends on the TEM performance parameters: S

_{m}, R

_{m}, K

_{m}, TEC drive current I, the system thermal resistances (R

_{1}, R

_{2}andR

_{3}), the upper surface temperature of the heat sink (T

_{1}) and the ambient environment temperature (T

_{a}). If it is assumed that T

_{1}is 293.15 K at which the pump laser module could work steadily and normally, I and T

_{a}are set to regular values, and S

_{m}, R

_{m}and K

_{m}are calculated according to the TEM parameters of I

_{max}, ΔT

_{max}, T

_{h}and V

_{max}(which are given by the manufacturer), then we just need to know the system’s thermal resistances (R

_{1}, R

_{2}and R

_{3}) to calculate Q

_{c}. If Q

_{c}multiplied by 16 is greater than Q

_{pump}, we can make the conclusion that the pump laser module can work at a suitable and stable temperature. The temperature of heat sink T

_{1}can also be written as the following expression:

_{pump}is at its maximum value, then we can obtain Q

_{c}as a fixed constant, setting I and T

_{a}at regular values, and calculate S

_{m}, R

_{m}and K

_{m}, allowing the temperature (T

_{1}) to be calculated out by the expression. Finally, it can be concluded whether the pump laser module is working at a suitable temperature by comparing T

_{1}with the normal operating temperature range.

#### 3.3. Numerical Simulation

^{3}, and the fin spacing was 20 mm. Seven fans were defined in the software, and the flow rate was set at 0.011 m

^{3}/s. The thermal conductivity of the heat pipe was set in segmented mode to make a closer equivalent simulation of its physical features. The thermal conductivity of the evaporation section was set at 2 × 10

^{4}W/(m·K), while the thermal conductivity of the condensation section was set at 500 W/(m·K).

_{3}) for the TEMs was 0.04 K/W. The other two groups of TEMs in the middle of the cabinet almost had a 15 K temperature rise at the hot side and the thermal resistance (R

_{3}) for them was 0.03 K/W.

_{m}, K

_{m}and S

_{m}, for T

_{h}= 50 °C and the following parameters were obtained: R

_{m}= 0.985 Ω, K

_{m}= 0.946 K/W and S

_{m}= 0.048 V/K. Using Equation (11), in the first situation, T

_{a}= 298.15 K (25 °C), the TEC drive current (I) was defined as 5A, and it was assumed that R

_{1}= R

_{2}= 0.1 K/W and T

_{1}= 293.15 K (20 °C) at which the pump source can work stably. For the two groups of TEMs with R

_{3}= 0.04 K/W, the cooling output of each TEM was Q

_{c}

_{1}= 39.5 W, and for the other two groups of TEMs with R

_{3}= 0.03 K/W, the cooling output of each TEM was Q

_{c}

_{2}= 40 W. Consequently, the total cooling output (Q

_{c}) of the 16 TEMs was about 636 W.

_{a}= 318.15 K (45 °C) with the same other parameters, the two groups of TEMs with R

_{3}= 0.04 K/W had Q

_{c}

_{1}= 24 W, and the other two groups of TEMs with R

_{3}= 0.03 K/W had Q

_{c}

_{2}= 24.4 W. Thus, the total cooling output (Q

_{c}) of the 16 TEMs was about 387.2 W. The calculated results indicate that the temperature of the LD modules and the fiber in the pump source can be controlled at the setting value in the ambient temperatures of 25 °C and 45 °C. The estimated cooling capacity of the system in different ambient environments is shown in Table 3.

## 4. Experiment Results and Discussion

_{max}, P

_{min}and P

_{avr}are the maximum, minimum and average output powers of the OPO laser with the measured values. The calculated output power stability values of the laser in room and high temperature environment were ±0.7% and ±1%, respectively. The one-hour output power stability of the laser in room temperature environment was within ±1%. The experimental results above show that the thermal control system has a strong cooling capacity to keep the substrate temperature of the pump laser module at the setting value.The laser was able to work normally in both the room and high temperature environments, and when pump power of the laser changed, the temperature control circuit was able to adjust the output drive voltage on TEMs according to the measured temperature value, keeping the temperature of the pump laser at a stable and suitable value.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The schematic diagram of the designed tunable all-fiber laser pumped optical parametric oscillator (OPO).

**Figure 2.**The variation in the curve of the laser wavelength with changes in the temperature of the crystal at different polarization periods.

Parameters | ||
---|---|---|

Internal resistance | 1 Ω ±10% | |

I_{max} | 12 A | |

V_{max} | 15.4 V | |

- | T_{h} = 27 °C | T_{h} = 50 °C |

Q_{max} | 110 W | 134 W |

ΔT_{max} | 68 °C | 75 °C |

Solder melting point | 138 °C |

Material | Thermal Conductivity (W/m·K) | Size | Number | Flow Rate (m^{3}/s) | |
---|---|---|---|---|---|

Cabinet | Aluminum 6063-T83 | 201 | 330 × 330 × 115 mm^{3}(L × W × H) Wall thickness: 10mm | / | / |

Fin | Aluminum 6063-T83 | 201 | 300 × 50 mm^{2} (L × W)Fin thickness: 2mm Fin spacing: 20mm | 14 | / |

Heat pipe | / | Evaporation section:2 × 10^{4}Condensation section: 500 | 280 × 12 × 5 mm^{3}(L × W × H) | 2 | / |

Fan | / | / | 40 × 40 × 10 mm^{3} | 6 | 0.011 |

Ambient Environment Temperature (T_{a}) | T_{1} | TEC Driving Current | Position of TEMs | R_{3} | TEM Cooling Output (Q_{c}_{1}) | System Cooling Capacity (Q_{c}) |
---|---|---|---|---|---|---|

298.15 K (25 °C) | 293.15 K (20 °C) | 5 A | TEMs near the edge | 0.04 K/W | 39.5 W | 636 W |

TEMs in the middle | 0.03 K/W | 40 W | ||||

318.15 K (45 °C) | 293.15 K (20 °C) | 5 A | TEMs near the edge | 0.04 K/W | 24 K/W | 387.2 W |

TEMs in the middle | 0.03 K/W | 24.4 W |

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## Share and Cite

**MDPI and ACS Style**

Yu, D.; He, Y.; Zhang, K.; Pan, Q.; Chen, F.; Guo, L. A Tunable Mid-Infrared Solid-State Laser with a Compact Thermal Control System. *Appl. Sci.* **2018**, *8*, 878.
https://doi.org/10.3390/app8060878

**AMA Style**

Yu D, He Y, Zhang K, Pan Q, Chen F, Guo L. A Tunable Mid-Infrared Solid-State Laser with a Compact Thermal Control System. *Applied Sciences*. 2018; 8(6):878.
https://doi.org/10.3390/app8060878

**Chicago/Turabian Style**

Yu, Deyang, Yang He, Kuo Zhang, Qikun Pan, Fei Chen, and Lihong Guo. 2018. "A Tunable Mid-Infrared Solid-State Laser with a Compact Thermal Control System" *Applied Sciences* 8, no. 6: 878.
https://doi.org/10.3390/app8060878