Comprehensive Thermal Analysis of Diamond in a High-Power Raman Cavity Based on FVM-FEM Coupled Method

At a Glance

Metadata	Details
Publication Date	2021-06-15
Journal	Nanomaterials
Authors	Zhenxu Bai, Zhanpeng Zhang, Kun Wang, Jia Gao, Zhendong Zhang
Institutions	Hebei University of Technology, Macquarie University
Citations	28
Analysis	Full AI Review Included

Executive Summary

This study provides a comprehensive thermal and mechanical analysis of single-crystal diamond operating in a high-power Raman laser cavity using a coupled Finite Volume Method (FVM) and Finite Element Method (FEM) simulation.

Rapid Thermal Stabilization: Despite operating at absorbed powers up to 200 W (corresponding to kilowatt-level output), the diamond crystal achieves thermal steady-state for the temperature gradient in an extremely short period, typically 53 µs (for a 60 µm beam radius).
High Repetition Rate Feasibility: This rapid stabilization and cooling (50 µs heating, 50 µs cooling) confirms that long-term, kilowatt-level quasi-continuous-wave (QCW) Raman lasing is feasible at repetition rates up to 10 kHz without significant heat accumulation.
Minimal Deformation: The maximum thermal-induced deformation of the millimeter-sized diamond crystal is extremely small, reaching only 2.456 µm at the highest simulated absorbed power (200 W).
Manageable Thermal Lensing: This minimal deformation results in a thermal focal length (f) of 54.5 mm at maximum power. This effect is easily compensated by minor adjustments to the resonator length (e.g., increasing the cavity length by ~3.4 mm).
Waist Dependence: The thermal constant time is primarily determined by the Stokes beam waist radius, ranging from 45 µs (40 µm radius) to 62 µs (100 µm radius), and is independent of the absorbed power level.
Design Optimization: The results provide critical theoretical guidance for optimizing the design and thermal management of high-power diamond Raman lasers (DRLs) operating in the thermal-affected regime.

Technical Specifications

Data extracted from Table 1 and Section 3 of the source material.

Parameter	Value	Unit	Context
Diamond Thermal Conductivity	2200	W/(m·K)	Single crystal
Diamond Thermal Expansion Coefficient	10^-6	K^-1
Diamond Density	3.51	g/cm³
Diamond Specific Heat Capacity	0.519	J/(g·K)
Diamond Size (Volume)	8 x 4 x 1.2 (0.0384)	mm (cm³)	Used in DRL setup
Copper Thermal Conductivity	385	W/(m·K)	Heat sink material
Heat Sink Temperature	298 (25)	K (°C)	Constant cooling temperature
Pump/Stokes Beam Radius (Range)	40 to 100	µm	Simulation variable
Absorbed Power (Range)	5 to 200	W	Corresponds to >1 kW output power
Thermal Constant Time (60 µm radius)	53	µs	Time for temperature gradient to reach 99% steady-state
Thermal Constant Time (Range)	45 to 62	µs	Dependent on beam radius (40 µm to 100 µm)
Maximum Thermal Deformation	2.456 ± 0.004	µm	At 200 W absorbed power
Minimum Thermal Focal Length (f)	54.5	mm	At 2.5 µm deformation (200 W absorbed)
Required Cavity Length Adjustment	~3.4	mm	To compensate 2.5 µm deformation (201 mm cold cavity)
Maximum QCW Repetition Rate	10	kHz	Based on 50 µs heating/cooling cycle

Key Methodologies

The thermal and mechanical analysis utilized a coupled FVM-FEM approach to model the complex thermo-fluid-mechanical interactions within the high-power diamond Raman laser (DRL) system.

Physical Model Definition:
- The DRL setup used an 8 mm x 4 mm x 1.2 mm single-crystal diamond placed in a near-concentric cavity (201 mm cold cavity length).
- The heat source was modeled as a spherical volume (40-100 µm radius) located at the diamond center, accounting for absorption and quantum defect (η = λ_P/λ_S).
Thermal Simulation (FVM):
- The governing energy equations for the solid (diamond and copper sink) and fluid (air) domains were solved using the Finite Volume Method (FVM) via ANSYS Fluent.
- The simulation accounted for heat conduction, air natural convection, and thermal radiation.
- The Discrete Ordinate (Do) model was used to simulate radiation heat transfer.
- A highly refined grid system of 28,667,369 elements was used, with a time step (∆τ) of 1 µs for transient analysis.
Boundary Conditions:
- The bottom surface of the copper heat sink was fixed at a constant wall temperature of 298 K.
- Interfaces between the air domain and solid domain were set as coupled surfaces.
Thermo-Elasticity Simulation (FEM):
- The temperature distribution results from the FVM simulation were used as input for the thermo-elasticity model.
- The equilibrium differential equations and constitutive equations for thermo-elasticity were solved using the Finite Element Method (FEM) via ANSYS Static Structural.
- The diamond and copper sink were allowed to freely expand, except for the bonded interface between them.
- A grid system of 113,187 elements was adopted for the FEM analysis.

Commercial Applications

The robust thermal performance and high-power capability demonstrated by diamond in this analysis are critical for several advanced engineering and commercial sectors:

High-Power Industrial Processing:
- Enabling next-generation high-power lasers (kW-level and above) for material processing, including high-speed cutting, precision welding, and surface treatment, where beam quality must be maintained under heavy thermal load.
Defense and Security:
- Development of high-brightness, high-power directed energy weapons (DEW) and long-range illumination systems, benefiting from diamond’s superior thermal shock resistance and minimal thermal lensing.
Scientific Research and High-Energy Physics:
- Providing stable, high-quality laser sources necessary for driving advanced research facilities, particle accelerators, and fusion experiments.
Spectral Diversity and Conversion:
- Efficiently shifting the wavelength of existing high-power fiber lasers (e.g., 1 µm) into eye-safe or application-specific spectral regions (e.g., 1.24 µm, 2.52 µm) using the Raman effect, expanding the utility of commercial laser platforms.
Aerospace and Space Exploration:
- Utilizing compact, thermally robust diamond laser systems for remote sensing, atmospheric monitoring, and laser communication in harsh environments.

View Original Abstract

Despite their extremely high thermal conductivity and low thermal expansion coefficients, thermal effects in diamond are still observed in high-power diamond Raman lasers, which proposes a challenge to their power scaling. Here, the dynamics of temperature gradient and stress distribution in the diamond are numerically simulated under different pump conditions. With a pump radius of 100 μm and an absorption power of up to 200 W (corresponding to the output power in kilowatt level), the establishment period of thermal steady-state in a millimeter diamond is only 50 μs, with the overall thermal-induced deformation of the diamond being less than 2.5 μm. The relationship between the deformation of diamond and the stability of the Raman cavity is also studied. These results provide a method to better optimize the diamond Raman laser performance at output powers up to kilowatt-level.

Tech Support

Original Source

DOI: https://doi.org/10.3390/nano11061572

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