A Thermal Modeling Toolkit for Continuous-Wave Gaussian Second-Harmonic Generation in KTP Crystal

We release an open-source finite-difference toolkit for computing temperature fields in continuous-wave (CW) second-harmonic generation (SHG) using potassium titanyl phosphate (KTP) crystals under Gaussian end-pumping. The toolkit includes modules for geometry and material definitions, boundary and cooling models, and transient and steady-state finite-difference solvers. Users provide beam and crystal parameters along with cooling profiles, and the solver returns spatiotemporal temperature fields with radial and axial profiles as exportable datasets. This implementation consolidates previous work into a single versioned repository with reproducible pipelines and parameterized scenario sweeps covering temperature-dependent versus constant conductivity, convection with or without radiation, and heat-transfer coefficients from $6.5$ to $2.0 \times 10^{4}$Wm$^{-2}$~K$^{-1}$. The compiled Fortran kernels include built-in benchmark reporting. Validation is performed by reproducing published temperature distributions and trends for KTP under Gaussian CW pumping. The code is available as an open-source GitHub repository and is released under the MIT license as version v1.0.0, with an archived release on Zenodo identified by DOI 10.5281/zenodo.17266421 for citation and long-term access.

💡 Research Summary

This paper presents the development and release of an open-source, finite-difference-based thermal modeling toolkit specifically designed for analyzing temperature fields in potassium titanyl phosphate (KTP) crystals under continuous-wave (CW) Gaussian beam pumping for second-harmonic generation (SHG). The toolkit addresses a critical need in photonics, where thermal management in nonlinear crystals is paramount for maintaining high SHG efficiency and beam quality at high power levels. Absorption-induced heating causes thermal lensing and phase mismatch, and accurate modeling is essential for system design.

The toolkit consolidates and extends previous analytical and numerical work into a single, version-controlled codebase. Its architecture comprises several core modules: a Geometry and Materials module for defining the cylindrical crystal and KTP properties, a Boundary and Cooling module implementing realistic convection (with a wide range of heat-transfer coefficients, h) and optional radiative boundary conditions, and a Core Solver that numerically integrates the heat equation in cylindrical coordinates (r, z). A key advanced feature is the implementation of temperature-dependent thermal conductivity, K(T), which is shown to significantly impact peak temperatures compared to a constant-K model.

Validation is performed by meticulously reproducing published temperature distributions and trends from a reference CW Gaussian KTP study. The toolkit successfully replicates results showing that using K(T) leads to a center temperature approximately 70K higher than using constant K at 80W pump power. It also demonstrates the insensitivity of surface temperature to h in the range for air cooling (6.5–50 W/m²K), the significant cooling effect of high-conductance mounts (h ~15,000–20,000 W/m²K), and the non-negligible role of radiation for crystals with larger radii and beam spots. The solver outputs spatiotemporal temperature fields and steady-state radial/axial profiles as plain-text files, facilitating direct comparison and use in downstream analyses like phase-mismatch calculation.

The implementation is in Intel Fortran for Linux systems, and the repository includes build instructions, example parameter sets, and reference output files to ensure reproducibility. The current scope is limited to azimuthally symmetric, CW Gaussian heating in KTP. The authors acknowledge limitations, such as the lack of support for pulsed excitation or non-Gaussian beams, and outline a roadmap for future extensions, including adding material properties for other nonlinear crystals (e.g., LBO, BBO) and providing hooks for post-processing the temperature data.

Released under the MIT license, the code is available on GitHub and archived on Zenodo with a DOI (10.5281/zenodo.17266421) for permanent citation and access. This work provides a standardized, reproducible foundation for benchmarking thermal models, comparing the effects of different physical assumptions (constant vs. temperature-dependent conductivity, convection vs. convection+radiation), and serves as a reliable starting point for researchers and engineers working on thermally coupled SHG system design.