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Unified analysis of spatially-coupled absorption and saturation dynamics in multi-pass pumped thin-disk lasers

Hanjin Jo, Jiří Mužík, Pawel Sikocinski, Magdalena Sawicka-Chyla, Michal Chyla, Yuya Koshiba, Yoann Levy, Kohei Hashimoto, Martin Smrž, Tomáš Mocek

TL;DR

The paper develops a self-consistent framework that unifies pump absorption, gain saturation, thermo-optic distortion, and cavity diffraction in multi-pass pumped solid-state lasers, proving a unique fixed-point solution for the coupled dynamics. It extends the model to 2D intra-cavity fields and validates it on a multi-pass Yb:YAG thin-disk module, achieving quantitative agreement in absorption, output power, beam size, and M^2. By coupling temperature-dependent cross-sections with saturation through a nonlinear absorption relation and rigorous roundtrip propagation, the method yields accurate predictions of high-power resonator behavior and diffraction losses due to disk deformation. The work provides actionable guidelines for pump-power scaling and pass-number optimization, improving design predictability for high-power thin-disk lasers.

Abstract

We present a theoretical framework that unifies pump absorption, gain saturation, thermo-optic distortion, and cavity diffraction into a self-consistent model of multi-pass pumped solid-state lasers. By deriving a theoretical formulation of the nonlinear coupling of the superimposed pump energy and effective absorption, we prove an unique steady-state solution exists. Applied to the multi-pass Yb:YAG thin-disk module, the framework is quantitatively validated with experiments, reproducing a well matched absorption tendency, errors in output power, beam diameter and M^2 within 3.0%, 1.7%, and 0.05 respectively. This approach provides predictive guidelines for pump-power scaling and pass-number optimization in high-power lasers.

Unified analysis of spatially-coupled absorption and saturation dynamics in multi-pass pumped thin-disk lasers

TL;DR

The paper develops a self-consistent framework that unifies pump absorption, gain saturation, thermo-optic distortion, and cavity diffraction in multi-pass pumped solid-state lasers, proving a unique fixed-point solution for the coupled dynamics. It extends the model to 2D intra-cavity fields and validates it on a multi-pass Yb:YAG thin-disk module, achieving quantitative agreement in absorption, output power, beam size, and M^2. By coupling temperature-dependent cross-sections with saturation through a nonlinear absorption relation and rigorous roundtrip propagation, the method yields accurate predictions of high-power resonator behavior and diffraction losses due to disk deformation. The work provides actionable guidelines for pump-power scaling and pass-number optimization, improving design predictability for high-power thin-disk lasers.

Abstract

We present a theoretical framework that unifies pump absorption, gain saturation, thermo-optic distortion, and cavity diffraction into a self-consistent model of multi-pass pumped solid-state lasers. By deriving a theoretical formulation of the nonlinear coupling of the superimposed pump energy and effective absorption, we prove an unique steady-state solution exists. Applied to the multi-pass Yb:YAG thin-disk module, the framework is quantitatively validated with experiments, reproducing a well matched absorption tendency, errors in output power, beam diameter and M^2 within 3.0%, 1.7%, and 0.05 respectively. This approach provides predictive guidelines for pump-power scaling and pass-number optimization in high-power lasers.

Paper Structure

This paper contains 7 sections, 17 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. MATERIALS AND METHODS
  3. Theoretical approach
  4. Roundtrip propagation
  5. Experimental details and numerical implementation
  6. RESULTS AND DISCUSSION
  7. CONCLUSION

Figures (3)

  • Figure 1: (a) experimental configuration of measuring unabsorbed power measurement. (b) Typical calculation results of the absorption behavior with (Eq. (\ref{['eqn:FP']})) and without saturation effects (Ideal absorption) for pump intensities of 1 $\mathrm{kW/cm^2}$ and 4 $\mathrm{kW/cm^2}$. Note pump intensity $I_p$ is defined as the incident pump power divided by the pump beam area. Pump beam radius is 2.05 mm. Abbreviations are following; LD: laser diode, PM: power-meter and BS: beam splitter.
  • Figure 2: (a) Experimental setup: simultaneous measurement of output power, disk wavefront during pumping. Typical example has been shown for the pump intensity of 4 $\mathrm{kW/cm^2}$ (b) Temperature-dependent absorption and emission cross-section of Yb:YAG. (c) Typical example of simulated 2D distributions: temperature, inversion, and gain when pumping intensity of 4 $\mathrm{kW/cm^2}$. Abbreviations as follows; WFS: wavefront sensor, LD: laser diode, PM: power-meter, BD: beam dump, PBS: polarized beam splitter and OC: output coupler.
  • Figure 3: (a) Representative example illustrating the evolution of the intracavity wave. (b) Typical example of the output beam, simulated beam profile, phase and the population inversion ratio of the disk in the steady state. (c) Summary of results: comparison between experiment and simulation, where a radius of curvature of 40 m obtained from the wavefront sensor was applied. Unabsorbed ratio, output power, major beam diameter($D_\mathrm{maj}$), and beam quality factor ($\mathrm{M^2}$) are compared. Note, $\varepsilon_{abs}$ is difference of unabsorbed ratio between the experiment and derived value from Eq. (\ref{['eqn:FP']}), $\varepsilon$ is relative errors and $\varepsilon_{M^2}$ absolute errors between the experiment and measured OPD applied simulation results.