A reduced-order analysis for multi-reflection-driven laser absorptance in vaporization-induced cavities
Abstract
Multiple internal reflections enhance laser absorption in vaporization-induced cavities, but connecting ray histories, cavity geometry, and absorptance typically requires full ray tracing. We develop a reduced-order framework based on Beer-Lambert-type attenuation governed by an effective per-reflection optical depth (EPROD). A power-weighted formulation defines an absorptance-equivalent interaction count under constant effective single-interaction absorptance, while a cumulant expansion separates the EPROD-independent mean interaction count from ray-path heterogeneity corrections. Across nine simulation groups spanning three alloys and three spot diameters, the mean interaction count follows a unit-intercept linear depth relation with R-squared values of 0.7824-0.9843. Its slope varies by only 3.4%-6.3% across alloys at fixed spot diameter and decreases with increasing spot diameter. Fixing this slope from ray statistics yields an absorptance-depth model with one fitted parameter and a median prediction error (MAPE) of 2.61%. An independent synchronized Ti-64 experiment yields model parameters within approximately 2.4% of corresponding simulation values. This framework separates geometric interaction accumulation from optical attenuation, enabling efficient energy-coupling prediction and absorptance-based keyhole characterization.
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BibTeX
@misc{liu2026reducedorder,
title = {{A reduced-order analysis for multi-reflection-driven laser absorptance in vaporization-induced cavities}},
author = {Haolin Liu and Haoran Shi and Xuzhe Zeng and Brian J. Simonds and Wenda Tan and Anthony D. Rollett and Levent Burak Kara},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32089},
eprint = {2609.32089},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32089},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A reduced-order analysis for multi-reflection-driven laser absorptance in vaporization-induced cavities
AU - Haolin Liu
AU - Haoran Shi
AU - Xuzhe Zeng
AU - Brian J. Simonds
AU - Wenda Tan
AU - Anthony D. Rollett
AU - Levent Burak Kara
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.32089
UR - https://arxiv.org/abs/2609.32089
AB - Multiple internal reflections enhance laser absorption in vaporization-induced cavities, but connecting ray histories, cavity geometry, and absorptance typically requires full ray tracing. We develop a reduced-order framework based on Beer-Lambert-type attenuation governed by an effective per-reflection optical depth (EPROD). A power-weighted formulation defines an absorptance-equivalent interaction count under constant effective single-interaction absorptance, while a cumulant expansion separates the EPROD-independent mean interaction count from ray-path heterogeneity corrections. Across nine simulation groups spanning three alloys and three spot diameters, the mean interaction count follows a unit-intercept linear depth relation with R-squared values of 0.7824-0.9843. Its slope varies by only 3.4%-6.3% across alloys at fixed spot diameter and decreases with increasing spot diameter. Fixing this slope from ray statistics yields an absorptance-depth model with one fitted parameter and a median prediction error (MAPE) of 2.61%. An independent synchronized Ti-64 experiment yields model parameters within approximately 2.4% of corresponding simulation values. This framework separates geometric interaction accumulation from optical attenuation, enabling efficient energy-coupling prediction and absorptance-based keyhole characterization.
ER -