Multiscale Numerical Modelling of Ultrafast Laser-Matter Interactions: Maxwell Two Temperature Model Molecular Dynamics (M-TTM-MD)

TL;DR

The paper develops a Maxwell–Two-Temperature–Molecular Dynamics (M-TTM-MD) framework that self-consistently couples electromagnetic field propagation (FDTD) with electron–phonon energy exchange (TTM) and atomic dynamics (MD) to model ultrafast laser–metal interactions. Energy deposition is computed as $Q_{ ext{las}} = -\nabla \cdot (\mathbf{E} \times \mathbf{H})$, with a temperature-dependent dielectric function updated via the ADE method, allowing a dynamic feedback between field distribution and material response. The model is validated on thin Au films under femtosecond pulses, revealing a spatiotemporally modulated absorption landscape, stress confinement up to $\sim$6 GPa, heterogeneous melting with cavitation, and the emergence of periodic surface features consistent with laser-induced structuring. This approach provides a predictive, atomistic view of ultrafast laser interactions with metals and paves the way for optimized laser patterning and surface engineering in complex geometries.

Abstract

In this work, we present a comprehensive numerical framework that couples numerical solutions of Maxwell's equations using the Finite-Difference Time-Domain (FDTD) approach, Molecular Dynamics (MD), and the Two-Temperature Model (TTM) to describe ultrafast laser-matter interactions in metallic systems at the atomic scale. The proposed Maxwell-Two-Temperature Model-Molecular Dynamics (M-TTM-MD) bridges the gap between electromagnetic field propagation, electron-phonon energy exchange, and atomic motion, allowing for a self-consistent treatment of energy absorption, transport, and structural response within a unified simulation environment. The calculated electromagnetic fields incorporate dispersive dielectric properties derived using the Auxiliary Differential Equation (ADE) technique, while the electronic and lattice subsystems are dynamically coupled through spatially and temporally resolved energy exchange terms. The changes in the material topography are then reflected in the updated grid for the FDTD scheme. The developed M-TTM-MD model provides a self-consistent numerical framework that offers insights into laser-induced phenomena in metals, including energy transport and surface dynamics under extreme nonequilibrium conditions.

Figures (9)

• Figure 1: Schematic representation of the different interactions accounted for in the M-TTM-MD model. The electromagnetic (EM) wave propagates through the material, where it is absorbed by the electronic subsystem, leading to a rapid increase of the electron temperature $T_e$. The energy is then transferred to the lattice subsystem via electron-phonon coupling, raising the lattice temperature $T_l$. The elevated lattice temperature induces atomic motion and structural changes, which in turn affect the material's optical properties and modify the EM wave scattering and absorption. This feedback loop continues throughout the laser--matter interaction process.
• Figure 2: Schematic representation of the relationship between the FDTD and TTM-MD continuum cells. Lower density of atoms in the MD cells, leads to decreased values in the dielectric function of the material in the FDTD approach.
• Figure 3: Schematic representation of the computational domain used in the algorithm. The domain consists of several regions: the central TTM-MD region represents the simulated material. The surrounding total field region (red dashed border) contains the incident electromagnetic field interacting with the material, while the scattered field region (green dashed border) accounts for the outgoing scattered waves. The outermost Perfectly Matched Layers (blue shaded region) absorb outgoing waves to prevent reflections back into the simulation box.
• Figure 4: Schematic illustration of the M-TTM-MD cycle, highlighting the interaction between the different subroutines. The FDTD source term drives the electron temperature elevation, influencing the lattice temperature via electron--phonon (e-ph) coupling. The increase in lattice temperature causes matter reorganization, altering the interatomic forces acting on individual particles. These forces are used to compute new positions and velocities of the particles, leading to updated atomic configurations. If the surface topology of the material changes, the scattering of the electromagnetic (EM) pulse is also affected, leading to further updates in the energy deposition profile and completing the cycle.
• Figure 5: Basic implementation of the M-TTM-MD algorithm. The FDTD module, the TTM energy equation, and the MD integrator exchange data at each global timestep, ensuring a self-consistent coupling between the different components.