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Modelling the full picture of femtosecond laser ablation

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Ultrashort laser pulses are an incredibly useful tool for removing small amounts of material from solid surfaces. So far, however, the computer models required for this technique have only considered the thermal processes involved in melting and evaporating material. In their research, Dr Xu Mao from the China Agricultural University and Dr C Steve Suh at Texas A&M University show that thermal stresses and electron emissions are also crucial factors to consider when modelling laser ablation. By introducing an updated model, the pair hope that laser ablation on metals, including steel and gold, could soon be carried out far more safely.
Laser ablation is a widely used technique for removing small amounts of material from solid surfaces, with exceptional degrees of precision. It involves irradiating a surface with a series of extremely short, low-intensity laser beam pulses, each lasting up to just hundreds of femtoseconds – or millionths of a nanosecond. When exposed to these pulses, materials will ideally either melt and evaporate, or sublimate straight from a solid to a gas.

Crucially, the durations of these laser pulses are so short that the heat they impart cannot be absorbed by other parts of the material. This allows researchers to carry out a variety of important operations: from carving out intricate patterns to removing coatings down to highly specific depths. However, Dr Xu Mao of the China Agricultural University and Dr C Steve Suh from Texas A&M University in the US argue that our conventional understanding of this technique doesn’t present the full picture.

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In reality, the molecular structures of solid surfaces can be partially fragmented and mechanically ejected during laser ablation, without either melting, evaporating, or sublimating – which suggests that other mechanisms are responsible for removing the material. For Mao and Suh, researchers’ current lack of consideration of these effects is presenting the technique with a serious problem.

Building a comprehensive model

When conducting femtosecond laser ablation, it is crucial for researchers to consider the differing molecular compositions of solid surfaces. In different materials, factors including pulse duration, intensity, and laser wavelength must be tightly controlled. Without adequate precautions, researchers risk damaging parts of the surface which were supposed to remain untouched.

In a series of 2019 studies, Mao and Suh aimed to address this issue by developing an advanced computer model, which could accurately recreate the coupled thermal and mechanical responses of metals to ultrafast laser pulses. In constructing their model, they considered how energy is transported and dissipated when incorporating the equations describing its flow. This involved ensuring that energy was conserved in each interaction: a fundamental necessity in all physical systems. In addition, they accounted for the heat carried by electrons, which is transferred to the metal as the particles interact with its atomic lattice.

For Mao and Suh, demonstrating the accuracy of their computer model was a monumental step. Not only did it pave the way for a reliable exploration of the ablation process; it also provided vital guidance for feasible damage-prevention techniques. However, the mechanical and electron-related factors the model described, along with the thermal effects accounted for in existing models, still wouldn’t be enough to prevent unwanted distortions in the remaining material.

“With accurate models, researchers could remove material from metal surfaces with molecular-level precision.”

Through a new pair of studies, the duo has developed a more comprehensive model which, for the first time, can fully account for the non-thermal ablations triggered by femtosecond laser pulses.

Accounting for multiple effects

Mao and Suh’s latest model can describe femtosecond laser ablation as a complex interplay between multiple physical processes, including the absorption of laser energy, the laser-generated charge-carrier dynamics, the interaction between electrons and ‘phonons’ – a quantised form of sound waves, which play a major role in transporting heat energy around the lattice – the diffusion of heat, and the subsequent mechanical motions of the material in response to these effects.

In addition, the researchers incorporated equations which obeyed the physical laws of energy conservation, while accounting for the differing timescales of each process. Furthermore, the model also considers factors including the finite speeds of electrons and phonons within the molecular lattice, and the energy it loses due to electrons being emitted from the material’s surface.

Gabor Wavelet Transform (GWT) of stress wave and its power density indicates high-cycle fatigue is probable at location (z=50nm, r=0) where micro-cracking is expected. Adapted from Mao & Suh, 2019, J Thermal Stresses, 42(3), with permission of the publisher Taylor & Francis Ltd.

This emission occurs as electrons gain enough energy from the heat surrounding them to leave the surface, and also by absorbing photons of just the right frequency. Together, these mechanisms generate a plume of hot, charged plasma, which propels evaporated material away from the material’s surface.

Impacts on polycrystalline metals

In their study, Mao and Suh considered how this complex interplay between processes would be affected when femtosecond laser ablation is carried out on ‘polycrystalline’ metals: a family of materials including gold and steel alloys. These metals are made up of ‘grains’ – within which molecular lattices are ordered in reliably repeating patterns.

However, the grains themselves can be oriented in completely random directions – creating boundaries between regions of drastically differing molecular arrangements within the metal. This structure introduces an extra layer of complexity in the computer models required for femtosecond laser ablation.

Evolutions of normal stress, its strain energy density rate, and predicted ablation depth based on ablation threshold. Adapted from Mao & Suh, 2021, J Thermal Stresses, 44(2), with permission of the publisher Taylor & Francis Ltd.

Mechanical stresses and electron emissions

Using their new model, Mao and Suh revealed that the sizes of grains within polycrystalline materials can affect factors including their thermal conductivity, the degree of interaction between the electrons and phonons travelling through them. When the diameters of these grains become larger, electrons will transport less heat through the metal, and will also interact more strongly with phonons – leading to a sharp rise in local temperatures.

Subsequently, grain sizes can have a profound influence over the metal’s mechanical response to femtosecond laser ablation. In this case, these responses come in the form of powerful, high-frequency stress waves, which can initiate cracking as they travel through molecular lattices – deteriorating their mechanical stability.

Losses of energy due to thermionic and photoelectric electron emissions are also crucially important to consider in this process. If they are not accounted for, models could calculate that the metals are far hotter than they actually are. This may lead them to inaccurately assume that metals have melted – which would entirely change their thermal and mechanical properties.

Updating the ablation process

Based on these robust results, Mao and Suh now propose that new mechanisms are required to model the removal of material from polycrystalline metal surfaces during exposure to ultrafast laser pulses. When assessing the results of their model, Mao and Suh found a close agreement with data gathered in real experiments – making a strong case for its more widespread use in future research.


With models that can accurately correlate the parameters of incident laser pulses with the physical damage they inflict on materials, the duo ultimately hopes that researchers could virtually eliminate the damage caused by femtosecond laser ablation – allowing them to remove material from metal surfaces with molecular-level precision.

In turn, this could improve capabilities in a wide variety of advanced manufacturing applications: from the production of intricate holes, channels, and other geometric structures found in advanced 2D materials, to the safe removal of ultra-thin coatings when they are no longer needed.

What steps will need to be taken to roll out the new model on larger scales?
More experimental studies are being planned to validate the current model. Upon validation, the model can be applied to investigate heterogeneous and/or homogeneous nucleation. A broad range of materials including poly-crystalline silicon and graphene, along with the underlying ablation mechanism, need be considered to realise high-accuracy modelling essential for achieving high manufacturing precision for electronics and digital devices. This also has significant implications for allowing the fabrication of materials on a large scale with a high repetition rate using femtosecond lasers.



  • Mao, X, Suh, CS, (2019) Generalized Thermo-Elastodynamics for Polycrystalline Metallic Thin Films in Response to Ultrafast Laser Heating. Journal of Thermophysics and Heat Transfer, 33.
  • Mao, X, Suh, CS, (2019) Ultrashort pulse-induced elastodynamics in polycrystalline materials. Part I: Model validation. Journal of Thermal Stresses, 42(3), 374–387.
  • Mao, X, Suh, CS, (2019) Ultrashort pulse induced elastodynamics in polycrystalline materials. Part II: Thermal–mechanical response. Journal of Thermal Stresses, 42(3), 388–400.
  • Mao, X, Suh, CS, (2021) Thermo-elasto-plasto-dynamics of ultrafast optical ablation in polycrystalline metals. Part I: Theoretical formulation. Journal of Thermal Stresses, 44(2), 163–179.
  • Mao, X, Suh, CS, (2021) Thermo-elasto-plasto-dynamics of ultrafast optical ablation in polycrystalline metals. Part II: Response and damage evaluation. Journal of Thermal Stresses, 44(2), 180–196.

Research Objectives

Developing a new computer model for ultrashort laser ablation of metals.


Dissemination of the research results are made available by Grant TC200H02D


Xu Mao has been an associate professor in the College of Engineering at China Agricultural University since 2021. He received his PhD from the Mechanical Engineering Department at Texas A&M University, then joined the Mechanical and Industrial Engineering Department at Northeastern University, where he was a postdoctoral fellow in 2019. His research interests focus on ultrafast laser dynamics, intelligent measurement and control, and multimodal sensing, imaging and fusion, with applications to advanced manufacturing, agricultural products, and smart agricultural devices.

C Steve Suh C Steve Suh is faculty member in the Mechanical Engineering Department at Texas A&M University, and an ASME Fellow. His interests in nonlinear time-frequency control, advanced manufacturing, engineering design theory, ultrafast laser dynamics, and complex networks have resulted in exceeding 180 scientific publications, ten book volumes and book chapters. He is currently the Editor of Vibration Testing and System Dynamics, an interdisciplinary journal serving as the forum for promoting dialogues among engineering practitioners and research scholars on the synergy of system dynamics, testing, design, modeling, and education. He is also serving as an Associate Editor for three internationally renowned archival journals: International Journal of Dynamics and Control, Journal of Applied Nonlinear Dynamics, and Discontinuity, Nonlinearity, and Complexity.


Dr Xu Mao
Room 457, College of Engineering,
China Agricultural University,
Beijing, 100083, PR China
Dr Xu Mao
E: [email protected]
T: +86 137 160 76675

Dr C Steve Suh
J Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA
E: [email protected]

T: +1 979 845 1417

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