Linear resonance (LR) absorption of an intense 800 nm laser light in a nano-cluster requires a long laser pulse > 100 fs when Mie-plasma frequency (ω M ) of electrons in the expanding cluster matches the laser frequency (ω). For a short duration of the pulse the condition for LR is not satisfied. In this case, it was shown by a model and particle-in-cell (PIC) simulations [Phys. Rev. Lett. 96, 123401 (2006)] that electrons absorb laser energy by anharmonic resonance (AHR) when the position-dependent frequency Ω[r(t)] of an electron in the selfconsistent anharmonic potential of the cluster satisfies Ω[r(t)] = ω. However, AHR remains to be a debate and still obscure in multi-particle plasma simulations. Here, we identify AHR mechanism in a laser driven cluster using molecular dynamics (MD) simulations. By analyzing the trajectory of each MD electron and extracting its Ω[r(t)] in the self-generated anharmonic plasma potential it is found that electron is outer ionized only when AHR is met. An anharmonic oscillator model, introduced here, brings out most of the features of MD electrons while passing the AHR. Thus, we not only bridge the gap between PIC simulations, analytical models and MD calculations for the first time but also unequivocally prove that AHR processes is a universal dominant collisionless mechanism of absorption in the short pulse regime or in the early time of longer pulses in clusters.

Pronounced maximum absorption of laser light irradiating a rare-gas or metal cluster is widely expected during the linear resonance (LR) when Mie-plasma wavelength λ M of electrons equals the laser wavelength λ . On the contrary, by performing molecular dynamics (MD) simulations of an argon cluster irradiated by short 5-fs (fwhm) laser pulses it is revealed that, for a given laser pulse energy and a cluster, at each peak intensity there exists a λ -shifted from the expected λ M -that corresponds to a unified dynamical LR at which evolution of the cluster happens through very efficient unification of possible resonances in various stages, including (i) the LR in the initial time of plasma creation, (ii) the LR in the Coulomb expanding phase in the later time and (iii) anharmonic resonance in the marginally over-dense regime for a relatively longer pulse duration, leading to maximum laser absorption accompanied by maximum removal of electrons from cluster and also maximum allowed average charge states for the argon cluster. Increasing the laser intensity, the absorption maxima is found to shift to a higher wavelength in the band of λ ≈ (1 − 1.5)λ M than permanently staying at the expected λ M . A naive rigid sphere model also corroborates the wavelength shift of the absorption peak as found in MD and un-equivocally proves that maximum laser absorption in a cluster happens at a shifted λ in the marginally over-dense regime of λ ≈ (1 − 1.5)λ M instead of λ M of LR. Present study may find importance for guiding an optimal condition laser-cluster interaction experiment in the short pulse regime.

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In the few-cycle pulse regime of laser-cluster interaction (intensity $$>10^{16}\,\text{ W/cm}^{2}$$ > 10 16 W/cm 2 , wavelength $$> 780$$ > 780  nm), laser absorption is mostly collisionless and may happen via anharmonic resonance (AHR) process in the overdense (cluster) plasma potential. Many experiments, theory and simulation show average absorbed energy per cluster-electron ($${\mathcal {E}_A}$$ E A ) close to the electron’s ponderomotive energy ($$U_\mathrm {p}$$ U p ) in the collisionless regime. In this work, by simple rigid sphere model (RSM) and detailed particle-in-cell (PIC) simulation, we show enhanced $${\mathcal {E}_A}\approx$$ E A ≈ 30–70$$U_\mathrm {p}$$ U p —a 15–30 fold increase—with an external (crossed) magnetic field near the electron-cyclotron resonance (ECR). Due to relativistic mass increase, electrons quickly deviate from the standard (non-relativistic) ECR, but time-dependent relativistic-ECR (RECR) happens which also contributes to enhanced $${\mathcal {E}_A}$$ E A . Here laser is coupled to electrons in two stages, i.e, AHR and ECR/RECR. To probe further we retrieve the phase-difference $$\Delta \psi$$ Δ ψ between the driving electric field and corresponding velocity component for each electron (in PIC and RSM). We find absorption by electron via AHR happens in a very short interval $$\Delta \tau$$ Δ τ for less than half a laser period where $$\Delta \psi$$ Δ ψ remains close to $$\pi$$ π (necessary condition for maximum laser absorption) and then $$\Delta \psi$$ Δ ψ drops to its initial $$\pi /2$$ π / 2 (meaning no absorption) after such short-lived AHR. On the contrary, auxiliary magnetic field near the ECR modifies AHR scenario inside the cluster and also helps maintaining the required phase $$\Delta \psi \approx \pi$$ Δ ψ ≈ π for the liberated cluster-electron accompanied by frequency matching for ECR/RECR for a prolonged $$\Delta \tau$$ Δ τ (which covers 50–60% of the laser pulse through pulse maxima) even after AHR—leading to jump in $${\mathcal {E}_A}\approx$$ E A ≈ 30–70$$U_\mathrm {p}$$ U p . We note that to realize the second stage of enhanced energy coupling via ECR/RECR, the first stage via AHR is necessary.