Periodic nanoparticle arrays have attracted considerable interest recently since the lattice effect can lead to spectrally narrow resonances and tune the resonance position in a broad range. Multipole decomposition is widely used to analyze the role of the multipoles in the resonance excitations, radiation, and scattering of electromagnetic waves. However, previous studies have not addressed the validity and accuracy of the multipole decomposition around the lattice resonance. The applicability of the exact multipole decomposition based on spherical harmonics expansion has not been demonstrated around the lattice resonance with the strong multipole coupling. This work studies the two-dimensional periodic arrays of both plasmonic and dielectric nanospheres and compares the multipole decomposition results with the analytic ones around their lattice resonances. We study both the effective polarizabilities of multipoles and the scattering spectra of the structures. The analytical results are calculated from the coupled dipole–quadrupole model. This study demonstrates that the exact multipole decomposition agrees well with the numerical simulation around lattice resonances. Only a small number of multipoles are required to represent the results accurately.
that different mechanisms are involved in SHG from non-centrosymmetric and centrosymmetric semiconductor materials. The latter ones inherit the inversion symmetry that forbids electric dipole secondorder susceptibility. Nevertheless, the symmetry is broken by bulk quadrupole and surface dipole contributions. [17,18] In order to describe the nonlinear optical response of centrosymmetric materials such as silicon (Si), a phenomenological model was proposed by Bloembergen et al. [9] and applied to specific nanostructures in the recent studies. [3,19] In the pioneering work, [9] the correspondence between pheno menological and a hydrodynamic model for free electrons, commonly applied to describe second-order nonlinear response from metals, [13] was demonstrated. These two approaches, originally designed for bound and free electrons and coupled to Maxwell equations by the nonlinear polarization, form the basis to describe the perturbative nonlinear response of arbitrary nanostructures.Upon ultrashort laser excitation of all-dielectric materials, optical properties swiftly change due to photo-ionization processes, while free carrier absorption may lead to the local material damage. On the one hand, these effects are commonly considered as the limiting factors for the operating frequency conversion nanodevices. [1,2,[20][21][22][23] On the other hand, inhomogeneous free carriers can serve as an additional source for symmetry breaking [24,25] and for high-order harmonics generation in non-perturbative regimes, [7,8,26,27] and participate in ultrafast self-action, all-optical switching, and modulation at the nanoscale. [20,[28][29][30][31][32] While the applicability of the perturbative approaches is limited to describe weak intensity regimes, the extended hydrodynamic model for electron-hole plasma kinetics and electron-ion transfer gives a reliable estimate for the inhomogeneous absorption and heating processes inside the laser-excited nanostructures and describes the non-perturbative mechanism of harmonic generation due to direct electron transitions from valence to conduction band. To date, a self-consistent approach, considering both nonlinear sources and laser-induced electron-hole dynamics has not been proposed and applied in the context of SHG and THG.In the current work, a multi-physical approach is developed in order to explore the natural material limitations for nonlinear conversion efficiency achievable by ultrashort laser irradiation of Reaching the optimal second-and third-order nonlinear conversion efficiencies while avoiding undesirable free carrier absorption losses and material damage in ultrashort laser-excited nanostructures is a challenging obstacle in all-dielectric ultrafast nanophotonics. In order to elucidate the main aspects of this problem, a multi-physical model is developed, coupling nonlinear Maxwell equations supplied by surface and bulk nonlinearities with free carrier hydrodynamic equations for electron-hole plasma kinetics and electron-ion transfer for silicon. The maximum feasible effic...
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