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Register a new userA classical theory for second-harmonic generation from metallic nanoparticles
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In this article, we develop a classical electrodynamic theory to study the optical nonlinearities of metallic nanoparticles. The quasi-free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an external electromagnetic field is described by the plasma equations. This theory is further tailored to study second-harmonic generation. Through detailed experiment-theory comparisons, we validate this classical theory as well as the associated numerical algorithm. It is demonstrated that our theory not only provides qualitative agreement with experiments, it also reproduces the overall strength of the experimentally observed second-harmonic signals.
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Strong second-harmonic generation has recently been experimentally observed from metamaterials consisting of periodic arrays of metal split ring resonators with an effective negative magnetic permeability [Science, 313, 502 (2006)]. To explore the underlying physical mechanism, a classical model derived from microscopic theory is employed here. The quasi-free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an external electromagnetic field is described by the cold-plasma wave equations. Through numerical simulations, it is demonstrated that the microscopic theory includes the dominant physical mechanisms bothqualitatively and quantitatively.
The resonance effects on the optical second harmonic generation from 140 nm silver nanoparticles is studied experimentally by hyper-Rayleigh scattering and numerically by finite element method calculations. We find that the interferences between the broad dipolar and narrow octupolar surface plasmon resonances leads to nonlinear Fano profiles that can be externally controlled by the incident polarization angle. These profiles are responsible for the nonlinear plasmon-induced transparency in the second harmonic generation.
On the basis of the Edward-Kornfeld formulation, we study the effective susceptibility of secondharmonic generation (SHG) in colloidal crystals, which are made of graded metallodielectric nanoparticles with an intrinsic SHG susceptibility suspended in a host liquid. We find a large enhancement and redshift of SHG responses, which arises from the periodic structure, local field effects and gradation in the metallic cores. The optimization of the Ewald-Kornfeld formulation is also investigated.
The generation process of second harmonic (SH) radiation from holes periodically arranged on a metal surface is investigated. Three main modulating factors affecting the optical response are identified: the near-field distribution at the wavelength of the fundamental harmonic, how SH light couples to the diffraction orders of the lattice, and its propagation properties inside the holes. It is shown that light generated at the second harmonic can excite electromagnetic modes otherwise inaccessible in the linear regime under normal incidence illumination. It is demonstrated that the emission of SH radiation is only allowed along off-normal paths precisely due to that symmetry. Two different regimes are studied in the context of extraordinary optical transmission, where enhanced linear transmission either occurs through localized electromagnetic modes or is aided by surface plasmon polaritons (SPPs). While localized resonances in metallic hole arrays have been previously investigated, the role played by SPPs in SH generation has not been addressed so far. In general, good agreement is found between our calculations (based on the finite difference time domain method) and the experimental results on localized resonances, even though no free fitting parameters were used in describing the materials. It is found that SH emission is strongly modulated by enhanced fields at the fundamental wavelength (either localized or surface plasmon modes) on the glass metal interface. This is so in the transmission side but also in reflection, where emission can only be explained by an efficient tunneling of SH photons through the holes from the output to the input side. Finally, the existence of a dark SPP at the fundamental field is identified through a noninvasive method for the first time, by analyzing the efficiency and far-field pattern distribution in transmission at the second harmonic.
We study second harmonic generation in nonlinear, GaAs gratings. We find large enhancement of conversion efficiency when the pump field excites the guided mode resonances of the grating. Under these circumstances the spectrum near the pump wavelength displays sharp resonances characterized by dramatic enhancements of local fields and favorable conditions for second harmonic generation, even in regimes of strong linear absorption at the harmonic wavelength. In particular, in a GaAs grating pumped at 1064nm, we predict second harmonic conversion efficiencies approximately five orders of magnitude larger than conversion rates achievable in either bulk or etalon structures of the same material.
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