Third-harmonic generation in the presence of classical nonlocal effects in gap-plasmon nanostructures

Abstract

Classical nonlocality in conducting nanostructures has been shown to dramatically alter the linear optical response, by placing a fundamental limit on the maximum field enhancement that can be achieved. This limit directly extends to all nonlinear processes, which depend on field amplitudes. A numerical study of third-harmonic generation in metal film-coupled nanowires reveals that for sub-nanometer vacuum gaps the nonlocality may boost the effective nonlinearity by five orders of magnitude as the field penetrates deeper inside the metal than that predicted assuming a purely local electronic response. We also study the impact of a nonlinear dielectric placed in the gap region. In this case the effect of nonlocality could be masked by the third harmonic signal generated by the spacer. By etching the dielectric underneath the nanowire however it is possible to muffle such contribution. Calculations are performed for both silver and gold nanowire.

Role of electron tunneling in the nonlinear response of plasmonic nanogaps

“…We thus adopt the freeelectron jellium model 103 (JM) of metal. Similar to the hydrodynamic treatments 60,[90][91][92] , this approach does not capture excitations involving electrons from the localized bands, as e.g. d-band in case of noble metals.…”

“…At optical frequencies, the nonlinearity of the tunneling current was demonstrated using time-dependent density functional theory (TDDFT) calculations for the case of a plasmonic dimer formed by spherical nanoparticles 67,69 . Recently reported hydrodynamic methods demonstrate the impact of the non-local screening on the nonlinear response of individual nanoparticles 60,[90][91][92] , and a model study based on the theory of PAT addressed the effect of tunneling in the nonlinear response of the gap nanoantenna [93][94][95][96] . However, a parameter-free quantum approach that allows to elucidate the rich variety of effects in the nanogap plasmonic system and the contribution of the different mechanisms driving the optical frequency conversion has not been attempted so far.…”

Nonlinear Duffing oscillator model for third harmonic generation

“…In reality, just as the linear dielectric constant is affected by both free electrons and interband transitions from electrons in the valence band, SHG can also arise from both conduction and inner-core electrons [2], due to a combination of the mere presence of interfaces, the magnetic portion of the Lorentz force, to a lesser extent the interaction of third harmonic and pump photons (downconversion), and other effective nonlinearities induced by quantum tunneling mechanisms [3][4][5] if metal components are in close proximity. By the same token, the third-order nonlinearity, χ 3 , arising from bound charges generates most of the third harmonic signal, subject to screening due to a free-electron spill-out effect and other geometrical considerations [5,6]. To a much smaller degree the interaction of pump and second harmonic photons also produces cascaded THG.…”

Study of second and third harmonic generation from an indium tin oxide nanolayer: Influence of nonlocal effects and hot electrons

“…The crucial physical differences between noble metals and conducting oxides are that: (1) free electron densities of the former can be several orders of magnitude larger than the free electron densities of the latter. This leads to significant differences in field penetration and the excitation of surface and volume nonlinearities, and nonlocal effects [16]; (2) interband excitations, increased free carrier density and a dynamic blueshift of plasma frequency characterize noble metals; conducting oxides are prone to display intraband transitions and increased electron gas temperature that lead to increased effective electron mass and a dynamic redshift of the plasma frequency [17]. Compared to noble metals, these effects make conducting oxides intriguing for the experimental and theoretical study of nonlinear optical interactions.…”

“…For instance, it is known that nonlocal effects tend to blueshift the plasmonic resonance [14][15][16]. In contrast, absorption, which is in turn modified by nonlocal effects, can change the free electron effective mass, causing the plasma frequency to redshift [17]. Nonlocal effects and modulation of the plasma frequency are dynamic, time dependent factors that can strongly influence the propagation, and can easily combine to impress unique dynamical features on measurable quantities, such as spatial and temporal modulation of dielectric constant and refractive index.…”