Nonlinear Duffing oscillator model for third harmonic generation

Scalora, Michael; Vincenti, Maria Antonietta; Ceglia, Domenico de; Cojocaru, C.; Grande, M.; Haus, Joseph W.

doi:10.1364/josab.32.002129

Cited by 33 publications

(41 citation statements)

References 31 publications

(59 reference statements)

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“…In contrast, for RTL incidence, Fig. 6(b), the gold shields the ITO to the extent that the intensity inside the ITO is nearly one order of magnitude smaller compared to LTR incidence, shifting maxima closer to 70⁰, thus limiting conversion efficiencies with little or no influence from the ITO and mimicking a metal-only response [49].…”

Section: Ito/gold Bilayermentioning

confidence: 98%

“…Therefore, the bulk metal nonlinearity becomes more consequential for THG because the fields penetrate into both layers. The conversion efficiency profiles are thus strongly impacted by the direction of approach, and are more metal-like for the RTL direction of incidence [49]. Worthy of note are the THG minima that occur for both transmitted and reflected components near a 20⁰ angle of incidence for LTR incidence, at the ENZ condition of ITO, which also appears for the ITO layer without gold backing.…”

Section: Ito/gold Bilayermentioning

confidence: 99%

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Harmonic generation from metal-oxide and metal-metal boundaries

et al. 2018

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We explore the outcomes of detailed microscopic models by calculating second-and thirdharmonic generation from thin film surfaces with discontinuous free-electron densities. These circumstances can occur in structures consisting of a simple metal mirror, or arrangements composed of either different metals or a metal and a free electron system like a conducting oxide.Using a hydrodynamic approach we highlight the case of a gold mirror, and that of a two-layer system containing indium tin oxide (ITO) and gold. We assume the gold mirror surface is characterized by a free-electron cloud of varying density that spills into the vacuum, which as a result of material dispersion exhibits epsilon-near-zero conditions and local field enhancement at the surface. For a bilayer consisting of a thin ITO and gold film, if the wave is incident from the ITO side the electromagnetic field is presented with a free-electron discontinuity at the ITO/gold interface, and wavelength-dependent, epsilon-near-zero conditions that enhance local fields and conversion efficiencies, and determine the surface's emission properties. We evaluate the relative significance of additional nonlinear sources that arise when a free-electron discontinuity is present, and show that harmonic generation can be sensitive to the density of the screening free-electron cloud, and not its thickness. Our findings also suggest the possibility to control surface harmonic generation through surface charge engineering.

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Section: Ito/gold Bilayermentioning

confidence: 98%

Section: Ito/gold Bilayermentioning

confidence: 99%

Harmonic generation from metal-oxide and metal-metal boundaries

et al. 2018

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“…We have carried out detailed numerical simulations of these phenomena using the approach outlined in [9][10][11]. The method employs a NL Lorentz oscillator model that naturally captures both linear and NL material dispersions, while simultaneously accounting for surface and magnetic nonlinearities.…”

Section: Modelmentioning

confidence: 99%

“…1 below), each describing a set of bound charges. Newton's second law for one such species of bound electrons leads to the following effective polarization equation [9][10][11][12]:…”

Section: Modelmentioning

confidence: 99%

Harmonic generation in the opaque region of GaAs: the role of the surface and magnetic nonlinearities

Rodríguez-Suné¹,

Trull²,

Scalora³

et al. 2019

Opt. Express

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Phase-locked second and third harmonic generation in the opaque region of a GaAs wafer is experimentally observed and analyzed both in transmission and reflection. These harmonic components, which are generated close to the surface, can propagate through an opaque material as long as the pump is tuned to a region of transparency or semitransparency and correspond to the inhomogeneous solutions of Maxwell's equations with nonlinear polarization sources. We show that measurement of the angular and polarization dependence of the observed harmonic components allows one to infer the different nonlinear mechanisms that trigger these processes, including not only the bulk nonlinearity but also the surface and magnetic Lorentz contributions, which usually are either hidden by the bulk contributions or assumed to be negligible. The experimental results are compared with a detailed numerical model that takes into account these different effects, including for the first time combined linear and nonlinear material dispersions in a nonlinear Lorentz oscillator model of the bulk nonlinearities. Our results suggest that the intensity of the second harmonic signal generated by the surface can be more intense than the signal generated by the bulk. These findings have significant repercussions and are consequential in nanoscale systems, which are usually investigated using only dispersionless bulk nonlinearities, with near-complete disregard of surface and magnetic contributions and their microscopic origins.

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“…The oscillators (dipoles) generally experience linear and nonlinear internal restoring forces, damping, and external forces in the form of the applied electromagnetic field that couples the equations. In turn, the fields are expanded near the surface, where they vary rapidly, yielding hydrodynamic-like equations [17,18] that contain the spatial derivatives of the electric field (or polarizations) that drive most of the second harmonic signal generated at the surface: 2 2 1 1 1 1 01 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 02 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2…”

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confidence: 99%

Resonant, broadband, and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths

et al. 2019

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Using a hydrodynamic approach we examine bulk-and surface-induced second and third harmonic generation from semiconductor nanowire gratings having a resonant nonlinearity in the absorption region. We demonstrate resonant, broadband and highly efficient optical frequency conversion: contrary to conventional wisdom, we show that harmonic generation can take full advantage of resonant nonlinearities in a spectral range where nonlinear optical coefficients are boosted well beyond what is achievable in the transparent, long-wavelength, nonresonant regime. Using femtosecond pulses with approximately 500 MW/cm 2 peak power density, we predict third harmonic conversion efficiencies of approximately 1% in a silicon nanowire array, at nearly any desired UV or visible wavelength, including the range of negative dielectric constant.We also predict surface second harmonic conversion efficiencies of order 0.01%, depending on the electronic effective mass, bistable behavior of the signals as a result of a reshaped resonance, and the onset fifth order nonlinear effects. These remarkable findings, arising from the combined effects of nonlinear resonance dispersion, field localization, and phase-locking, could significantly extend the operational spectral bandwidth of silicon photonics, and strongly suggest that neither linear absorption nor skin depth should be motivating factors to exclude either semiconductors or metals from the list of useful or practical nonlinear materials in any spectral range.The advent of metamaterials and the search for efficient nonlinear frequency converters have mediated the growth of theoretical and experimental studies of second and third harmonic generation (SHG and THG) from all types of metallic, semiconductor, and all-dielectric

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Nonlinear Duffing oscillator model for third harmonic generation

Cited by 33 publications

References 31 publications

Harmonic generation from metal-oxide and metal-metal boundaries

Harmonic generation from metal-oxide and metal-metal boundaries

Harmonic generation in the opaque region of GaAs: the role of the surface and magnetic nonlinearities

Resonant, broadband, and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths

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