Nonlinear Plasmonics Research Articles

Dissimilar permittivity and permeability sensitivities in nonlinear plasmons and spoof plasmons.

We show that employing localized surface plasmon resonators to probe environmental media will always lead to dissimilar optical sensitivities to permittivity and permeability. We find that while the permittivity sensitivities of diverse plasmonic structures display a geometry-independent universal scaling relation, the permeability sensitivities are highly dependent on the metals' geometries and resonant modes. Similar results are also found in mixed real/spoof localized surface plasmon resonators, and the phenomena can be universally scaled to the normalized effective plasmon frequencies. Importantly, the results put a fundamental constraint for all plasmonic-assisted nonlinear magneto-optical phenomena, including the Faraday effect, magneto-optical Kerr effect, and Cotton-Mouton effect.

Nonlinear TE-Polarized Surface Plasmons at the Interface between Graphene and Metamaterials

Nonlinear TE-polarized surface plasmons localized at the interface between graphene and metamaterials are investigated analytically. The normalized momentum of graphene surface plasmons at the interface between graphene and metamaterials composed of arrays of wires and split-ring resonators (SRR) embedded into a nonlinear dielectric exhibits bistable behavior with the magnetic field intensity. The effect is explained by the hysteresis-type dependence of the nonlinear permeability of metamaterials on the field intensity.

Plasmon-enhanced four-wave mixing by nanoholes in thin gold films

Nonlinear plasmonics opens up for wavelength conversion, reduced interaction/emission volumes, and nonlinear enhancement effects at the nanoscale with many compelling nanophotonic applications foreseen. We investigate nonlinear plasmonic responses of nanoholes in thin gold films by exciting the holes individually with tightly focused laser beams, employing a degenerated pump/probe and Stokes excitation scheme. Excitation of the holes results in efficient generation of both narrowband four-wave mixing (FWM) and broadband multiphoton excited luminescence, blueshifted relative to the excitation beams. Clear enhancements were observed when matching the pump/probe wavelength with the hole plasmon resonance. These observations show that the FWM generation is locally excited by nanoholes and has a resonant behavior primarily governed by the dimensions of the individual holes.

Emergence of a nonlinear plasmon in the electronic response of doped graphene

The electronic response of self-doped graphene supported on metal substrates shows two well-distinct plasmon modes: the acoustic plasmon, characterized by a linear dispersion, and a nonlinear plasmon. The nonlinear plasmon originates from the anisotropy of the electron bands of graphene around the K point. The existence of two plasmons with a different dispersion relation demonstrates that charge carriers with different group velocity may coexist within the same band in epitaxial graphene.

Investigation on the electron dynamics of periodic nano ripple formation on fused silica induced by temporally shaped femtosecond laser

We investigate the electron dynamic process of periodic nano ripples formation on fused silica induced by temporally shaped femtosecond laser. The dynamic model for predictions of ripple period is proposed by introducing the mechanisms of non-linear ionization and surface plasmon polaritons (SPPs) interaction. The quantitative relation between nano ripple period and temporally shaped pulse separation is obtained by using the proposed model. It is revealed that the nano ripple period can be manipulated by adjusting the temporal intervals of the temporally shaped pulses due to the transient adjustment of the wavevector matching process during ripple formation via temporally shaped pulses. The theoretical predictions of the ripple period match well with the experimental data. This study provides the fundamental understanding of transient formation mechanism of ripples, and the precise manipulating of ripple period.

Dissipative plasmon‐solitons in multilayer graphene

AbstractNonlinear properties of a multi‐layer stack of graphene sheets are studied. It is predicted that such a structure may support dissipative plasmon‐solitons generated and supported by an external laser radiation. Novel nonlinear equations describing spatial dynamics of the nonlinear plasmons driven by a plane wave in the Otto configuration are derived and the existence of single and multi‐hump dissipative solitons in the graphene structure is predicted.

Dispersion characteristics of surface plasmon polariton modes in a metallic slab waveguide with nonlinear magnetic cladding

We investigate the propagation characteristics of surface plasmon polaritons along a slab waveguide with a nonlinear magnetic cladding characterized by permeability μ =μl+μnlH2 and a linear substrate. The dispersion relation for the surface plasmon polariton modes supported by the structure was derived and numerically solved. The dependance of mode behavior on input power was studied. As the input power increases, the propagation constant of the modes increases. The effect of self focussed peak on the mode confinement near the interface and the resulting propagation characteristics of the plasmon modes were investigated. Increase in metal film thickness lifts the degeneracy of nonlinear plasmon modes supported by the waveguide. It has been observed that the propagation length is not a single valued function of input power which is crucial in understanding optical nano-switches.

Surfaces, films, and multilayers for compact nonlinear plasmonics

We present a step-by-step analysis of four-wave mixing (FWM) in one-dimensional stacks of metallo-dielectric structures, pointing out various channels of plasmonic and Fabry–Perot enhancement. We start from the derivation of oblique incidence FWM at a single interface and then extend these expressions into a transfer-matrix-based formalism to quantitatively study films and multilayer geometries. Throughout our analysis, we consider typical examples, such as a single silver interface, a thin silver film, and Fabry–Perot multilayers. In this way, we offer an intuitive view of the surprisingly rich dynamics supported by even the simplest of nonlinear plasmonic systems.

Universal aspects of localized excitations in graphene

Unique features of nonlinear solitary plasmon excitations in two and three dimensional massless Dirac fluids, with respect to their normal Fermi counterparts, are explored using the Bernoulli pseudopotential method. It is revealed that graphene, as a two dimensional Dirac fluid, possesses some unique characteristics with respect to the propagation of the localized plasmon excitations, which is absent in other ordinary solids. It is also shown that the Mach number limit below/above, which the localized solitary/periodic excitations propagate in a monolayer graphene has a universal value independent of the other environmental parameters such as the electron number-density and the ambient temperature. The amplitude of nonlinear solitary or periodic waves is also remarked to be independent of such parameters and depend only on the Mach-number value of the solitary or periodic excitations. These unique hydrodynamic wave features of the massless Dirac fluid are attributed to the remarkable photon-like linear energy dispersion in Dirac points of graphene material.

Thermal transport and quench relaxation in nonlinear Luttinger liquids

One-dimensional electrons with a linearized dispersion relation are equivalent to a collection of harmonic plasmon modes, which represent long wavelength density oscillations. An immediate consequence of this Luttinger model of one-dimensional electron systems is the absence of inelastic scattering processes responsible for the relaxation of nonequilibrium states. In a generic nonlinear Luttinger liquid plasmons may decay and thus acquire a finite lifetime. We show that equilibration of plasmons is hierarchical and has profound implications for the dynamics after a thermal quench. We also develop a thermal transport theory and compute thermal conductance of the nonlinear Luttinger liquid by treating the collision integral of plasmons in a manifestly nonperturbative way.

Unified hydrodynamic approach to laser field plasmon excitations in metal nanoparticles with general shape

We present a unified hydroelectrodynamical approach to study electron dynamics in a laser field in cold metal nanoparticles with a general nonspherical surface. This is the generalization to complex shapes of the model used earlier to study both linear and nonlinear plasmon excitations in thin metal films and spherical nanoparticles. Along with a general formulation allowing a direct nonlinear extension of the model for nanoparticles with nonspherical shapes, the linear plasmon excitations in metal cubic and rectangular parallelepiped nanoparticles are calculated as an example of using the hydrodynamic model in a cold charge-compensated electron plasma approximation. The results obtained for the cubic and parallelepipedlike nanoparticles are analyzed and compared with the ones of earlier approaches such as the discrete dipole approximation.

Enhanced Second Harmonic Generation by Photonic–Plasmonic Fano-Type Coupling in Nanoplasmonic Arrays

In this communication, we systematically investigate the effects of Fano-type coupling between long-range photonic resonances and localized surface plasmons on the second harmonic generation from periodic arrays of Au nanoparticles arranged in monomer and dimer geometries. Specifically, by scanning the wavelength of an ultrafast tunable pump laser over a large range, we measure the second harmonic excitation spectra of these arrays and demonstrate their tunability with particle size and separation. Moreover, through a comparison with linear optical transmission spectra, which feature asymmetric Fano-type lineshapes, we demonstrate that the second harmonic generation is enhanced when coupled photonic-plasmonic resonances of the arrays are excited at the fundamental pump wavelength, thus boosting the intensity of the electromagnetic near-fields. Our experimental results, which are supported by numerical simulations of linear optical transmission and near-field enhancement spectra based on the Finite Difference Time Domain method, demonstrate a direct correlation between the onset of Fano-type coupling and the enhancement of second harmonic generation in arrays of Au nanoparticles. Our findings enable the engineering of the nonlinear optical response of Fano-type coupled nanoparticle arrays that are relevant to a number of device applications in nonlinear nano-optics and plasmonics, such as on-chip frequency generators, modulators, switchers, and sensors.

Nonlinear Plasmonics: Four-photon Near-field Photolithography using Optical Antennas

Recent experiments on four-photon nonlinear exposure of photoresist near nanoplasmonic structures raise a question: What nonlinear processes are responsible for the observed profile? Here, we study the nonlinear exposure of poly(methyl methacrylate) (PMMA) in the near-field of gold nanoantennas. We consider six possible nonlinear processes and study them in terms of the developed volumes and the exposure profiles in photoresist. We find that the direct fourth harmonic generation (4HG) in gold is the dominant nonlinear process. The developed volume from 4HG and the exposure profiles both match closely with the experiments. The next strongest process is direct four-photon absorption (4PA) in PMMA. The strength of 4PA process is about one order of magnitude weaker than 4HG. The developed volume and exposure profiles predicted from 4PA process clearly deviate from experiments.

Nonlinear graphene plasmonics: Amplitude equation for surface plasmons

Using perturbation expansion of Maxwell equations, the amplitude equation is derived for nonlinear TM and TE surface plasmon waves supported by graphene. The equation describes interplay between in-plane beam diffraction and nonlinerity due to light intensity induced corrections to graphene conductivity and susceptibility of dielectrics. For strongly localized TM plasmons, graphene is found to bring the superior contribution to the overall nonlinearity. In contrast, nonlinear response of the substrate and cladding dielectrics can become dominant for weakly localized TE plasmons.

Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with J-aggregates

Researchers observe Rabi oscillations in a metal structure with a J-aggregate nonlinear medium and coherent energy transfer between excitonic quantum emitters and surface plasmons. The coupling energy is controlled on the 10 fs timescale by varying the exciton density. This work demonstrates the potential of nonlinear ultrafast plasmonics.

Nonlinear hybrid plasmonic slot waveguide for second-harmonic generation

A nonlinear hybrid plasmonic slot waveguide composed of periodically poled lithium niobate (PPLN) and two separated silver films is investigated. The effective refractive index, propagation length, and energy confinement of the hybrid anti-symmetric mode in this waveguide are calculated using the structure parameters at the fundamental wavelength of \lambda=1550 nm and its second harmonic (SH) \lambda= 775 nm. Through the above indices, coupling efficiency (maximum SH conversion efficiency during propagation) and peak position (propagation location of the conversion efficiency) of SH generation are analyzed. Finally, higher conversion efficiency can be achieved at a shorter propagation distance by changing the waveguide into a tapered structure.

Coexistence of plasmonic and magnetic properties in Au89Fe11 nanoalloys

We describe an environmentally friendly, top-down approach to the synthesis of Au89Fe11 nanoparticles (NPs). The plasmonic response of the gold moiety and the magnetism of the iron moiety coexist in the Au89Fe11 nanoalloy with strong modification compared to single element NPs, revealing a non-linear surface plasmon resonance dependence on the iron fraction and a transition from paramagnetic to a spin-glass state at low temperature. These nanoalloys are accessible to conjugation with thiolated molecules and they are promising contrast agents for magnetic resonance imaging.

Plasmon hybridization in stacked metallic nanocups

We investigate hybridized electric and magnetic plasmon modes in stacked nanocups. To elucidate the coupling mechanism we demonstrate the analogy between split-ring-resonators and nanocups in the case of dipolar excitation and compare the behavior of stacked nanocups to stacked split-ring-resonators. The interplay of electric coupling with the symmetric and antisymmetric coupling of magnetic moments in effective split-ring-resonator resonances in the nanocups leads to experimentally observed hybridized modes in the coupled nanocup system. Our stacked nanocups are easily manufacturable at low cost, they cover a large-area, and can serve as SERS or SEIRA substrates. They might also serve as novel plasmonic nanoantennas, as templates for nonlinear plasmonics, and as stacked meander surfaces for metamaterial-assisted imaging.

Excitation of a nanowire “molecule” in gold-filled photonic crystal fiber

A pair of gold nanowires, incorporated into a photonic crystal fiber, acts as a plasmonic "molecule." Hybridized modes are excited at specific wavelengths by launching light into the glass core. The formation of bonding and antibonding solutions results in a modal splitting of more than 100 nm, even though the spatial separation between the wires is larger than 3 μm. The study provides insight into multiwire plasmonic devices with applications as polarizers or filters in near-field optics, nonlinear plasmonics, optical sensing, and telecommunications.

Nonlinear spoof surface plasmon polariton phenomena based on conductor metamaterials

We present nonlinear phenomena produced from spoof surface plasmon polariton (SSPP) modes. Below the THz spectrum, artificially textured conducting metastructures on a subwavelength scale generate surface-bound modes and are called SSPP modes, similar to surface plasmon polariton (SPP) modes in the visible spectrum. Even though nonlinear effects in the THz domain are negligible, subwavelength metallic gap structures are ideal candidates to realize nonlinear behavior in the THz domain because of slow light propagation, strong electromagnetic confinement, and a high quality factor Q. In particular, when SSPP structures are combined with Kerr nonlinear materials, nonlinear-bistable curves can be observed below the THz spectrum.