Nonlinear Plasmonics Research Articles

Quasi-phase matching for efficient long-range plasmonic third-harmonic generation via graphene.

We propose and numerically investigate an efficient method for long-range third-harmonic generation (THG) of propagating surface plasmon polaritons (SPP) waves on graphene sheets for nonlinear plasmonic purposes in the terahertz (THZ) gap region of the electromagnetic spectrum via a developed nonlinear finite-difference time-domain technique. We reveal that although extended and unmodulated graphene sheets with low Fermi levels can offer high-conversion efficiency (CE) for SPP THG at short distances, suitable for miniaturized plasmonic circuits, they suffer from inherent absorption loss induced by graphene that noticeably reduces the CE of the THG at long ranges. We suggest a structure benefiting from low Fermi-level graphene regions of strong nonlinear response as oscillators and high Fermi-level ones of low loss as a propagating medium in a periodic manner, which satisfies the quasi-phase matching condition and shows considerable efficiency improvement at long propagation distances. We predict that such a configuration can find valuable potential applications in the realm of nonlinear THz plasmonics for generating new frequencies and also in spectroscopy, signal processing, and so on.

Optical bistability induced by nonlinear surface plasmon polaritons in graphene in terahertz regime

We demonstrate optical bistability in a prism-air-graphene-dielectric structure. Under a moderate electric field in the terahertz frequency regime, the third order nonlinear optical conductivity is comparable to the linear conductivity. The nonlinear conductivity enhances the energy of surface plasmon polaritons. Both the energy and frequency of the surface plasmon polaritons depend on the strength of the nonlinear current in the graphene layer. When considering excitation in the Kretschmann configuration, the reflectance as a function of frequency exhibits bistability. The origin of the bistability is the field dependence of the plasmon mode. We have determined the parameter regime for the occurrence of bistability in this structure.

Nonlinear Cavity and Frequency Comb Radiations Induced by Negative Frequency Field Effects.

Optical Kerr frequency combs (KFCs) are an increasingly important optical metrology tool with applications ranging from ultraprecise spectroscopy to time keeping. KFCs may be generated in compact resonators with extremely high quality factors. Here, we show that the same features that lead to high quality frequency combs in these resonators also lead to an enhancement of nonlinear emissions that may be identified as originating from the presence of a negative frequency (NF) component in the optical spectrum. While the negative frequency component of the spectrum is naturally always present in the real-valued optical field, it is not included in the principal theoretical model used to model nonlinear cavities, i.e., the Lugiato-Lefever equation. We therefore extend these equations in order to include the contribution of NF components and show that the predicted emissions may be studied analytically, in excellent agreement with full numerical simulations. These results are of importance for a variety of fields, such as Bose-Einstein condensates, mode-locked lasers, nonlinear plasmonics, and polaritonics.

Optical meta-atom for localization of light with quantized energy.

The capacity to confine light into a small region of space is of paramount importance in many areas of modern science. Here we suggest a mechanism to store a quantized ‘bit' of light—with a very precise amount of energy—in an open core-shell plasmonic structure (‘meta-atom') with a nonlinear optical response. Notwithstanding the trapped light state is embedded in the radiation continuum, its lifetime is not limited by the radiation loss. Interestingly, it is shown that the interplay between the nonlinear response and volume plasmons enables breaking fundamental reciprocity restrictions, and coupling very efficiently an external light source to the meta-atom. The collision of an incident optical pulse with the meta-atom may be used to release the trapped light ‘bit'.

Optical Second Harmonic Generation in Plasmonic Nanostructures: From Fundamental Principles to Advanced Applications.

Plasmonics has emerged as an important research field in nanoscience and nanotechnology. Recently, significant attention has been devoted to the observation and the understanding of nonlinear optical processes in plasmonic nanostructures, giving rise to the new research field called nonlinear plasmonics. This review provides a comprehensive insight into the physical mechanisms of one of these nonlinear optical processes, namely, second harmonic generation (SHG), with an emphasis on the main differences with the linear response of plasmonic nanostructures. The main applications, ranging from the nonlinear optical characterization of nanostructure shapes to the optimization of laser beams at the nanoscale, are summarized and discussed. Future directions and developments, made possible by the unique combination of SHG surface sensitivity and field enhancements associated with surface plasmon resonances, are also addressed.

Nonlinear magneto-plasmonics

Nonlinear magneto-plasmonics (NMP) describes systems where nonlinear optics, magnetics and plasmonics are all involved. In such systems, nonlinear magneto-optical Kerr effect (nonlinear MOKE) plays an important role as a characterization method, and Surface Plasmons (SPs) work as catalyst to induce many new effects. Magnetization-induced second-harmonic generation (MSHG) is the major nonlinear magneto-optical process involved. The new effects include enhanced MSHG, controlled and enhanced magnetic contrast, etc. Nanostructures such as thin films, nanoparticles, nanogratings, and nanoarrays are critical for the excitation of SPs, which makes NMP an interdisciplinary research field in nanoscience and nanotechnology. In this review article, we organize recent work in this field into two categories: surface plasmon polaritons (SPPs) representing propagating surface plasmons, and localized surface plasmons (LSPs), also called particle plasmons. We review the structures, experiments, findings, and the applications of NMP from various groups.

Nanoscale Imaging of Local Few-Femtosecond Near-Field Dynamics within a Single Plasmonic Nanoantenna.

The local enhancement of few-cycle laser pulses by plasmonic nanostructures opens up for spatiotemporal control of optical interactions on a nanometer and few-femtosecond scale. However, spatially resolved characterization of few-cycle plasmon dynamics poses a major challenge due to the extreme length and time scales involved. In this Letter, we experimentally demonstrate local variations in the dynamics during the few strongest cycles of plasmon-enhanced fields within individual rice-shaped silver nanoparticles. This was done using 5.5 fs laser pulses in an interferometric time-resolved photoemission electron microscopy setup. The experiments are supported by finite-difference time-domain simulations of similar silver structures. The observed differences in the field dynamics across a single particle do not reflect differences in plasmon resonance frequency or dephasing time. They instead arise from a combination of retardation effects and the coherent superposition between multiple plasmon modes of the particle, inherent to a few-cycle pulse excitation. The ability to detect and predict local variations in the few-femtosecond time evolution of multimode coherent plasmon excitations in rationally synthesized nanoparticles can be used in the tailoring of nanostructures for ultrafast and nonlinear plasmonics.

Curved Gratings as Plasmonic Lenses for Linearly Polarised Light

The ability of curved gratings as sectors of concentric circular gratings to couple linearly polarised light into focused surface plasmons is investigated by theory, simulation, and experiment. The experimental and simulation results show that increasing the sector angle of the curved gratings decreases the width of the lateral distribution of surface plasmons resulting in focusing of surface plasmons, which is analogous to the behaviour of classical optical lenses. We also show that two faced curved gratings, with their groove radius mismatched by half of the plasmon wavelength (asymmetric configuration), can couple linearly polarised light into a single focal spot of concentrated surface plasmons with smaller depth of focus and higher intensity in comparison to single curved gratings. The major advantage of these structures is the coupling of linearly polarised light into focused surface plasmons with access to, and control of, the plasmon focal spot, which facilitate their potential applications in sensing, detection, and nonlinear plasmonics.

Nonlinear effective behavior of a dispersion of randomly oriented coated ellipsoids with arbitrary temporal dispersion

This work deals with the determination of the linear and nonlinear effective properties of an heterogeneous material composed of a dispersion of coated ellipsoidal particles (core–shell structure). The particles are considered randomly oriented and positioned within the matrix. Moreover, all constitutive equations (matrix, cores, shells) exhibit an hereditary behavior, leading to an arbitrary temporal dispersion. While matrix and shell are considered linear, the particles core shows an additional third-order nonlinearity. We develop an effective medium theory, which allows us to calculate the linear and nonlinear response in terms of the microstructure features. In particular, we can investigate the effects of the inter-phase on the overall behavior, in combination with the randomness of the orientations and with the linear and nonlinear hereditary phenomena. The results may find relevant applications in material science and, more specifically, in nonlinear optics, bulk plasmonics and metamaterials.

Unidirectional All-Optical Absorption Switch Based on Optical Tamm State in Nonlinear Plasmonic Waveguide

We demonstrate that unidirectional absorption can be achieved and efficiently tuned in an asymmetrical and nonlinear metal-dielectric-metal plasmonic waveguide by inserting a one-dimensional photonic crystal and a metal layer into the waveguide core. We show that optical Tamm state is excited when the surface impedance of the photonic crystal and that of the metallic layer match with each other. Owing to the strong field confinement induced by the optical Tamm state, high absorption of the surface plasmon can be achieved in the proposed waveguide. The geometric asymmetry of the considered system makes its absorption performance quite different for different incident directions, which is useful for the design of unidirectional plasmonic absorber. Furthermore, Fano resonance, originating from the quantum interference between the optical Tamm state and the traveling waveguide mode, occurs and can be tuned through the nonlinear optical effect. Based on the tunable Fano asymmetric line shape of the considered system, absorption contrast ratio up to 43.5 dB is achieved by varying the intensity of the pumping light, which can be used for all-optical Fano absorption switching. Our results may find potential applications in integrated optical circuits and photodetection.

Nonlinear organic plasmonics: Applications to optical control of Coulomb blocking in nanojunctions

Purely organic materials with negative and near-zero dielectric permittivity can be easily fabricated. Here, we develop a theory of nonlinear non-steady-state organic plasmonics with strong laser pulses that enable us to obtain near-zero dielectric permittivity during a short time. Our consideration is based on the model of the interaction of strong (phase modulated) laser pulse with organic molecules developed by one of the authors before, extended to the dipole-dipole intermolecular interactions in the condensed matter. We have proposed to use non-steady-state organic plasmonics for the enhancement of intersite dipolar energy-transfer interaction in the quantum dot wire that influences on electron transport through nanojunctions. Such interactions can compensate Coulomb repulsions for particular conditions. We propose the exciton control of Coulomb blocking in the quantum dot wire based on the non-steady-state near-zero dielectric permittivity of the organic host medium.

Giant colloidal silver crystals for low-loss linear and nonlinear plasmonics.

The development of ultrasmooth, macroscopic-sized silver (Ag) crystals exhibiting reduced losses is critical to fully characterize the ultimate performance of Ag as a plasmonic material, and to enable cascaded and integrated plasmonic devices. Here we demonstrate the growth of single-crystal Ag plates with millimetre lateral sizes for linear and nonlinear plasmonic applications. Using these Ag crystals, surface plasmon polariton propagation lengths beyond 100 μm in the red wavelength region are measured. These lengths exceed the predicted values using the widely cited Johnson and Christy data. Furthermore, they allow the fabrication of highly reproducible plasmonic nanostructures by focused ion beam milling. We have designed and fabricated double-resonant nanogroove arrays using these crystals for spatially uniform and spectrally tunable second-harmonic generation. In conventional ‘hot-spot'-based nonlinear processes such as surface-enhanced Raman scattering and second-harmonic generation, strong enhancement can only occur in random, localized regions. In contrast, our approach enables uniform nonlinear signal generation over a large area.

Effective wavelength scaling of rectangular aperture antennas.

We investigate the resonances of aperture antennas from the visible to the terahertz regime, with comparison to comprehensive simulations. Simple piecewise analytic behavior is found for the wavelength scaling over the entire spectrum, with a linear regime through the visible and near-IR. This theory will serve as a useful and simple design tool for applications including biosensors, nonlinear plasmonics and surface enhanced spectroscopies.

Determination of the polarization states of an arbitrary polarized terahertz beam: vectorial vortex analysis.

Vectorial vortex analysis is used to determine the polarization states of an arbitrarily polarized terahertz (0.1–1.6 THz) beam using THz achromatic axially symmetric wave (TAS) plates, which have a phase retardance of Δ = 163° and are made of polytetrafluorethylene. Polarized THz beams are converted into THz vectorial vortex beams with no spatial or wavelength dispersion, and the unknown polarization states of the incident THz beams are reconstructed. The polarization determination is also demonstrated at frequencies of 0.16 and 0.36 THz. The results obtained by solving the inverse source problem agree with the values used in the experiments. This vectorial vortex analysis enables a determination of the polarization states of the incident THz beam from the THz image. The polarization states of the beams are estimated after they pass through the TAS plates. The results validate this new approach to polarization detection for intense THz sources. It could find application in such cutting edge areas of physics as nonlinear THz photonics and plasmon excitation, because TAS plates not only instantaneously elucidate the polarization of an enclosed THz beam but can also passively control THz vectorial vortex beams.

Analytical Approach of the Nonlinear Surface Plasmon at a Left-Handed Material

The surface wave dispersion relations of surface Plasmon at the interface of a left-handed material and a non-linear Kerr medium of arbitrary nonlinearity are derived based on a generalized first integral approach. The normalized power flow is also investigated for various values of frequency. The above study is conducted for both cases: self-focusing (αp0) and de-focusing (αs0) nonlinear Kerr coefficient.

Electrically tunable nonlinear plasmonics in graphene nanoislands.

Nonlinear optical processes rely on the intrinsically weak interactions between photons enabled by their coupling with matter. Unfortunately, many applications in nonlinear optics are severely hindered by the small response of conventional materials. Metallic nanostructures partially alleviate this situation, as the large light enhancement associated with their localized plasmons amplifies their nonlinear response to record high levels. Graphene hosts long-lived, electrically tunable plasmons that also interact strongly with light. Here we show that the nonlinear polarizabilities of graphene nanoislands can be electrically tuned to surpass by several orders of magnitude those of metal nanoparticles of similar size. This extraordinary behaviour extends over the visible and near-infrared spectrum for islands consisting of hundreds of carbon atoms doped with moderate carrier densities. Our quantum-mechanical simulations of the plasmon-enhanced optical response of nanographene reveal this material as an ideal platform for the development of electrically tunable nonlinear optical nanodevices.

Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre.

Brillouin scattering in optical fibres is a fundamental interaction between light and sound with important implications ranging from optical sensors to slow and fast light. In usual optical fibres, light both excites and feels shear and longitudinal bulk elastic waves, giving rise to forward-guided acoustic wave Brillouin scattering and backward-stimulated Brillouin scattering. In a subwavelength-diameter optical fibre, the situation changes dramatically, as we here report with the first experimental observation of Brillouin light scattering from surface acoustic waves. These Rayleigh-type surface waves travel the wire surface at a specific velocity of 3,400 m s−1 and backscatter the light with a Doppler shift of about 6 GHz. As these acoustic resonances are sensitive to surface defects or features, surface acoustic wave Brillouin scattering opens new opportunities for various sensing applications, but also in other domains such as microwave photonics and nonlinear plasmonics.

Point spread function analysis with saturable and reverse saturable scattering.

Nonlinear plasmonics has attracted a lot of interests due to its wide applications. Recently, we demonstrated saturation and reverse saturation of scattering from a single plasmonic nanoparticle, which exhibits extremely narrow side lobes and central peaks in scattering images [ACS Photonics 1(1), 32 (2014)]. It is desirable to extract the reversed saturated part to further enhance optical resolution. However, such separation is not possible with conventional confocal microscope. Here we combine reverse saturable scattering and saturated excitation (SAX) microscopy. With quantitative analyses of amplitude and phase of SAX signals, unexpectedly high-order nonlinearities are revealed. Our result provides greatly reduced width in point spread function of scattering-based optical microscopy. It will find applications in not only nonlinear material analysis, but also high-resolution biomedical microscopy.

Manipulating the Optical Bistability in a Nonlinear Plasmonic Nanoantenna Array with a Reflecting Surface

The influence of a reflecting surface on the optical bistability in a nanoantenna array is investigated theoretically. The optical response of the array is modeled using a surface integral equation method developed for periodic structures, and the description of the Kerr effect is based on an analytical model. Different behaviors are observed when the distance between the nanoantenna array and the silver layer is changed. Indeed, a modification of the nanoantennas radiative properties permit to control important parameters of the nonlinear response such as the intensity threshold and the area of the hysteresis cycle. The results presented in this article demonstrate that a reflecting surface is a convenient and flexible tool for controlling the operating of nonlinear optical systems based on the Kerr effect.

Amplification of surface plasmon polaritons in nonlinear medium with full saturation susceptibility model

In this paper, a numerical analysis to model the amplification of nonlinear surface plasmon polaritons (SPPs) propagating along a metal active dielectric interface is presented. Nonlinearity of the medium with gain is considered through the full saturation susceptibility parameter of a two-level model. Above the linear threshold of the gain and loss balance, the nonlinear performance of the amplified SPPs is verified, which agrees well with the experimental results reported in the literature. An important feature of the proposed method is to predict an abrupt increase in output intensity due to amplified spontaneous emission.