A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures

In this paper, we develop a nested hybridizable discontinuous Galerkin (HDG) method to numerically solve the Maxwell's equations coupled with the hydrodynamic model for the conduction-band electrons in metals. By means of a static condensation to eliminate the degrees of freedom of the approximate solution defined in the elements, the HDG method yields a linear system in terms of the degrees of freedom of the approximate trace defined on the element boundaries. Furthermore, we propose to reorder these degrees of freedom so that the linear system accommodates a second static condensation to eliminate a large portion of the degrees of freedom of the approximate trace, thereby yielding a much smaller linear system. For the particular metallic structures considered in this paper, the resulting linear system obtained by means of nested static condensations is a block tridiagonal system, which can be solved efficiently. We apply the nested HDG method to compute the second harmonic generation (SHG) on a triangular coaxial periodic nanogap structure. This nonlinear optics phenomenon features rapid field variations and extreme boundary-layer structures that span multiple length scales. Numerical results show that the ability to identify structures which exhibit resonances at $\omega$ and $2\omega$ is paramount to excite the second harmonic response.Comment: 31 pages, 7 figure

Nanophotonics: Optical time reversal with graphene

Would you ever guess that a microscopic flake of graphite could reverse the diffraction of light? An experiment that demonstrates just such an effect highlights the exciting optical applications of graphene — an atomic layer of carbon with a two-dimensional honeycomb lattice

Going beyond Axisymmetry: 2.5D Vector Electromagnetics

Linear wave propagation through inhomogeneous structures of size R≫λ (Fig.1) is a computationally challenging problem, in particular when using finite element methods, due to the steep increase of the number of degrees of freedom as a function of R/λ. Fortunately, when the geometry of the problem possesses symmetries, one may choose an appropriate basis in which the stiffness matrix of the discretized problem is block-diagonal. A particular scenario is the case of a cylindrically-symmetric geometry, where an appropriate basis is the set of cylindrical waves with all possible azimuthal numbers (m). Each of the excited cylindrical harmonics propagate through the structure independently of all other harmonics, and therefore the fields associated with that harmonic can be found by solving an essentially two-dimensional PDE problem in the ρ-z (half)-plane. The cylindrical waves have a prescribed dependence on the azimuthal angle variable (φ), hence the name – 2.5D electromagnetics. This novel approach is applied to the problem of cloaking and wave scattering off a spherical nanoparticle on metallic and/or dielectric substrates.COMSOL, Inc

Nonlocality in metallo-dielectric multilayers: numerical tools and physical analysis

We provide theoretical and numerical tools to quantitatively study the impact of nonlocality arising from free electrons in metals on the optical properties of metallo-dielectric multilayers. Though effects due to nonlocality are in general quite small, they nevertheless can be important for very thin (typically below 10 nm) metallic layers - as are used in structures characterized by relatively flat dispersion curves. Such structures include those with negative refractive index; hyperbolic meta-materials; and materials with index near zero. We find in all cases that the inclusion of nonlocal effects through application of the hydrodynamic model to the electron response leads to a higher transmission through the considered medium. Finally, we examine the excitation of gap-plasmon resonances, where nonlocality plays a much greater role, and suggest possible routes for experimental investigation

Theory of backward second-harmonic localization in nonlinear left-handed media

Recent research on photonic crystals possessing a quadratic nonlinear response has revealed a second-harmonic light localization phenomenon that originates from an all-angle phase matching between counterpropagating Bloch modes at the fundamental and double frequencies [E. Centeno , Phys. Rev. Lett. 98, 263903 (2007)]. In this paper, we develop an electromagnetic theory describing the nature of this parametric light localization, which appears in properly design metamaterials or photonic crystals exhibiting nonlinear left-handed behaviors. We demonstrate that interferences between converging phase-matched and diverging anti-phase-matched waves create a localized second-harmonic wave focused on the pump emitter on the scale of half the wavelength. This light trapping is accompanied by the enhancement of the second-harmonic intensity, which linearly increases with the size of the two-dimensional domain. We finally show that the second-harmonic localization effect previously proposed for GaN photonic crystals can also be obtained with LiNbO3 material

Etude de la génération de second harmonique dans des matériaux non-linéaires nano-structurés

Au cours de ces 20 dernières années, une attention particulièrement soutenue a été donnée à l'étude et à la fabrication de matériaux nano-structurés permettant le contrôle de la lumière. Cependant, les propriétés de non-linéarité optique de ces nouveaux matériaux n'ont que très peu été explorées. Partant de ce constat, cette thèse se propose de pourvoir cette insuffisance. L'accent est mis en particulier sur le processus de génération de seconde harmonique à travers deux aspects fondamentaux: (i) le contrôle de l'émission de seconde harmonique pour des matériaux nano-structurés non-linéaires et (ii) l'augmentation de conversion dans des dispositifs photoniques intégrés. Nous présentons un nouveau phénomène de localisation non-linéaire qui a lieu dans des matériaux main-gauche et qui implique un accord de phase isotrope. Nous démontrons analytiquement le processus de localisation dans un milieu homogène main-gauche, avant de mettre en évidence un tel effet dans des cristaux photoniques non-linéaires à l'aide de simulations numériques. L'effet de localisation contra-propagative du second harmonique est utilisé pour le design d'une lentille de second-harmonique. Ce résultat théorique a été démontré numériquement pour une structure réalisable fonctionnant aux fréquences optiques. L'augmentation de génération de seconde harmonique constitue l'aspect complémentaire. En tirant parti de la forte localisation de lumière dans une chaîne de nano-tiges de dimension finie, nous montrons que, pris ensemble, le confinement transverse sub-longueur d'onde et la condition de résonance d'accord de phase contribuent de manière importante à l'augmentation de la génération de seconde harmonique. Les capacités de guidage sub-longueur d'onde de chaînes de nano-tiges sont mis en évidence en examinant leurs propriétés de propagation linéaire. Pour finir, nous nous penchons sur la condition d'accord de phase assurant l'interaction non-linéaire optimale.The past twenty years have been exceptionally rich on the study and fabrication of nanostructured materials to control light, but no much attention was given to nonlinear optical properties of these novel materials. In this context, the present thesis would partially address this gap. In particular, we focus on the second-harmonic generation process, by considering two fundamental aspects: the second-harmonic emission control by means of nanostructured nonlinear materials and the conversion enhancement in integrated photonic devices. A novel nonlinear localization phenomenon occurring in left-handed materials and involving isotropic phase-matching is presented. We analytically demonstrate the localization process in a homogenous left-handed material and by numerical simulation we show the effect for nonlinear photonic crystals. The backward second-harmonic localization effect is used to design a second-harmonic lens. This interesting theoretical result is numerically shown for a feasible structure working at optical frequencies. The second-harmonic generation enhancement is the complementary aspect. By taking advantage of the strong light localization achieved in finite size dielectric nonlinear nanorod chains, we show that sub-wavelength transversal confinement, together with the resonant phase-matching condition, adds an important property to the second-harmonic generation enhancement. A study of linear propagation properties of nanorod chain structures first evidences its sub-wavelength guiding capabilities. Finally, the phase-matching condition that assures the maximal nonlinear interaction in this kind of structure is presented.MONTPELLIER-BU Sciences (341722106) / SudocSudocFranceF

Influence of spatial dispersion on surface plasmons, nanoparticles and grating couplers

International audienceRecent experiments have shown that spatial dispersion may have a conspicuous impact on the response of plasmonic structures. This suggests that in some cases the Drude model should be replaced by more advanced descriptions that take spatial dispersion into account, like the hydro-dynamic model. Here we show that nonlocality in the metallic response affects surface plasmons propagating at the interface between a metal and a dielectric with high permittivity. As a direct consequence, any nanoparticle with a radius larger than 20 nm can be expected to be sensitive to spatial dispersion whatever its size. The same behavior is expected for a simple metallic grating allowing the excitation of surface plasmons, just as in Woods famous experiment. Finally, we carefully set up a procedure to measure the signature of spatial dispersion precisely, leading the way for future experiments. Importantly, our work suggests that for any plasmonic structure in a high permittivity dielectric, nonlocality should be taken into account

Plasmonic Nanopatch Antennas for Large Purcell Enhancement

We demonstrate Purcell enhancements of-1000 from fluorescent molecules embedded in a plasmonic antenna with sub-10 nm gap between metals. Simulations and experiments reveal the high radiative efficiency and directionality of the antenna

Directional plasmonic nanoantennas to enhance the purcell effect

We will present plasmonic nanoantennas, composed of silver nanocubes strongly coupled to gold films, which are the optical and infrared (IR) frequency counterparts to the well-established patch antennas used in microwave frequencies for mobile communications. These nanoantennas are ideal platforms to boost several photodynamic processes, such as spontaneous emission. Interestingly, they can be built based on bottom-up chemical synthesis approaches and their radiation spectrum can be easily controlled