Second-harmonic generation in the scattering of light by two-dimensional particles

Valencia, Claudio I.; Mendez, Eugenio Rafael Mendez; Mendoza, Bernardo S.

doi:10.1364/josab.20.002150

Cited by 50 publications

(39 citation statements)

References 33 publications

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“…The method of calculation is based on the integral equations resulting from the application of Green's second integral theorem (with Sommerfeld radiation condition) [26,27,30,32,33]. Employing Green's integral theorem outside the scatterers, the magnetic field for p polarization can be written in parametric coordinates as…”

Section: P Polarizationmentioning

confidence: 99%

Calculations of light scattering from isolated and interacting metallic nanowires of arbitrary cross section by means of Green's theorem surface integral equations in parametric form

Giannini

Sánchez‐Gil

2007

J. Opt. Soc. Am. A

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We study theoretically the light scattering from metal wires of arbitrary cross section, with emphasis on the occurrence of plasmon resonances. We make use of the rigorous formulation of the Green's theorem surface integral equations of the electromagnetic wave scattering, written for an arbitrary number of scatterers described in parametric form. We have investigated the scattering cross sections for nanowires of various shapes (circle, triangles, rectangles, and stars), either isolated or interacting. The relationship between the cross sectional shape and the spectral dependence of the plasmon resonances is studied, including the impact of nanoparticle coupling in the case of interacting scatterers. Near-field intensity maps are also shown that shed light on the plasmon resonance features and the occurrence of local field enhancements.

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Section: P Polarizationmentioning

confidence: 99%

Calculations of light scattering from isolated and interacting metallic nanowires of arbitrary cross section by means of Green's theorem surface integral equations in parametric form

Giannini

Sánchez‐Gil

2007

J. Opt. Soc. Am. A

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“…Past this value, the scattering efficiency grows slowly with the size parameter and exhibits several resonances somehow similar to those found in the linear Mie scattering theory. Theoretical studies of two-dimensional circular geometries that considered a Mie-type solution arrived at similar conclusions [12,13]. A simpler approach than the full Mie scattering theory, the nonlinear Rayleigh-Gans-Debye theory assumes that the index contrast between the sphere and the surrounding medium is sufficiently small such that the fundamental field inside the sphere is an unperturbed plane wave [4,7].…”

Section: Laser and Photonics Reviewsmentioning

confidence: 92%

Nonlinear optics in spheres: from second harmonic scattering to quasi‐phase matched generation in whispering gallery modes

Kozyreff

Domínguez-Juárez

Martorell

2011

Laser & Photonics Reviews

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Over the last fifteen years, a series of theoretical and experimental investigations have demonstrated the usefulness of circular geometries to tailor second-order nonlinear optical effects. However, until recently, such effects have remained rather weak, calling for their enhancement. In parallel, developments in the field of high quality factor spherical or ring resonators have shown that many different types of light-matter interactions can be dramatically amplified when light is coupled in the whispering gallery modes of such resonators. In high-quality spherical micro-resonators, close to one million interactions can occur between a nonlinear molecule and a circulating light pulse. Recent research on nonlinear optics in spherical geometry is reviewed, from micrometer-size spheres to whispering gallery mode resonators.

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“…Firstly, we have to explicitly choose the surface magnitudes that are unknowns in the system of integral equations. In the literature, sources are chosen with different criteria [26][27][28][29][30]. In this work our unknown surface magnitudes are the (two) tangential and (one) normal components of the surface electromagnetic field, namely:…”

Section: System Of Integral Equations: Surface Em Fieldsmentioning

confidence: 99%

“…On the other hand, the Green's theorem method (GTm) became an appealing method in the early nineties to study 2D semi-infinite rough surfaces [22]. The GTm has been implemented in many different ways, for many different geometrical configurations: 1D semi-infinite rough surfaces [22,23], 2D semi-infinite rough surfaces [26][27][28][29], 2D closed surfaces in parametric equations [30,31], 3D closed surfaces in electrostatic approximation [32,33], and 3D closed surfaces with axial symmetry [34]. However, it remains still undone a general implementation of the GTm for 3D closed surfaces without any approximation.…”

Section: Introductionmentioning

confidence: 99%

Localized surface-plasmon resonances on single and coupled nanoparticles through surface integral equations for flexible surfaces

Rodríguez-Oliveros¹,

Sánchez‐Gil²

2011

Opt. Express

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Abstract:We present an advanced numerical formulation to calculate the optical properties of 3D nanoparticles (single or coupled) of arbitrary shape and lack of symmetry. The method is based on the (formally exact) surface integral equation formulation, implemented for parametric surfaces describing particles with arbitrary shape through a unified treatment (Gielis' formula). Extinction, scattering, and absorption spectra of a variety of metal nanoparticles are shown, thus determining rigorously the localised surface-plasmon resonances of nanocubes, nanostars, and nanodimers. Far-field and near-field patterns for such resonances are also calculated, revealing their nature. The flexibility and reliability of the formulation makes it specially suitable for complex scattering problems in Nano-Optics & Plasmonics. References and links1. X. Lu, M. Rycenga, S. E. Skrabalak, B. Wiley, and Y. Xia, "Chemical synthesis of novel plasmonic nanoparticles," Annu. Rev. Phys. Chem. 60, 167-92 (2009). 2. T. R. Jensen, G. C. Schatz, and R. P. V. Duyne, "Nanosphere lithography: surface plasmon resonance spectrum of a periodic array of silver nanoparticles by ultraviolet-visible extinction spectroscopy and electrodynamic modeling," J. Phys. Chem. B 103, 2394-2401 (1999). 3. A. Ono, J. Kato, and S. Kawata, "Subwavelength optical imaging through a metallic nanorod array," Phys. Rev. Lett. 95, 267407 (2005). 4. E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006). 5. V. Giannini, A. Fernandez-Dominguez, Y. Sonnefraud, T. Roschuk, R. Fernandez-García, and S. A. Maier, "Controlling light localization and light-matter interactions with nanoplasmonics," Small 6, 2498-2507 (2010). 6. L. Novotny and N. van Hulst, "Antennas for light," Nat. Photonics 5, 83-90 (2011). 7. J. A. Sánchez-Gil and J. V. García-Ramos, "Local and average electromagnetic enhancement in surface-enhanced Raman scattering from self-affine fractal metal substrates with nanoscale irregularities," Chem. Phys. Lett. 367, 361-366 (2003). 8. E. J. Zeman and G. C. Schatz, "An accurate electromagnetic theory study of surface enhancement factors for Ag, Au, Cu, Li, Na, Al, Ga, In, Zn, and Cd," J. Phys. C 91, 634-643 (1987 14, 302-307 (1966). 17. R. Clough, "The finite element method after twenty-five years: a personal view," Comput. Struct. 12, 361-370 (1980). 18. C. Girard and A. Dereux, "Near-field optics theories," Rep. Progr. Phys. 59, 657 (1996)

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Second-harmonic generation in the scattering of light by two-dimensional particles

Cited by 50 publications

References 33 publications

Calculations of light scattering from isolated and interacting metallic nanowires of arbitrary cross section by means of Green's theorem surface integral equations in parametric form

Calculations of light scattering from isolated and interacting metallic nanowires of arbitrary cross section by means of Green's theorem surface integral equations in parametric form

Nonlinear optics in spheres: from second harmonic scattering to quasi‐phase matched generation in whispering gallery modes

Localized surface-plasmon resonances on single and coupled nanoparticles through surface integral equations for flexible surfaces

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