Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit

Abstract

The electromagnetic theory of optical second-harmonic generation from small spherical particles comprised of centrosymmetric material is presented. The interfacial region where the inversion symmetry is broken provides a source of the nonlinearity. This response is described by a general surface nonlinear susceptibility tensor for an isotropic interface. In addition, the appropriate weak bulk terms for an isotropic centrosymmetric medium are introduced. The linear optical response of the sphere and the surrounding region is assumed to be isotropic, but otherwise arbitrary. The analysis is carried out to leading order in the ratio of (a/), the particle radius to the wavelength of the incident light, and can be considered as the Rayleigh limit for secondharmonic generation from a sphere. Emission from the sphere arises from both induced electric dipole and electric quadrupole moments at the second-harmonic frequency. The former requires a nonlocal excitation mechanism in which the phase variation of the pump beam across the sphere is considered, while the latter is present for a local-excitation mechanism. The locally excited electric dipole term, analogous to the source for linear Rayleigh scattering, is absent for the nonlinear case because of the overall inversion symmetry of the problem. The second-harmonic field is found to scale as (a/) 3 and to be completely determined by two effective nonlinear susceptibility coefficients formed as a prescribed combination of the surface and bulk nonlinearities. Characteristic angular and polarization selection rules resulting from the mechanism of the radiation process are presented. Various experimental aspects of the problem are examined, including the expected signal strengths and methods of determining the nonlinear susceptibilities. The spectral characteristics associated with the geometry of a small sphere are also discussed, and distinctive localized plasmon resonances are identified.

Anisotropic Second- and Third-Order Nonlinear Optical Response from Anisotropy-Controlled Metallic Nanocomposites

“…In particular, the anisotropic nonlinear optical response, for given wavelength and incident polarization, reveals a complex contribution from all the different, nonzero, linearly independent third-order susceptibility tensor's components Rodríguez-Iglesias et al, 2009). Besides, given this anisotropy, although the nanocomposite remains being centrosymmetric, there is the possibility of measuring a nonzero optical second-order nonlinearity in the form of a second harmonic generation (SHG) signal, as it has been shown in previous results (Aktsipetrov et al, 1995;Brevet et al, 2011;Dadap et al, 1999Dadap et al, , 2004Figliozze et al, 2005;Gallet et al, 2003;Mendoza et al, 2006), and also verified by us experimentally (Rocha-Mendoza et al, 2011).…”

Effect of Ni2+ - ions on the Structural, Optical and Mechanical Properties of Ninhydrin Crystals

“…Hence, it is concluded that pure and nickel nitrate doped ninhydrin crystals are also soft materials. The study of nonlinear optical conversion efficiency was carried out using the modified experimental setup of Kurtz and Perry [9,10]. A Q-switched Nd:YAG laser beam of wavelength 1064 nm, with input energy 0.701 Joule with a repetition rate of 10 Hz was used.…”

Light wave driven electron dynamics in clusters

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