Second-Harmonic Rayleigh Scattering from a Sphere of Centrosymmetric Material

Abstract

We describe the electromagnetic theory of second-harmonic generation from the surface of a sphere that is small compared to the wavelength of light. In a leading-order expansion, the second-harmonic radiation is emitted in nonlocally excited electric dipole and locally excited electric quadrupole modes. We analyze the problem with particular emphasis on experimental aspects, such as the radiation pattern, polarization selection rules, determination of nonlinear susceptibilities, radiation efficiency, and spectral characteristics.

Second harmonic generation in suspensions of spherical particles

“…10 and is not a subject of the present paper. We note, however, that, in general, 1 χ and 2 χ are complex-valued functions of frequency.…”

“…moments of this new charge distribution being nonzero [9,10]. These multipole moments oscillate in time due to the oscillations of the incident electric field and hence the particle re-radiates electromagnetic waves.…”

“…On the other hand, the lowest-order nonlinear effects -those quadratic in the wave field -have also been considered in the limit l * << l NL [8]. Recent theoretical [9,10] and experimental [11] work suggests that even the simplest realization of a nonlinear disordered medium, a dilute suspension of spherical particles, exhibits a rather unexpected and nontrivial behavior: second harmonic (SH) is generated by a single spherical particle despite its central symmetry and seemingly prohibited second-order nonlinear effects, and a measurable SH signal can be obtained from a dilute suspension of such particles in a single scattering regime [11]. Note that although SHG in 1D disordered systems of spheres has been studied theoretically in…”

Nonlinear optics on nano/micro-hierarchical structures on metals: focus on symmetric and plasmonic effects

“…Thus, we considered the dephasing of the light field induced by the NSs on the Ni microstructures seen in Figure 17(a). In general, SH radiation collected from nanometer-scale areas is strongly dephased [53]. Stockman [46] has discussed the dephasing effect in terms of the roughness of metal surfaces on the optical processes upon them.…”

Second harmonic surface response of a composite

“…However, for a nonuniform polarizing field, this cancellation is no longer exact and dipolar radiation becomes possible. Recently Dadap et al 16,17 presented a model that permits an arbitrary nonlinear intrinsic response, and calculated the SH Rayleigh scattering from a small sphere of centrosymmetric material illuminated by a linearly or circularly polarized plane wave. Retardation of the incoming field across the particle leads to a total dipole moment that scales as R/λ for small spheres, where R is the radius of the sphere and λ the wavelength.…”