Optical second harmonic generation from a thin chiral film

We present a simple model for calculating the second-order optical response of a film of chiral molecules. The difference in the output signal for right or left circularly polarized input is analyzed. A strong enhancement in the normalized differential signal is found for p-polarized output. This is due to the existence of Brewster angles which are slightly different for R or L circular input. This feature has no analog in the linear signal, since in that case the two Brewster angles coincide

Second-harmonic generation from spherical particles

We calculate the nonlinear dipole and quadrupole moments induced at the second-harmonic (SW) frequency 2 omega in a small dielectric sphere by an inhomogeneous monochromatic electric field of frequency omega. We neglect finite-size effects and assume that the selvedge region of the sphere is thin enough so that the surface may be considered locally flat. The second-order dipole displays resonances corresponding to the excitation of dipolar and quadrupolar plasmons at w and a dipolar plasmon at 2 omega, besides the resonances in the nonlinear surface response parameters a, b, and f. The second-order quadrupole, on the other hand, has resonances corresponding to those of a, b, and f, and to the excitation of dipolar surface plasmons at omega only. Depending on the relation between the size of the sphere and the spatial scale of variation of the field, the SH radiation may be dominated by either dipolar or quadrupolar scattering, with a crossover region. As an application, we calculate the SH scattering of a Si sphere lying at various distances above a dielectric substrate

Second-harmonic generation in arrays of spherical particles

We calculate the optical second harmonic (SH) radiation generated by small spheres made up of a homogeneous centrosymmetric material illuminated by inhomogeneous transverse and/or longitudinal electromagnetic fields. We obtain expressions for the hyperpolarizabilities of the particles in terms of the multipolar bulk susceptibilities and dipolar surface susceptibilities of their constitutive material. We employ the resulting response functions to obtain the nonlinear susceptibilities of a composite medium made up of an array of such particles and to calculate the radiation patterns and the efficiency of SH generation from the bulk and the edge of thin composite films illuminated by finite beams. Each sphere has comparable dipolar and quadrupolar contributions to the nonlinear radiation, and the composite has comparable bulk and edge contributions which interfere among themselves yielding nontrivial radiation and polarization patterns. We present numerical results for Si spheres and we compare our results with recent experiments

Depth resolved nonlinear optical nanoscopy

An electromagnetic field forced to vary along a plane with a spatial scale d much smaller than its free space wavelength lambda decays exponentially along its normal with a decay length similar tod. This decay, similar to that of the wavefunction of tunneling electrons, has allowed the development of scanning near-field optical microscopes (SNOMs), reminiscent of scanning tunneling and atomic force microscopes, which have been able to resolve structures in the nanometer scale. However, existing SNOMs are unable to determine the depth below the surface from which the optical signals arise due to the monotonic decay of the optical evanescent probe fields. In this paper we study the optical second harmonic generation (SHG) produced by mixing of the evanescent fields produced by a SNOM tip. We show that employing an appropriately spatially-patterned tip, a non-monotonic non-linear probing field may be produced which has a maximum at a given distance beyond the tip, yielding a novel microscopy which may attain depth resolution with nanometric lengthscales. We estimate the size of the optical signal and we compare it with that arising in the usual SHG-based surface spectroscopy of centrosymmetric materials. (C) 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Energy conservation and the Manley-Rowe relations in surface nonlinear-optical spectroscopy

We consider the energy conservation problem for nonlinear-optical three-wave mixing processes at the surface and in the bulk of semi-infinite centrosymmetric lossless media. Because of the intrinsic nonlocality of these processes, the corresponding Manley-Rowe relations differ from those of noncentrosymmetric media. The ensuing restrictions link the surface and bulk nonlinear susceptibility components and may be used to test theories of nonlinear response. Our analysis permits a clear separation of the intrinsic surface contribution that contains the information about the surface structure