Nonlinear surface susceptibilities

Gavrilenko V I and Rebentrost F 1995 Nonlinear optical susceptibility of the surfaces of silicon and diamond Surf. Sc/. B 331-3 1355-60... 

The theoretical framework developed above is valid in the electric dipole approximation. In this context, it is assumed that the nonlinear polarization Ps 2a)) is reduced to the electric dipole contribution as given in Eq. (1). This assumption is only valid if the surface susceptibility tensor co, m) is large enough to dwarf the contribution from higher... 

The SHG signal intensity, 1(2 ), arising at the liquid-liquid interface is known to be proportional to the square of the second-order nonlinear electric susceptibility, c , at the surface [18,28,29],... 

The red PL band of PS can not only be excited by above bandgap photons, but also by an intense IR (1064 nm) pulse [Di6]. Such a thermostimulated luminescence is known for the case of glasses. This observation was attributed to PS having about 100 times the third-order nonlinear optical susceptibility of bulk Si, as discussed in Section 7.3. Multiphoton excitation of the red PL band by resonant pumping of the vibrational modes of surface groups like Si-O [Di4] or Si-H [Ch8] provided evidence for excitation modes that involve the porous skeleton surface. 

The standard method of treating the electric dipole contribution from the surface region is to view the nonlinear polarization as a dipole sheet which can be described by the surface susceptibility tensor, xf. This is equivalent to considering the three layer system shown in Fig. 3.1 with the dipole sheet placed just below the surface at z = 0+ and allowing the surface layer thickness, d, to approach zero. The surface contribution to the polarization can then be written as... 

The theoretical framework developed above is valid in the electric dipole approximation. In this context, it is assumed that the nonlinear polarization PfL(2 >) is reduced to the electric dipole contribution as given in Eq. (1). This assumption is only valid if the surface susceptibility tensor x (2 > >, a>) is large enough to dwarf the contribution from higher orders of the multipole expansion like the electric quadrupole contribution and is therefore the simplest approximation for the nonlinear polarization. At pure solvent interfaces, this may not be the case, since the nonlinear optical activity of solvent molecules like water, 1,2-dichloroethane (DCE), alcohols, or alkanes is rather low. The magnitude of the molecular hyperpolarizability of water, measured by DC electric field induced second harmonic... 

A monolayer at an interface between air and water can be considered as an infinitely thin dielectric sheet represented by an induced polarization, which is usually a complicated nonlinear function of the electric field (E) of the incident laser beam. In the linear case, the induced polarization is a simple linearized form, P = XgE where Xs is the surface susceptibility xs = Xs (z)f for simplicity here taken as a scalar, i.e. the monolayer is assumed to be isotropic and z is the direction normal to the surface. With the light incident from air, the phase retardation between the reflected S and P waves (A = " p) which is measured by... 

The nonlinear response of the interface may then be characterized in tenns of a surface (or interface) nonlmear susceptibility tensor. This quantity relates the applied electromagnetic fields to the induced... 

An alternative scheme for extracting all tliree isotropic nonlinear susceptibilities can be fomuilated by examining equation B 1.5.39. By choosing an appropriate configuration and the orientation of the polarization of die SH radiation e 2a) such that the SHG signal vanishes, one obtains, assuming only surface contribution with real elements, ... 

Spatial synnnetry is one of the basic properties of a surface or interface. If the syimnetry of the surface is known a priori, then this knowledge may be used to simplify the fomi of the surface nonlinear susceptibility as discussed in section Bl,5,2,2. Conversely, in the absence of knowledge of the surface synnnetry, we may characterize the fonn of -iexperimentally and then make inferences about the synnnetry of the surface... 

All of the symmetry classes compatible with the long-range periodic arrangement of atoms comprising crystalline surfaces and interfaces have been enumerated in table Bl.5,1. For each of these syimnetries, we indicate the corresponding fonn of the surface nonlinear susceptibility With the exception of surfaces... 

Given the interest and importance of chiral molecules, there has been considerable activity in investigating die corresponding chiral surfaces [, and 70]. From the point of view of perfomiing surface and interface spectroscopy with nonlinear optics, we must first examhie the nonlinear response of tlie bulk liquid. Clearly, a chiral liquid lacks inversion synnnetry. As such, it may be expected to have a strong (dipole-allowed) second-order nonlinear response. This is indeed true in the general case of SFG [71]. For SHG, however, the pemiutation synnnetry for the last two indices of the nonlinear susceptibility tensor combined with the... 

A schematic diagram of the surface of a liquid of non-chiral (a) and chiral molecules (b) is shown in figure Bl.5.8. Case (a) corresponds to oom-synnnetry (isotropic with a mirror plane) and case (b) to oo-symmetry (isotropic). For the crj/ -synnnetry, the SH signal for the polarization configurations of s-m/s-out and p-m/s-out vanish. From table Bl.5.1. we find, however, that for the co-synnnetry, an extra independent nonlinear susceptibility element, is present for SHG. Because of this extra element, the SH signal for... 

For other purposes, obtaining a measure of the adsorbate surface density directly from the experiment is desirable. From this perspective, we introduce a simple model for the variation of the surface nonlinear susceptibility with adsorbate coverage. An approximation that has been found suitable for many systems is... 

We now consider this issue in a more rigorous fashion. The inference of molecular orientation can be explamed most readily from the following relation between the surface nonlinear susceptibility tensor and the molecular nonlinear polarizability... 

For adsorbates on a metal surface, an SFG spectmm is a combination of resonant molecular transitions plus a nonresonant background from the metal. (There may also be a contribution from the water-CaF2 interface that can be factored out by following electrode potential effects see below.) The SFG signal intensities are proportional to the square of the second-order nonlinear susceptibility [Shen, 1984] ... 

Another determination of the surface equilibrium entails the use of the coupling of the DC electric field present at charged interfaces with the electromagnetic field, as described in the theoretical section. Integration of the nonlinear polarization over the whole double layer leads to the following expression of the effective susceptibility tensor ... 

Chen, Y. J. Carter, G. M. "Measurement of Third Order Nonlinear Susceptibilities by Surface Plasmons," Appl. Phys. 

There are different paths to achieving surface specificity. One can exploit optical susceptibilities and resonances that are nonzero only at the surface or only for the molecular species of interest adsorbed on the surface. Examples include the use of second-order nonlinear mixing processes such as second harmonic generation7-9 for which the nonlinear susceptibility tensor is nonzero only where inversion symmetry is broken. Spectroscopic techniques with very high selectivity for molecular resonances such as surface-enhanced infrared or Raman spectroscopy10-12 may also be used. 

---