Surface second harmonic generation
[8][9] Just as bulk second harmonic generation, surface SHG arises out of the second-order susceptibility tensor χ(2).
When determining molecular orientation, it is assumed that χ(2) is rotationally invariant around the z-axis (normal to the surface).
The number of tensor elements reduces from 27 to the following 7 independent quantities: χZZZ, χZXX = χZYY, χXZX = χYZY, χXXZ = χYYZ, χXYZ = −χYXZ, χXZY = −χYZX, χZXY = −χZYX.
These four terms give rise to the second harmonic signal, and allow for calculation of material properties such as electronic structure, atomic organization, and molecular orientation.
Typical measurements of SHG from crystalline surfaces structures are performed by rotating the sample in an incident beam (Figure 1).
The second harmonic signal will vary with the azimuth angle of the sample due to the symmetry of the atomic and electronic structure (Figure 2).
[12] SHG sensitivity to surface structure approach was effectively demonstrated by Heinz, Loy, and Thompson, working for IBM in 1985.
SHG measurements allow the incident laser beam to pass without interaction through higher level materials to the target interface where the second harmonic signal is generated.
In cases where the transmitting materials do interact with the beam, these contributions to the second harmonic signal can be resolved in other experiments and subtracted out.
Bourguignon et al.[15] showed that as carbon monoxide is adsorbed onto a Pd(111) surface, the SHG signal decreased exponentially as predicted by the Langmuir isotherm.
The beam is incident on the sample in a total internal reflection geometry which improves the second harmonic signal because as the wave propagates along the interface, additional second harmonic photons are generated,[1] By rotating either the polarizer or the analyzer, the s- and p-polarized signals are measured which allow for the calculation of the second-order susceptibility tensor χ(2).
Typically, SHG measurements of this type are only able to extract a single parameter, namely the molecular orientation with respect to the surface normal.
The si terms depend on the experimental geometry are functions of the total internal reflection angles of the incident and second harmonic beams and the linear and nonlinear Fresnel factors respectively which relate the electric field components at the interface to incident and detected fields.
The second-order susceptibility tensor, χ(2), is the parameter which can be measured in second order experiments, but it does not explicitly provide insight to the molecular orientation of surface molecules.
In monolayer microscopy the second harmonic signal is magnified and surface features are imaged with a resolution on the order of a wavelength.
