Response signal harmonic generation

Unlike linear optical effects such as absorption, reflection, and scattering, second order non-linear optical effects are inherently specific for surfaces and interfaces. These effects, namely second harmonic generation (SHG) and sum frequency generation (SFG), are dipole-forbidden in the bulk of centrosymmetric media. In the investigation of isotropic phases such as liquids, gases, and amorphous solids, in particular, signals arise exclusively from the surface or interface region, where the symmetry is disrupted. Non-linear optics are applicable in-situ without the need for a vacuum, and the time response is rapid. 

Figure 9.20 Intensity of s-polarized second-harmonic signal generated in transmitted direction for glass-side incidence as function of rotation angle of quarter waveplate. Note significant difference in response for right- (45° and 225°) and left-hand (135° and 315°) circularly polarized light. Points represent experimental data, solid line fit to the model described in Section 3 with nonvanishing g, and the dashed line the fit with vanishing g.

An electrical system with linear properties does not generate harmonics in response to the perturbation signal, and the response to two or more superimposed excitation signals is equal to the sum of the two responses obtained by excitation independently. With electrochemical systems this linearity is possible to a good approximation for perturbations rather less than the thermal potential (lcBT/e) = 25 mV at 298K. 

The integration over many cycles of the generator is highly effective in averaging out random noise from the input signal. Also, only the response at the fundamental frequency is detected, since terms like cos (mot+ntp) sin tot with n = 2, 3,4. .. average to zero over a complete cycle harmonics are totally... 

When an intense laser beam strikes a medium with a structure that is not centrosymmetric, a second harmonic of the laser frequency is generated. A boundary between uniform media lacks inversion symmetry, and a second harmonic can therefore be generated at an interface. If the signal comes mainly from a monolayer on the surface, then the nonlinear susceptibility that is responsible for SHG has the form ... 

Other nonlinear optical spectroscopies have gained much prominence in recent years. Two techniques in particular have become quite popular among surface scientists, namely, second harmonic (SHG) [55] and sum-frequency (SFG) [56] generation. The reason why both SHG and SFG can probe interfaces selectively without being overwhelmed by the signal from the bulk is that they rely on second-order processes that are electric-dipole forbidden in centrosymmetric media by breaking the bulk symmetry, the surface places the molecular species in an environment where their second-order nonlinear susceptibility, the term responsible for the absorption of SHG and SFG signals, becomes non-zero. 

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