Sum-frequency intensities

In addition to the tensor element dependence of the sum-frequency intensity, there is also a dependence on the geometry of the experiment that manifests itself in the linear and non-linear Fresnel factors that describe the behaviour of the three light beams at the interface. Fresnel factors are the reflection and transmission coefficients for electromagnetic radiation at a boundary and depend on the frequency, polarization and incident angle of the electromagnetic waves and the indices of refraction for the media at the boundary [16,21]. 

Equation (6) shows that the sum-frequency intensity is dependent on the second-order polarization However, that polarization is a vector quantity P f. Within the electric dipole approximation the local fields E and re coupled by the second-order non-linear susceptibility, [16], inducing the following non-linear polarization at... 

The sum-frequency response at aqueous interfaces is very weak because of the small number of adsorbed molecules present and the poor polarizability of most liquids. To compensate for the low sum-frequency efficiency, pulsed lasers are used. Since the sum-frequency intensity increases with the peak intensity of the incident beams, picosecond and femtosecond pulses are optimal, although these shorter pulses result in larger IR bandwidths. Nanosecond systems are generally much simpler to operate and have narrower IR bandwidths, but can contribute to significant heating of the interface unless an optical coupling scheme such as total internal reflection (TIR) [6] or other mechanisms such as sample rotation [32] are employed. 

FIGURE 2.8. Square root of the sum-frequency intensity of the phenyl mode W2 as a function of surface concentration for (a) DBS at the CCE/water interface with 0.1M NaCl. (The line is a fit to the data.) (h) DBS at the air/water interface. The solid data points correspond to surface concentrations at and near full monolayer coverage. Adapted from Ref. [40]. 

Gemini North Observatory/CTI Mode-locked SFG Laser. CTT is developing the first commercial solid-state Na LGS system. It will be installed on the center section of the 8-m Gemini North telescope, with the output beam relayed to a projector behind the secondary mirror. The projected beam is required to be 10-20 W power, with M2 < 1.5. The architecture is based on sum-frequency mixing two mode-locked solid-state Nd YAG lasers. The mode-locked format provides significantly higher peak intensity than CW, enabling more efficient SFG conversion. The laser is also free of the thermal and intensity transients that are inherent in the macro pulse format. The chosen... 

A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a high-frequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to 400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pezolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The (P2) values were determined... 

The intensity of the sum frequency light /sum at a given delay time r between the probe pulse and the fluorescence beam co( is proportional to the correlation function of the fluorescence intensity with the intensity of the probe pulse co ... 

If not one but two light beams, at frequencies Vq and v, impinge upon a crystal, a I3E(vq)E(vi) term can produce beats at Vq v, and at appropriate crystal angles this interaction can be used to generate intense coherent radiation at a sum frequency in the visible or ultraviolet region or at the difference frequency in the infrared. 

As mentioned above, the intensity of the VSFS signal is dependent on the nonlinear polarization induced in the medium. The polarization that gives rise to sum-frequency generation, P f, is in mm dependent on the surface non-linear susceptibility... 

---