Sum frequency generation spectroscopy (SFG) is a nonlinear laser spectroscopy technique based on sum-frequency generation and used to analyze surfaces and interfaces. It can be expressed as a sum of a series of Lorentz oscillators. In a typical SFG setup, two laser beams mix at an interface and generate an output beam with a frequency equal to the sum of the two input frequencies, traveling in a direction given by the sum of the incident beams' wavevectors. The technique was developed in 1987 by Yuen-Ron Shen and his students as an extension of second harmonic generation spectroscopy and rapidly applied to deduce the composition, orientation distributions, and structural information of molecules at gas–solid, gas–liquid and liquid–solid interfaces. Soon after its invention, Philippe Guyot-Sionnest extended the technique to obtain the first measurements of electronic and vibrational dynamics at surfaces. SFG has advantages in its ability to be monolayer surface sensitive, ability to be performed in situ (for example aqueous surfaces and in gases), and its capability to provide ultrafast time resolution. SFG gives information complementary to infrared and Raman spectroscopy.
Theory IR-visible sum frequency generation spectroscopy uses two laser beams (an infrared probe, and a visible pump) that spatially and temporally overlap at a surface of a material or the interface between two media. An output beam is generated at a frequency of the sum of the two input beams. The two input beams must be able to access the surface with sufficiently high intensities, and the output beam must be able to reflect off (or transmit through) the surface in order to be detected. Broadly speaking, most sum frequency spectrometers can be considered as one of two types, scanning systems (those with narrow bandwidth probe beams) and broadband systems (those with broad bandwidth probe beams). For the former type of spectrometer, the pump beam is a visible wavelength laser held at a constant frequency, and the other (the probe beam) is a tunable infrared laser — by tuning the IR laser, the system can scan across molecular resonances and obtain a vibrational spectrum of the interfacial region in a piecewise fashion. In a broadband spectrometer, the visible pump beam is once again held at a fixed frequency, while the probe beam is spectrally broad. These laser beams overlap at a surface, but may access a wider range of molecular resonances simultaneously than a scanning spectrometer, and hence spectra can be acquired significantly faster, allowing the ability to perform time-resolved measurements with interfacial sensitivity.
Nonlinear susceptibility For a given nonlinear optical process, the polarization P → {\displaystyle {\overrightarrow {P}}} which generates the output is given by
P → = ϵ 0 ( χ ( 1 ) E → + χ ( 2 ) E → 2 + χ ( 3 ) E → 3 + ⋯ + χ ( n ) E → n ) = ϵ 0 ∑ i = 1 n χ ( i ) E → i {\displaystyle {\overrightarrow {P}}=\epsilon _{0}\left(\chi ^{(1)}{\overrightarrow {E}}+\chi ^{(2)}{\overrightarrow {E}}^{2}+\chi ^{(3)}{\overrightarrow {E}}^{3}+\dots +\chi ^{(n)}{\overrightarrow {E}}^{n}\right)=\epsilon _{0}\sum _{i=1}^{n}\chi ^{(i)}{\overrightarrow {E}}^{i}}
… excerpt ends here. Continue reading the full article.
