generation spectroscopy

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Sum Frequency Generation Spectroscopy (SFG) is a technique used to analyze surfaces and interfaces. This spectroscopy method utilizes Sum Frequency Generation, where two light beams mix at a surface and generate an output beam with a frequency equal to the sum of the two input frequencies. From the experiment setup and the output beam, one can deduce the composition, orientation distributions, and some structural information of molecules on a surface. 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 not causing much damage to the sample surface. SFG is comparable to Second Harmonic Generation (SFG is a more general form) and Infrared and Raman Spectroscopy.

Contents

1 Theory

1.1 SFG Intensity

1.2 Orientation Information

2 Experimental Setup

3 References

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Theory

IR-visible sum frequency generation spectroscopy uses two laser beams that overlap at a surface of a material or the interface between two materials. An output beam is generated at a frequency of the sum of the two input beams. The geometry of this effect is shown in Figure 1. The two input beams have to be able to access the surface, and the output beam needs to be able to leave the surface to be picked up by a detector. One of the beams is a visible wavelength laser held at a constant frequency and the other is a tunable infrared laser. By tuning the IR laser, the system can scan over resonances and obtain the vibrational spectrum of the interfacial region.

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Figure 1: Diagram of SFG geometry. Two input beams, ?1 and ?2 coincide at the interface between materials n1 and n2. A resulting beam ?3 is generated. The axes are labeled where z is normal to the interface and x and y are parallel to the surface.

As a nonlinear optical process, the polarization which generates the output depends on the electric fields of the two input beams.



As a second-order nonlinear process, SFG is dependent on the 2nd order susceptibility ?(2). The fact that the 2nd order susceptility, a third rank tensor, becomes zero in Centrosymmetric media, limits what samples are accessible for SFG. Centrosymmetric media include the bulk of gases, liquids, and most solids under the assumption of the electric-dipole approximation, which neglects the signal generated by multipoles and magnetic moments. At an interface between two different materials or two centrosymmetric media, the inversion symmetry is broken and an SFG signal can be generated. This suggests that the resulting spectra represent a thin layer of molecules. A signal is found when there is a net polar orientation.

SFG Intensity

The output beam is collected by a detector and its intensity is measured. The intensity of the beam is given by



Here, intensity is directly proportional to the susceptibility squared and the product of the intensities of the incoming beams. The IR frequency is given as ?2 and the visible frequency is given as ?1. The constant of proportionality varies across literature, many of them including the product of the square of the output frequency, ?2 and the squared secant of the reflection angle, sec2?. Other factors include index of refractions for the three beams.

The second order susceptibility has two contributions

? = ?nr + ?r

where ?nr is the non-resonating contribution and ?r is the resonating contribution. The non-resonating contribution is from electronic transitions, and is considered constant if the visible light is held constant. An ei? term can be attached to ?nr to account for any phase difference between the non-resonant and resonant terms.

The resonating contribution is from the vibrational modes and shows changes in resonance. It can be expressed as a sum of a series of Lorentz oscillators



where A is the strength or amplitude, ? is the frequency or energy, ? is the damping or linewidth coefficient, and each q is a resonance mode. The amplitude is a product of ?, the induced dipole moment, and ?, the polarizability. Together, this indicates that the transition must be both IR and Raman active.

The above equations can be combined to form



which used to model the SFG output over a range of wavenumbers. When the SFG system scans over a vibrational mode of the surface molecule, the output intensity is resonantly enhanced. In a graphical analysis of the output intensity versus wave number, this is represented by peaks. Depending on the system, inhomogeneous broadening and interference between peaks may occur. The Lorentz profile can be convoluted with a Gaussian intensity distribution to better fit the intensity distribution.

Orientation Information

From the second order susceptibility, it is possible to ascertain information about the orientation of molecules at the surface….(and so on)
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