Characterization of Soft Matter at Interfaces by Optical Means

Abstract

In this chapter, I give a brief overview, which is biased by personal experience, on how various optical techniques can be used for characterization of soft matter at interfaces, including ellipsometry, light scattering, and total internal reflection geometries. Without discussing the technical details and theoretical foundations of the methods, I focus on what can be learned by applying the individual techniques.

Appendix 1: Total Internal Reflection and Evanescent Field

Electromagnetic near fields designate non-radiative fields that are localized near an object, so to say at the surface of the object. Optical near fields offer a convenient way to probe interfaces. They extend over one wavelength or so. In particular they can be used to excite scattering or fluorescence.

One such near field is the evanescent waves present in the medium of lower refractive index at total internal reflection. When reflectivity coefficients are one, there is nonetheless a near field penetrating the medium of lower refractive index. It is well described by the reflectivity coefficients, with r _p and r _s being complex numbers of module 1 (Fig. 13.4).

Fig. 13.4

Optical field at TIR the bottom correspond to the low refractive index medium (wiki-commons). The white line is added to materialize the interface. Below is the medium of low refractive index and above the one with high refractive index. The brightness relates to the amplitude of the electric field (the brighter the higher) The standing waves due to the interference between the incoming and reflected beam is clearly seen. The evanescent field is also clearly visible below the white line. (image wiki-commons)

In particular it is possible to compute the penetration depth.

The evanescent field writes [2] as $E_{ev} = E_{0} \,e^{ - \kappa z} e^{i(kx - \omega t)}$ with the “penetration wave vector” $\kappa = 1/d_{p} = \frac{{2\pi n_{1} }}{\lambda }\sqrt {\sin^{2} \theta - \frac{{n_{2}^{2} }}{{n_{1}^{2} }}}$ and the “propagation wave vector” along the interface $k = \frac{{2\pi n_{1} }}{\lambda }\sin \theta$.

The other may be less appreciated length scale associated with TIR is the Goss Haenchen shift, that describes the lateral shift of the beam [2]. Looking into the reflectivity coefficient, a phase shift appears under TIR, which also depends on the polarization and the incidence angle. This phase shift is the sign of a time (length) associated with the TIR.

The EW produced at TIR can be associated with many different detection schemes [22], ellipsometry, light scattering, fluorescence, Raman, IR, and recently optical rotation.

The critical angle is independent of the polarization for non-birefringent materials, and so is the penetration depth. However the s and p polarized light undergo different phase shift under TIR. The difference of phase shift is what ellipsometry under total internal reflection will measure. The penetration depth can be varied by changing the incidence angle. A larger optical contrast between the two materials will provide a shorter penetration depth, as will larger incidence angles. As an example, the field penetration depth d _p at interface between high refractive index incidence medium (n ₁ = 2) with water (n ₂ = 1.33) can become as low as 60 nm for a wavelength of 532 nm.