Penetration of the evanescent wave

Figure 10.4. Total internal reflection at the interface of an internal reflection element (IRE). Depth of penetration of the evanescent wave is approximately 1 pm. The top picture depicts the evanescent beam in more detail. The sample is coated on both sides of the IRE.

Figure 3.38, which schematically illustrates three beams A, B and C at different angles of incidence to the cladding and the depth of penetration of the evanescent wave for each. E is the electric-field intensity and it can be seen that this decays exponentially into the cladding. 

The wavelength and angle dependences of the depth of penetration, d, were given earlier (Equation (3.22)), and this principle is used in the MIR for the sampling technique of ATR spectroscopy. Figure 3.13(c) illustrated this, and, for typical refractive indices of fibre core and sample of 2.5 and 1.5, respectively, and an angle of incidence of 45°, the depth of penetration of the evanescent wave is about 0.152. The effect of the evanescent wave on fibre-optic spectroscopy may be illustrated by the example of plastic-clad silica (PCS) fibre optics for remote spectroscopy in the NIR spectral region, as discussed below. 

It is useful to calculate the depth of penetration of the evanescent wave as a function of incidence angle and X-ray wavelength. This has been done for quartz, hematite and calcite, using the X-ray optics calculator on the Center for X-ray Optics web page http //www-cxro.lbl.gov/optical-constants/ Taking hematite as an example, it is clear from Figure 10 that there is a dramatic effect from increased absorption. At 7100 eV, below the Fe edge, the penetration function resembles those of other solids. However,... 

Figure 2. Three common configurations for spectroscopic monitoring of solution components generated at an electrode. With an optically transparent electrode, a beam passes through the electrode and absorbance U governed by an effective path length of approximately y l)t. The wavy line indicates an imaginary boundary layer of electrogenerated material (P) moving out into the solution. In the case of internal reflection, absorbance is determined by penetration of the evanescent wave into the solution. R indicates a reactant initially present in solution P is an electrogenerated product.

Internal reflection spectra are not exact duplicates of transmission spectra. First of all, the effective penetration of the evanescent wave into the sample is a direct function of the wavelength of the radiation. This means that as the wavelength increases, bands get deeper relative to those in a transmission spectrum. Secondly, the effective penetration of the evanescent wave is an inverse function of the quantity [sin i — This means that band... 

The photothermal signal is proportional to the sample s thermal expansion, to the absorbed energy per unit area t/abs> for short laser pulses to the duration of the thermal excitation in the sample. The sample s thermal expansion is proportional to its thickness z while is approximately proportional to z. Thus, the photothermal signal S should be proportional to the product of and z. The absorption by the sample will depend on the exponentially decaying evanescent electric field intensity. For thicknesses less than the depth of penetration of the evanescent wave d, the AFM-IR signal increases with an increase in sample thickness z. For nonabsorbing samples, the value of is given by the well-known equation ... 

At higher ethanol concentrations, ATR spectra should contain the contribution from bnUc species, becanse of the long penetration depth of the evanescent wave, 250 nm. To examine the bulk contribution, the integrated peak intensities of polymer OH peaks of transmission (Ats) and ATR (Aatr) spectra are plotted as a function of the ethanol concentration in Figure 5. The former monitors clnster formation in the bulk liquid, and the latter contains contributions of clusters both on the snrface and in the bulk. A sharp increase is seen in A tr... 

Simply visualised, the infrared beam penetrates (of the order 0.3-3 pm, dependent on its wavelength) just beyond the ATR crystal-specimen boundary before it is reflected back and makes its way through the crystal to the detector. On this short path (of the evanescent wave) into the sample surface layer, light is absorbed, and the reflected beam carries characteristic spectral information of the sample. The decaying amplitude of the evanescent wave and the depth of penetration dp at which it has decreased to a proportion of 1 /e is defined by the Harrick equation (Equation (2)), where X is the wavelength of the incoming... 

From the three-layer mode equation, (15.3), the values cutoff and the penetration depth of the evanescent wave in the cover media, dv c, can be found for the three-layer structure as ... 

The depth of penetration (at which the intensity of the evanescent wave has decayed to 1/e of its original value) is given by Eq. (1) ... 

An important issue to consider when probing powders with ATR spectroscopy is the match between particle size and penetration depth of the evanescent wave, as outlined schematically in Fig. 1. For large particles (Fig. 7, case (a)), only the part closest to the IRE is probed by the evanescent field. For large spherical particles, the overlap between the particle and the evanescent field is reduced for geometrical reasons. As shown by Fig. 7(a), the point of contact (the point of highest density) of... 

From an experimental point of view it is important to recognize that the profile of (Ey2 as a function of z is proportional to the profile of the intensity of electromagnetic radiation in the proximity of the interface in medium 2. Such a profile will determine the surface sensitivity of the evanescent wave the depth of penetration is smaller if ... 

What is even more relevant to the present subject is that a thin dielectric layer of polymer can be situated between two media without grossly distorting the optical nature of the interface, i.e. total internal reflection would occur as if no polymer layer is present even if its refractive index is unmatched to both media. Such a layer will, however, affect the intensity of the evanescent wave and particularly its depth of penetration. ... 

An important parameter for the use of ATR in electrochemistry is the penetration depth of the evanescent wave. This is defined as the distance where the amplitude... 

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