Evanescent wave penetration depth

Table 3.1 Critical angles of total Internal reflection and evanescent wave penetration depths...

Fig. 2.12 Schematic diagram of an ATR prism, d denotes the evanescent wave penetration depth into the sample. ni and n2 are the indexes of refraction of the prism and sample, respectively. X is the light wavelength and 9 its the angle of incidence...

Problem 7.3. The fluorescence spectrum will be sensitive to the population of the scattered atoms if the evanescent wave penetration depth, S, is less than, or comparable to, the population memory length Ip (see Section 2.4.3). This condition is fulfilled at incidence angles above 0, satisfying the equation... 

Problem 7.4. The vapor spectra excited by an evanescent wave will depend strongly on the change of the vapor polarization in vapor-surface scattering if the evanescent wave penetration depth is less than or comparable with the polarization memory length, i.e.,... 

ATR is one of the most useful and versatile sampling modes in IR spectroscopy. When radiation is internally reflected at the interface between a high-refractive index ATR crystal (usually Ge, ZnSe, Si, or diamond) and the sample, an evanescent wave penetrates inside the sample to a depth that depends on the wavelength, the refractive indices, and the incidence angle. Because the penetration depth is typically less than 2 pm, ATR provides surface specific information, which can be seen as an advantage or not if surface orientation differs from that of the bulk. It also allows one to study thick samples without preparation and can be used to characterize highly absorbing bands that are saturated in transmission measurements. 

While planar optical sensors exist in various forms, the focus of this chapter has been on planar waveguide-based platforms that employ evanescent wave effects as the basis for sensing. The advantages of evanescent wave interrogation of thin film optical sensors have been discussed for both optical absorption and fluorescence-based sensors. These include the ability to increase device sensitivity without adversely affecting response time in the case of absorption-based platforms and the surface-specific excitation of fluorescence for optical biosensors, the latter being made possible by the tuneable nature of the evanescent field penetration depth. 

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 ... 

Delta is of the order of 10 and is typically of the order of a few milliradians. As long as the beam is incident below this critical angle, it is totally reflected and only an evanescent wave penetrates the substrate. This has two very important consequences. First, the penetration depth is of the order of 20 A and thus one can signiflcantly discriminate in favor of a surface-contained material. Compton and elastic scattering are also minimized. In addition, the reflection enhances the local intensity by as much as a factor of 4 as well as the effective path length. All of these factors combined enhance the surface sensitivty of the technique and when combined with solid-state fluorescence detection, submonolayer amounts of material can be detected. ... 

As originally described by Eisenberger and Marra, the angle of incidence is kept below the critical angle for the material under study so that the x-ray beam undergoes total external reflection. As mentioned previously, this has two very important consequences. First of all, since only an evanescent wave penetrates the substrate, the sampling depth is very shallow and of the order of 10 to 20 A. 

An electromagnetic disturbance termed the evanescent wave penetrates the rarer medium to a finite depth. It has a wavelength A. and is continuous with the sinusoidal field of the standing wave, but the electric field amplitude E decreases exponentially with distance from the surface z as... 

In ATR, a beam of infrared light is totally reflected inside a specially cut infrared transparent material that has a high index of refraction. Typical materials used for ATR prisms are Ge, Si, and ZnSe. Because the index of refraction differs between the polymer and the prism, an evanescent wave penetrates the polymer if it intimately contacts the prism. The infrared radiation will interact with molecular vibrations in the same manner as in conventional infrared spectroscopy. The amplitude of the evanescent wave decays exponentially from the surface, so the depth of penetration is arbitrarily taken as the point where the amplitude decays to 1/e (37%) of its initial value. The depth of penetration depends on the ratio of the refractive indices between the polymer and the prism, the angle of incidence, and frequency of radiation in the following manner (Ishida, 1987) ... 

When the phenomenon of total reflection is examined in detail, it becomes clear that the evanescent radiation plays a central role in ATR spectrometry [3,4]. The electric field of this evanescent wave penetrates the sample and decays exponentially with increasing depth of penetration. If no absorption of the incident radiation occurs, the radiation is totally reflected, but if the energy of radiation is transferred to the sample at a wavenumber at which an absorption by the sample occurs, the reflectance at this wavenumber is reduced by the amount of the absorbed energy. Accordingly, if the spectrum of the total reflection is measured, a spectrum similar to a transmission spectrum is obtained. 

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... 

A more direct approach to the photoinduced ET dynamics involves monitoring the lifetime of the excited state at the interface. By illuminating the interface in TIR from the electrolyte phase containing the quencher species, the generation of excited state is limited to the characteristic penetration depth given by the evanescent wave (/ ) [127],... 

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... 

As the mode propagates within the waveguide by total internal reflection, its exponentially decaying evanescent tail extends into both cover and substrate layers over a distance that is characterised by the penetration depth, dp. The extent to which the evanescent field penetrates the cover layer is of vital importance to the operation of evanescent-wave-based sensors. The penetration depth can be calculated from Equation (1) and is typically of the order of the wavelength of the propagating light. 

The background problem can be further overcome when using a surface-confined fluorescence excitation and detection scheme at a certain angle of incident light, total internal reflection (TIR) occurs at the interface of a dense (e.g. quartz) and less dense (e.g. water) medium. An evanescent wave is generated which penetrates into the less dense medium and decays exponentially. Optical detection of the binding event is restricted to the penetration depth of the evanescent field and thus to the surface-bound molecules. Fluorescence from unbound molecules in the bulk solution is not detected. In contrast to standard fluorescence scanners, which detect the fluorescence after hybridization, evanescent wave technology allows the measurement of real-time kinetics (www.zeptosens.com, www.affinity-sensors.com). 

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 ... 

From Snell s Law, sin(0j) m = sin(0j) nr. We have TIR when sin(Oj) > nr/rii, while we will have refraction and reflection when sin(0j) < nr/ni. In practical cases properties of light, such as phase, polarization and intensity, can be modulated inside the wave guide by a given measurand, which is interacting, for instance, with a CIM lying within the penetration depth for the evanescent field of the light localized near the external guide surface. 

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) ... 

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