Evanescent field wave, penetration depth

For infinite film thickness the two waves in the film will just act as freely propagating waves with minimal influence from the surrounding medium hence, practically all the mode power will be flowing in the film, resulting in vm -> c/riy and Nm -> tip. However, the total internal reflection at the boundaries still results in evanescent fields with penetration depths of dp>b = k l (nP - ax) 1/2 int0 the highest-RI medium and dp>c = k l (n - M in) 1/2 into the lowest-RI medium. 

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. 

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. 

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 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. 

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... 

The second (real) term accounts for the exponential decay of the electric field intensity in the direction normal to the interface. The reflected beam combines with the incident beam, forming a standing electromagnetic wave at the interface (Fig. 9.9). The electric field that penetrates to the optically rarer medium of refractive index n, the evanescent field, plays a critical role in many optical sensors based on the waveguiding principle. Its depth of penetration dv is defined as the distance at which the initial intensity Eq decays to 1/e of its value. Thus from (9.18), dv is... 

Figure 8.2 (a) The incident angle is 0 > 0c, where 0c is critical angle where total reflection on interface starts to produce, (b) The electric field of evanescent wave in the surrounding medium. Dp is the penetration depth of evanescent wave in surrounding medium. 

In ATR-FTIR excitation occurs only in the immediate vicinity of the surface ol the reflection element, in an evanescent wave resulting from total internal reflection. The intensity of the evanescent field decays exponentially in the direction normal to the interface with a penetration depth given by (1.7.10.121, which for IR radiation is of the order of a few hundreds of nm. Absorption leads to an attenuation of the totally reflected beam. The ATR spectrum is similar to the IR transmission spectrum. Only for films with a thickness comparable to, or larger than, the penetration depth of the evanescent field, do the band intensities depend on the film thickness. Information on the orientation of defined structural units can be obtained by measuring the dichroic ratio defined as R = A IA, where A and A are the band absorbances for radiation polarized parallel and perpendicular with respect to the plane of incidence, respectively. From this ratio the second-order parameter of the orientation distribution (eq. [3.7.13]) can be derived ). ATR-FTIR has been extensively used to study the conformation and ordering in LB monolayers, bilayers and multilayers of fatty acids and lipids. Examples of various studies can be found... 

Figure 3.38. The penetration depth, d, for the evanescent wave from the core into the cladding for three beams A, B and C E is the electric field strength.

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... 

Precise control of the incidence angle is important to generate evanescent fields in a reproducible manner because the intensity and the depth of the evanescent fields depend on the angle. For intensity and penetration depth of the evanescent wave, and d, respectively, we have. 

The polarization of the incident beam does not affect the penetration depth, but it does affect the amplitude of the evanescent field. For plane waves incident on the interface with intensity /j in the dense medium, the amplitude of the field in the less dense medium /q is given by... 

Evanescent wave microscopy has already yielded a number of contributions to the fields of micro-and nanoscale fluid and mass transport, including investigation of the no-slip boundary condition, applications to electrokinetic flows, and verification of hindered Brownian motion. With more experimental data and improvements to TIRE techniques, the accuracy and resolution of these techniques are certain to improve. Areas of potential improvements include development of rmiform-sized and bright tracer particles, creation of high-NA imaging optics and high-sensitivity camera systems, and further development of variable index materials for better control of the penetration-depth characteristics. 

Evanescent-wave microscopy uses the evanescent wave produced by the total intemal reflection of light at a dielectric interface to illuminate a layer of material within the penetration depth of the evanescent field. The material of interest is imaged using a microscope objective typically within 100-200 nm of the interface. 

Simultaneous with the light s reflection off the internal surface of the fiber is the creation of an electromagnetic field at the external surface of the fiber core. This field extends into the surrounding media and is called the evanescent wave. The intensity of the field decays exponentially as the distance from the surface of the probe increases. The effective distance this field penetrates the external media is less than one wavelength of light and is very sensitive to the incident angle the refractive indexes of the internal media (n ), and external media (n2). For the typical optical fiber used in an immunoassay with a fused silica core surrounded by an aqueous media, the penetration depth of the evanescent wave is on the order of 100 nm. 

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