Incidence, plane total internal reflection

Based on the director distribution we can derive the electrooptical response of a nematic liquid crystal cell (such as birefringence), rotation of the polarization plane of the incident light, total internal reflection, absorption, or some other important characteristics of the cell. In this chapter we will consider in detail these particular features of the electrooptical phenomena in uniform structures. Special attention will be paid to their possible applications. Electrooptics of the isotropic phase and polymer nematics, including Polymer Dispersed Liquid Crystals (PDLC), are also discussed. 

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... 

The form of the Fresnel equations is deceptively simple. They encapsulate the different reflectivity in the p and s planes referred to, but also describe such phenomena as internal reflection, where the refractive index of the incident medium is higher than that of the substrate, and total and frustrated total internal reflection. 

The simplest case for the existence of an evanescent wave is the well-known total internal reflection of a plane electromagnetic wave at the base of a glass prism (index of refraction rii) in contact with an optically less dense medium (with ri2 < Hi), for example, air (Hj = ) This geometry is schematically sketched in Figure 4a (top). If the reflected light intensity is recorded as a function of the angle of incidence, 6, the reflectivity R reaches unity as one... 

Figure 4. Two configurations for evanescent wave optics, (a) Top total internal reflection of a plane wave at the base of a glass prism. Bottom the reflectivity R recorded by a detector as a function of the angle of incidence shows the increase to unity at 6, the critical angle for total reflection, (b) ATR setup for the excitation of surface plasmons (PSPs) in Kretschmann geometry. Top a thin metal film (thickness 50 nm) is evaporated onto the base of the prism and acts as resonator driven by the photon field. Bottom the resonant excitation of the PSP wave is seen in the reflectivity curve as a sharp dip at coupling angle 6g.

A film of metal evaporated onto a glass microscope slide dramatically increases the internal reflectance at angles below the critical angle for to internal reflectance, 0., and causes some loss in the total internal reflection (TIR) region. For monochromatic light incident on a metal film roughly 50 nm thick, polarized in the plane of incidence (p-polarized), a resonant absorption is observed just above 0. . For metals with loss loss at optical frequencies, particularly silver, the reflectance at the resonance angle may fall to practically zero, with a resonance width typically less than 0.5. Fig. 1 shows such a resonance in the reflectance curve for a film of silver. 

Fig. 2 Illustration of geometry and parameters for an evanescent wave produced by the total internal reflection of plane waves incident on the interface of two dielectric media...

A few polymer chains chemically end labeled with a fluorescent probe (NBD) are mixed to the polymer melt (4). The sample is a drop of this mixture (optical index, 03), squeezed between a moving plate and the upper surface of a silica prism (optical index, ni > n2) which form the walls of a plane Couette cell. Two laser beams (wavelength in vacuum Xq) impinge on the prism surface at an incidence angle 0i greater than the critical angle for total internal reflection, 0c = sin (n2/ni). They both... 

For SPR measurement the incident beam should be p-polarized (the electric vector is parallel to the plane of incidence) since s-polarized light will not excite the surface plasmon and will not decrease reflectivity at some angles of incidence. Similarly to a total internal reflection (TIR), the incident beam which excites surface plasmons creates an evanescent field. This evanescent field penetrates the medium next to the metal up to a few hundred nanometers [27-29] and can provide effective excitation of fluorophores. 

Conversely, in the above example, the variation of the phase change with polarization of the plane wave electric field is small when the difference between and ng is small, although the incident wave is still totally reflected. Thus, if the refractive indices are nearly equal, the slight nonuniformity maintains total internal reflection, but the medium is virtually homogeneous as far as polarization effects are concerned. Further, the fields associated with plane-wave reflection satisfy the scalar wave equation, as discussed in Section 35-6. With this perspective, we anticipate that waveguides of arbitrary refractive-index profile have some analogous simplification in the description of their modal fields, provided only that the profile height parameter is small, i.e. A < 1, or n,. ... 

Fluctuations in the dielectric properties near the interface lead to scattering of the EW as well as changes in the intensity of the internally reflected wave. Changes in optical absorption can be detected in the internally reflected beam and lead to the well-known technique of attenuated total reflectance spectroscopy (ATR). Changes in the real part of the dielectric function lead to scattering, which is the main topic of this review. Polarization of the incident beam is important. For s polarization (electric field vector perpendicular to the plane defined by the incident and reflected beams or parallel to the interface), there is no electric held component normal to the interface, and the electric field is continuous across the interface. For p polarization (electric field vector parallel to the plane defined by the incident and reflected beams), there is a finite electric field component normal to the interface. In macroscopic electrodynamics this normal component is discontinuous across the interface, and the discontinuity is related to the induced surface charge at the interface. Such discontinuity is unphysical on the molecular scale [4], and the macroscopic formalism may have to be re-examined if it is applied to molecules within a few A of the interface. 

Infrared Imaging and Mapping for Biosensors, Fig. 2 Schematic of transmission, external reflection, and internal reflection modes at multiple incidence angles (p. For the internal reflection, a single reflection in attenuated total reflection (ATR) geometry is shown exemplar-ily. The polarization of the E-field of the incident radiation parallel (p-polarized) and perpendicular to the incidence plane (s-polarized) is marked in the transmission and... 

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