Evanescent-wave mode

As shown in Eq. (13.46), the Galerkin solution consists of a free propagating wave mode and nonpropagating evanescent modes. The evanescent wave modes would be of importance in the region near the breakwater. However, since we are interested in the reflected wave far from the breakwater, we focus on the solution for the propagating mode. Massed showed that in region 2, the function (po x) satisfies the following ordinary differential equation ... 

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. 

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 fabrication and characterization of a fiber optic pH sensor based on evanescent wave absorption was presented by Lee63. The unclad portion of a multi-mode optical fibre was coated with the sol-gel doped with pH sensitive dye. The sensitivity of the device increased when the multiple sol-gel coatings were used in the sensing region. The dynamic range and the temporal response of the sensor were investigated for two different dyes -bromocresol purple and bromocresol green. 

The same observations are true for the evanescent wave of the modes in the surrounding medium. Moreover, these changes in the field distributions are accompanied by an increase of the effective refractive indices of the cladding modes, as will be clarified later. For this reason and by virtue of (3.1), the resonance wavelengths of the coated LPG are expected to blue-shift in response to an overlay thickness change. 

Rosenberger, A. T. Rezac, J. P., Whispering gallery mode evanescent wave microsensor for trace gas detection, In Biomedical Instrumentation Based on Micro and Nanotechnology Mariella, R. P., Jr. Nicolau, D. V., Eds. Proc. SPIE 2001, 4265, 102 112... 

Evanescent Waves of Guided and Leaky Waveguide Modes... 

The sensor systems outlined in the present chapter use evanescent electromagnetic radiation to monitor various analytes in aqueous solutions. Therefore, as a beginning, the basic properties of evanescent electromagnetic waves and the so-called TIR phenomena are summarized. Afterwards, two types of waveguide modes will be briefly discussed guided and leaky modes, which both generate evanescent waves at a solid/liquid boundary. 

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 ... 

As mentioned in Sect. 15.2, sometimes a 4th thin layer (M) of metal or die is incorporated between the substrate and waveguide film to decrease the radiation loss into the substrate of the substrate radiation modes. These modes are referred to as leaky modes and the obtained structure is the MCLW. This configuration is also broadly used in evanescent wave sensor systems. 

Rowland, D.R. and Love, J.D., 1993, Evanescent wave coupling of whispering gallery modes of a dielectric cylinder. TEE Proc.Pt. J 140(3) 177-188. 

Fig. 8.9 Set-up for infrared measurements in attenuated total reflection mode on a planar model catalyst. The silicon ATR crystal has a top layer of SiC>2 which serves as the supported for the catalyst particles. In reality, the infrared beam undergoes 25 reflections with the surface in the crystal the evanescent waves protruding outside the crystal are used...

This split-off discrete state rejoins, for cK co0, the exciton energy ha>0 it behaves qualitatively in the same way as the lower branch of the 3D polariton.33 35 For this reason we call it the 2D polariton. It is the projection of the exciton K> on this 2D polariton (radiatively stable) that constitutes (1) the finite limit value of the curves AK t) for t- oo (Fig. 3.8), and (2) the weight of the discrete peak in the spectrum PK((o) (Fig. 3.9). The transition, in the 2D polariton branch, between the photon and the pure exciton characters occurs around the value K0 = co0/c in an area of width AK = r0/c (with ro = 15cm 1). Thus, the 2D polariton may be considered as a photon mode trapped in the 2D lattice, where it acquires its own dispersion.115,116,126 Therefore, the 2D polaritons cannot be excited by free photons, but they may be coupled to evanescent waves, by ATR for example.115,116... 

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