Leaky modes excitation

A substantial linewidth broadening of the adlayer modes in the whole region near T where they overlap the bulk phonon bands of the substrate the excited adlayer modes may decay by emitting phonons into the substrate they become leaky modes. These anomalies were expected to extend up to trilayers even if more pronounced for bi- and in particular for monolayers. 

While this longitudinal loss is detrimental for communications or applications involving transport of energy over long distances, this property is potentially very beneficial for sensors utilizing capillaries. Most of the leaky modes will directly excite molecules immobilized on the inner surface of the capillary. The effective attenuation for each of the leaky modes is found to be inversely proportional to the diameter of the capillary and exhibits unacceptable values for all modes with the exception of a few lower order modes, corresponding to almost normal incidence at the proximal end of the capillary, i.e., Oq < 5", ... 

The fractional power in the cladding increases with mode number and capillary length. Thus, for sensor application, excitation of higher-order leaky modes leads to direct illumination of the immobilized fluorophores on the surface. 

The products of hybridization are detected through the use of fluorescent labeling. These molecular complexes can either be homogeneously distributed in the liquid core or be bound to the interior surface of the capillary through covalent bonding. In both cases, labeled molecules can be excited either by direct illumination with the leaky modes of the liquid filled core, or by the evanescent waves arising from the guided modes of the capillary wall. Direct excitation is less wasteful of incident photon flux and is the method of choice in conventional fluorometers. Evanescent wave excitation becomes a necessity when direct excitation is either not feasible or results in undesirable sensor performance. Both methods of illumination are possible for the CWBP. 

Fig. 8 Excitation geometry for direct illumination of surface bound molecules. Image on the left shows the modified fiber optic cormector with a fluid port and adjacent optical fiber. Measured nearfield intensity distribution of the distal end confirms propagations of leaky modes...

As discussed in Sect. 2.3, capillary selection may be undertaken by independent consideration of the excitation and emission geometries. Larger ID capillaries are preferred for direct excitation of leaky modes. Capillaries with thinner walls, i.e.. 

Fig. 5—Prism coupler for exciting (a) guided or (b) leaky modes in liquid-crystal (LC) layers.

Fig. 24-2 (a) Intuitive description of power flow on a fiber when a leaky mode is excited at z = 0 and (b) a differential section of length dz of a step-profile fiber, showing the element of leaky-mode power dP lost to radiation. 

As we now have orthogonality relations and normalization expressions for leaky modes, results which were derived for bound modes in earlier chapters can simply be extended to apply to leaky modes. These include the perturbation expressions of Chapter 18, the modal amplitudes due to illumination in Chapter 20, and the excitation and scattering effects of current sources in Chapters 21 to 23. We give an example of leaky-mode excitation by a source in Section 24—23. 

So far we have presented all the properties necessary for understanding the physical attributes of leaky modes, and for determining their excitation. All these properties, though, require a knowledge of the complex propagation constant for each leaky mode. The solution of the eigenvalue equation for values of F below cutoff must, in general, be performed numerically. Only for weakly leaky modes when V is close to cutoff are analytical solutions available [13]. We now consider examples. 

U and Q are defined in terms of 6 by Eq. (21-37). Consequently, as 0 Varies, the peak values of Cf(6) occur at the minima of G([/). Now G(U) vanishes only at a leaky-mode solution of the eigenvalue equation of Eq. (24-30) in these cases U is not real. Since Eq. (21-37) requires U to be real, we deduce that G([/) has small but finite minima when U is approximately equal to the real part of the leaky-mode solution. Thus the peaks in Cj(6) correspond to the finite minima of G U ) and, therefore, to the excitation of leaky modes, i.e. to resonances in the fiber cross-section, as illustrated in Fig. 21-6(0). 

Close to and within the core, the radiation fields are composed of both leaky modes and a space wave, as expressed by Eq. (24-1). Thus, only when the source excites mainly leaky modes is the radiation field given approximately by the leaky-mode fields. This is the case at each p>eak in Fig. 24-7. We next consider a source which is efficient in exciting individual leaky modes. 

In Section 22-5 we determined the attenuation of the fundamental mode on a weakly guiding, step-profile fiber due to radiation from a sinusoidal perturbation of the interface, using free-space antenna methods and correction factors. Here we consider the situation when the radiation field is well approximated by a single leaky mode, which can be realized by having an on-axis sinusoidal nonuniformity of the form of Eq. (22-14). The azimuthal symmetry ensures that only HEi leaky modes are excited. Further, the direction of radiation should coincide with the direction of the leaky-mode radiation [23]. If we represent the nonuniformity and the incident fundamental-mode fields by the induced current method, as in Section 22-5, the direction condition is satisfied by setting C = in Eq. (24-43), whence... 

Sammut, R. and Snyder A. W. (1976) Leaky modes on a dielectric waveguide-orthogonality and excitation. Appl. Opt., 15, 1040-4. 

Oblique ultrasonic waves sent to a composite at frequencies that excite plate wave modes induce the leaky lamb wave phenomenon. When the leaky Lamb wave is generated, the specular reflection is distorted. When the specular reflection and the leaky Lamb wave interfere, a phase cancellation occurs, and two components are generated with a phase between them. Because each type of defect has a unique response, this technique can be used to determine material eleastic constants and to estimate the volume content of resin as well as porosity content. Detection of transverse cracking and delamination in a 24-layer unidirectional graphite-epoxy laminate has also been reported [140], and oblique incidenee back-scattering techniques give accurate fiber orientation of the first composite layers [15],... 

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