Normalization leaky modes

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", ... 

It follows from the discussion in the previous section that the normalization N of each leaky mode is defined by... 

We emphasize that the definition of N given by Eq. (24-27) is formally correct for leaky modes of arbitrary attenuation. However, although the power of a bound mode on a nonabsorbing fiber is directly related to normalization in Eq. (11-22), there is no corresponding expression for the power of a leaky mock-The leaky-mode power P of Eq. (24-16) is an intuitive concept for understanding leaky modes. Only for weakly leaky modes can we express power in terms of normalization using Eq. (11-22). However, if we are only concerned with the power in the core, then Eq. (11-28) applies rigorously to both bound and leaky modes. 

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. 

In Eq. (24-53), we substitute for Cu and Cji from Eq. (24-48) with Uf = Uj. The normalization Nj is given by Eq. (24-29) and Af, follows from Table 14-3, page 313. Using the condition G([//) = 0 to express the Hankel functions in terms of Bessel functions leads to Eq. (24-56). Weare reminded that this equivalence holds only for the leaky-mode radiation direction of Eq. (24-9). 

Radiation inodes of the scalar wave equation 33-7 Orthogonality and normalization 33-8 Leaky modes... 

Transvascular transport involves both convection and diffusion. Under normal physiological conditions, diffusion is the dominant mode of transport for small molecules and convection is more important for transport of macromolecules and nanoparticles. However, interstitial fluid pressure (IFF) at the center of solid tumors is elevated uniformly, and is approximately equal to the microvascular pressure. In addition, the osmotic pressure difference across the microvessel wall is minimal because of the vascular leakiness. Therefore, the driving force for convection is negligible in the middle of sohd tumors. At the periphery, convection can be the dominant mode of transvascular transport of macromolecules due to the rapid decrease in the IFR The convection can make systemically administered macromolecules preferentially accumulate at the edge of tumors (see also the discussion on interstitial transport). ... 

---