Index effective

We now define a quantitative measure of the magnitude of the gel effect the gel effect index, y ... 

Experimental conversion-time data, obtained from the literature, on the bulk free radical polymerization of MMA initiated by AIBN at several temperatures and initiator concentrations, were described by the model. However, the expressions for the rate of conversion and gel effect index were first simplified and rearranged. ... 

Assuming that no chain transfer reaction was sufficiently important to be considered, useful simplifications result for equations (la), (3) and (4), so that the gel effect index, y, is given by the expression ... 

If equations (7) and (9) are then introduced into equation (6), as well as the correct expressions for n and the variation of with conversion, the expression for tfie gel effect index may be written as ... 

The general equation for the gel effect index, equation (la) which incorporates chain transfer, was used in those cases where there was not a good agreement between model predictions and experimental data. The same values of and (derived from the values of and C2 found at high rates) were used in the integration of equation (1) and the value of the constant of chain transfer to monomer, C, was taken as an adjustable parameter and used to minimize tfie error of fitting the time-conversion data by the model. 

The calculation of the cladding mode effective index can be accomplished by an extension of the model for doubly clad fibers28 or by following the transfer matrix method (TMM) proposed by Anemogiannis et al.26 and successively widely adopted for the analysis of coated LPGs29 30. 

Fig. 8.26 Effective index variation is calculated as a function of the refractive index of top cladding. The result shows that slot microrings have higher waveguide sensitivity than conven tional microrings...

The two important properties of the waveguide mode are its cross-sectional electric field amplitude profile A(x,y) and the effective index /VelT. Here x and y are the coordinates in the plane perpendicular to z, the waveguide propagation direction. The electric field at any point along the waveguide is given by... 

Fig. 9.6 The calculated effective index change in the silicon PWEF waveguide of Fig. 9.3 induced by adsorbed films of constant optical thickness (a) Dopt 0.4 nm and (b) Dopt 0.1 nm for film thickness between 0.5 and 16 nm. As the film thickness changes, the refractive index is adjusted so that the optical thickness remains constant. For comparison, the graphs also show 8iVeff and the corresponding SPR angle shift A6 for an SPR experiment...

Therefore Z)opt provides a convenient single parameter that can be used to estimate the response of guided modes to very thin adsorbed layers. To assess and compare surface sensitivity, in this chapter, we will use the differential change of mode effective index with the optical thickness ... 

Guided mode calculations were also carried out to compare the sensor response of several waveguide systems. In these simulations a model molecular monolayer is represented by a 2-nm thick layer with a refractive index of n 1.5. The optical properties of this model layer are typical of a dense layer of organic molecules on a substrate1 41, and are a reasonable approximation for a streptavidin protein layer bound to a biotinylated surface, the experimental model system we use to characterize our sensors. The ambient upper cladding was assumed to be water with a refractive index of n 1.32. For all examples, the lower cladding was assumed to be Si02 with an index of n 1.44. In the simulations, the effective index of... 

Fig. 9.7 The effective index change induced by the adsorption of a 2 nm thick molecular layer with index n 1.5, calculated as a function of core thickness for the TM mode propagating in glass, polymer, silicon nitride, and silicon waveguides. The right vertical axis shows the equiva lent modal sensitivity...

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