Intensity match conditions

Equation (9.22) is the intensity match condition for the reflectance at the resist-air interface to be zero, and its significance lies in the fact that it encapsulates within it the optimal refractive index of the top antireflection coating that is associated with the least reflectivity at the resist-air interface. 

In summary, for the reflectivity to be zero, both the phase match and the intensity match conditions must be satisfied. 

The Hartmann-Hahn match can be found by varying the B S) power level so that maximum intensity is observed. It is important to ensure that the observed spectrum results from the CP (the best indication of this is the absence of the signal after increase of the power beyond the H-H matching condition). 

I i Intensity of incident light, 1 sample path length, 1 c coherent length, n, refractive index If phase matching condition A k =0 does not hold, I decreases, i.e., 1 m depends on the incident angle 0. m = 2 second harmonic generation (SHG) m=3 third harmonic generation (THG)... 

Nevertheless, Morris and Ellis [29] demonstrated the feasibility of the Al/ H CP experiment. For a hydrated 7-alumina, they were able to observe Oh and Tj Bronsted acid sites on the surface. In the original work, the matching conditions favored CP to the Of, sites relative to Tj sites. Subsequent experiments, represented in Fig. 7, illustrate more balanced CP conditions for surface and Of, sites. Upon partial dehydration, the population of Tj sites is reduced relative to that of Of, sites. These findings are consistent with the relative acidity of the sites. Concomitant with these observations in dehydration experiments was a significant reduction in Al signal intensity, which is consistent with the surface Hs being the source of the Al magnetization. 

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