Theoretical Results for a Distribution of Dipoles. Random Orientations

Theoretical Results for a Distribution of Dipoles Random Orientations 

The collected fluorescence 3F [from Eq. (7.39)] clearly depends on the orientation distribution of the dipoles and the incident polarization through the dependences on 0 and E. We will assume a special but common case here randomly oriented dipoles with a z-dependent concentration near the surface, excited by a p-polarized evanescent wave. 

In this case, C(z, ) , 6 ) = C(z). Equation (7.39) can then be written as an integral over the dipole distance z  

The remaining functions of z that are needed in order to do the integral in Eq. (7.41) are the excitation intensity ,p(z) 2 and the concentration profile C(z). The excitation intensity is easily obtained from Eq. (7.10). Note that the exp(—zJd) implicit in the (z) 2 factor can be written as exp(—zk ), where 

The concentration profile may be known, for example, a delta function at a particular z (say, z = 0) for closely adsorbed material, or a step function out 

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