Macroscopic surface excitons and polaritons in isotopically mixed crystalline solutions

1 Macroscopic surface excitons and polaritons in isotopically mixed crystalline solutions 

We will start the discussion of the problem of surface excitons in disordered media considering macroscopic states. It is necessary to know the dielectric constant tensor to determine these states.We will use here the mean polarizability method, which we discussed in Chapter5 and which we apply for a cubic molecular crystal whose molecules differ only in the isotopic composition of the nuclei. 

In the mean polarizability approximation indicated above there exists a Lorenz-Lorentz relation (Lorenz-Lorentz formula) 

Using this relation and also eqn (12.17) and assuming a boundary with vacuum, we obtain the dispersion relation for surface polaritons  

If the polarizabilities a are known, eqn (12.78) determines the surface polariton dispersion as a function of the isotopic composition of the mixture. 

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