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For this, express \(\hat e_\lambda (Q)\) exp (iQ·r) appearing in (7.28) in terms of the solutions of the Maxwell equation (7.95) which is possible because \(\hat e_\lambda (Q)\) exp (iQ·r) is also a solution of (7.95). Then use the orthogonality relations to obtain (7.109-112). For more details see [Ref. 7.83, p. 768]. Also note that the surface mode A slm (r) is orthogonal to the bulk modes A klm(r) [i.e., also to \(\hat e_\lambda (Q)\) exp (iQ·r)] because of phase space
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Arya, K., Zeyher, R. (1984). Theory of surface-enhanced Raman scattering. In: Cardona, M., Güntherodt, G. (eds) Light Scattering in Solids IV. Topics in Applied Physics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11942-6_25
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