Advances in chemical physics by I Prigogine

Optics

By I Prigogine

Advances in Chemical Physics, quantity 127 covers contemporary advances on the innovative of study relative to chemical physics. The sequence, Advances in Chemical Physics, presents a discussion board for serious, authoritative reviews of advances in each quarter of the self-discipline.

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N -00 eij,a w,k) = - - t (xk) V,a' dx. x-w If the medium is nongyrotropic, i. 1 The Tensor Gi/W, k) and Its Properties 33 Im{eij(w,k)} = - Im {eij( - w,k)}. 22 a) to eij'( w, k) - t5ij = _2 -f 00 7C 0 x eij"(x, k ) ~ dx, 2 x -w (2. 1. 27 a) eU"( .. wk)' - - -- 2w -f 7C 0 00 e'·(x ~ u 2' k) -u - IJ.. dx . 27, 28) as a parameter and remains arbitrary [it is assumed that the tensor eij(w,k) exists for the k values under consideration, and has no singularities in the upper half-plane and on the real w axis].

Since in the optical range considered the medium is always nonmagnetic (disregarding ferromagnetie substances), we have in practice no limitations (see below). 7) is not at all trivial though quite natural. As a matter of fact there exist quantities which are still functions of s = k/k even when k-+O and thus are not analytic funetions of k if k-+O. In the ease of eij(w,k), however, regularity when k -+0 results from physical considerations, since there are no reasons of either a thearetical ar an experimental nature far the induetion D(w,k) as a function of the field E (w, k) to depend on the magnitude or direction of k in the limiting case of sufficiently long wavelengths, i.

The most important property used above is due to causality. 3 - 5) for D(r, t). 27,28) for special cases only. 9). In general, the tensors eij and eij 1 can be equally weIl applied over a wide range, but, in general, the use of eij is somewhat more convenient and more widespread. At the same time, as we have already indicated above, when k =1= 0, eij(w,k) can have singularities, in principle, when w" > 0, while the tensor e;/(w,k) is an analytic function in the upper half w plane (i. 9]. 27, 28) for the tensor eijl(w,k) are also valid for all values of k.

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