By W. Lauterborn, T. Kurz

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**Extra resources for Coherent Optics - Fundamentals and Applns**

**Example text**

Hence, it follows, in partieular, that the function u has no zeros in the upper half-plane. 32,33); for dielectries eij(W) = at the point w = 0, but in this case u = eij(W = O)aial > 1 as follows from thermodynamies [Ref. 7, § 14]). We thus have for the upper half-plane and the real axis 5 ° * = eij(w,k,Bext)aial 0, w = w' + iw", w" ~ 0. 35) This inequality involves another one, namely leij(w,k ,Bext ) 1* ° °, w = w' + i w" , w" > 0. 35) equals zero. 36) the inverse tensor eijl(w,k,B ext ) exists and has no singularity.

An isotropie medium can be gyrotropic since its elements (e. , certain moleeules in agas or in a solution) do not have to have a center of symmetry. In this case isotropy means that aIl directions are equivalent in the sense that normal waves of a given type have the same values of n(w) and the same polarization for all values of s. The presence of gyrotropy in an isotropie medium corresponds formally to the appearance of some pseudoscalar g, i. , of a quantity that changes its sign in the case of mirror reflection.

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].