Crystal Optics with Spatial Dispersion, and Excitons by Professor Dr. Vladimir M. Agranovich, Professor Dr. Vitaly

Optics

By Professor Dr. Vladimir M. Agranovich, Professor Dr. Vitaly Ginzburg (auth.)

Spatial dispersion, particularly, the dependence of the dielectric-constant tensor at the wave vector (i.e., at the wavelength) at a hard and fast frequency, is receiving elevated cognizance in electrodynamics and condensed-matter optics, partic­ ularly in crystal optics. unlike frequency dispersion, particularly, the frequency dependence of the dielectric consistent, spatial dispersion is of curiosity in optics generally while it results in qualitatively new phenomena. One such phenomenon has been weH identified for a few years; it's the normal optical task (gyrotropy). yet there are different attention-grabbing results because of spatial dispersion, specifically, new common waves close to absorption traces, optical anisotropy of cubic crystals, and so forth. Crystal optics that takes spatial dispersion into consideration contains classical crystal optics with frequency dispersion in basic terms, as a different case. In our opinion, this truth by myself justifies efforts to advance crystal optics with spatial dispersion taken under consideration, even though admittedly its effect is smaH on occasion and it truly is observable basically below fairly distinctive stipulations. additionally, spatial dispersion in crystal optics merits consciousness from one other aspect to boot, particularly, the research of excitons that may be interested by gentle. We contend that crystal optics with spatial dispersion and the speculation of excitons are fields that overlap to an excellent quantity, and that it's occasionally rather most unlikely to split them. it's our goal to teach the genuine interaction be­ tween those interrelations and to mix the macroscopic and microscopic techniques to crystal optics with spatial dispersion and exciton theory.

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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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