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

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 recognition 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 customarily while it ends up in qualitatively new phenomena. One such phenomenon has been weH recognized for a few years; it's the traditional optical job (gyrotropy). yet there are different fascinating results because of spatial dispersion, particularly, new basic 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 purely, as a distinct case. In our opinion, this truth on my own justifies efforts to boost crystal optics with spatial dispersion taken into consideration, even if admittedly its effect is smaH every so often and it truly is observable in simple terms less than fairly distinct stipulations. in addition, spatial dispersion in crystal optics merits realization from one other aspect to boot, particularly, the research of excitons that may be serious about gentle. We contend that crystal optics with spatial dispersion and the speculation of excitons are fields that overlap to a good volume, and that it truly is occasionally really most unlikely to split them. it really is our goal to teach the genuine interaction be­ tween those interrelations and to mix the macroscopic and microscopic methods to crystal optics with spatial dispersion and exciton theory.

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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].

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