On the Propagation of Light in Incommensurately Modulated Dielectric Crystals

Microscopic Dielectric and Gyration Tensors of Incommensurately Modulated Insulators

“…Assuming that the modulation phase factors are fixed (see [24]) and putting cot ðD=2Þ $ 1, q I =k $ 10-50, and e a ; g a $ 10 --6 -10 --4 [1,24,27], one can obtain from (45), (46) a rough estimate c $ 10 --8 -5 Â 10 --6 . This is about two orders of magnitude larger when compared to the normal wave ellipticity predicted in the study [36] where the term linear in the mesoscopic modulation wave vector is not accounted for. The value of the c parameter according to the upper limit gets into the typical sensitivity ranges characteristic of the polarimetric apparatus HAUP (see [6][7][8]) and can be, in principle, detected experimentally.…”

“…The microscopic model testifies that the spatial dispersion and the gyration in the IC insulating systems turn out to be much more complex phenomena than usually believed (see also [36]). They are demonstrated rigorously to be associated with the spatial inhomogeneity of both the electromagnetic wave (the wave vector k) and the optical medium itself (the mesoscopic modulation wave vector q I ), and the latter are even more important.…”

“…with n n ¼ ðe 0 11 e 0 22 Þ 1=4 the mean refractive index. A comparison with the results [36] shows the presence of a relatively large term linear in k=q I in (46), originated from the gradient term r n g ijn in formula (35). Assuming that the modulation phase factors are fixed (see [24]) and putting cot ðD=2Þ $ 1, q I =k $ 10-50, and e a ; g a $ 10 --6 -10 --4 [1,24,27], one can obtain from (45), (46) a rough estimate c $ 10 --8 -5 Â 10 --6 .…”

“…should be taken into consideration for the plane-wave modulation region in the IC phase (see the analyses [24,36]), where the gyration pseudotensor g qn is defined through the relation ðw=cÞ g ijn ¼ e ijq g qn , and e a ðwÞ and g a ðwÞ denote the corresponding modulation amplitudes. Following [36] and solving the standard wave equation in the approximation linear in e a and g a , one can calculate the ellipticity of the normal light waves propagated in the crystal, the parameter that characterizes quantitatively the gyration effect in the birefringent crystal section:…”

Spatial dispersion in incommensurately modulated insulators

“…The material SD in such non-scattering media would mainly modify a polarization state of the light waves but not their phase velocities. As shown in [23], the latter situation just occurs in crystals with the IC superstructure (see also section 4.2). Without pretending to have achieved completeness, let us finally point out the situations in which the material SD in the non-scattering media may be of some practical importance.…”