Dear Colleagues,
From relation:
P=ε_0 χ^((1)) E
I suppose that in an isotropic medium, χ^((1)) is the scalar quantity, vector P and E are in the same direction, while for an anisotropic medium, χ^((1)) is the tensor quantity, vector P and E are different in direction. However, my professor said that the above statement is not true in some special cases. Could you tell me which is the those cases?
Thank you and hoping for your insightful response.
This depends on the crystal system. For triclinic systems the above statement that P and E are not in the same direction is generally true. For monoclinic systems it is not true for E parallel to the crystallographic b-axis. For orthorhombic systems it is not true for E parallel to the 3 crystallographic axes. For uniaxial materials it is not true for E parallel to the optical axis and in all directions perpendicular to this axis.
Thank you very much, Prof.Thomas Mayerhöfer. The important issue is first statement which is also not true (according to my professor): χ^((1)) is the scalar quantity, vector P and E are in the same direction. What do you think about this?
May be your Professor refers to chiral media, for which the polarization vector also depends on magnetic field for isotropic and anisotropic systems.
Or he refers to the fact that isotropy is somewhat ill-defined. In case of cubic crystals the first statement should be true as long as the wavelength of the incoming radiation does not become too small (keyword: "intrinsic birefringence"). For randomly oriented polydomain media where the domains themselves are anisotropic, it is also the wavelength of the incident light that is decisive. If the domains are small compared to the resolution limit of light, the first statement is true. If they are not small, then double refraction occurs in each domain, and the first statement is no longer true. See e.g.
Article Optical isotropy in polycrystalline Ba_ {2} TiSi_ {2} O_ {8}...
I really appreciate your help, Prof.Thomas Mayerhöfer and Prof.Pablo Acebal !
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