I am writing regarding a statement on the invited paper of Prof. Boardman Allan and Dr. Xie Ming, appeared in SPIE proceedings 2001, and also in the book "Introduction to Complex Mediums for Optics and Electromagnetics" chapter of complex magnetic materials, which I could not understand, or find an answer.
The statement is: "it is clear that (g × E) is normal to E, so that the overall dielectric property tensor of a magneto-optic material must have off-diagonal elements."
My questions are:
1) How can one relate / understand the off-diagonal elements in the permittivity tensor are due to the fact that g x E is normal to E (are there any mathematical aspects hidden beneath that)?
2) And, why the other off-diagonal elements equal to zero ? (is tehre any coordiantes' sytem transformation)
Thank you inadavance for your answers !
Dear Mr. Abdedaim,
the equation which you are referring to is
(1) D = ε0 ( ε E + i g x E ) ,
where ε is the dielectric tensor in the absence of the applied static magnetic field, while g depends on the magnetic field. In a component form, this equation reads
(2) Dk = ε0 ( εkl El + i εknl gn El ) ,
where in the second term εkln denotes the Levi-Civita symbol. One can also write this as
(3) Dk = ε0 (ε')kl El ,
with the "overall" dielectric tensor (including the effects of the static magnetic field)
(4) (ε')kl = εkl + i εknl gn .
This tensor has obviously off-diagonal elements (where k ≠ l). For example,
(5) (ε')13 = ε13 + i g2 .
I hope this might be a helpful answer. With best regards, Giulio
Dear Dr. Schober,
Thank you very much for your answer ! Definitely, it gave me more insights.
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