Why is the fact that N(-E) = N*(E), where N(E) = n(E) +ik(E), a condition of time reversal symmetry? N(E) represents the complex index of refraction and E is photon energy,
Yes, E is photon energy. And, I cannot define negative energy of a photon. But, according to Jellison and Modine (Appl. Phys. Lett. 69, 371, 1996) the Forouhi-Bloomer (FB) dispersion equations violate time reversal symmetry because k(E) is not equal to -k(-E) in FB equations. However, I cannot find a specific scientific reference where the extinction coefficient, k, is explicitly associated with time reversal symmetry. Can you help?
It is well known that complex character of refraction index is resulted from solution of Maxwell wave equation for electromagnetic waves. Like mass, charge and some other index refraction is nondynamical parameter and therefore it dose not change sign at operation of time reversal. If you change formally both signs it could be connected with reversal direction of wave propagation and amplification of wave instead damping. Kramers -Kronig integral relation in positive frequency region on the base of this complex form gave us useful method to connect real and imagine parts of IR and showed that connection between reason and results exists in nature. Some similarity to time reversal effect we can meet in nonlinear optics. It is effect of wave front reversal or phase reversal at stimulated Brilluin light scattering to backward and some other effect that You can find in VIKI. So good lack in search this interesting question.
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