The relationship of the Poynting vector and the dispersion surface in the absorbing crystal

Abstract

The relationship of the Poynting vector and the dispersion surface in the absorbing crystal is studied in detail. It is found that the long-accepted concept in which the physical energy flow of waves in the absorbing crystal is normal to the real part of the dispersion surface is not valid when the contribution of the imaginary part of the atomic scattering factor to the diffraction is comparable to that of the real part.

The relationship between the Poynting vector and the dispersion surface in the Bragg case

“…In our previous work [1], we found that, in the symmetrical Laue case, when the contribution of the imaginary part of the atomic scattering factor to the diffraction is comparable to that of the real part near the absorption edge, the direction Poynting vector within the crystal deviates from the normal of the real part of the complex dispersion surface. As we know, the diffraction and the dispersion surface in the Bragg case are quite different from those in the Laue case.…”

“…So we address the question of whether the above-mentioned relationship is valid or not in the symmetrical Bragg case, which is the purpose of this letter. The notation is the same as in reference [1].…”

“…According to equation (22) in reference [1], the dispersion equation in the symmetrical Bragg case (β = 0) is as follows:…”

“…As shown in figure 1, the direction of the averaged Poynting vector S corresponding to the point (X, Y ) is determined by the angle . According to equations (10) and (25) in reference [1], we get and…”