Dispersion relations


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Dispersion relations

Relations between the real and imaginary parts of a response function. A response function relates a cause and its effect through an integral equation. The term dispersion refers to the fact that the index of refraction of a medium is a function of frequency. In 1926 H. A. Kramers and R. Kronig showed that the imaginary part of an index of refraction (that is, the absorptivity) determines the real part (that is, the refractivity); this is called the Kramers-Kronig relation. The term dispersion relation is now used for the analogous relation between the real and imaginary parts of the values of any response function.

References in periodicals archive ?
Kumar, "Towards dispersion relations for tapered core dielectric elliptical fibers," Optik, Vol.
The paper is organized as follow: in Section 2 the dispersion relation of the proposed structure is given.
2004) presented the dispersion relation resulting from linear stability analysis and also its long wave approximation.
Next, having studied the dispersion relation for the eastern Baltic Proper, we present the first derivative in the series as
In this paper, the dispersion relation for the TE and TM modes supported by a vane-loaded circular cylindrical waveguide are derived from an exact solution of a homogeneous boundary value problem for Maxwell's equations, i.
Furthermore, the numerical dispersion relation is derived analytically.
As we observe from dispersion relation profiles in Figure 2 (the dotted lines), the range of frequency where the dispersion relations are discontinuous correspond to photonic band gaps so that no propagating modes exist, and in the regions the dispersion relation are continuous, we have propagating modes (wave number) for each frequency.
In this section, the dispersion relations of the proposed methods are derived by following a similar procedure described in [5].
From these values, the dispersion relations on 4 major directions of the reciprocal lattice of the square lattice are plotted in Fig.
By using the method presented in [22], the numerical dispersion relations of the proposed method and the ADI-FDTD method are as follows.
The present communication aims at the investigation of the dispersion relations of the liquid crystal tapered optical fiber (LCTOF) structure for which Maxwell's equations are implemented for a rigorous analysis.