LITMIR.BIZ

Figure 2.3 Experimental dispersion curves of the permittivity of silver, gold, and aluminum [72, 102]. (a) Real part. (b) Imaginary part.

Note that an extensive treatment of the topic of spatial dispersion would be beyond the scope of this book. Here, we thus limit ourselves to a brief and simplified description of this phenomenon, while more advanced presentations may be found in [9, 29, 52, 148].

      In order to show how spatial dispersion brings about bianisotropy and artificial magnetism in the constitutive relations, consider a medium with the conventional constitutive relations

(2.24a)

      (2.24b)

      where we have expressed the material polarization density, , in terms of the induced current density, (A/). Spatial dispersion is now introduced via the relationship between the induced current and the electric field [29],

(2.25)

where the dyadic tensor represents the response of the medium and is a volume of integration, centered at . We next restrict our attention to the case of weak spatial dispersion, where . We can then simplify (2.25) by using the three-dimensional Taylor expansion of truncated to the second order [29],

(2.26)

where the subscripts and run over , , and , which decomposes the second term in three terms and the third term in nine terms. Substituting (2.26) into (2.25) leads, after somewhat involved manipulations and simplifications [29], to

(2.27)

where the parameters are related to . Inserting then (2.27) into 2.24a yields

(2.28)

where is the Kronecker delta. The relation ( Скачать книгу