ABSTRACT
We will present in this appendix, principally for the benefit of the less experienced reader, a derivation of the dispersion in a bianisotropic medium and the Fresnel coefficients across the interface between an isotropic medium and a bianisotropic medium. This is primarily to only demonstrate the manner of calculating them. By following the procedure the reader should be able to derive all the cases (anisotropic, bi-isotropic or bianisotropic) that (s)he would confront in the book. We will consider the case when the constitutive relations for the bianisotropic medium are given by
D = ε0
⎛ ⎝ εx 0 00 εy 0
0 0 εz
⎞ ⎠E + 1
c
⎛ ⎝0 iξxy 00 0 0
0 iξzy 0
⎞ ⎠H, (B.1)
B = 1 c
⎛ ⎝ 0 0 0iζyx 0 iζyz
0 0 0
⎞ ⎠E + μ0
⎛ ⎝ 1 0 00 μy 0
0 0 1
⎞ ⎠H. (B.2)
These relations are seen to be reciprocal if ζyx = −ξxy and ζyz = −ξzy. An array of split-ring resonators with their axes along the y direction (or cylinders along the y directions) would be well described by these constitutive relations (see Chapter 3). This is a special case of a bianisotropic medium where the modes in the medium are linearly polarized.
