ABSTRACT
Up to this point we have assumed that the electric field is scalar, that is, polarized invariably in some particular direction, and that the medium re sponds along this direction. This is often a good approximation, but in general a more realistic assumption is that the field is vectorial with two transverse degrees of freedom. A particularly convenient choice of representation is that with circularly polarized components:
E(z, 0 = £{!+£+(/) ex p [- j(M + jS+)] + £_£_(/) exp[—i(y~t + fi-)]} U(z) + c.c., (1)
where the complex circularly polarized unit vectors s ± = 2~1/2(x ± iy) (see Fig. 12-1), and amplitudes E+, £_, and phases ^+, are slowly varying functions of time. A related generalization of the previous theory is the inclusion of cavity anisotropy, for example, different losses for different polarizations. A strong anisotropy favoring one linear polarization over another can be produced by a Brewster window. Similarly, different polarizations may see different cavity lengths.
