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.