  Within the frame of quantum optics we analyze the properties of spontaneous
emission of two-level atom in media with indefinite permittivity tensor where
the geometry of the dispersion relation is characterized by an ellipsoid or a
hyperboloid(hyperbolic medium). The decay rate is explicitly given with the
orientation of the dipole transition matrix element taken into account. It
indicates that for the ellipsoid case the intensity of the photons coupled into
different modes can be tuned by changing the direction of the matrix element
and for the hyperboloid case it is found that spontaneous emission in
hyperbolic medium can be dramatically enhanced compared to the dielectric
background. Moreover, spontaneous emission exhibit the strong directivity and
get the maximum in the asymptote direction.

Optics;Quantum Physics