  In this paper we study photon pairs generated in a nonlinear cavity, composed
of a nonlinear crystal surrounded by mirrors, by the process of spontaneous
parametric downconversion. We analyze two different regimes: singly-resonant
cavities where the signal and idler modes are resonant, and doubly-resonant
cavities where the pump mode is also resonant. We present analytic expressions
for the joint spectral amplitude in these two cases, and study the reduction in
emission bandwidth as the cavity coefficient finesse is increased. We also
study the enhancement of the source brightness resulting from the presence of
the cavity.
