  Quantum models for synchronously pumped type I optical parametric oscillators
(SPOPO) are presented. The study of the dynamics of SPOPOs, which typically
involves millions of coupled signal longitudinal modes, is significantly
simplified when one considers the ?supermodes?, which are independent linear
superpositions of all the signal modes diagonalizing the parametric
interaction. In terms of these supermodes the SPOPO dynamics becomes that of
about a hundred of independent, single mode degenerate OPOs, each of them being
a squeezer. One derives a general expression for the squeezing spectrum
measured in a balanced homodyne detection experiment, valid for any temporal
shape of the local oscillator. Realistic cases are then studied using both
analytical and numerical methods: the oscillation threshold is derived, and the
spectral and temporal shapes of the squeezed supermodes are characterized.
