  We report the implementation and performance of a double servo-loop for
intensity and phase-difference active stabilization of a dual-frequency
vertical external--cavity surface-emitting laser (DF-VECSEL) for coherent
population trapping (CPT) of cesium atoms in the framework of compact atomic
clocks. In--phase fully correlated pumping of the two laser modes is identified
as the best scheme for intensity noise reduction, and an analytical model
allows the optimization of the active stabilization strategy. Optical
phase-locking the beat-note to a local oscillator leads to a phase noise level
below -103~dBc/Hz at 100~Hz from the carrier. The laser contribution to the
short-term frequency stability of the clock is predicted to be compatible with
a targeted Allan deviation below $\sigma_y = 5\,\times 10^{-13}$ over one
second.

Instrumentation and Detectors;Optics