We have designed and fabricated a set of AlGaAs multilayer waveguides, which can serve as a source of entangled photons at 1.55 μm through parametric fluorescence. In our scheme two counterpropagating, orthogonally polarized signal/idler modes are nonlinearly generated by a pump wave impinging on the upper surface of the waveguide. To check the compliance with design specifications on phase-matching wavelength and parametric gain, we have systematically measured effective indices and surface-emitting second-harmonic generation, respectively. This characterization allowed us to single out a nominal sample with optimum performances, which we numerically modeled for counterpropagating parametric fluorescence. We predict a pair generation efficiency ηPF=4×10-13 (signal photons per pump photon). For a 1 W (peak), 100 ns pump pulse at normal incidence, this corresponds to about 14 photons per dark count with state-of-the-art avalanche photodiodes.