We propose a novel concept for the implementation of 2-dimensional (2D) optical phased arrays (OPAs) with end-fire waveguides as antenna elements (AEs), and we present its theoretical model and experimental proof. The concept is based on the use of 3-dimensional (3D) photonic integrated circuits (PICs) with multiple waveguiding layers on the PolyBoard platform. In their simplest form, the 3D PICs comprise AEs at different layers, vertical and lateral couplers for the distribution of light among the AEs, and phase shifters for the execution of the 2D beam scanning process. Using the field equivalence principle, we model the radiated field from the single-mode waveguide of the platform at 1550 nm, and we find that the expected beam width is 12.7^o. We also investigate the perturbation that is induced into propagating fields inside parallel waveguides in proximity, and we conclude that waveguide spacings down to 6 µm can be safely used for development of uniform OPAs in the PolyBoard platform. For OPAs with 6 µm pitch and 4 AEs, we find that the maximum steering angle is 14.0^o and the expected angular clearance, wherein the main radiation lobe is higher than any grating lobe by at least 3, 6 and 10 dB is 10.8^o, 7.6^o and 2.8^o, respectively. Based on our simulations, we design and fabricate single- and 2-layer PICs with 1×4 and 2×4 OPAs. The lateral pitch of the OPAs ranges from 10 down to 6 µm, while the vertical pitch is 7.2 µm. We experimentally characterize these OPAs and validate the potential of the 2-layer PICs for 2D beam scanning on the azimuthal and elevation plane. The beam profiles and the main scanning parameters such as the maximum steering angle and the relative intensity between the main and the grating lobes are found in excellent agreement with our simulations.