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Planar arrays of coupled synchronous waveguides are analyzed with regard to full power transfer between the outermost guides. It is shown analytically, that in an -guide synchronous system the coupling coefficients have to be tapered parabolically, in agreement with previous empirical results; the propagation constants of this system are equi-spaced. We prove that full transfer indeed occurs and determine the coupling length of the system. The mode interference picture provides a physical interpretation of the full transfer phenomenon. This multiple waveguide system is a discrete analog of the quantum mechanical harmonic oscillator.