Coupled waveguides mediated by the engineered refractive indexes are the central devices in integrated optical system. Generically, the coupled-mode equations describing the optical transports in the multiple waveguide-coupled structure are relatively complexity and hard to be analytically solved. In this paper we first show that the waveguides with the nearest-neighbor interactions possess simply a SU(2) dynamical symmetry, and then the analytical solutions of the relevant coupled-mode equations can be easily obtained. As a consequence, by setting properly the coupling coefficients between the waveguides, the optical transports in these waveguides can be controlled and the relevant optics devices can be designed robustly. Specifically, we show how the famous geometric phase acquired by the cyclic evolution of a parameter-driven three-level quantum system can be analogously demonstrated with the classical optical pulses transporting in a three-waveguide structure with the transverse interactions. Hopefully, the optical analogue of geometric phase might be applied to design and fabricate various novel phase-modulated integrated devices.