Arrayed waveguide grating (AWG) is a promising technology for constructing high-speed large-capacity WDM switches, because it can switch fast, is scalable to large size and consumes little power. To take the full advantage of high-speed AWG, the routing control of a massive AWG-based switch should be as simple as possible. In this paper, we focus on the self-routing design of AWG-based switches with O(1) constant routing complexity and propose a novel construction of self-routing AWG switches that can guarantee the attractive nonblocking property for both the wavelength-to-wavelength and wavelength-to-fiber request models. We also fully analyze the proposed design in terms of its blocking property, hardware cost and crosstalk performance and compare it against traditional designs. It is expected that the proposed construction will be useful for the design and all-optical implementation of future ultra high-speed optical packet/burst switches.