Constructing wavelength division multiplexing (WDM) switches with cheap components and low complexity is an important problem in optical networking. Typically, there are two request models widely considered. In one model, a connection request asks to go from a wavelength on an input finer of the WDM switch to a particular wavelength on an output fiber. In the other, a connection only needs to get to a particular output fiber, irrespective of what wavelength it will be on. We give novel constructions of strictly nonblocking and rearrangeably nonblocking WDM switches for both request models using limited range wavelength converters and arrayed waveguide grating routers. We fully analyze their blocking characteristics. Our designs are all relatively simple and easy to be laid out, and are useful for both optical circuit-switching and optical packet/burst switching. As far as we know, these are the first of such constructions.