Partial image revivals in a multi-channel directional-coupler

We describe and analyze the phenomenon of partial image revivals in a multi-channel directional-coupler (MCDC) structure. Using supermodes, a MCDC is described as a composite waveguide structure and then analyzed in terms of multi-mode interference and the principle of self-imaging. As we bring the waveguides in the array closer together the supermodes beat to form partial images in between the complete mirror- and self-images. In this case, we have the advantage of the increased coupling and hence shorter image lengths, but with the disadvantage that the images are partial revivals of the input field. Nonetheless, we can take advantage of the partial image revivals that occur near complete mirror- and self-images, as they are almost complete images themselves. To demonstrate the use of this phenomenon we describe the simple design of a compact 1×2 wavelength division multiplexer based on a MCDC. The design highlights a trade-off between device length and isolation ratio, where although we use the partial self-image at 1.55 μm for a more compact device, the trade-off is a reduced isolation ratio when compared to 1.3 μm where a complete mirror-image is present.