Investigation of self-imaging position dependence on relative modal phase shifts in MMI waveguides

Multimode Interference Devices (MMI) play an important role in optical switches and power splitters. The MMI work on the formation of self-images of any input optical field at various distances along the optical axis of MMI. The length Lπ is an important parameter to calculate the distances where these self-images will be formed. In this paper we show that the calculations of Lπ given in [1] are only approximate and we present an improved method to calculate this parameter. We also show that the error in Lπ calculations is different for single, double and triple images, and therefore requires separate calculations for all these images.