Self-imaging effects in curved gradient index multimode interference structures made by K⁺-Na⁺ ion exchange

The paper presents an analysis of self-imaging phenomena in gradient multimode interference (MMI) structures produced by K⁺-Na⁺ ion exchange in glass. This investigation concerned curved MMI structures with various geometries - for the linear, concave function described by an exponential function, and the convex structure connected with a cosine course. The relations derived characterizing the relative shortening of the length of propagation for N-fold images have been confirmed by numerical simulations using the beam propagation method (BPM) of symmetrically excited gradient splitters 1×2.