Analysis of giant waveguide tapers with funnel geometry: multi-mode Interference regime to single mode

In this study, we are interested in giant tapers operating in a totally Multi-Mode Interference (MMI) regime capable of producing still an adequate single-mode field at the output. The idea is therefore to provide an answer on a possible giant acceptable limit of such MMI tapers still causing a single-mode output and then determining which opto-geometric parameters on this simple mathematical object and geometry act on the behavior. To this end, we have defined energy criteria per volume at the output. We consider families of tapers with a constant height corresponding to the output rib waveguide and a triangle shape. Each taper is defined by its input size, its length and its output size. The objective is to determine the minimum length of the taper to get enough energy or the desired guided mode(s) in the output waveguide. Two various approaches have been investigated and compared: numerical simulations by a finite element method (COMSOL) and a pure mathematical and geometrical study in conditions of total reflection on the walls of the taper plus a specific plane transformation. When the length of the taper increases, the energy increases in the core up to a limit value and decreases in the cladding. The size of the output guide is fixed to w_s = 2 microns and the input size of the taper varies from typically 6 microns to `giant' 400 microns. Four kinds of behavior were identified. For small lengths all the energy is reflected by the walls of the taper. For first intermediate lengths a part of the light is difused in the cladding and the other part is guided to the output guide. For following intermediate lengths the major part of the light is guided to the output guide with multi-modes propagation. Lastly for greater lengths only the fundamental guided mode appears in the output guide.