Analysis of mode separation in multichannel branching waveguides

Spatial separation of modes is important in multiport switching and wavelength multiplexing for integrated optics, and in controlling the spatial modes in multimode semiconductor laser structures. It has been recently shown that the
m
normal modes of an
m
- mode channel waveguide can be separated by branching into
m
single-mode channels whose propagation constants are all different. By means of examples, we answer two questions about this mode separation scheme. 1) How widely separated must the channels be in order for each mode to be concentrated in a different one of the channels? 2) How small must the branching angle be in order for the power to remain in the launched mode? The effects of wavelength, dimensions, and refractive index step are discussed. Important conclusions are that the branching angle must be rather small, of the order of a few milliradians, and that it is helpful to have the largest possible difference in the widths of the guiding channels, thereby giving them the largest possible difference in uncoupled propagation constants.