Wavelength-Selective Switches for Mode-Division Multiplexing: Scaling   and Performance Analysis
  Wavelength-selective switches for mode-division-multiplexing systems are designed by scaling switches from single-mode systems. All modes at a given wavelength are switched as a unit, which is necessary in systems with substantial mode coupling, and minimizes the number of ports required to accommodate a given traffic volume. When a pure mode is present at the input, modal transmission and coupling coefficients are mode-dependent and may be computed using a simple mode-clipping model. When multiple modes are present, interference between modes alters the transmission and coupling coefficients, shifting the passband center frequency and changing its bandwidth. Mode-coupling matrices are used to compute mixed modes having the narrowest or widest bandwidths, or having the largest center-frequency offsets. In a specific design for graded-index fiber, five mode groups and 50-GHz channel spacing, the one-sided bandwidth may change up to $\pm$3.6 GHz. In a system with many cascaded switches and strong mode coupling, the end-to-end response per switch may be characterized by a mode-averaged transmission coefficient. 
Keang-Po Ho, Joseph M. Kahn and Jeffrey P. Wilde
physics.optics