  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.
