  We present an optimization framework based on Lagrange duality and the
scattering $\mathbb{T}$ operator of electromagnetism to construct limits on the
possible features that may be imparted to a collection of output fields from a
collection of input fields, i.e., constraints on achievable optical
transformations and the characteristics of structured materials as
communication channels. Implications of these bounds on the performance of
representative optical devices having multi-wavelength or multiport
functionalities are examined in the context of electromagnetic shielding,
focusing, near-field resolution, and linear computing.
