Fundamental limit for two-dimensional passive devices

There is an upper limit to the number of electromagnetic communication channels in two-dimensional linear passive components that depends only on the geometrical dimensions but is independent of the permittivity function, the actual external shape, or the internal design. The limit applies to both weakly and strongly scattering waves. When the permittivity contrast is low, a tighter limit exists that includes only multiple scattering waves. A detailed analysis helps compare these two limits and leads to insights that apply to devices, such as photonic crystals and microresonators, as well as lossless metamaterials, superlenses, and cloaking devices. As an example, we establish a rigorous scaling relation for the upper bound of the number of demultiplexing channels in superprisms.