Fan in loss in electrical and optical circuits and systems

Analogies between the fan-in limitations of linear electrical circuits and linear optical circuits are explored. In both cases, the second law of thermodynamics sets the limits as to the amount of power that can be coupled from multiple inputs into a single output. The limitation applies to the power coupled into a single (properly defined) output "mode" from a set of input modes. While fan-in limitations of optics have generally been stated in terms of power coupled into a single outgoing spatial mode from incoming spatial modes, a more general view makes use of temporal and polarization modes as well. It is then possible to show that the usual fan-in restrictions stated with respect to only spatial modes can be violated, while the more general restriction in terms of space-time-polarization modes remains satisfied. The results have direct application to wavelength multiplexed optical interconnects.<>