Finding and counting channels with waves

Increasingly, we need to find and count channels for waves. In nanophotonics, knowing how many optical channels can usefully enter or leave a small structure is critical for understanding what the structure can do and how to design it efficiently. Though conventional diffraction theory gives useful answers for large objects, for nanostructure on wavelength scales, there has been no clear picture. We show how understand such channels based on a concept of tunneling escape of waves from small volumes. We also show how to find the best coupled channels automatically through arbitrary optics, based on self-configuring photonic integrated circuit processors, which function as real-time optical analog processing systems.