All linear optical devices are mode converters

Understand

We show that every linear optical component can be completely described as a device that converts one set of orthogonal input modes, one by one, to a matching set of orthogonal output modes.

• This result holds for any linear optical structure with any specific variation in space and/or time of its structure.
• There are therefore preferred orthogonal "mode converter" basis sets of input and output functions for describing any linear optical device, in terms of which the device can be described by a simple diagonal operator.
• This result should help us understand what linear optical devices we can and cannot make.