All linear optical devices are mode converters

TL;DR

This paper proves that all linear optical devices function as mode converters, transforming orthogonal input modes into orthogonal output modes, simplifying their analysis and revealing fundamental limitations and design principles.

Contribution

It establishes that any linear optical device can be fully described as a mode converter, providing a universal framework for understanding and designing such devices.

Findings

Any linear optical device can be represented as a diagonal mode conversion operator.

Derived a general expression for alignment tolerance in mode couplers.

Proved that lossless combining of orthogonal modes is impossible.

Abstract

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. As illustrations, we use this approach to derive a general expression for the alignment tolerance of an efficient mode coupler and to prove that loss-less combining of orthogonal modes is impossible.