How complicated must an optical component be?

TL;DR

This paper introduces a method to quantify the complexity of linear optical components by analyzing the number of parameters needed for various functions, aiding in the design of simpler or more advanced optical devices.

Contribution

It develops a universal approach based on singular value decomposition to evaluate the complexity of linear optical devices across different systems and functionalities.

Findings

The method applies to space-, frequency-, and time-dependent systems.

Limits of simple optical devices are analyzed.

Potential for advanced functionalities with nanophotonics is discussed.

Abstract

We analyze how complicated a linear optical component has to be if it is to perform one of a range of functions. Specifically, we devise an approach to evaluating the number of real parameters that must be specified in the device design or fabrication, based on the singular value decomposition of the linear operator that describes the device. This approach can be used for essentially any linear device, including space-, frequency-, or time-dependent systems, in optics or in other linear wave problems. We analyze examples including spatial mode converters and various classes of wavelength demultiplexers. We consider limits on the functions that can be performed by simple optical devices such as thin lenses, mirrors, gratings, modulators, and fixed optical filters, and discuss the potential for greater functionalities using modern nanophotonics.