Tapered Photonic Switching

TL;DR

This paper develops a general analytical framework for understanding and designing wave control via temporal inhomogeneities in nonlinear materials, enabling broadband frequency conversion and filtering.

Contribution

It introduces a formalism based on electromagnetic momentum conservation to quantify and tailor time-reversal effects in temporally inhomogeneous media.

Findings

Analytical formalism for time-reversal due to temporal inhomogeneities.

Design methodology for broadband frequency converters and filters.

Demonstration of tailored spectral responses using the formalism.

Abstract

The advent of novel nonlinear materials has stirred unprecedented interest in exploring the use of temporal inhomogeneities to achieve novel forms of wave control, amidst the greater vision of engineering metamaterials across both space and time. When the properties of an unbounded medium are abruptly switched in time, propagating waves are efficiently converted to different frequencies, and partially coupled to their back-propagating phase-conjugate partners, through a process called time-reversal. However, in realistic materials the switching time is necessarily finite, playing a central role in the resulting temporal scattering features. By identifying and leveraging the crucial role of electromagnetic momentum conservation in time-reversal processes, here we develop a very general analytical formalism to quantify time-reversal due to temporal inhomogeneities of arbitrary profile. Finally, we deploy our analytic theory to develop a formalism, analogous to spatial tapering theory, that enables the tailoring of a desired time-reversal spectral response, demonstrating its use for the realization of broadband frequency converters and filters.