Fundamental limits to multi-functional and tunable nanophotonic response

Abstract

Tunable and multi-functional nanophotonic devices are used for applications from beam steering to sensing. Yet little is understood about fundamental limits to their functionality. The difficulty lies with the fact that it is a single structure that must exhibit optimal response over multiple scenarios. In this article, we present a general theoretical framework for understanding and computing fundamental limits to multi-functional nanophotonic response. Building from rapid recent advances in bounds to light-matter interactions, we show that after rewriting the design problems in terms of polarization fields, the introduction of suitable cross-correlation constraints imposes the crucial "single-structure" criteria. We demonstrate the utility of this approach for two applications: reflectivity contrast for optical sensing, and maximum efficiency for optical beam switching. Our approach generalizes to any active or multi-functional design in linear optics.

Designing disordered multi-functional metamaterials using the discrete dipole approximation

“…In this section we give expansions of the figures of merit used in the main text and the gradients that result from these expansions. To write these, we will need to use the expressions for the changes in the fields that are given by (14) in the main text. Unpacking the notation, we have,…”

“…This condition, equivalent to reciprocity, places a stringent constraint on the two wave-fields if they are to be supported by the same material, which can be used to derive fundamental bounds on the performance of multi-functional devices [14]. Equation ( 4) is a generalization of Poynting's theorem, representing the conservation of the norm of the system modes; ensuring for example, their orthogonality.…”

Thickness bound for nonlocal wide-field-of-view metalenses

“…Each of these studies concerns one specific type of design. The powerconcentration bound of Zhang et al [56] and the multifunctional bound of Shim et al [57] are more general, though they bound the performance rather than the device footprint. However, the relationship between thickness and angular diversity remains unknown.…”