Computational Bounds to Light–Matter Interactions via Local Conservation Laws

Kuang, Zeyu; Miller, Owen D.

doi:10.1103/physrevlett.125.263607

Cited by 37 publications

(39 citation statements)

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“…In this Letter, we develop a general framework for identifying fundamental limits to achievable response in multifunctional devices. Despite significant recent interest in identifying nanophotonic bounds [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], such works have almost exclusively applied only to devices with only a single function. Here, building from recent discoveries that design problems can be transformed to quadratically constrained quadratic programs [26,30], we introduce a simple mechanism for constructing "cross-correlation" constraints that encapsulate simultaneous requirements on a single device.…”

Section: Introductionmentioning

confidence: 99%

“…Despite significant recent interest in identifying nanophotonic bounds [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], such works have almost exclusively applied only to devices with only a single function. Here, building from recent discoveries that design problems can be transformed to quadratically constrained quadratic programs [26,30], we introduce a simple mechanism for constructing "cross-correlation" constraints that encapsulate simultaneous requirements on a single device. Such constraints can be utilized for maximum functionality across multiple frequencies, incident fields, and constituent-material properties, as well as active modulation.…”

Section: Introductionmentioning

confidence: 99%

“…One can accommodate multiple functionalities in the sense of, for example, maximizing scattering while constraining absorption [17,29], but multiple scenarios cannot be accounted for. It is possible to combine the contour-integral, broad-bandwidth approach with the energy-conservation-based, single-frequency approach to identify bounds over any frequency range [19], but such bounds are feasible only for response functions with very special optical-theorem-like structure, such as local den-sity of states [19] and extinction [26]. Tighter singlefrequency bounds can be achieved with a recently developed computational approach in which many "local" conservation laws are identified that must necessarily be satisfied by any design [26,30].…”

Section: Introductionmentioning

confidence: 99%

“…It is possible to combine the contour-integral, broad-bandwidth approach with the energy-conservation-based, single-frequency approach to identify bounds over any frequency range [19], but such bounds are feasible only for response functions with very special optical-theorem-like structure, such as local den-sity of states [19] and extinction [26]. Tighter singlefrequency bounds can be achieved with a recently developed computational approach in which many "local" conservation laws are identified that must necessarily be satisfied by any design [26,30]. The mathematical framework of this approach appears to generalize to physical design problems across many domains; one successful application has been to quantum optimal control [58].…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we combine the recently developed integral-equation framework for optical-response bounds [26,30] with a new approach to capturing constraints that must be satisfied in multi-functional devices. The key is to identify generalized conservation laws that relate the polarization fields induced in one scenario to the incident and scattered fields in another (Sec.…”

Section: Introductionmentioning

confidence: 99%

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Fundamental limits to multi-functional and tunable nanophotonic response

Shim¹,

Kuang²,

Lin³

et al. 2021

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fundamental limits to multi-functional and tunable nanophotonic response

Shim¹,

Kuang²,

Lin³

et al. 2021

Preprint

Self Cite

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Fundamental Limits to the Refractive Index of Transparent Optical Materials

2021

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Increasing the refractive index available for optical and nanophotonic systems opens new vistas for design, for applications ranging from broadband metalenses to ultrathin photovoltaics to high‐quality‐factor resonators. In this work, fundamental limits to the refractive index of any material are derived, given only the underlying electron density and either the maximum allowable dispersion or the minimum bandwidth of interest. In the realm of small to modest dispersion, the bounds are closely approached and not surpassed by a wide range of natural materials, showing that nature has already nearly reached a Pareto frontier for refractive index and dispersion. Conversely, for narrow‐bandwidth applications, nature does not provide the highly dispersive, high‐index materials that the bounds suggest should be possible. The theory of composites to identify metal‐based metamaterials that can exhibit small losses and sizeable increases in refractive index over the current best materials is used. Moreover, if the “elusive lossless metal” can be synthesized, it is shown that it would enable arbitrarily high refractive index in the high‐dispersion regime, nearly achieving the bounds even at refractive indices of 100 and beyond at optical frequencies.

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How Thin and Efficient Can a Metasurface Reflector Be? Universal Bounds on Reflection for Any Direction and Polarization

Abdelrahman

Monticone

2022

Advanced Optical Materials

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such as negative refraction, invisibility, artificial magnetism, and light manipulation over thin surfaces. [2][3][4][5][6][7][8] Because of the capacity to create nanostructures in virtually unlimited forms and with high precision, the design space of all conceivable geometrical configurations for a given volume is vast, possibly spanning thousands to millions of optimization variables. Design methods that involve large-scale simulations, either via brute-force parametric sweeps or using more advanced inverse-design and optimization algorithms, are the typical approach to arrive at components with superior performance. There is no doubt that this approach is successful in achieving efficient designs; [9][10][11][12][13] however, it suffers from a fundamental weakness: no matter how many simulations are performed, there is typically no guarantee that a globally maximal/minimal solution could be identified. If a structure's performance metrics are already close to the optimal solution, significant computing work could be wasted for the sake of finding a better design with no noticeable enhancement.In this context, the question of how to determine a fundamental bound on a certain physical response in a specific volume (such as absorption, scattering, reflection, etc.), no matter how finely structured the system is, has become critically important both from a scientific and a practical perspective. To obtain universal bounds on optical response, these questions should be approached from a fundamental perspective, by examining basic physics constraints like energy conservation, causality, passivity, and symmetries, which govern the totality of electromagnetic interactions. Several fundamental bounds have already been identified in the literature, such as bounds on the scattering cross section, absorption, near-field radiative heat transfer, antenna performance, the local density of states, the refractive index, and other physical responses. [14][15][16][17][18][19][20] In a design approach informed by fundamental bounds, inversedesign methods can then be used to determine an actual feasible design as close as possible to the global optimum.A particularly significant optical function that has only received marginal attention in this context is the ability to optimally control the reflected field in terms of magnitude, phase, direction, and polarization, which is important for a plethora of Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single material represented by a complex scalar susceptibility. The problem of optimal light-matter interactions to maximize reflection is formulated as the solution of an optimization problem in terms of the induced currents, subject to energy conservation and passivity, which admits a global upper bound by using Lagrangian duality. The derived upper bounds apply to a broad range of planar structures, in...

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Computational Bounds to Light–Matter Interactions via Local Conservation Laws

Cited by 37 publications

References 70 publications

Fundamental limits to multi-functional and tunable nanophotonic response

Fundamental limits to multi-functional and tunable nanophotonic response

Fundamental Limits to the Refractive Index of Transparent Optical Materials

How Thin and Efficient Can a Metasurface Reflector Be? Universal Bounds on Reflection for Any Direction and Polarization

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