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Physical limits in electromagnetism

Nature Reviews Physics volume 4, pages 543–559 (2022)Cite this article

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Abstract

Photonic devices play an increasingly important role in advancing physics and engineering. Although improvements in nanofabrication and computational methods have driven progress in expanding the range of achievable optical characteristics, they have also greatly increased design complexity. These developments motivate the study of fundamental limits on optical response. Here we review recent progress in our understanding of these limits with special focus on an emerging theoretical framework that combines computational optimization with conservation laws to yield physical limits capturing all relevant wave effects. Results pertaining to canonical electromagnetic problems such as thermal emission, scattering cross-sections, Purcell enhancement and power routing are presented. Finally, we identify areas where further research is needed, including conceptual extensions and efficient numerical schemes for handling large-scale problems.

Key points

  • Limits provide a rigorous theoretical basis to quantify the trade-offs and scaling laws associated with almost any common design parameter (device footprint, material choices, fixed separations and so on).

  • Limits may guide practical design efforts and complement computational inverse design methods by confirming the achievement of near-optimality or clarifying possibilities for further improvement.

  • Inverse design methods, such as topology optimization, involve a large number of degrees of freedom subject to non-convex constraints (Maxwell’s wave equations); although gradient-based methods can efficiently find local optima, it is generally infeasible to determine the global optimum.

  • Many limits are derived by simplifying the design problem in some fashion: for example, by working with geometric optics, maximizing per-mode contributions ignoring inter-mode constraints, only enforcing a subset of the relevant physics and so on.

  • Mathematical optimization theory formalizes the notion of simplified (‘relaxed’) physics and offers tools for bounding the design performance in such settings. In turn, these values bound realistic design performance.

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Fig. 1: Applications of photonics and computational design.
Fig. 2: Overview of representative electromagnetic limits.
Fig. 3: Schematic of scattering theory.
Fig. 4: Bounds on angle-integrated absorption based on the conservation of resistive power.
Fig. 5: Bounds on scattering cross-sections based on the conservation of total power.
Fig. 6: Impact of localized constraints.
Fig. 7: From performance bounds to structural optimization.

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Acknowledgements

The authors acknowledge support from the National Science Foundation under the Emerging Frontiers in Research and Innovation (EFRI) programme, grant no. EFMA-1640986, the Cornell Center for Materials Research (MRSEC) through award no. DMR-1719875, and the Defense Advanced Research Projects Agency (DARPA) under grant agreements no. HR00112090011, no. HR00111820046 and no. HR0011047197. R.K.D. acknowledges financial support from the Princeton Presidential Postdoctoral Research Fellowship.

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  1. Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ, USA

    Pengning Chao, Benjamin Strekha, Rodrick Kuate Defo & Alejandro W. Rodriguez

  2. Department of Engineering Physics, Polytechnique Montréal, Montréal, Québec, Canada

    Sean Molesky

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Chao, P., Strekha, B., Kuate Defo, R. et al. Physical limits in electromagnetism. Nat Rev Phys 4, 543–559 (2022). https://doi.org/10.1038/s42254-022-00468-w

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