[Enlarge image]Left: Scattered fields from plane-wave excitation of a cylinder. One could fit these curves with a few dozen parameters in coupled-mode theory, but with little design guidance. Right: The same scattering scenario, now visualized in the diagonal elements of the scattering “T” matrix. The lineshapes resemble Drude–Lorentz oscillators of optical materials, but here emerge entirely from complex multiple-scattering physics. Causality and passivity principles impose strong constraints on the lineshapes of the matrix, leading to strong constraints on the extreme limits of wave-scattering engineering, for applications from linear isolators to multi-functional metasurfaces to near-field radiative heat transfer.
Scattering theory underpins all linear optics and photonics. It has benefited enormously from decades of development in coupled-mode theory,1 quasinormal modes2 and numerical computation. But these approaches only model: They reduce given configurations to minimally descriptive degrees of freedom such as resonances. They are less well-suited for answering design questions: Out of all possible complex systems, what are the extreme limits to performance? How do these limits depend on available materials, size constraints and application objectives?
In recent work, we introduced a new framework for scattering theory that offers exactly such guidance.3 We found that the fundamental principles of causality and passivity alone are enough to strongly constrain scattering “T ” matrices for arbitrarily complex scattering systems. We discovered a new representation via Drude–Lorentz oscillators with matrix-valued (spatially nonlocal) coefficients.
The representation we developed can transform seemingly random spectral undulations in scattered fields into surprising, intuitively understandable lineshapes. This is not a reformulation of material oscillators; it emerges de novo, entirely from multiple scattering processes.
This previously unseen structure offers tantalizing promise for general wave-scattering guidance. Following through on that promise, we developed the first general theory of the ultimate limits to near-field radiative heat transfer,3 with ramifications for thermophotovoltaics, photonic refrigeration, heat-assisted magnetic recording and more.4 Previous theories predicted orders-of-magnitude gaps (greater than 750×) from known designs, as well as incorrect material trends. Our approach offers insights into optimal patterning, predicts unconventional plasmonic materials to be superior, and yields material-independent bounds within a small factor (5×) from state-of-the-art designs.
We believe the theoretical approach we have developed can be seamlessly applied to many high-interest applications across nanophotonics; it also appears extensible to classical and quantum scattering theory. Other areas of engineering, such as communications and photovoltaics, have benefited from fundamental limits (for example, Shannon’s bounds), but wave physics seemed too complex for similar bounds. Our work has shown that this is not the case.
Researchers
Lang Zhang and Owen D. Miller, Yale University, New Haven, CT, USA
Francesco Monticone, Cornell University, Ithaca, NY, USA
References
1. S. Fan et al. J. Opt. Soc. Am. A 20, 569 (2003).
2. P. Lalanne et al. Laser Photonics Rev. 12, 1700113 (2018).
3. L. Zhang et al. Nat. Commun. 14, 7724 (2023).
4. K. Kim et al. Nature 528, 387 (2015).