# Global T operator bounds on electromagnetic scattering: Upper bounds on far-field cross sections

Published on Jul 30, 2020

· DOI :10.1103/PHYSREVRESEARCH.2.033172

Published on Jul 30, 2020

· DOI :10.1103/PHYSREVRESEARCH.2.033172

References179

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The design of the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success in applying local optimization methods to electromagnetic device design, it is unclear whether the performance of the resulting designs is close to that of the best possible design. This question remains open for absorptionless electromagnetic devices, since the absence of material loss makes it difficult to provide prov...

We derive upper and lower bounds on the Casimir--Polder force between an anisotropic dipolar body and a macroscopic body separated by vacuum via algebraic properties of Maxwell's equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We find that the attractive Casimir--Polder force between...

Extended depth of focus (EDOF) lenses are important for various applications in computational imaging and microscopy. In addition to enabling novel functionalities, EDOF lenses can alleviate the ne...

The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic device design, it is unclear whether the performance of resulting designs is close to that of the best possible design. This question remains unsettled for absorptionless electromagnetic devices since the absence of material loss makes it difficult to provide...

Fundamental Limits to Radiative Heat Transfer: The Limited Role of Nanostructuring in the Near-Field.

In a complementary article, we exploited algebraic properties of Maxwell's equations and fundamental principles such as electromagnetic reciprocity and passivity, to derive fundamental limits to radiative heat transfer applicable in near- through far-field regimes. The limits depend on the choice of material susceptibilities and bounding surfaces enclosing arbitrarily shaped objects. In this article, we apply these bounds to two different geometric configurations of interest, namely dipolar part...

Near-field radiative heat transfer between bodies at the nanoscale can surpass blackbody limits on thermal radiation by orders of magnitude due to contributions from evanescent electromagnetic fields, which carry no energy to the far-field. Thus far, principles guiding explorations of larger heat transfer beyond planar structures have assumed utility in surface nanostructuring, which can enhance the density of states, and further assumed that such design paradigms can approach Landauer limits, i...

We derive fundamental per-channel bounds on angle-integrated absorption and thermal radiation for arbitrarily structured bodies-for any given material susceptibility and bounding region-that simultaneously encode both the per-volume limit on polarization set by passivity and geometric constraints on radiative efficiencies set by finite object sizes through the scattering T operator. We then analyze these bounds in two practical settings, comparing against prior limits as well as near optimal str...

The low efficiency of Raman spectroscopy can be overcome by placing the active molecules in the vicinity of scatterers, typically rough surfaces or nanostructures with various shapes. This surface-enhanced Raman scattering (SERS) leads to substantial enhancement that depends on the scatterer that is used. In this work, we find fundamental upper bounds on the Raman enhancement for arbitrary-shaped scatterers, depending only on its material constants and the separation distance from the molecule. ...

The brightness theorem—brightness is nonincreasing in passive systems—is a foundational conservation law, with applications ranging from photovoltaics to displays, yet it is restricted to the field of ray optics. For general linear wave scattering, we show that power per scattering channel generalizes brightness, and we derive power-concentration bounds for systems of arbitrary coherence. The bounds motivate a concept of “wave etendue” as a measure of incoherence among the scattering-channel amp...

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Photonic devices play an increasingly important role in advancing physics and engineering, and while improvements in nanofabrication and computational methods have driven dramatic progress in expanding the range of achievable optical characteristics, they have also greatly increased design complexity. These developments have led to heightened relevance for the study of fundamental limits on optical response. Here, we review recent progress in our understanding of these limits with special focus ...

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 a...

Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related inequalities, but such bounds utilize only coarse system information, and loosen significantly in the presence of constraints and complex interaction dynamics. We show that an integral-equation-based formulation of conservation laws in quantum dynamics leads to a syste...

Fundamental bounds on the performance of monochromatic scattering-cancellation and field-zeroing cloaks made of prescribed linear passive materials occupying a predefined design region are formulated by projecting field quantities onto a sub-sectional basis and applying quadratically constrained quadratic programming. Formulations are numerically tested revealing key physical trends as well as advantages and disadvantages between the two classes of cloaks. Results show that the use of low-loss m...

Causality, Passivity and Optimization: Strong Duality in Quadratically Constrained Quadratic Programs for Waves

We prove that a special variety of quadratically constrained quadratic programs, occurring frequently in conjunction with the design of wave systems obeying causality and passivity (i.e. systems with bounded response), universally exhibit strong duality. Directly, the problem of continuum ("grayscale" or "effective medium") device design for any (complex) quadratic wave objective governed by independent quadratic constraints can be solved as a convex program. The result guarantees that performan...

\mathbb{T}Operator Limits on Optical Communication: Metaoptics, Computation, and Input-Output Transformations.

We present an optimization framework based on Lagrange duality and the scattering \mathbb{T}operator of electromagnetism to construct limits on the possible features that may be imparted to a collection of output fields from a collection of input fields, i.e., constraints on achievable optical transformations and the characteristics of structured materials as communication channels. Implications of these bounds on the performance of representative optical devices having multi-wavelength or mu...

Topology optimization (TopOpt) methods for inverse design of nano-photonic systems have recently become extremely popular and are presented in various forms and under various names. Approaches comprise gradient- and non-gradient-based algorithms combined with more or less systematic ways to improve convergence, discreteness of solutions, and satisfaction of manufacturing constraints. We here provide a tutorial for the systematic and efficient design of nano-photonic structures by TopOpt. The imp...

In the photonic design problem, a scientist or engineer chooses the physical parameters of a device to best match some desired device behavior. Many instances of the photonic design problem can be naturally stated as a mathematical optimization problem that is computationally difficult to solve globally. Because of this, several heuristic methods have been developed to approximately solve such problems. These methods often produce very good designs, and, in many practical applications, easily ou...

We develop a computational framework for identifying bounds to light-matter interactions, originating from polarization-current-based formulations of local conservation laws embedded in Maxwell's equations. We propose an iterative method for imposing only the maximally violated constraints, enabling rapid convergence to global bounds. Our framework can identify bounds to the minimum size of any scatterer that encodes a specific linear operator, given only its material properties, as we demonstra...