Abstract:At visible and infrared frequencies, metals show tantalizing promise for strong subwavelength resonances, but material loss typically dampens the response. We derive fundamental limits to the optical response of absorptive systems, bounding the largest enhancements possible given intrinsic material losses. Through basic conservation-of-energy principles, we derive geometry-independent limits to per-volume absorption and scattering rates, and to local-density-of-states enhancements that represent the power radiated or expended by a dipole near a material body. We provide examples of structures that approach our absorption and scattering limits at any frequency; by contrast, we find that common "antenna" structures fall far short of our radiative LDOS bounds, suggesting the possibility for significant further improvement. Underlying the limits is a simple metric, |χ| 2 / Im χ for a material with susceptibility χ, that enables broad technological evaluation of lossy materials across optical frequencies. 4. H. A. Atwater and A. Polman, "Plasmonics for improved photovoltaic devices," Nat. Mater. 9, 205-213 (2010). 5. G. V. Naik, J. Kim, and A. Boltasseva, "Oxides and nitrides as alternative plasmonic materials in the optical range [Invited]," Opt. Mater. Express 1, 1090-1099 (2011). 6. P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, "A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics," Nat. Photonics 6, 259-264 (2012). 7. M. D. Arnold and M. G. Blaber, "Optical performance and metallic absorption in nanoplasmonic systems," Opt.Express 17, 3835-3847 (2009). 8. J. B. Khurgin and G. Sun, "In search of the elusive lossless metal," Appl. Phys. Lett. 96, 181102 (2010). 9. A. Raman, W. Shin, and S. Fan, "Upper bound on the modal material loss rate in plasmonic and metamaterial systems," Phys. Rev. Lett. 110, 183901 (2013). 10. J. B. Khurgin, "How to deal with the loss in plasmonics and metamaterials," Nat. Nanotechnol. 10, 2-6 (2015). 11. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2012), 2nd ed. Electrons, and Plasmons, vol. 5 (W. A. Benjamin, 1964). 35. V. J. Keast, "Ab initio calculations of plasmons and interband transitions in the low-loss electron energy-loss spectrum," J. Electron Spectros. Relat. Phenomena 143, 97-104 (2005). 36. D. R. Lytle, P. S. Carney, J. C. Schotland, and E. Wolf, "Generalized optical theorem for reflection, transmission, and extinction of power for electromagnetic fields," Phys. Rev. E 71, 056610 (2005). 37. R. G. Newton, "Optical theorem and beyond," Am. J. Phys. 44, 639-642 (1976). Johnson, "Fundamental limits to extinction by metallic nanoparticles," Phys. Rev. Lett. 112, 123903 (2014).46. R. Fuchs, "Theory of the optical properties of ionic crystal cubes," Phys. Rev. B 11, 1732Rev. B 11, -1740Rev. B 11, (1975 14, 2783-2788 (2014). 142. U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866Rev. 124, -1878Rev. 124, (1961. 143. K. Petermann, ...

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Purpose We compute the ultimate signal-to-noise ratio (uSNR) and G-factor (uGF) in a realistic head model from 0.5 to 21 Tesla. Methods We excite the head model and a uniform sphere with a large number of electric and magnetic dipoles placed at 3 cm from the object. The resulting electromagnetic fields are computed using an ultrafast volume integral solver, which are used as basis functions for the uSNR and uGF computations. Results Our generalized uSNR calculation shows good convergence in the sphere and the head and is in close agreement with the dyadic Green’s function approach in the uniform sphere. In both models, the uSNR versus B0 trend was linear at shallow depths and supralinear at deeper locations. At equivalent positions, the rate of increase of the uSNR with B0 was greater in the sphere than in the head model. The uGFs were lower in the realistic head than in the sphere for acceleration in the anterior-posterior direction, but similar for the left-right direction. Conclusion The uSNR and uGFs are computable in nonuniform body models and provide fundamental performance limits for human imaging with close-fitting MRI array coils.

We describe a fluctuating volume-current formulation of electromagnetic fluctuations that extends our recent work on heat exchange and Casimir interactions between arbitrarily shaped homogeneous bodies [Phys. Rev. B. 88, 054305] to situations involving incandescence and luminescence problems, including thermal radiation, heat transfer, Casimir forces, spontaneous emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike previous scattering formulations based on field and/or surface unknowns, our work exploits powerful techniques from the volume-integral equation (VIE) method, in which electromagnetic scattering is described in terms of volumetric, current unknowns throughout the bodies. The resulting trace formulas (boxed equations) involve products of well-studied VIE matrices and describe power and momentum transfer between objects with spatially varying material properties and fluctuation characteristics. We demonstrate that thanks to the low-rank properties of the associated matrices, these formulas are susceptible to fast-trace computations based on iterative methods, making practical calculations tractable. We apply our techniques to study thermal radiation, heat transfer, and fluorescence in complicated geometries, checking our method against established techniques best suited for homogeneous bodies as well as applying it to obtain predictions of radiation from complex bodies with spatially varying permittivities and/or temperature profiles.

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Objective: In this paper, we introduce Global Maxwell Tomography (GMT), a novel, volumetric technique that estimates electric conductivity and permittivity by solving an inverse scattering problem based on magnetic resonance measurements. Methods: GMT relies on a fast volume integral equation solver, MARIE, for the forward path and a novel regularization method, Match Regularization, designed specifically for electrical properties estimation from noisy measurements. We performed simulations with three different tissue-mimicking numerical phantoms of different complexity, using synthetic transmit sensitivity maps with realistic noise levels as the measurements. We performed an experiment at 7T using an 8-channel coil and a uniform phantom. Results: We showed that GMT could estimate relative permittivity and conductivity from noisy magnetic resonance measurements with an average error as low as 0.3% and 0.2%, respectively, over the entire volume of the numerical phantom. Voxel resolution did not affect GMT performance and is currently limited only by the memory of the Graphics Processing Unit. In the experiment, GMT could estimate electrical properties within 5% of the values measured with a dielectric probe. Conclusion: This work demonstrated the feasibility of GMT with Match Regularization, suggesting that it could be effective for accurate in vivo electrical property estimation. GMT does not rely on any symmetry assumption for the electromagnetic field and can be generalized to estimate also the spin magnetization, at the expenses of increased computational complexity. Significance: GMT could provide insight into the distribution of electromagnetic fields inside the body, which represents one of the key ongoing challenges for various diagnostic and therapeutic applications.

A fast frequency domain full-wave electromagnetic simulation method is introduced for the analysis of MRI coils loaded with the realistic human body models. The approach is based on integral equation methods decomposed into two domains: 1) the RF coil array and shield, and 2) the human body region where the load is placed. The analysis of multiple coil designs is accelerated by introducing the precomputed magnetic resonance Green functions (MRGFs), which describe how the particular body model used responds to the incident fields from external sources. These MRGFs, which are precomputed once for a given body model, can be combined with any integral equation solver and reused for the analysis of many coil designs. This approach provides a fast, yet comprehensive, analysis of coil designs, including the port S-parameters and the electromagnetic field distribution within the inhomogeneous body. The method solves the full-wave electromagnetic problem for a head array in few minutes, achieving a speed up of over 150 folds with root mean square errors in the electromagnetic field maps smaller than 0.4% when compared to the unaccelerated integral equation-based solver. This enables the characterization of a large number of RF coil designs in a reasonable time, which is a first step toward an automatic optimization of multiple parameters in the design of transmit arrays, as illustrated in this paper, but also receive arrays.

Purpose We introduce a method for calculation of the ultimate specific absorption rate (SAR) amplification factors (uSAF) in non-uniform body models. The uSAF is the greatest possible SAF achievable by any hyperthermia (HT) phased array for a given frequency, body model and target heating volume. Methods First, we generate a basis-set of solutions to Maxwell’s equations inside the body model. We place a large number of electric and magnetic dipoles around the body model and excite them with random amplitudes and phases. We then compute the electric fields created in the body model by these excitations using an ultra-fast volume integral solver called MARIE. We express the field pattern that maximises the SAF in the target tumour as a linear combination of these basis fields and optimise the combination weights so as to maximise SAF (concave problem). We compute the uSAFs in the Duke body models at 10 frequencies in the 20–900 MHz range and for twelve 3 cm-diameter tumours located at various depths in the head and neck. Results For both shallow and deep tumours, the frequency yielding the greatest uSAF was ~900 MHz. Since this is the greatest frequency that we simulated, we hypothesise that the globally optimal frequency is actually above that. Conclusions The uSAFs computed in this work are very large (40–100 for shallow tumours and 4–17 for deep tumours), indicating that there is a large room for improvement of the current state-of-the-art head and neck HT devices.