Real-space Hopfield diagonalization of inhomogeneous dispersive media

We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields, and we invert the Hopfield transformation expressing the microscopic fields as functions of the polaritonic operators. As an example, we apply our approach to the case of a planar interface between vacuum and a polar dielectric, showing how we can consistently treat both propagative and surface modes, and express their nonlinear interactions, arising from phonon anharmonicity, as polaritonic scattering terms. We also show that our theory can be naturally extended to the case of dissipative materials

Theoretical Investigation of Phonon Polaritons in SiC Micropillar Resonators

Of late there has been a surge of interest in localised phonon polariton resonators which allow for sub-diffraction confinement of light in the mid-infrared spectral region by coupling to optical phonons at the surface of polar dielectrics. Resonators are generally etched on deep substrates which support propagative surface phonon polariton resonances. Recent experimental work has shown that understanding the coupling between localised and propagative surface phonon polaritons in these systems is vital to correctly describe the system resonances. In this paper we comprehensively investigate resonators composed of arrays of cylindrical SiC resonators on SiC substrates. Our bottom-up approach, starting from the resonances of single, free standing cylinders and isolated substrates, and exploiting both numerical and analytical techniques, allows us to develop a consistent understanding of the parameter space of those resonators, putting on firmer ground this blossoming technology.Comment: 10 Pages, 8 Figure

Palate shape and depth : a shape matching and machine learning method for assessment of ancestry from skeletal remains

The assessment of ancestry from skeletal remains is a vital aspect of forensic anthropology. As such, a myriad of techniques exists for estimating this particular component of the biological profile. The most traditional of these methods utilizes the naked eye and the observer’s experience. As replicability has become more important, objective, metric techniques have been developed. This study attempts to merge these two subfields: by taking a traditionally non-metric feature, palate shape, and using a computer, evaluating it quantitatively. Using 3D digitizer technology in conjunction with shape matching and machine learning methods common in computer science, palate shape curves were collected from 376 individuals of varying backgrounds from mixed historic and modern contexts. Additionally, measurements were taken to capture palate depth, which is a novel measurement in this study. Results of the computer analysis indicated palate shape was an accurate indicator of ancestry 58% of the time. This number improved slightly when the historic sample was examined on its own (61%), but not to such a degree as to indicate a significant difference. This result may indicate that secular change in the human skeleton is not affecting this region, or at least that secular change does not affect the shape of the palate as it relates to ancestry. Cluster analysis of the curves revealed that the parabolic, hyperbolic, and elliptical shapes are relatively discrete from one another, with the only major overlap in shape being between white and Hispanic individuals. The results regarding depth are rudimentary at this stage; however, results indicate that the depth of the palate in Hispanic individuals is significantly deeper than in other ancestry groups

Coherent coupling between localised and propagating phonon polaritons

Following the recent observation of localised phonon polaritons in user-defined silicon carbide nano-resonators, here we demonstrate coherent coupling between those localised modes and propagating phonon polaritons bound to the surface of the nano-resonator's substrate. In order to obtain phase-matching, the nano-resonators have been fabricated to serve the double function of hosting the localised modes, while also acting as grating for the propagating ones. The coherent coupling between long lived, optically accessible localised modes, and low-loss propagative ones, opens the way to the design and realisation of phonon-polariton based quantum circuits

PYRO-NN: Python Reconstruction Operators in Neural Networks

Purpose: Recently, several attempts were conducted to transfer deep learning to medical image reconstruction. An increasingly number of publications follow the concept of embedding the CT reconstruction as a known operator into a neural network. However, most of the approaches presented lack an efficient CT reconstruction framework fully integrated into deep learning environments. As a result, many approaches are forced to use workarounds for mathematically unambiguously solvable problems. Methods: PYRO-NN is a generalized framework to embed known operators into the prevalent deep learning framework Tensorflow. The current status includes state-of-the-art parallel-, fan- and cone-beam projectors and back-projectors accelerated with CUDA provided as Tensorflow layers. On top, the framework provides a high level Python API to conduct FBP and iterative reconstruction experiments with data from real CT systems. Results: The framework provides all necessary algorithms and tools to design end-to-end neural network pipelines with integrated CT reconstruction algorithms. The high level Python API allows a simple use of the layers as known from Tensorflow. To demonstrate the capabilities of the layers, the framework comes with three baseline experiments showing a cone-beam short scan FDK reconstruction, a CT reconstruction filter learning setup, and a TV regularized iterative reconstruction. All algorithms and tools are referenced to a scientific publication and are compared to existing non deep learning reconstruction frameworks. The framework is available as open-source software at \url{https://github.com/csyben/PYRO-NN}. Conclusions: PYRO-NN comes with the prevalent deep learning framework Tensorflow and allows to setup end-to-end trainable neural networks in the medical image reconstruction context. We believe that the framework will be a step towards reproducible researchComment: V1: Submitted to Medical Physics, 11 pages, 7 figure

Precision Learning: Towards Use of Known Operators in Neural Networks

In this paper, we consider the use of prior knowledge within neural networks. In particular, we investigate the effect of a known transform within the mapping from input data space to the output domain. We demonstrate that use of known transforms is able to change maximal error bounds. In order to explore the effect further, we consider the problem of X-ray material decomposition as an example to incorporate additional prior knowledge. We demonstrate that inclusion of a non-linear function known from the physical properties of the system is able to reduce prediction errors therewith improving prediction quality from SSIM values of 0.54 to 0.88. This approach is applicable to a wide set of applications in physics and signal processing that provide prior knowledge on such transforms. Also maximal error estimation and network understanding could be facilitated within the context of precision learning.Comment: accepted on ICPR 201