Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDecomposition of scattered electromagnetic fields into vector spherical wave functions on surfaces with general shapes
325
0
0.0
(
0
)
Added by
Xavier Garcia Santiago
Publication date
2018
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Decomposing the field scattered by an object into vector spherical harmonics (VSH) is the prime task when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the scattered field is available on a spherical surface enclosing the scatterer; being with that adapted to the spatial dependency of the VSHs but being rather incompatible with many numerical solvers. To mitigate this problem, we propose an orthogonal expression for the decomposition that holds for any surface that encloses the scatterer, independently of its shape. We also show that the orthogonal relations remain unchanged when the radiative VSH used for the expansion of the scattered field are substituted by the VSH used for the expansion of the illumination as test functions. This is a key factor for the numerical stability of our decomposition. As example, we use a finite-element based solver to compute the multipole response of a nanorod illuminated by a plane wave and study its convergence properties.
rate research
Read More
The derivation of the Helmholtz theorem of vector decomposition of a 3-vector field requires that the field satisfy certain convergence properties at spatial infinity. This paper investigates if time-dependent electromagnetic radiation wave fields, which are of long range, satisfy these requirements. It is found that the requirements are satisfied because the fields give rise to integrals over the radial distance r of integrands of the form sin(kr)/r and cos(kr)/r. These Dirichlet integrals converge at infinity as required.
Recent studies have shown convolutional neural networks (CNNs) can be trained to perform modal decomposition using intensity images of optical fields. A fundamental limitation of these techniques is that the modal phases can not be uniquely calculated using a single intensity image. The knowledge of modal phases is crucial for wavefront sensing, alignment and mode matching applications. Heterodyne imaging techniques can provide images of the transverse complex amplitude & phase profile of laser beams at high resolutions and frame rates. In this work we train a CNN to perform modal decomposition using simulated heterodyne images, allowing the complete modal phases to be predicted. This is to our knowledge the first machine learning decomposition scheme to utilize complex phase information to perform modal decomposition. We compare our network with a traditional overlap integral & center-of-mass centering algorithm and show that it is both less sensitive to beam centering and on average more accurate.
The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for computation of electromagnetic fields in a device with rough textures. The method allows for efficient computations on meshes with strong variations in element sizes. This enables to use precise geometry resolution of the rough textures. Convergence to highly accurate results is observed.
Unless another thing is stated one works in the $C^infty$ category and manifolds have empty boundary. Let $X$ and $Y$ be vector fields on a manifold $M$. We say that $Y$ tracks $X$ if $[Y,X]=fX$ for some continuous function $fcolon Mrightarrowmathbb R$. A subset $K$ of the zero set ${mathsf Z}(X)$ is an essential block for $X$ if it is non-empty, compact, open in ${mathsf Z}(X)$ and its Poincare-Hopf index does not vanishes. One says that $X$ is non-flat at $p$ if its $infty$-jet at $p$ is non-trivial. A point $p$ of ${mathsf Z}(X)$ is called a primary singularity of $X$ if any vector field defined about $p$ and tracking $X$ vanishes at $p$. This is our main result: Consider an essential block $K$ of a vector field $X$ defined on a surface $M$. Assume that $X$ is non-flat at every point of $K$. Then $K$ contains a primary singularity of $X$. As a consequence, if $M$ is a compact surface with non-zero characteristic and $X$ is nowhere flat, then there exists a primary singularity of $X$.
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 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 for additional research, including conceptual extensions and efficient numerical schemes for handling large-scale problems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
