Related papers: T-matrix representation of optical scattering resp…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
The raster model is widely used in Geographic Information Systems to represent data that vary continuously in space, such as temperatures, precipitations, elevation, among other spatial attributes. In applications like weather forecast…
The interaction of light with short light pulses is relevant in optical traps, optical tweezers, and many other applications. The theoretical description of such polychromatic light-matter interaction is challenging, and more so when the…
We adapt the transfer matrix ($\T$-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. In similarity to one-dimensional…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
We present, discuss and validate an adapted S-matrix formalism for an efficient, simplified treatment of stacked homogeneous periodically structured metasurfaces operated under normally incident plane wave excitation. The proposed formalism…
This is the second paper in a series on light scattering from optically anisotropic scatterers embedded in an isotropic medium. The apparently complex T-matrix theory involving mixing of angular momentum components turns out to be an…
We derive the $\mathcal{T}$-matrix formalism tailored for numerical analysis of second-harmonic (SH) generation from arbitrarily shaped particles made of centrosymmetric optical materials. First, the transfer matrix of a single particle is…
We propose a conceptually new method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology and other applications. The method is inspired by the theory of…
A data matrix may be seen simply as a means of organizing observations into rows ( e.g., by measured object) and into columns ( e.g., by measured variable) so that the observations can be analyzed with mathematical tools. As a mathematical…
We analyze further a recently proposed S-matrix description of transplanckian scattering in the specific case of axisymmetric collisions of extended sources, where some of the original approximations are not necessary. We confirm the claim…
We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries, as well as dispersive objects in relative motion. A general (trace) formula is derived for the radiation from…
Scattering thresholds and their associated spectral square root branch points are ubiquitous in photonics. In this Letter, we show that the scattering matrix has a simple universal behavior near scattering thresholds. We use unitarity,…
The scattering problem can be implemented in a square-integrable basis via the so-called $J$-matrix method. While methods to compute the phase shift in the $J$-matrix approach are known, we introduce a novel formula in square-integrable…
Transfer matrix method is a well-known and extensively used tool to compute the reflection and transmission coefficients of electromagnetic waves when interacting with a system of layers parallel to each other. We present here a modified…
Semi-analytic expressions for the static limit of the T-matrix for electromagnetic scattering are derived for a circular torus, expressed in bases of both toroidal and spherical harmonics. The scattering problem for an arbitrary static…
This paper introduces a new spreadsheet tool for adoption by high school or college level physics teachers who use common assessments in a pre-instruction/post-instruction mode to diagnose student learning and teaching effectiveness. The…
The scattering matrix (S-matrix), relating the initial and final states of a physical system undergoing a scattering process, is a fundamental object in quantum mechanics and quantum field theory. The study of factorised S-matrices, in…
Multiple scattering theory is applied to low-energy electron collisions with a complex target formed of two molecular scatterers. The total T-matrix is expressed in terms of the T-matrix for each isolated molecule. We apply the approach to…
Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…