t matrix
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2022 ◽  
Vol 130 (2) ◽  
pp. 273
Author(s):  
В.Г. Фарафонов ◽  
В.Б. Ильин ◽  
Д.Г. Туричина

The relations between the T-matrices emerging when solving the problem of light scattering by a spheroid by applying the expansions of the electro-magnetic fields in the employing spheroidal and spherical bases are found. The behavior of the obtained relations is numerically studied, and it is noted that in a wide range of the task parameter values the calculation of the spheroidal T-matrix and its corresponding transformation is the only practical way to derive the spherical T-matrix often used in applications.


2021 ◽  
Vol 0 (4) ◽  
pp. 9-15
Author(s):  
R.F. AKHMETYANOV ◽  
◽  
E.S. SHIKHOVTSEVA ◽  

Scalar power functions of the form x1 + + xN -v Î are in some cases found in physical problems and applications, especially in many-body problems with paired interactions. There are known decompositions for two vectors in three-dimensional space. In this paper, we consider analogous decompositions with any number of N arbitrary M-dimensional vectors in Euclidean space as a product of a multidimensional rational series with respect to spatial variables and hyperspheric functions on the unit sphere SM-1. Such an advantage of expansion arises in three-body problems when solving the Faddeev equation, where it is known that the main problem is the approximate choice of approximation of interaction potentials, in which the t-matrix scattering elements acquired a separable form.


2021 ◽  
Author(s):  
◽  
Matt Majic

<p>This thesis is concerned with electrostatic boundary problems and how their solutions behave depending on the chosen basis of harmonic functions and the location of the fundamental singularities of the potential.  The first part deals with the method of images for simple geometries where the exact nature of the image/fundamental singularity is unknown; essentially a study of analytic continuation for Laplace's equation in 3 dimensions. For the sphere, spheroid and cylinder, new deductions are made on the location of the images of point charges and their linear or surface charge densities, by using different harmonic series solutions that reveal the image.  The second part looks for analytic expressions for the T-matrix for electromagnetic scattering of simple objects in the low frequency limit. In this formalism the incident and scattered fields are expanded on an orthogonal basis such as spherical harmonics, and the T-matrix is the transformation between the coefficients of these series, providing the general solution of any electromagnetic scattering problem by a given particle at a given wavelength. For the spheroid, bispherical system and torus, the natural basis of harmonic functions for the geometry of the scatterer are used to determine T-matrix expressed in that basis, which is then transformed onto a basis of canonical spherical harmonics via the linear relationships between different bases of harmonic functions.</p>


2021 ◽  
Author(s):  
◽  
Matt Majic

<p>This thesis is concerned with electrostatic boundary problems and how their solutions behave depending on the chosen basis of harmonic functions and the location of the fundamental singularities of the potential.  The first part deals with the method of images for simple geometries where the exact nature of the image/fundamental singularity is unknown; essentially a study of analytic continuation for Laplace's equation in 3 dimensions. For the sphere, spheroid and cylinder, new deductions are made on the location of the images of point charges and their linear or surface charge densities, by using different harmonic series solutions that reveal the image.  The second part looks for analytic expressions for the T-matrix for electromagnetic scattering of simple objects in the low frequency limit. In this formalism the incident and scattered fields are expanded on an orthogonal basis such as spherical harmonics, and the T-matrix is the transformation between the coefficients of these series, providing the general solution of any electromagnetic scattering problem by a given particle at a given wavelength. For the spheroid, bispherical system and torus, the natural basis of harmonic functions for the geometry of the scatterer are used to determine T-matrix expressed in that basis, which is then transformed onto a basis of canonical spherical harmonics via the linear relationships between different bases of harmonic functions.</p>


2021 ◽  
Vol 88 (3) ◽  
pp. 295-311
Author(s):  
P. SAHOO ◽  
U. LAHA ◽  
B. KHIRALI ◽  
A.K. BEHERA

Author(s):  
P. Sahoo ◽  
U. Laha

Within the framework of non-relativistic quantum scattering theory we treat the charged hadron scattering by replacing the nuclear interaction by a separable nonlocal one and the electromagnetic part by the Manning-Rosen potential. The off-energy-shell scattering is studied by this additive interaction by including the effect of electromagnetic interaction rigorously. The exact analytical expressions for the off-shell solutions and half-shell T-matrix are obtained in maximal reduced form. The half-shell T-matrix for the proton-oxygen system is computed and the resultant phase shifts are found in order.


2021 ◽  
Vol 2015 (1) ◽  
pp. 012160
Author(s):  
N Ustimenko ◽  
K V Baryshnikova ◽  
R Melnikov ◽  
D Kornovan ◽  
V Ulyantsev ◽  
...  

Abstract Metalens is a planar device for light focusing. In this work, we design and optimize c-Si nanosphere metalenses working on the magnetic dipole and quadrupole resonances of the c-Si nanoparticle. Resonant optical response of c-Si nanostructures is simulated by the multipole decomposition method along with the zero-order Born approximation. Limitations of this approach are investigated. The obtained results of optimization are verified by simulation via the T-matrix method.


Atmosphere ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1231
Author(s):  
Antonio Valenzuela Gutierrez

Levitation of single trapped particles enables the exploration of fundamental physicochemical aerosol properties never previously achieved. Experimental measurements showed that (NH4)2SO4’s particle shape deviated from sphericity during the crystallization process. Despite that, salt aerosols are assumed to be spheres even in low relative humidity (RH) in most climate models. In the analysis performed here, Mie and T-Matrix codes were operated to simulate crucial parameters needed to estimate the radiative forcing efficiency: extinction efficiency, asymmetry parameter and backscattering fraction. The incorporation of non-spherical effects in (NH4)2SO4 particles can cause a difference of up to 46% radiative forcing efficiency compared to the assumption of sphericity in the 0.3–0.6 µm particle radius range.


Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 747-756
Author(s):  
Haifeng Hu ◽  
Qiwen Zhan

A superchiral field, which can generate a larger chiral signal than circularly polarized light, is a promising mechanism to improve the capability to characterize chiral objects. In this paper, Mie scattering by a chiral sphere is analyzed based on the T-matrix method. The chiral signal by circularly polarized light can be obviously enhanced due to the Mie resonances. By employing superchiral light illumination, the chiral signal is further enhanced by 46.8% at the resonance frequency. The distribution of the light field inside the sphere is calculated to explain the enhancement mechanism. The study shows that a dielectric sphere can be used as an excellent platform to study the chiroptical effects at the nanoscale.


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