A new guideline for proper allocation of multipoles in the multiple multipole method (MMP) is proposed. In an ‘a posteriori’ approach, subspace fitting (SSF) is used to find the best location of multipole expansions for the two dimensional dielectric scattering problem. It is shown that the best location of multipole expansions (regarding their global approximating power) coincides with the medial axis of the object. The subspace analysis is performed for various scenarios including objects with different shapes and sizes relative to the wavelength, different permittivities and both TEz and TMz polarizations. Numerical examples for both TEz and TMz cases are also presented. The results are in a very good agreement with the finite element method (FEM) results. Two challenging test cases are presented. First, a large object compared to the wavelength and second, a small object with field singularities close to the boundary. Accuracy of the final MMP results shows the effectiveness of the new allocation rule.

A Modified Single-Level Fast Multipole Method (MSLFMM) for large-scale heat conduction problems is presented. This method is obtained by embedding the far-field approximation (FFA) within the traditional single-level fast multipole method (SLFMM). The FFA is used to compute the influence coefficients of the far elements within adjacent cells, and also to determine the moments of the elements within far cells. This approximation not only reduces the difficulty of procedures and programming, but also causes a significant decrease in the CPU time. Several problems are considered to verify and evaluate the proposed method. The computational cost of the MSLFMM is demonstrated by comparing the Conventional Boundary Element Method (CBEM), the SLFMM, and the Multi-Level Fast Multipole Method (MLFMM). It is shown that the MSLFMM is much faster than the SLFMM, and comparable with the MLFMM due to its ease of use. Finally, to check the ability of the proposed method in modeling a complicated problem, steady-state heat conduction in an engine block is solved. The numerical results show a good agreement with those obtained by a Finite Volume Method (FVM), and its difference is less than 1.5%.

In this paper، the Mutiple Multipoles method is employed to solve nonlinear eigenvalue problem and calculate band structure for a 2D photonic crystal. Band structure is calculated for both TE and TM polarizations. Simulation space is implemented for the first Brillouin zone by using physical properties such as rods radius، permittivity and susceptibility. To model fields inside and outside of object، Multipole centers were located around it and Bessel series inside the object is shown complex fields. We used Bloch theory to implement fictitious periodic boundary conditions for the first Brillouin zone. To validate the code، we simulated the band structure of a cubic lattice and compare the results with Plane Wave Expansion Method which illustrates the accuracy of the code. It is shown that this method can be applied to investigate photonic crystals with irregular shapes and different materials for different lattices such as cubic، trigonal and honeycomb. Furthermore it could be used for dielectric or dispersive material and experimental data. Numerical calculation shows that MMP method is accurate، fast and it can be used on Personal Computers.

In this paper, we investigate the evolution of supercontinuum and femtosecond optical pulses generation through square lattice elliptical-core photonic crystal fiber (PCF) at 1550 nm by using both full-vector multipole method (M.P.M) and novel concrete algorithms: symmetric split-step Fourier (SSF) and fourth order Runge Kutta (RK4) which is an accurate method to solve the general nonlinear Schrodinger equation (GNLSE). We propose a novel square lattice PCF structure featuring a minimum anomalous group velocity dispersion (GVD), nearly zero third-order dispersion (TOD) and enhanced nonlinearity for efficient soliton–effect compression of femtosecond optical pulses and supercontinuum generation(SCG) with lowest input pulse energies over discrete distances of the fiber.

Metamaterial is defined as an artificial, macroscopic, and effectively homogeneous structure (with an average unit cell size much smaller than the guide wavelength). In the electromagnetic literature, the response of a system to an electric or magnetic field is largely determined by the characteristics of the materials in question. Two examples of these microscopic properties are the electric permittivity and magnetic permeability coefficients, both of which are positive in ordinary materials. By arranging an array of metal wires, a negative electric permittivity can be obtained, and by arranging an array of periodic split ring resonator structures, a negative magnetic permeability coefficient can be obtained. To model metamaterial structures, integral equations of electric field or magnetic field are used, which can be studied based on the numerical method of moment. One of the advantages of this method is that it only segregates the source, although the required memory increases in proportion to the size of the geometry of the structure. To solve this problem, today, alternative methods such as fast multipole method (single level and multi-level) are used, which in addition to the source, the basic functions and observation points are also segmented. In this paper, using surface integral equations and multi-level fast multipole method, the diffraction and calculation of scattering fields of some metamaterial surfaces are investigated and the importance of this method compared to the direct moment method is greatly reduced in the computation time, approximately 75%.

In present study, we intend to investigate the evolution of supercontinuum generation (SCG) through triangular photonic crystal fiber (PCF) at 1310nm by using both full-vector multipole method (M.P.M) and novel concrete algorithms: symmetric split-step fourier (SSF) and fourth order runge kutta (RK4) which is an accurate method to solve the general nonlinear schrodinger equation (GNLSE). We propose an ideal solid-core PCF structure featuring a minimum anomalous group velocity dispersion (GVD), small higher order dispersions (HODs) and enhanced nonlinearity for appropriate supercontinuum generation with low input pulse energies over discrete distances of the PCF. We also investigate the impact of linear and nonlinear effects on supercontinuum spectra in detail and compare the results with different status.

Magnetic Measurement Lab is one of the most significant divisions of Research and Development (R&D) Lab of Iranian Light Source Facility. The main duty of this lab is to measure and check qualification of the accelerator magnets, including permanent and electromagnets, being applied in Iran for the fisrt time. The ILSF measurement lab consists of precise measurement equipment, in proportion to synchrotron needs, such as Hall Effect probe measurement bench, rotating coil and Helmholtz coil. Recently, the lab has been provided with Hall probe measurement bench and uncompensated rotating coil and has made it possible to measure prototype magnets. In this article, the results of measuring quadrupole prototype are studied using Hall probe and rotating coil, to determine and compare errors in measuring multipole magnets and their sources

In this paper, we present a solid-core Silica-based photonic crystal fiber (PCF) composed of hexagonal lattice of air-holes and calculate the effective index and chromatic dispersion of PCF for different physical parameters using the empirical relations method (ERM). These results are compared with the data obtained from the conventional multipole method (MPM). Our simulation results reveal that the ERM is an accurate and fast method for dispersion analysis of PCFs with large pitch sizes. However, for small pitch sizes of PCFs, it is not as accurate as the MPM method. Therefore, ERM is a fast, simple and accurate method for modelling and analysis of Silica-based PCFs with large pitch sizes.

By studying the polarizability of a spherical metallic nanoparticle on a dielectric substrate, the optical properties of the system is investigated. Since the size of nanoparticle is much smaller than the wavelength of the incident light, by solving the Laplace equation, the electric potential at different regions is expanded in terms of multipoles. By using the polarizability tensor, expressions for the parallel and normal polarizability are derived and then numerical results discussed. In addition to the impact of the size of plasmonic nanoparticle, by defining a geometrical parameter that called the truncation parameter, the impact of this parameter on the parallel and normal components of polarizability tensor is shown. It is demonstrated that the optical dispersion and absorption strongly depends on the particle size, the type of metal particle and the truncation parameter. The type of nanoparticle is gold and silver, because these noble metals have predominately been the materials of choice for plasmonic applications around the optical frequencies.

‎In this paper‎, ‎dose uniformity ratio in irradiation cell of GC-220 is specifiedutilizing an analytical method based on the multipole moment expansion‎. ‎In this method‎, ‎the values of monople‎, ‎dipole and quadrupole moments for source arrangements of GC-220 are calculated by numerical integrating‎. ‎Appling these values‎, ‎the dose uniformity ratio in the irradiation cell of GC-220 is calculated equal to 1.92‎. ‎Monte Carlo simulation is applied to validate calculations‎. ‎There is a relative difference about 12% between the results obtained from the analytical calculation and Monte Carlo simulation‎, ‎which confirm the used method‎. ‎In comparison with Monte Carlo methods‎, ‎this method is not time consuming‎, ‎so‎, ‎this method can be used for the conceptual designing and the source load planning of irradiators‎.