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Interference-Based All-Optical Photonic Crystal Logic Gates
Published in Narendra Kumar, Bhuvneshwer Suthar, Advances in Photonic Crystals and Devices, 2019
Enaul Haq Shaik, Nakkeeran Rangaswamy
In order to simulate the structures, input light is launched with Gaussian profile at 1550 nm. To absorb the waves and avoid the reflections at the boundaries, simulation has been done by using perfectly matched boundary conditions. The electromagnetic waves propagate in the (x, z) plane and the magnetic field polarization has been chosen in such a way that it is parallel to the axis of the Si rods, that is, y-axis. The FDTD method must solve the Maxwell’s equations by discretizing the fields into space and time. Space grids are chosen such that Δx < λ/10 and Δz < λ/10, to ensure convergence in the simulation, where x- and z-axes are the horizontal and vertical direction coordinates, respectively. To obtain stable simulations, the space grid and the time grid are chosen in order to satisfy the following Courant condition (Wu et al. 2012): () cΔt<1(Δx)−2+(Δz)−2
Finite Difference Methods
Published in Matthew N.O. Sadiku, Computational Electromagnetics with MATLAB®, 2018
The FDTD method is a robust, flexible (adaptable to complex geometries), efficient, versatile, easy-to-understand, easy-to-implement, and user-friendly technique to solve Maxwell's equations in the time domain. Although the method did not receive as much attention as it deserved when it was suggested, it is now becoming the most popular method of choice in computational EM. It is finding widespread use for solving open-region scattering, radiation, penetration/absorption, electromagnetic interference (EMI), electromagnetic compatibility (EMC), diffusion, transient, bioelectromagnetics, and microwave circuit modeling problems. However, the method exhibits some problems such as slow convergence for solving resonant structures, requirement of large memory for inhomogeneous waveguide structures due to the necessity of a full-wave analysis, inability to properly handle curved boundaries due to its orthogonal nature, low stability, and low accuracy unless fine mesh is used, to mention a few. These problems prohibit the application of the standard FDTD technique and have led to various forms of its modifications [81–91] and hybrid FDTD methods [92–94]. Although these new FDTD methods have enhanced the standard FDTD (increase accuracy and stability, etc.), some researchers still prefer the standard FDTD.
Diffractive optical elements
Published in Neil Collings, Fourier Optics in Image Processing, 2018
The rigorous design of DOEs is required when the feature size of the DOE is reduced to the order of magnitude of the wavelength of the illuminating light beam. This is currently a research field, although there are a number of application areas, such as wire grid polarizers. High resolution DOEs could also be used in Fourier optical systems when the size of the system shrinks or when it is desired to construct the system in solid optics and high resolution gratings are required. The mathematical techniques for solving Maxwell’s equations have been researched under a variety of names, such as Rigorous Coupled Wave Analysis (RCWA), Fourier Expansion Modal Methods (FMM), Finite Element Methods (FEM), and Finite Difference Time Domain (FDTD) techniques. The first two, RCWA and FMM, are synonymous, and cover the mathematical techniques used to expand the electromagnetic field as a Fourier series for which the propagation through the DOE can be computed relatively easily. Commercial software packages for RCWA include GSolver and DiffractMOD (Rsoft). FEM divide the DOE into a mesh of elements, commonly triangular, where the electromagnetic field is expressed as a linear combination of elementary basis functions. The conjunction of these linear approximations over the constellation of elements and the matching with the boundary constraints form the essentials of the method. JCMwave is an example of an FEM solver that can be used for DOE design. FDTD is a numerical solver based on finite-difference approximations to the derivative operators in Maxwell’s differential equations. A number of FDTD solvers are available, for example that of Lumerical Inc.
Characterization of microwave heating for hyperthermia cancer treatment
Published in Waves in Random and Complex Media, 2021
A. R. Niknam, Sh. Dodge, M. Hajian, M. A. Ansari
The analytical study of microwave propagation in biological tissue is often difficult. Therefore, a numerical solution is used in such problems. Among the various numerical methods used to solve partial differential equations, the FDTD method is the most widely used, as it has a simple structure and high accuracy. FDTD method is a numerical method based on solving Maxwell's equations to obtain the distribution of electric and magnetic fields in space and time domains. Maxwell's curl equations are as follows: where is the electric field and is the magnetic field. In the one-dimensional case, we can use only and . In the FDTD method, using the Yee algorithm, the continuous derivatives in space and time in Maxwell's equations are approximated by second-order accurate, two-point centered difference forms and the distribution of electric and magnetic fields in time and space is obtained [56, 57]. We need to determine the time and space steps necessary according to our resolution and excitation wave characteristics. We consider s and m.
Perfect cylindrical cloak under gyration, non-inertial effects make perfect cloak visible
Published in Waves in Random and Complex Media, 2021
Saeed Hasanpour Tadi, Babak Shokri
As the electromagnetic pulse is split into two parts while passing the cloak (top and bottom sides), movement in two separate paths with different flying times creates a phase difference between these two parts, similar to the Sagnac phenomenon. The phase difference makes deformation in the electric field pattern compared to that in the inertial state when these two splits interfere. This issue can warp the pulse and damage the cloak. In the present study, the FDTD method is employed to simulate the impact of rotation on the gyrating 2D cylindrical cloak by transforming Maxwell’s equations from the non-inertial form to the inertial form. FDTD is one of the most widely applied computational methods in solving electromagnetic problems. This method is significant because of to its high speed and accuracy in problem solving. This method has been used to solve various problems in the interaction of electromagnetic waves with complex electromagnetic structures such as metamaterials, anisotropic materials, nanophotonics, plasma, biophotonics, and bioelectromagnetism. In the present paper, the effect of rotation on the perfect cloak’s structure is investigated using the upgraded FDTD method [19], which is used to simulate the Sagnac effect of a rotating optical waveguide. First a simple dielectric structure is simulated and then the FDTD equations are rewritten for the cloak structure because the perfect cloak has complex electromagnetics parameters. Making objects invisible with transformation optics methods needs a complex medium provided by metamaterial structures.
Novel Subthreshold Modelling of Advanced On-Chip Graphene Interconnect Using Numerical Method Analysis
Published in IETE Journal of Research, 2021
Nikita R. Patel, Yash Agrawal, Rutu Parekh
This paper innovatively analyses graphene interconnects in the subthreshold region of operation. It is discussed that the subthreshold region of operation is of prime importance for low power applications, while graphene interconnects are necessary for nanoscale technology nodes. For the effective analyses and comparisons, linear model and conventional copper interconnects have also been considered. This study has shown that MLGNR is better interconnect in terms of delay, power dissipation and PDP in both the subthreshold and linear regions as compared to copper interconnect. The subthreshold modelling of graphene interconnects has been distinctly formulated using the proposed FDTD-based model. For the various analyses performed, it is analysed that the proposed FDTD-based model is highly accurate to the simulation model. It is seen that with the subthreshold region of operation, power dissipation is nearly 26% lesser than the linear region. Also, PDP in the subthreshold region of operation is nearly three times lower than the linear region. Hence, the subthreshold region of operation is good for low power applications. Consequently, it can be conveniently stated that graphene interconnects and its operation in the subthreshold region shall be very prominent to meet ultra-low power requirements in next-generation era.