Posted on Categories:Electrodynamics, 物理代写, 电动力学

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## 物理代写|电动力学代考Electrodynamics代写|On dispersion in 1D metamaterial

A concept of a metamaterial from a formal point of view is directly based on dispersion relation [1], that develops on the Drude model, see chapter 6 , subsection 6.3.2 as a particular case of Lorentz model. The term ‘metamaterial’ itself has an interesting history [1]. One of the important applications of such a model relates to metamaterials that are characterized by negative values of the parameters $\varepsilon$ and $\mu$, that must be anomalous dispersive, i.e. their permittivity and permeability must be frequency dependent, otherwise they would not be causal [2]. The two-time derivative Lorentz material (2TDLM) model encompasses the metamaterial models most commonly discussed; it has the frequency domain susceptibility [3]:
$$\chi_e=\frac{\omega_p^2 \chi_\alpha+i \omega_p \chi_\beta \omega-\chi_\gamma \omega^2}{\omega_0^2+i \omega \Gamma-\omega^2},$$
its particular case is the 2TDLM model, which produces a resonant response at $\omega=\omega_0$ when $\Gamma=0$. The natural $1 \mathrm{D}$ metamaterials construction originated from layered medium $[4]$

The nonlinear behavior of electromagnetic (EM) wave propagation depends on relations between the field and induced polarization. It is obvious that it is necessary to use either a numerical scheme or approximations to obtain an analytical solution of a nonlinear problem. The first successful approach of such a reduction was the use of a set of slowly varying envelopes. The simplest model scalar equation for a directed wave propagation, based on this approach, have a form of the nonlinear Schrödinger equation, derived by Zakharov in 1968 [5, 6]. Its integrability [7] made the model very attractive because of the rich ‘zoo’ of the equation explicit solutions [8].

## 物理代写|电动力学代考Electrodynamics代写|Maxwell’s equations for matter inside a waveguide

For such a problem, for points inside a waveguide, more close to engineering, we would present the Maxwell system in SI units as:
$$\begin{gathered} \operatorname{div} \vec{D}=0, \ \operatorname{div} \vec{B}=0, \ \operatorname{rot} \vec{E}=-\frac{\partial \vec{B}}{\partial t}, \ \operatorname{rot} \vec{H}=\frac{\partial \vec{D}}{\partial t}, \end{gathered}$$
that is formulated for the case of absence of charges and currents. The material operator relations for an isotropic dispersive medium in a waveguide we write as in section 13.2 from [25] in SI units:
$$\vec{D}=\varepsilon_0 \hat{\varepsilon} \vec{E}, \vec{H}=\frac{1}{\mu_0} \hat{\mu}^{-1} \vec{B}$$

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代写|On dispersion in 1D metamaterial

$$\chi_e=\frac{\omega_p^2 \chi_\alpha+i \omega_p \chi_\beta \omega-\chi_\gamma \omega^2}{\omega_0^2+i \omega \Gamma-\omega^2}$$

## 物理代写|电动力学代考Electrodynamics代写|Maxwell’s equations for matter inside a waveguide

$$\operatorname{div} \vec{D}=0, \operatorname{div} \vec{B}=0, \operatorname{rot} \vec{E}=-\frac{\partial \vec{B}}{\partial t}, \operatorname{rot} \vec{H}=\frac{\partial \vec{D}}{\partial t},$$

$$\vec{D}=\varepsilon_0 \hat{\varepsilon} \vec{E}, \vec{H}=\frac{1}{\mu_0} \hat{\mu}^{-1} \vec{B}$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

Posted on Categories:Electrodynamics, 物理代写, 电动力学

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

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## 物理代写|电动力学代考Electrodynamics代写|Linear problem

We start directly with the Maxwell system, chapter 10 , section 10.1 .1 , in cylindrical coordinates $\rho, \varphi, z$, see figure 11.3. Bessel functions satisfy orthogonality conditions hence form convenient basis. To complete the statement of the problem, we define the boundary problem with conditions at the point $z=0$ that fix the transversal components (polarizations) of the electric field as a function of time.

The procedure of the projecting is properly described in [45], firstly we expand basic fields in series with respect to the orthogonal waveguide Hondros-Debye basis
$$N_{n l}^{-1} J_l\left(\alpha_{n l} \rho\right) e^{i l p}$$
$N_{n l}$ are the normalization constants for the transverse modes $n l$,
\begin{aligned} E_z(\rho, \varphi, z, t)= & \sum_{l, n} \mathcal{A}{l n}(z, t) J_l\left(\alpha{n l} \rho\right) e^{i l \varphi}+c . c ., \ E_r(\rho, \varphi, z, t)= & \sum_{l, n} \mathcal{B}{l n}(z, t) \frac{i l}{\rho} J_l\left(\alpha{l n} \rho\right) e^{i l \varphi} \ & +\mathcal{C}{l n}(z, t) \frac{\partial}{\partial \rho} J_l\left(\alpha{l n} \rho\right) e^{i l \varphi}+c . c ., \end{aligned}

## 物理代写|电动力学代考Electrodynamics代写|Transformation to frequency domain

Fourier transformation from time to frequency domain provides the solution for the system and leads to the current form
$$\begin{gathered} \frac{\partial}{\partial z} \tilde{\mathcal{A}}{l n}(z, \omega)=-\tilde{\alpha}{l n}^2 \tilde{\mathcal{C}}{l n}(z, \omega), \ \frac{\partial}{\partial z} \tilde{\mathcal{C}}{l n}(z, \omega)=\left(\omega^2 \frac{\varepsilon \mu}{\tilde{\alpha}{l n}^2 c^2}+1\right) \tilde{\mathcal{A}}{l n}(z, \omega), \ \frac{\partial}{\partial z} \tilde{\mathcal{K}}{l n}(z, \omega)=-\tilde{\alpha}{l n}^2 \tilde{\mathcal{M}}{l n}(z, \omega), \ \frac{\partial}{\partial z} \tilde{\mathcal{M}}{l n}(z, \omega)=\left(\frac{\varepsilon \mu}{\tilde{\alpha}{l n}^2 c^2} \omega^2+1\right) \tilde{\mathcal{K}}{l n}(z, \omega) . \end{gathered}$$

This form of the ordinary differential equations with constant coefficients allows us to propose a solution $\tilde{\mathcal{A}}{l n}(z, \omega)=\breve{\mathcal{A}}{l n}(k, \omega) e^{i k z}$, which will be adopted to other variables. Applying this solution to our system, the result
$$\begin{gathered} i k \breve{\mathcal{A}}{l n}(k, \omega)=-\tilde{\alpha}{l n}^2 \breve{\mathcal{C}}{l n}(k, \omega), \ i k \breve{\mathcal{C}}{l n}(k, \omega)=\left(\omega^2 \frac{\varepsilon \mu}{\tilde{\alpha}{l n}^2 c^2}+1\right) \breve{\mathcal{A}}{l n}(k, \omega), \ i k \breve{\mathcal{K}}{l n}(k, \omega)=-\tilde{\alpha}{l n}^2 \breve{\mathcal{M}}{l n}(k, \omega), \ i k \breve{\mathcal{M}}{l n}(k, \omega)=\left(\frac{\varepsilon \mu}{\tilde{\alpha}{l n}^2 c^2} \omega^2+1\right) \breve{\mathcal{K}}{l n}(k, \omega) \end{gathered}$$

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代写|Linear problem

$$N_{n l}^{-1} J_l\left(\alpha_{n l} \rho\right) e^{i l p}$$
$N_{n l}$ 是横向模式的归一化常数 $n l$,
$$E_z(\rho, \varphi, z, t)=\sum_{l, n} \mathcal{A l n}(z, t) J_l(\alpha n l \rho) e^{i l \varphi}+\text { c.c. }, E_r(\rho, \varphi, z, t)=\quad \sum_{l, n} \mathcal{B l n}(z, t) \frac{i l}{\rho} J_l(\alpha \ln \rho) e^{i l \varphi}+\mathcal{C l n}(z, t) \frac{\partial}{\partial \rho} J_l(\alpha \ln \rho) e^{i l \varphi}+c . c .$$

## 物理代写|电动力学代考Electrodynamics代写|Transformation to frequency domain

$$i k \breve{\mathcal{A}} \ln (k, \omega)=-\tilde{\alpha} \ln ^2 \breve{\mathcal{C}} \ln (k, \omega), i k \breve{C} l n(k, \omega)=\left(\omega^2 \frac{\varepsilon \mu}{\tilde{\alpha} l^2 c^2}+1\right) \breve{\mathcal{A}} \ln (k, \omega), i k \breve{\mathcal{K}} \ln (k, \omega)=-\tilde{\alpha} \ln ^2 \breve{\mathcal{M}} \ln (k, \omega), i k \breve{\mathcal{M}} \ln (k, \omega)=\left(\frac{\varepsilon \mu}{\tilde{\alpha} l n^2 c^2} \omega^2+1\right) \breve{\mathcal{K}} \ln (k, \omega$$

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。