### 物理代写|光学代写Optics代考|PHYSICS 3540

statistics-lab™ 为您的留学生涯保驾护航 在代写光学Optics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写光学Optics代写方面经验极为丰富，各种代写光学Optics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|光学代写Optics代考|Cloak for Dielectric Resonator

Many different applications are in pressing need of effectively cloaking resonators (or sensors and detectors), which can efficiently detect signals but has negligible disturbance on the surrounding environment. For example, in physics and engineering experiments, this means that a probe, e.g., the tip of a near-field scanning optical microscope or a microwave antenna, may have a minimal scattering effect on the quantity it is designed to measure $[1,2]$. With the development of transformation optics, the old dream of a device which render an object invisible to the human eye is already within reach $[33,40]$. By transformation optics, the cloak/anticloak interaction has been investigated to realize the sensor cloaking [17]. However, the derived cloak/anticloak has extreme optical properties, permittivity and permeability. And they normally are implemented by exotic metamaterials [9]. The tailored microstructure of such metamaterials has to be much smaller than the wavelength, and this makes it very challenging to realize the desired magnetic properties at optical frequencies. Would it be possible to design a cloaked resonator using conventional

simple isotropic dielectric readily available in nature instead of using metamaterials with extreme optical properties?

The topology optimization based inverse design approach can be adopted to address this question, by finding the geometrical configuration of the conventional nonmagnetic isotropic dielectric cloak for a resonator. Besides, the metasurfacesbased optical illusion or virtual shaping has also been demonstrated to be an alternative approach $[20,38,41]$. Topology optimization is a full-parameter method used to inversely determine the geometrical configuration, which represents distribution of materials [6]. It can be used to implement the structural design for the cases where the scale is large enough to ensure the reasonability for using physical parameters of materials fitting in with statistical hypothesis or continuum hypothesis. In contrast to designing devices by tuning a handful of structural parameters in size and shape optimization, topology optimization method utilizes the full-parameter space to design structures solely based on the user’s desired performance specification. Therefore, topology optimization is more flexible and robust, because of its low dependence on initial structure and implicitly expression of the material distribution in structures.

## 物理代写|光学代写Optics代考|Modelling

An infinitely long cylinder domain is illuminated in the free space with monochromatic propagating wave. Due to the invariance of the optical properties along the cylinder axis, the problem can be formulated in a plane perpendicular to the cylinder axis. A first-order absorbing boundary condition is used as an approximation to the Sommerfeld radiation condition in order to truncate the infinite domain. Thus, the computational domain is preset as shown Fig. $3.15$ with one circularly shaped resonator at the center. A time-harmonic optical wave propagates from the left boundary through the computational domain. In the computational domain, the resonator cloak is located in a ring-shaped domain with the same center as the resonator, and it is inversely determined using the topology optimization approach. The rest surrounding medium is set to be vacuum.

For transverse electric polarization, the waves are described by the governing equation as follows:
$$\left{\begin{array}{l} \nabla \cdot\left[\mu_{r}^{-1} \nabla\left(E_{z s}+E_{z i}\right)\right]+k_{0}^{2} \varepsilon_{r}\left(E_{z s}+E_{z i}\right)=0, \text { in } \Omega \ \mu_{r}^{-1} \nabla E_{z s} \cdot \mathbf{n}+j k_{0} \sqrt{\varepsilon_{r} \mu_{r}^{-1} E_{z s}}=0, \text { on } \partial \Omega \end{array}\right.$$
where $E_{z s}$ is the scattering transverse electric field; $E_{z i}$ is the incident transverse electric field; $\varepsilon_{r}$ and $\mu_{r}$ are the relative permittivity and permeability respectively; $k_{0}$ is the free space wave number; $j$ is the imaginary unit; $\Omega$ is the computational domain with trace $\partial \Omega$. This section considers the inverse design case for uniform plane incident waves with the incident transverse electric wave $E_{z i}$ set to be $e^{-j k_{0} \mathbf{k} \cdot \mathbf{x}}$, where $\mathbf{k}$ is the normalized wave vector and $\mathbf{x}$ is the spatial coordinate.

Topology optimization approach is based on the material interpolation between two different materials. And the material interpolation is implemented with the binary distribution defined in the design domain, where the binary distribution with values 0 and 1 respectively represent two material phases. This section considers nonmagnetic materials with unity relative permeability. Then the inverse design for the resonator cloaking is focused on the geometrical configuration corresponding to the spatial distribution of materials with two different relative permittivity. The binary distribution is set to be the design variable, which is relaxed to vary in the interval $[0,1]$ in the gradient information-based topology optimization.

## 物理代写|光学代写Optics代考|Results and Discussion

In this section, the resonator cloaking performance is investigated, with including the sensitivity to the incident angle. The inverse design method is further applied to the cases with dielectric materials $\mathrm{SU} 8, \mathrm{Si}$ and $\mathrm{SiO}_{2}$ to reveal the origin of inversely designed resonator cloaking.

The dielectric material with relative permittivity $\varepsilon_{r}=2$ is chosen for both the resonator and cloak. The incident wavelength is set to be $600 \mathrm{~nm}$. The radius of the resonator and exterior radius of the ring-shaped design domain are set to be $0.5$ – and 2 -fold of the incident wavelength respectively. Then, the resonator cloak is derived as shown in Fig. 3.16, where the inversely designed resonator is shown in Fig. $3.16 \mathrm{a}$, and the total fields for the cloaked and uncloaked resonator are plotted respectively in Fig. $3.16 \mathrm{~b}$ and c. With the inversely designed resonator cloak shown in Fig. $3.16 \mathrm{a}$, the scattering induced by the resonator is reduced to be $0.08$-fold compared with that of the uncloaked case; and the filed is kept to resonate in the central domain with $1.30$-fold enhancement. From the total field in Fig. 3.16b, one can conclude that the inversely designed resonator cloak achieves the phase matching by effectively weakening the scattering field in the outside surrounding and the total field is enhanced in the resonator by guiding and focusing the field in the cloak.
The resonator cloak in Fig. $3.16 \mathrm{a}$ is inversely designed for incident wave with fixed incident angle. Its performance has a strong dependence on the incident angle. Therefore, the incident angle-insensitive inverse design is implemented to extend the incident angle bandwidth. The inverse design procedure is implemented by setting the design objective to be the sum of equally weighted quotients corresponding to different incident angles valued in a specified incident bandwidth. By specifying the incident bandwidth to be $-5^{\circ} \sim 5^{\circ}$, the incident angle-insensitive inverse design of resonator cloak is derived as shown in Fig.3.17a with total field distribution corresponding to different incident angles respectively shown in Fig. $3.17 \mathrm{~b} \sim \mathrm{g}$. In Fig. $3.17 \mathrm{~h}$, the incident angle spectra of the inversely designed resonator cloak is plotted. These results demonstrate that reasonably good cloaking effect is achieved within the moderate angle range.

## 物理代写|光学代写Optics代考|Modelling

$$\left{ ∇⋅[μr−1∇(和和s+和和一世)]+ķ02er(和和s+和和一世)=0, 在 Ω μr−1∇和和s⋅n+jķ0erμr−1和和s=0, 上 ∂Ω\正确的。$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。