光学波导传播的MATLAB仿真教程

4星 · 超过85%的资源需积分: 47 32 浏览量更新于2024-07-22 收藏 2.02MB PDF 举报

"波导MATLAB仿真 - 一本关于利用MATLAB进行光学波导数值仿真的教材，包含可直接使用的源代码。" 在光学领域，波导是传输光信号的重要组件，广泛应用于光纤通信、光子集成电路和量子光学等多个方面。本书“Numerical Simulation of Optical Wave Propagation with examples in MATLAB”由Jason D. Schmidt撰写，是一本专为学习和研究光学波导数值模拟的教材。MATLAB作为强大的科学计算软件，因其易用性和丰富的数学函数库，被广泛用于各种物理现象的数值模拟，包括光学波导的分析。该书深入浅出地介绍了光学波导传播的基本理论，包括波动光学的基础知识，如电磁场方程、麦克斯韦方程组以及波导的传输特性等。通过MATLAB编程，作者提供了一系列实际的仿真例子，帮助读者理解并应用这些理论。这些源代码是书中的重要组成部分，读者可以直接运行和修改，以加深对波导传播特性的理解。书中的内容涵盖了以下几个关键知识点： 1. **波动光学基础**：讲解了光波的基本性质，如波长、频率、相位和振幅，以及光在不同介质中的传播规律，包括反射、折射、干涉和衍射等现象。 2. **波导理论**：阐述了波导的工作原理，如模式分析、传播常数和截止频率等概念，特别是对于单模和多模波导的区别进行了深入讨论。 3. **MATLAB编程基础**：介绍了MATLAB环境的使用，包括基本语法、数据类型、数组操作以及图形用户界面（GUI）的构建，为进行波导仿真打下基础。 4. **数值方法**：讲解了求解偏微分方程（如波动方程）的数值方法，如有限差分法、傅里叶变换和矩量法（MoM），以及如何在MATLAB中实现这些算法。 5. **波导仿真案例**：提供了多个实际的波导设计和仿真例子，如光纤通信中的单模光纤、平面光子晶体波导等，通过实际操作帮助读者掌握波导仿真技巧。 6. **结果解析与优化**：讲解如何解析仿真结果，评估波导性能，并根据结果调整设计参数以优化波导性能。 7. **参考文献与索引**：附带了详尽的参考文献列表，便于进一步研究，同时有索引方便查找特定主题。这本书对于学习光学、光电子学以及相关领域的学生和研究人员来说是一份宝贵的资源，它不仅提供理论知识，还通过MATLAB实践增强了学习效果，使得读者能够直接将理论应用到实际问题中，提高问题解决能力。

Taking the curl of Eq. (1.27) yields

∇ × (

∇ × E) = −µ

∂

∂t

(∇

× H) . (1.33)

Then, substituting in Eq. (1.28) gives

∇ × (∇× E) = −µ



∂

∂t

E. (1.34)

w, applying the vector identity ∇× (∇ ×E) = ∇(∇ · E) − ∇

E leads to

∇(∇ ·E) − ∇

E = −µ



∂

∂t

E. (1.35)

Finally

, substituting in Eqs. (1.17) and (1.23), and keeping in mind that  is inde-

pendent of position results in a wave differential equation:

∇

E − µ



∂

∂t

E = 0. (1.36)

Similar

manipulations beginning with the curl of Eq. (1.28) yield

∇

B − µ



∂

∂t

B = 0. (1.37)

When

the Laplacian is used on the Cartesian components of E and B, the result is

six uncoupled but identical equations of the form



∇

− µ



∂

∂t



U (x,

y, z) = 0, (1.38)

where the scalar U (x, y, z) stands for any of the x-, y- or z- directed components

of the vector ﬁelds E and B.

At this point, we can deﬁne index of refraction

n =



(1.39)

and the

vacuum speed of light

c =

√



(1.40)

so that



∇

−

∂

∂t



U (x, y, z) = 0. (1.41)

The electric and magnetic ﬁelds that compose light are traveling wave ﬁelds. There-

fore, ﬁelds with harmonic time dependence exp (−i2πνt) (where ν is the wave

Chapter 1

frequency) are the types of solutions sought for the purposes of this book. When

this is

substituted into Eq. (1.41), the result is

∇



2πnν



U = 0

. (1.42)

Typically, the wavelength is given by λ = c/ν, and the wavenumber is deﬁned as

k = 2π/λ so that



∇

+ k



U = 0. (1.43)

This is the Helmholtz equation, and it appears in many other branches of physics

including thermodynamics and quantum mechanics. At this point, we can dispense

with the time dependence since it is the same for all solutions of the Helmholtz

equation. From this point forward, the ﬁeld U (x, y, z) refers to the phasor por-

tion of the optical ﬁeld (i.e, no time dependence). Further, we deﬁne the units of

U (x, y, z) to be square-root watts per meter (1 W = 1 J/s = 1 N m/s) so that optical

irradiance I = |U|

is in units of watts per meter squared. The value of the electric

ﬁeld or magnetic induction can always be obtained by a simple conversion of units.

1.2.2 Simple traveling-wave ﬁelds

There are several simple traveling-wave ﬁelds that are useful in this book. These are

planar, spherical, and Gaussian-beam waves. With each of these solutions, the ﬁeld

at all points always maintains its planar, spherical, or Gaussian-beam form, and pa-

rameters like radius of curvature change in a simple manner as the wave propagates.

The next section on scalar diffraction theory handles more general cases.

A planar wave is the simplest possible traveling wave. It has uniform amplitude

and phase in any plane perpendicular to its direction of propagation. More gener-

ally, when the optical axis is not along the direction of propagation, a planar wave

ﬁeld is given by

(r) = A exp (ik · r) , (1.44)

where A is the amplitude of the wave and

k =

2π

(αˆ

x + βˆy + γˆz) (1.45)

is the wavevector with direction cosines given by α, β, and γ. Then, making the

direction cosines more explicit,

(r) = A exp



2π

(α

x + βy + γz)



. (1.46)

This wave travels at an angle cos

−1

α from the x-axis and cos

−1

β from the y-axis

as shown in Fig. 1.1.

Foundations of Scalar Diffraction Theory

剩余200页未读，继续阅读

bennet2014

粉丝: 1
资源: 10

光学波导传播的MATLAB仿真教程

MATLAB仿真矩形波导中电磁模态传播分析

Matlab仿真实现矩形波导场分布分析

Matlab仿真：光波导模式求解器实现方法

矩形波导MATLAB仿真

矩形波导matlab仿真

【波导仿真】基于matlab FDTD算法环状波导仿真【Matlab仿真 4299期】.zip

【矩形波导】基于matlab矩形波导仿真【Matlab仿真 7515期】.zip

【波导仿真】基于matlab GUI矩形波导和圆波导场分布【Matlab仿真 4300期】.zip

波导_射频通信系统simulink仿真_MATLAB仿真在现代通信中的应用_波导仿真_射频通信

【波导仿真】基于matlab FDTD算法环状波导仿真【含Matlab源码 4299期】.mp4

最新资源