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# 物理代写|傅立叶光学代写Fourier optics代考|SK2340 Fundamentals of Wave Propagation

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## 物理代写|傅立叶光学代写Fourier optics代考|Fundamentals of Wave Propagation

In this chapter and Chapter 4 , waves are considered in 3-D, in general. However, in some applications such as in integrated optics in which propagation of waves on a surface is often considered, 2-D waves are of interest. For example, see Chapter 19 on dense wavelength division multiplexing. Two-dimensional equations are simpler because one of the space variables, say, $y$ is omitted from the equations. Hence, the results discussed in 3-D in what follows can be easily reduced to the 2-D counterparts.

Electromagnetic (EM) waves will be of main concern. They are generated when a time-varying electric field $\mathbf{E}(\mathbf{r}, t)$ produces a time-varying field $\mathbf{H}(\mathbf{r}, t)$. EM waves propagate through unguided media such as free space or air and in guided media such as an optical fiber or the medium between the earth’s surface and the ionosphere. In this chapter, we will be mainly concerned with unbounded media.
Spherical waves result when a source such as an antenna emits EM energy as shown in Figure 3.1(a). At a far away distance from the source, the spherical wave appears like a plane wave with uniform properties at all points of the wavefront, as seen in Figure 3.1(b). Another example would be an electric dipole directed along the $z$-axis, located at the origin, and oscillating with the circular frequency $w$. It generates electric and magnetic fields with a complicated expression, but far from the origin where the fields look like plane waves. A perfect plane wave does not exist physically, but it is a component that is very useful in modeling all kinds of waves.
Waves propagate in a medium. In the case of optical waves, the optical medium is characterized by a quantity $n$ called the refractive index. It is the ratio of the speed of light in free space to that of the speed of light in the medium. The medium is homogeneous if $n$ is constant, otherwise, it is inhomogeneous. In this chapter, we will assume that the medium is homogeneous.

## 物理代写|傅立叶光学代写Fourier optics代考|WAVES

Nature is rich in a large variety of waves, such as electromagnetic, acoustical, water, and brain waves. A wave can be considered as a disturbance of some kind that can travel with a fixed velocity and is unchanged in form from point to point.

Let $u(x, t)$ denote a 1-D wave in the $x$-direction in a homogeneous medium. If $v$ is its velocity, $u(x, t)$ satisfies
$$u(x, t)=u(x-v t, 0)$$
if it is traveling to the right and
$$u(x, t)=u(x+v t, 0)$$
if it is traveling to the left.
Assuming the wave is traveling to the left, let $s$ be given by
$$s=x+v t$$

## 物理代写|傅立叶光学代写傅里叶光学代考|WAVES

$$u(x, t)=u(x-v t, 0)$$

$$u(x, t)=u(x+v t, 0)$$

$$s=x+v t$$ 给出

## MATLAB代写

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