# 光电子学-Background of Lightwave

• 参考书籍：Optoelectronics and Photonics
• [英] S.O.Kasap 著

emmmmmm去年11月11日建的post，结果…….拖延拖延，反正就是拖延，没有写光电子学笔记的兴致！也没有翻书温习的动力。如今还有$12$天就考试了，前两天课上复习了知识框架…恐怖！！原来已经落下了这么多东西了….淦！学期开始时候的豪言壮语…去TM的！！劳资只想快乐！懒有懒的报应，小小熬夜一下好了（接下来不会都是通宵吧？！），就是希望鼻子上别再长痘了。现在开始好好学吧，自己做的承诺没有完成才是打击最大的！！外人？管TM怎么看，自己快乐自己不后悔就够了！啊啊~好想回家啊~学习完就可以回家了。先改一下post的日期吧（2021.01.07-03:05）

# What does this course focus on

• Generation/Emission
• Interaction of light with matter,Optical Amplification
• Semiconductor Optics and Semiconductor Light Sources
• Amplification
• Principle of Laser and Typical Lasers
• Semiconductor Optics and Semiconductor Light Sources
• Transmission
• Resonator and Gaussian Optics
• Modulation
• Optical Modulation

# Light is an electromagnetic wave

## Propagation of light wave

An electromagnetic wave is a traveling wave that has time-varying electric and magnetic fields that are perpendicular to each other and the direction of propagation z. Optical field refers to the electric field.

## Wave function

This is a monochromatic plane wave（单色平面波） of infinite extent traveling in the positive $z$ direction.

$$E_x=E_0\cos(\omega t-kz+\phi_0)\\ E(\vec r,t)=E_0\cos(\omega t-\vec k\cdot \vec r+\phi_0)$$

$E_x$:Electric field along $x$ at position $z$ at time $t$

$k$:Propagation constant$=\frac{2\pi}{\lambda}$

$\lambda$:Wavelength

$\omega$:Angular frequency$=2\pi\nu(\nu=frequency)$

$E_0$:Amplitude of the wave

$\phi_0$:Phase constant;at $t=0$ and $z = 0$, $Ex$ may or may not necessarily be zero depending on the choice of origin.

$(\omega t-kz+\phi_0)=\phi=$Phase of the wave

When the electromagnetic (EM) wave is propagating along some arbitrary direction $\vec k$, then the electric field $E(\vec r,t)$ at a point $\vec r$.

## Exponential notation（指数计数法）

$E_x(z,t) = Re[E_0\exp(j\phi_0)\exp j(\omega t − kz)]$

where $Re$ refers to the real part.

## Wave vector

Direction of propagation is indicated with a vector $\vec k$,called the wave vector, whose magnitude is the propagation constant（传播常数）.$\vec k$ is perpendicular to constant phase plane.

## Wavefront

A surface over which the phase of a wave is constant is referred to as a wavefront.

A wavefront of a plane wave is a plane perpendicular to the direction of propagation

## Phase and phase change

The phase difference between two points separated by $\Delta z$ is simply $k\Delta z$ since $\omega t$ is the same for each point

$$\Delta\phi=k\Delta z$$

## Spherical wave

$$E=\frac{A}{r}\cos(\omega t -kr)$$

## Optical frequencies

Typical frequencies that are involved in optoelectronic devices are in the infrared (including far infrared), visible, and UV（紫外光，Ultraviolet）, and we generically refer to these frequencies as optical frequencies: Roughly $10^{12} \quad to\quad 10^{16}Hz$

# Photon nature of light

• Wave-particle duality of light
• Electromagnetic radiation (wave):$\lambda=\frac{c}{\nu}$
• Particle:$\varepsilon_k=mc^2=cp$
• Planck–Einstein relation:$\varepsilon_k=h\nu=h\frac{c}{\lambda}\quad h=6.63\times10^{-34}J\cdot s$
• Matter wave(de Broglie wave):$\lambda=\frac{h}{p}$
• Some parameters
• Number density of photons:$N$
• Light intensity:$I=N\cdot h\nu\cdot u$
• Optical power:$P=I\cdot S=N\cdot h\nu\cdot u\cdot S$
• Wave vector:$\vec k=\frac{2\pi}{\lambda}\vec{k_0}$
• Wave number:$k=\frac{2\pi}{\lambda}$
• Spectra
• If one frequency is close to another:$\Delta\nu=\nu_2-\nu_1\approx\frac{c}{\lambda^2}\Delta\lambda\quad \lambda=\frac{\lambda_1+\lambda_2}{2}$

## Photoelectric effect

The essence of photoelectric effect, is absorption and emission of energy.

$$1eV=1.602\times10^{-19}J$$

Relation between wavelength and energy(eV)

$$\lambda=\frac{hc}{\Delta E_{(J)}}\approx\frac{1.24\times10^{-6}}{\Delta E_{(eV)}}m=\frac{1.24}{\Delta E_{(eV)}}\mu m$$

# Refractive index（折射率）

When an EM(electromagnetic) wave is traveling in a dielectric medium, the oscillating electric field polarizes the molecules of the medium at the frequency of the wave

The stronger is the interaction between the field and the dipoles, the slower is the propagation of the wave

Phase Velocity:$v=\frac{1}{\sqrt{\varepsilon_r\varepsilon_0\mu_0}}$

Refractive index $n$ definition:$n=\frac{c}{v}=\sqrt{\varepsilon_r}$

porpagation constant:$k_{medium}=nk$

Wavalength:$\lambda_{medium}=\frac{\lambda}{n}$

Cauchy dispersion（柯西色散公式）

$$n=n_{-2}(h v)^{-2}+n_0+n_2(h v)^2+n_4(h v)^4$$

$n_{-2,0,2,4}$是常量