# 平面波

## 數學表述

$\nabla^2 f - \frac{1}{v^2}\frac{\partial^2 f}{\partial t^2}=0$

$\nabla^2 \tilde{\psi} - \frac{1}{v^2}\frac{\partial^2 \tilde{\psi}}{\partial t^2}=0$

$\tilde{\psi}(\mathbf{x},t) = \tilde{A} e^{i(\mathbf{k}\cdot\mathbf{x} - \omega t)}$

$\operatorname{Re}\{\tilde{\psi}(\mathbf{x},t)\} = |\tilde{A}| \cos (\mathbf{k}\cdot\mathbf{x} - \omega t + \arg \tilde{A})$

$\mathbf{k}\cdot\mathbf{x} - \omega t_0 + \arg \tilde{A}=c_1$

$\mathbf{k}\cdot\mathbf{x}=c_2$

$\nabla^2 \mathbf{E} - \frac{1}{v^2}\frac{\partial^2 \mathbf{E}}{\partial t^2}=0$
$\nabla^2 \mathbf{B} - \frac{1}{v^2}\frac{\partial^2 \mathbf{B}}{\partial t^2}=0$

$\tilde{\boldsymbol{\psi}}(\mathbf{x},\ t)=\tilde{\mathbf{A}}e^{i(\mathbf{k}\cdot\mathbf{x} - \omega t)}$

$v_p=\omega/k$

$v_g=\frac{\partial \omega}{\partial \mathbf{k}}$

## 參考文獻

1. ^ Hecht, Eugene, Optics 4th, United States of America: Addison Wesley, 2002, ISBN 0-8053-8566-5 （English）
• J. D. Jackson, Classical Electrodynamics (Wiley: New York, 1998 )。