Exercise 2:
Use $H_{oz} = F \cos(\frac{m\pi}{b}x) \cos(\frac{n\pi}{a}y)$ to find the transverse components $E_{ox}$, $E_{oy}$, $H_{ox}$ and $H_{oy}$ for the TE mode.
The expressions on the formula list, which are
Assignment 3 (last one)
Devoir 3 (le dernier)
$E_{ox} = -j(\mu_0 \omega \frac{\partial H_{oz}}{\partial y} + k_z \frac{\partial E_{oz}}{\partial x})/k_c^2$, $E_{oy} = -j(-\mu_0 \omega \frac{\partial H_{oz}}{\partial x} + k_z \frac{\partial E_{oz}}{\partial y})/k_c^2$, $H_{ox} = -j(-\epsilon_0 \omega \frac{\partial E_{oz}}{\partial y} + k_z \frac{\partial H_{oz}}{\partial x})/k_c^2$ and $H_{oy} = -j(\epsilon_0 \omega \frac{\partial E_{oz}}{\partial x} + k_z \frac{\partial H_{oz}}{\partial y})/k_c^2$ are useful.
Answers/ Réponses:
$H_{oy} = \frac{jk_z(m\pi/a)F}{[(\frac{m\pi}{b})^2 + (\frac{n\pi}{a})^2]} \cos(\frac{m\pi}{b}x) \sin(\frac{n\pi}{a}y)$
$H_{ox} = \frac{jk_z(n\pi/b)F}{[(\frac{m\pi}{b})^2 + (\frac{n\pi}{a})^2]} \sin(\frac{m\pi}{b}x) \cos(\frac{n\pi}{a}y)$
$E_{oy} = \frac{-j\mu_0 \omega (n\pi/b)F}{[(\frac{m\pi}{b})^2 + (\frac{n\pi}{a})^2]} \sin(\frac{m\pi}{b}x) \cos(\frac{n\pi}{a}y)$
$E_{ox} = \frac{j\mu_0 \omega (m\pi/a)F}{[(\frac{m\pi}{b})^2 + (\frac{n\pi}{a})^2]} \cos(\frac{m\pi}{b}x) \sin(\frac{n\pi}{a}y)$
Deadline: December 3 2024
Échéance: 3 décembre 2024