Rectangular Cavity Resonator for TE Mode

Editors：杜俊毅、陳禎祐

Advisor：江簡富教授

There are two sets of modes, TE modes and TM modes, that can exist in a rectangular cavity resonator as shown in Fig.1.13.

Following the same procedure as in the last section, the transverse electric and magnetic fields can be expressed in terms of the

E_z and H_z components which satisfy the wave equation. The boundary conditions require that

(1) E_y = E_z = 0 at x = 0 and x = a, (2) E_z = E_x = 0 at y = 0 and y = b, and (3) E_x = E_y = 0 at z = 0 and z = d.

As a result, standing-wave forms are taken in all the ,  and  directions, and three sets of guidance conditions are obtained

as k_x = mπ/a, k_y = nπ/b, and k_z = pπ/d.

For the TE mode, E_z = 0, and

with m, n = 0, 1, 2, · · ·, m² + n²≠0, p = 1, 2, · · ·. The wave numbers and the frequency satisfy the dispersion relation

(mπ/a)² + (nπ/b)² + (pπ/d)² = ω²με. Thus, the resonant frequency of the TE_mnp mode can be expressed as

                                a=5, b=5, d=5

(1) TE₁₀₁ Mode

(2) TE₀₁₁ Mode

(3) TE₁₁₁ Mode