Las guías de onda se analizan resolviendo las ecuaciones de Maxwell.
Comencemos escribiendolas:
∇ ⋅ E = 0 ( 1 ) {\displaystyle \nabla \cdot \mathbf {E} =0\quad \quad \quad (1)}
∇ ⋅ B = 0 ( 2 ) {\displaystyle \nabla \cdot \mathbf {B} =0\quad \quad \quad (2)}
∇ × E = − ∂ B ∂ t ( 3 ) {\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial \mathbf {t} }}\quad \quad \quad (3)}
∇ × E = 1 c 2 ∂ E ∂ t ( 4 ) {\displaystyle \nabla \times \mathbf {E} ={\frac {1}{\mathrm {c} ^{2}}}{\frac {\partial \mathbf {E} }{\partial \mathbf {t} }}\quad \quad \quad (4)}