baby_1
- 159
- 16
- Homework Statement
- This is my own question: Why do we intentionally include the imaginary unit jj in the propagation constant after taking its square root?
- Relevant Equations
- Helmholtz equation
Here is my question:
$$
\nabla^2 \bar{E} + \omega^2 \mu \left( 1 - j \frac{\sigma}{\omega} \right) \bar{E} = 0
$$
where
$$
\gamma = \alpha + j \beta
$$
$$
\gamma^2 = \omega^2 \mu \left( 1 - j \frac{\sigma}{\omega} \right)
$$
$$
\gamma = j \sqrt{ \omega^2 \mu \left( 1 - j \frac{\sigma}{\omega} \right) }
$$
why is there a factor of j in the expression for γ?
$$
\nabla^2 \bar{E} + \omega^2 \mu \left( 1 - j \frac{\sigma}{\omega} \right) \bar{E} = 0
$$
where
$$
\gamma = \alpha + j \beta
$$
$$
\gamma^2 = \omega^2 \mu \left( 1 - j \frac{\sigma}{\omega} \right)
$$
$$
\gamma = j \sqrt{ \omega^2 \mu \left( 1 - j \frac{\sigma}{\omega} \right) }
$$
why is there a factor of j in the expression for γ?