# Reactance of a dipole antenna

I am interested in calculating the input impedance $$\Z_{in}=R_{in}+jX_{in}\$$ of a dipole antenna numerically. However, I am unsure how I would compute the imaginary part of the impedance ($$\X_{in}\$$).

In order to compute $$\R_{in}\$$ of a dipole of length $$\l\$$ which is fed with a current of frequency $$\\omega\$$ and is oriented along the z-Axis, I would follow the following steps (conceptually):

1. Assume a standard sinusoidal current distribution on the antenna $$\\underline{I}(z)\$$.
2. Compute the vector potential $$\\underline{\vec{A}}(\vec{r})\$$ from this current distribution.
3. Compute the magnetic field $$\\underline{\vec{H}}(\vec{r})\$$ and the electric field $$\\underline{\vec{E}}(\vec{r})\$$ from the vector potential.
4. Compute the far-field energy-flux (Poynting-Vector) of the field $$\\underline{\underline{\vec{S_{ff}}}}(\vec{r})=\frac{1}{2}\underline{\vec{E}}(\vec{r})\times\underline{\vec{H}}^{*}\$$
5. Compute the overall power which is radiated by the dipole : $$\P_{\mathrm{rad}}=\iint_{B_{R}}\underline{\underline{\vec{S_{ff}}}}(\vec{r})\cdot d\vec{A}\$$

So in this case, since I know the input current which is fed into the antenna $$\\underline{I}(z=0):=\underline{I}_{0}\$$ and since I can calculate the radiated power $$\P_{\mathrm{rad}}(\underline{I}_{0})\sim I_{0}^2\$$ I would be able to calculate $$\R_{in}\$$ from $$\P_{\mathrm{rad}}=R_{in} I_{0}^2\$$.

Is there a way to calculate the reactance of the dipole antenna $$\X_{in}\$$ from the fields $$\\underline{\vec{E}}(\vec{r})\$$ and $$\\underline{\vec{H}}(\vec{r})\$$?

The result that I am looking for looks like this: