As it is completely useless and often also misleading to compare different pictures with current density plots, we proposed metric which should be equal to one for correctly calculated characteristic vector:
$$chi_n = displaystyle maxlimits_p sqrt{sumlimits_{q=-p}^{p} Bigg| intlimits_varOmega boldsymbol{hat{J}}_n left(boldsymbol{r}right) cdot boldsymbol{hat{J}}_{pq}^mathrm{TM/TE} left(boldsymbol{r}right) ,mathrm{d}S Bigg|^2},$$
where all the current densities are normalized so that
$$boldsymbol{hat{J}} = displaystylefrac{boldsymbol{J}}{displaystylesqrt{intlimits_varOmega boldsymbol{J} left(boldsymbol{r}right)cdot boldsymbol{J} left(boldsymbol{r}right) ,mathrm{d}S}},$$
$boldsymbol{hat{J}}_n$ is numerically calculated characteristic mode, and $boldsymbol{hat{J}}_{pq}^mathrm{TM/TE}$ is the analytically known characteristic mode (spherical harmonics).
Results:
Coefficient $chi_n$ for spherical shell discretized into 500 triangles (750 RWG functions) at ka = 3/2:
Matlab script generating characteristic currents for TM and TE spherical modes is HERE.
For details see IEEE Trans. Antennas and Propagation paper.
/Edited 17. 07. 2017, MC/
