# Spherical Mode Coefficients

Calculate spherical modes for use in a spherical mode equivalent source or export the modes to GRASP from TICRA.

The calculation of spherical mode coefficients is based on the far field values and the coefficients are written to the .out file.

Spherical modes have three indices s, m, and n with s = 1 for TE-modes, s = 2 for TM-modes, m = -N . . .N, and n = 1 . . .N, including a one-dimensional compressed indexing scheme j = 1. . . J and the normalisation of the modes and so forth. The input parameter Maximum mode index N can be used to manually set the maximum mode index N. Based on the choice for N a total number of J = 2N(N + 2) modes will be computed. If the Specify number of modes check box is not checked, Feko will automatically calculate the modes up to a maximum mode index based on factors such as the model size, the individual power in each mode and the total power captured in all the modes.

Tip: If only spherical modes are required, only a single far field point (position irrelevant) could be requested.
The origin for the modes is the same as for the far field computation in general (which is the global origin unless an OF card has been used to specify an offset). Due to the nature of the far field (propagating towards r = $\infty$ ) all computed mode coefficients refer to spherical cylinder functions ${\text{z}}_{n}^{\left(c\right)}$ with type c = 4.
Tip: Use the DA card before the FF card to request the export of the spherical expansion modes to an SWE file (.sph file) for import into GRASP from TICRA.
GRASP is a reflector antenna modelling code, and by means of the SWE file export it is possible to model a horn antenna as feed in Feko and then export this feed structure for use in GRASP.
Note: The gain in GRASP will only be correct if the radiated power in Feko has been set to $4\pi$ Watt.

The spherical mode expansion coefficients Qsmn as used by Feko are described in the AS card. In GRASP a slightly different convention is used:

• An additional factor $\frac{1}{\sqrt{8\pi }}$ is used.
• The coefficients are conjugate complex (that is GRASP assumes an ${e}^{-i\omega t}$ time dependency).
• The index m is exchanged with -m.
Note: In Feko the $\phi$ dependency is defined as ${e}^{jm\phi }$ but in GRASP it is defined as ${e}^{-jm\phi }$ .

The above conversions are done automatically by Feko when exporting the SWE file, so that this can readily be imported into GRASP.