# 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* =
2*N*(*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.

*c*= 4.

The spherical mode expansion coefficients *Q _{smn}* 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.