The Effective Number of Degrees of Freedom of the Far-Fields Radiated by Rectangular Current Sheets

The number of degrees of freedom (NDF) of the electromagnetic far-fields generated by current sheets under certain noise level in the environment is evaluated numerically by directly sampling on the constellation of the propagation modes in free space. The electric fields in the far region are efficiently calculated by using the far-field approximation, and the effective numbers of degrees of freedom (ENDFs) are obtained through singular value decomposition (SVD) incorporating noises. The results show that ENDF is proportional to the area of the current sheets. Due to the effect of noise, when two current sheets in parallel are closer within a threshold, the differential mode fields will be submerged by the noise, so the ENDF is only determined by the common modes. Although the threshold is signal-to-noise ratio (SNR) dependent, the ENDF provides a clear physical meaning. When two current sheets are located in the same plane, numerical results suggest that the ENDF is mainly determined by the total area of the two current sheets, and the spacing between them almost does not affect the ENDF.