Fractal Antennae and Coherence

Fractal antennae have very special properties: (1) They are broad band antennae, i.e. they radiate, and detect, very eeciently for a wide range of frequencies. The frequency range is speciied by the smallest and largest size present in the antenna. The radiation, and hence the detection, eeciency depends slowly on frequency between these two limits. (2) They can display considerable gain over normal dipole type of an-tennae and this gain depends slowly on frequency over a large frequency range. This antenna gain can be related to the spatio-temporal structure of the radiation pattern. (3) They can display spatial structure. The spatial structure is also related to the antenna gain, as the antenna concentrate radiated power in certain postions and now in others. This spatial structure can be very useful when directionality is required. For the purposes of this work, we assume that a fractal antenna can be formed as an array of "small" line elements having a fractal distribution in space. Such description is consistent with our understanding of fractal discharges and lightning observations as discussed by Appendix A develops the theory for the calculation of the elds produced by a fractal antenna composed of small line elements and for the calculation of the array factor in the far eld of the fractal.