Programmable Dispersion Matrix Using Bragg Fibre Grating for Optically Controlled Phased Array Antennas

( 3 ) where c is the velocity of light in free space, s = 7cr2 (area of the original circle) and (s Ax) is the overlapping area of the two circles. The theoretical resonant frequencies for ports 1 and 2 are 2.609 and 3.129GHz, respectively. The experiment has been repeated with substrates of different thickness and dielectric constant. The agreement between theoretical and experimental resonance frequencies is found to be good, except for a slight error that could be due to tolerances in dielectric constant, fabrication etc. Generally, the above analysis can predict the resonant frequencies with an error of less than 5%.