Abstract
A semi-analytical formulation is presented to quantify the effects of group delay ripple on the performance of an optical beam-former. For delay elements, implemented with commercially available multi-channel fiber Bragg gratings, an impulse response is introduced and calculated for the group delay ripple. To do this, the transfer function of the fiber Bragg grating is parted into two dispersive and non-dispersive sections. This will also ease the demonstration of the fiber Bragg grating as a true time delay element. The formulation is applied to an ultra-wideband pulsed array of antennas. As an example the array factor and electric field patterns of a four element antenna array is derived, using certain available measured data. The distortion in the temporal-angular radiation patterns due to the non-ideal true time delay behavior may be predicted using the presented work. It also facilitates to distinguish between the effects of long and short ripples. This new mathematical investigation is applicable to any linearly chirped fiber Bragg grating other than multi-channel ones. It also includes corrections to previously published formulations.
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