For an optical-modulator-based BAM, a decisive parameter of the pickup output signal is the slope steepness. We suggest a novel pickup with flat thin electrodes in a transverse gap. Increasing the electrode width makes the steepness greater in proportion to the signal increase. For a given width, reducing the electrode thickness allows the ultimate steepness to be reached. Wave processes in the pickup were investigated on a large scale model, using the technique described in [1]. The DESY 40GHz button pickup was used as a reference. It was found that for the same overall dimensions the steepness of the flat electrode pickup can be increased by the factor of two. A way is shown to keep the steepness as high with transition to a more practical bandwidth 20GHz. The investigation results are the basis of a final pickup optimisation using electrodynamic simulation.