Application of aperiodic phase reversals to the electrode pattern of a Mach-Zehnder traveling wave modulator according to suitable pseudorandom sequences considerably improves the high-frequency response for fixed drive voltage. Simulations for a family of devices based on the Barker codes are presented, in the presence of frequency dependent microwave losses and impedance mismatch, using a new theorem relating the modulation transfer function to the Laplace transform of the electrode pattern evaluated on a parabolic contour in the

-plane. Projecting from our recent experimental results on 4 and 5 bit Barker codes, at 1.3-μm wavelengths, a 2-cm-long 13-bit Barker code device fabricated in LiNbO
3will exhibit 5-dB optical modulation bandwidth in excess of 50 GHz with a half-wave voltage less than 8 V.