  We propose a composite acousto-optical modulation (AOM) scheme for wide-band,
efficient modulation of CW and pulsed lasers. We show that by adjusting the
amplitudes and phases of weakly-driven daughter AOMs, diffraction beyond the
Bragg condition can be achieved with exceptional efficiencies. Furthermore, by
imaging pairs of AOMs in a counter-propagating configuration, high contrast
switching of output orders can be achieved at the driving radio frequency (rf)
limit, thereby enabling efficient bidirectional routing of a synchronized
mode-locked laser. Here we demonstrate a simplest example of such scheme with a
double-AOM setup for efficient diffraction across an octave of rf bandwidth,
and for routing a mode-locked pulse train with up to $f_{\rm rep}=400$~MHz
repetition rate. We discuss extension of the composite scheme toward multi-path
routing and time-domain multiplexing, so as to individually shape each pulses
of ultrafast lasers for novel quantum control applications.
