  Acoustic phased arrays are capable of steering and focusing a beam of sound
via selective coordination of the spatial distribution of phase angles between
multiple sound emitters. Constrained by the principle of reciprocity,
conventional phased arrays exhibit identical transmission and reception
patterns which limit the scope of their operation. This work presents a
controllable space-time acoustic phased array which breaks time-reversal
symmetry, and enables phononic transition in both momentum and energy spaces.
By leveraging a dynamic phase modulation, the proposed linear phased array is
no longer bound by the acoustic reciprocity, and supports asymmetric
transmission and reception patterns that can be tuned independently at multiple
channels. A foundational framework is developed to characterize and interpret
the emergent nonreciprocal phenomena and is later validated against benchmark
numerical experiments. The new phased array selectively alters the directional
and frequency content of the incident signal and the frequency conversion
between the different wave fields is analyzed as a function of the imposed
modulation. The space-time acoustic phased array enables unprecedented control
over sound waves in a variety of applications ranging from ultrasonic imaging
to non-destructive testing and underwater SONAR telecommunication.
