An antenna array comprising: a plurality of antennae each configured to emit a main beam energy so that respective main beams of the plurality of antennae sum across the antenna array, the plurality of antennae including a first antenna and a second antenna, the first antenna including a first waveguide with a first input configured to receive a first signal at a first time, the first antenna further including a first plurality of emitters including a first emitter, the first waveguide arranged to propagate the first signal to the first plurality of emitters, wherein, of all emitters of the first plurality of emitters, the first emitter is an Nth closest emitter to the first input, wherein N is a positive integer; and the second antenna including a second waveguide with a second input configured to receive a second signal at the first time, the second antenna further including a second plurality of emitters including a second emitter, the second waveguide arranged to propagate the second signal to the second plurality of emitters, wherein, of all emitters of the second plurality of emitters, the second emitter is an Nth closest emitter to the second input; wherein a first phase difference between the first signal when at the first input and the second signal when at the second input is different from a second phase difference between the first signal, at a second time, when at the first emitter and the second signal, at the second time, when at the second emitter, wherein a difference between the first and second phase differences is configured to mitigate side lobes created by signals transmitted from the first and second antennae (410, 420); wherein the first antenna comprises a first medium having a first permittivity disposed in the first waveguide and extending along the entire length of the first antenna; and wherein the second antenna comprises a second medium and a third medium extending partially along the length of the second antenna, the third medium and the second medium having a second permittivity and a third permittivity respectively, the second permittivity and the third permittivity being other than the first permittivity; and wherein the difference between the first phase difference and the second phase difference is based at least in part on differences between the first permittivity and both the second and the third permittivity. a plurality of antennae each configured to emit a main beam energy so that respective main beams of the plurality of antennae sum across the antenna array, the plurality of antennae including a first antenna and a second antenna, the first antenna including a first waveguide with a first input configured to receive a first signal at a first time, the first antenna further including a first plurality of emitters including a first emitter, the first waveguide arranged to propagate the first signal to the first plurality of emitters, wherein, of all emitters of the first plurality of emitters, the first emitter is an Nth closest emitter to the first input, wherein N is a positive integer; and the second antenna including a second waveguide with a second input configured to receive a second signal at the first time, the second antenna further including a second plurality of emitters including a second emitter, the second waveguide arranged to propagate the second signal to the second plurality of emitters, wherein, of all emitters of the second plurality of emitters, the second emitter is an Nth closest emitter to the second input; wherein a first phase difference between the first signal when at the first input and the second signal when at the second input is different from a second phase difference between the first signal, at a second time, when at the first emitter and the second signal, at the second time, when at the second emitter, wherein a difference between the first and second phase differences is configured to mitigate side lobes created by signals transmitted from the first and second antennae (410, 420); wherein the first antenna comprises a first medium having a first permittivity disposed in the first waveguide and extending along the entire length of the first antenna; and wherein the second antenna comprises a second medium and a third medium extending partially along the length of the second antenna, the third medium and the second medium having a second permittivity and a third permittivity respectively, the second permittivity and the third permittivity being other than the first permittivity; and wherein the difference between the first phase difference and the second phase difference is based at least in part on differences between the first permittivity and both the second and the third permittivity.