Macroscopic emitters on origami structures: a group theoretic approach

Phased arrays steer electromagnetic radiation in a desired direction by electronically adjusting the phases of individual antennas. Each transmitting antenna functions as a macroscopic oscillator and produces electromagnetic radiation similar to that of a Hertzian oscillator. The fields generated by individual antennas in an array interfere constructively in the intended direction, resulting in significant power gain, while interfering destructively in most other directions, minimizing power output. In this paper, we use a model similar to the Hertzian model to represent a finite set of transmitting antennas. The antennas are positioned along the orbits of various discrete groups with one or two generators. Notably, a conventional phased array is a special case using a translation group. We observe that antenna positions constructed by this method are precisely consistent with the deformations of certain deployable origami structures constructed by the group orbit method. In this context, we consider the problem of manipulating the phases of the antennas to achieve constructive interference at an assigned far-field point. This gives intriguing interference patterns in parameter space. These patterns are adapted to various applications, such as monitoring the kinematics of deployable structures and encrypting messages in communication.