Disclosed are systems and methods for manufacturing energy relays for energy directing systems and Transverse Anderson Localization. Systems and methods include providing first and second component engineered structures with first and second sets of engineered properties and forming a medium using the first component engineered structure and the second component engineered structure. The forming step includes randomizing a first engineered property in a first orientation of the medium resulting in a first variability of that engineered property in that plane, and the values of the second engineered property allowing for a variation of the first engineered property in a second orientation of the medium, where the variation of the first engineered property in the second orientation is less than the variation of the first engineered property in the first orientation.