Superpositions of up to six plane waves without electric-field interference

Superpositions of coherent light waves typically interfere. We present superpositions of up to six plane waves which defy this expectation by having a perfectly homogeneous mean square of the electric field. For many applications in optics these superpositions can be seen as having a homogeneous intensity. Our superpositions show interesting one- two- and three dimensional patterns in their helicity densities, including several that support bright regions of superchirality. Our superpositions might be used to write chiral patterns in certain materials and, conversely, such materials might be used as the basis of an 'optical helicity' camera capable of recording spatial variations in helicity.