Exploiting design freedom in biaxial dielectrics to enable spatially overlapping optical instruments

The optical behavior of gradient biaxial dielectrics has not been widely explored in the literature due to their complicated nature, but the extra degrees of freedom in the index tensor have the potential of yielding useful optical instruments which are otherwise unachievable. In this work, a design method is described in detail which allows one to combine the behavior of up to four totally independent isotropic optical instruments in an overlapping region of space. This is non-trivial because of the mixing of the index tensor elements in the Hamiltonians; previously known methods only handled uniaxial dielectrics (where only two independent isotropic optical functions could overlap). The biaxial method introduced also allows three-dimensional multi-faced Janus devices to be designed; these are worked out in an example of what is possible to design with the method.