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

Abstract

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.

An analogy strategy for transformation optics

“…For devices performing a unidirectional behavior, the analogy idea bridges the transformation approach and ray optics formulae to create feasible 3D profiles, which are hardly achievable using either technique alone. Although the examples shown here are isotropic, some of which can be obtained as well by solving Laplaceʼs equation [38,63], we believe it is possible to find analogies to anisotropic systems for biaxial [64] or more advanced devices [65]. Meanwhile, numerical techniques should not be excluded for complex geometries.…”

Optically anisotropic media: New approaches to the dielectric function, singular axes, microcavity modes and Raman scattering intensities

“…The case of transparent biaxial crystals is still very interesting , historically well‐known for the effect of conical refraction , an optical singularity due to the diabolic (double cone) structure of the index of refraction around the optic axes. A simplified mathematical discussion of diabolic and exceptional points is given in Appendix A1.…”

“…For these directions the eigenstate is left-or right-circular polarized and accordingly allows the propagation of so-called Voigt waves. The case of transparent biaxial crystals is still very interesting [11], historically well-known for the effect of conical refraction [12,13], an optical singularity [14] due to the diabolic (double cone) structure of the index of refraction around the optic axes. A simplified mathematical Marius Grundmann received his Ph.D. (Dr. rer.…”