Modal-Domain Design of Layered Multiport Waveguide Crossings Based on Transformation Optics
Authors:
Nona Messhenas, Werner L. Schroeder, Thomas Kaiser
Abstract:
A systematic design methodology for transformation-optics-derived two-dimensional graded-index dielectric structures at millimeter-wave frequencies is presented using a modal-domain formulation. Instead of prescribing a bulk spatial permittivity distribution, the proposed approach specifies the local propagation velocity of the fundamental guided TE0 slab mode, yielding an equivalent spatial distribution of modal effective refractive index. The Maxwell’s fish-eye profile derived from transformation optics is mapped onto a layered dielectric configuration composed of mirror-symmetric two-material stacks selected from a precomputed lookup library. The approach explicitly considers fabrication-compatible layered realizations based on available dielectric materials and planar multilayer manufacturing constraints, ensuring compatibility with low-loss dielectric waveguide structures. An eight-port dielectric waveguide crossing operating at 77 GHz is used as a representative design example. Full-wave simulations indicate efficient transmission of the fundamental mode over the operating band, low crosstalk levels, and negligible higher-order mode conversion. The influence of dielectric loss and geometric design parameters is also investigated, confirming robust behavior under realistic material conditions. Compared with the preliminary conference contribution, this work introduces the modal-domain formulation, the layered dielectric synthesis strategy, and an extended performance analysis for multiport configurations. The presented framework provides a systematic approach for fabrication-compatible layered realizations of transformation-optics-derived guided-wave devices and supports scalable dielectric waveguide interconnects for 77 GHz automotive radar systems.
