Topological platforms in electromagnetic metamaterials with arbitrary auxiliary orbital freedom through Kekulé modulation

Photonic topological insulators have unique advantages regarding ensuring lossless transmission and realizing stable energy locality of electromagnetic waves. More complex requirements to manipulate discrete degrees of freedom (DOF) of photons, such as orbital DOF, show great foresight. In this paper, we design and demonstrate two kinds of topological metamaterials, A and B, with arbitrary auxiliary orbital DOF. By applying continuous generalized Kekul\'e modulations $\ifmmode\pm\else\textpm\fi{}{m}_{0}{e}^{i\ensuremath{\varphi}}$, the topological Chern numbers of the A and B configurations are inverse and the orbital DOF is controlled independently. This provides a completely new idea for the controllability and applicability of the photonic topology phase. We construct three kinds of topological platforms based on the more generic type of topological photonic insulators with arbitrary orbital DOF, including a perfect electrical conductor (PEC) boundary of a finite metamaterial structure, a domain wall interface consisting of two topological phases, and line-defect channels. The findings of our system provide a new pathway for exploring multifunctional topological electromagnetic metamaterials. It is expected that the present results can become an alternative means to manipulate topological phase transition and provide an underlying platform for the exploration of additional DOF.