Ohm's law of electromagnetic ideal fluids: impedance-governed supercoupling in complex near-zero-index networks

Supercoupling in near-zero-index (NZI) media enables geometry-insensitive electromagnetic (EM) transport through narrow channels with near-zero phase delay. However, most studies have focused on single-channel, point-to-point configurations, leaving EM power-flow distribution in complex structures largely unexplored. Here we extend NZI supercoupling to complex structures and show that EM power flow follows a passive, deterministic, and quasi-static distribution governed by boundary conditions and impedance contrasts, with PEC-terminated branches carrying no propagating power flow. We interpret this behavior using a pressure-driven flow analogy and directly visualize it in a waveguide-emulated plasmonic platform with photonic doping. This quasi-static power-flow distribution follows an "Ohm's law of ideal EM power flow", where the potential is set by boundary conditions and the effective impedance by each branch's length-to-width ratio. Beyond the physical interpretation, our results suggest an impedance-designed approach to passive multi-port EM interconnects, offering insights for NZI physics and on-chip networks at millimeter-wave and terahertz frequencies.