Epsilon-Near-Zero Supercoupling (2D)

An epsilon-near-zero (ENZ) channel is a slice of material whose permittivity is tuned toward zero, sending its refractive index toward zero and its phase velocity toward infinity. This 2D sibling renders the same wide–narrow–wide waveguide as a top-down schematic, computes exact Fabry–Pérot transfer-matrix transmission and reflection for the narrow throat, and animates wavefront markers squeezing through it — pan and zoom the view freely. Drag the channel's permittivity toward the value that matches its width (the "Match ε to width" button jumps straight there) and watch the reflection collapse and stay collapsed as you pinch the throat down or bend it sideways — the shape-independent "supercoupling" signature first predicted by Silveirinha and Engheta. Push permittivity negative and the same channel flips into a plasmonic barrier that reflects almost everything regardless of thickness.