Epsilon-Near-Zero Supercoupling

Channel Material

Permittivity ε_c 0.02

Channel Geometry

Channel width 0.10

Bend angle 25°

Channel length d/λ 1.00

Live Readouts

Epsilon-Near-Zero

Transmission T

0.0%

Reflection R

0.0%

Phase velocity v_p/c

—

|n_c|

0.14

How it works

The wide-narrow-wide channel is modelled as a 3-layer transfer-matrix (Fabry–Pérot) stack: an outer medium of index n₀ = 1, a channel of complex index n_c = √ε_c and optical thickness d/λ, then n₀ again:

n(ε) = √ε           (real for ε≥0, purely imaginary for ε<0)
r  = (n₀ − n_c) / (n₀ + n_c)
δ  = 2π n_c (d/λ)
r_total = r(1 − e^{i2δ}) / (1 − r² e^{i2δ})
T = 1 − |r_total|²,   R = |r_total|²

As ε_c → 0, n_c → 0 so the phase δ → 0 as well — the reflection numerator r(1−e^{i2δ}) collapses to zero regardless of how large the impedance mismatch r looks, and regardless of the channel's length or cross-section. That cancellation is supercoupling: an epsilon-near-zero (ENZ) channel transmits almost perfectly through arbitrarily narrow or bent geometry, because a near-zero index means an (almost) infinite phase velocity v_p = c/n and a spatially uniform phase across the whole channel (Silveirinha & Engheta, 2006). Push ε_c negative and n_c becomes imaginary — the channel behaves like a plasmonic/metallic barrier below cutoff, reflecting almost everything no matter how thin it is.

ε_c slider — sets the channel's relative permittivity; drag through zero to see the reflection dip.
Channel width — purely geometric pinch of the throat; notice transmission barely changes at ε_c≈0, the hallmark of supercoupling.
Bend angle — bends the narrow section sideways; the effect is shape-independent, so a bent channel transmits the same as a straight one at ε_c≈0.
Channel length d/λ — the throat's optical thickness; away from ε_c=0 this produces ordinary Fabry–Pérot fringes in T.

Transmitted wavefront Reflected wavefront

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