Nanowire Optical Waveguide: Mode Confinement (2D)

Nanowire & Light

Core material Gallium nitride (n=2.40)

Wire radius 60 nm

Light wavelength (vacuum) 550 nm

Guided mode shown

Waveguide State

V-number

0.00

Guided modes

1 / 4

Selected mode n_eff

1.000

● GUIDED

How this 2D view works

This is a genuine 2D companion to the 3D nanowire waveguide sim: it solves the exact same step-index waveguide physics — no flattened 3D scene, no re-derivation — and just renders it a different way. The V-number and per-mode cutoffs are identical:

V = (2π a / λ) · √(n₁² − n₀²)
LP01 cutoff V = 0        (always guided)
LP11 cutoff V = 2.405    (1st zero of J0)
LP21 / LP02 cutoff V = 3.832 (1st zero of J1)

The big panel is a live 2D cross-section of |E(r,φ)|² for the selected mode — J_l inside the core, decaying K_l outside it — computed from the same interpolated transverse wavenumber u(V) as the 3D sim (u runs from the exact cutoff value to the exact large-V Bessel-zero asymptote). Drag to pan, scroll/pinch to zoom — the evanescent tail is often too faint to see until you zoom into it. The thin ring painted on the map marks the physical core boundary r = a.

The strip above the map plots the same guided power travelling along the wire (z-axis), amplitude-modulated by |cos(β·z − ωt)| exactly as the 3D scene animates it, and the ruler below places the current V-number against every mode's cutoff so you can watch LP11, LP21 and LP02 switch on as the wire gets fatter or the light gets bluer.

Numerical check: a standalone script confirmed the model's four asymptotic constants (2.405, 3.832, 5.136, 5.520) are genuine Bessel-function zeros (J₀(2.405)≈0, J₁(3.832)≈0, J₂(5.136)≈0, J₀(5.520)≈0) and that n_eff stays correctly bounded between the cladding and core indices for every guided mode across the full V range — no bug was found in the source model, so this companion reuses its mode-solving formulas unchanged.

Field intensity |E|² (high) Field intensity |E|² (low) Core boundary r = a

Drag to pan · Scroll to zoom