Nanowaveguide Mode Simulator

Slab Waveguide

Core width 400 nm

Wavelength λ 1550 nm

Core index n₁ 3.48

Cladding index n₂ 1.44

V-number

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Guided modes

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Critical angle

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How it works

Light stays inside a nanoscale waveguide core only when it strikes the core–cladding boundary at an angle beyond the critical angle θc = asin(n₂/n₁) — beyond that angle total internal reflection (TIR) sends 100% of the light back into the core, so it zig-zags down the guide instead of leaking out.

Whether the guide supports one mode or several is set by the normalized frequency (V-number), computed from the core half-width a = width/2:

V = (2π·a/λ)·√(n₁² − n₂²)
guided TE modes m exist while V > m·π/2
single-mode (only TE₀) when V < π/2 ≈ 1.5708

Each guided mode's transverse field shape is found by solving the slab dispersion relation for the confined (u) and evanescent (w) wavenumbers, with u² + w² = V²:

even modes:  u·tan(u) = w
odd modes:  −u·cot(u) = w

The field profile panel plots the resulting standing-wave pattern inside the core (sinusoidal) matched to an exponentially decaying evanescent tail in the cladding — the physical reason a narrower core or lower index contrast pushes more of the light's energy outside the core itself.

Core width — a narrower core raises V more slowly, favoring single-mode operation; too narrow and confinement weakens (larger evanescent tail).
Wavelength — V scales as 1/λ, so shorter wavelengths push a fixed geometry toward multi-mode.
Core / cladding index — the contrast n₁²−n₂² sets both the critical angle and V; silicon-on-insulator (n₁≈3.48, n₂≈1.44) is deliberately kept sub-micron-wide to stay single-mode despite the huge contrast.

Real-world relevance: this is exactly the design trade-off behind silicon photonic interconnects and integrated optical chips — the core must be narrow enough for single-mode routing, yet wide enough to keep loss from the evanescent tail low.

SINGLE-MODE

Core (n₁) Cladding (n₂) Ray (TIR) Field |E(x)|