3D Nanowaveguide Fiber Modes

Step-Index Fiber

Core radius 400 nm

Wavelength λ 1550 nm

Core index n₁ 1.4682

Cladding index n₂ 1.4630

V-number

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Est. modes

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Mode field radius

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How it works

A step-index fiber confines light in a cylindrical core the same way a slab guide does — total internal reflection at the core/cladding boundary — but the circular symmetry means the guided modes are Bessel-like "LP" (linearly polarized) patterns instead of a simple sine wave. Whether the fiber carries one mode or many is set by the normalized frequency:

V = (2π·a/λ)·√(n₁² − n₂²),  a = core radius
single-mode (LP01 only) when V < 2.405
estimated mode count (V ≫ 1):  N ≈ V²/2

2.405 is the first zero of the Bessel function J₀ — the cutoff of the next mode, LP11. Below it the fiber is strictly single-mode; above it LP11 (and higher orders) also propagate, each with its own azimuthal lobe pattern.

The fundamental mode's radial intensity is rendered here with the Marcuse Gaussian approximation, the standard closed-form estimate of a step-index fiber's mode field radius w₀:

w₀/a ≈ 0.65 + 1.619·V^(−1.5) + 2.879·V^(−6)

When the fiber runs multi-mode, the visualization blends in the LP11 pattern (a cos(φ) azimuthal lobe with a radial node) so you can see the beating between LP01 and LP11 that real multi-mode fiber exhibits as modal noise.

Core radius — bigger core, bigger V, more modes; single-mode telecom fiber keeps this near 4–5 µm at 1550 nm.
Wavelength — V ∝ 1/λ, so a fiber that is single-mode at 1550 nm can become multi-mode at 800 nm.
Core / cladding index — real single-mode fiber uses a tiny contrast (Δn ≈ 0.003–0.006); this sim lets you push the contrast further to see how quickly V — and the mode count — grows.

Real-world relevance: this V-number trade-off is exactly why telecom fiber is drawn with a ~4 µm core and a lightly doped cladding — just enough contrast to guide light, deliberately kept single-mode so pulses don't smear from modal dispersion over long hauls.

SINGLE-MODE

Core glass LP01 intensity LP11 lobe (multi-mode)

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