Optical Fiber Mode Propagation Simulator

simulator intermediate ~10 min
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V = 2.06 — Single-mode operation at 1310 nm with 9 µm core. 1 guided mode, cutoff at 1119 nm.

A standard telecom single-mode fiber with 9 um core and 0.12 NA operates with V=2.06 at 1310 nm wavelength, supporting only the fundamental LP01 mode.

Formula

V = (π · d · NA) / λ
M ≈ V²/2 (step-index), M ≈ V²/4 (graded-index)
MFD ≈ d · (0.65 + 1.619/V^1.5 + 2.879/V^6)

Guided Modes in Optical Fibers

An optical fiber guides light through total internal reflection between a high-index core and lower-index cladding. The number and shape of guided modes depend on core geometry, refractive index contrast, and wavelength. The normalized frequency parameter V encapsulates these variables and serves as the key design metric.

Single-Mode vs Multimode Operation

When V falls below 2.405, only the fundamental LP01 mode propagates — the single-mode condition essential for high-bandwidth long-haul telecommunications. Above this cutoff, additional LP modes appear, each with a distinct transverse intensity pattern. Multimode fibers intentionally operate at high V numbers for easier coupling with LED sources.

Index Profile Engineering

Step-index fibers have a uniform core refractive index, creating an abrupt boundary with the cladding. Graded-index fibers use a parabolic profile that equalizes mode group velocities, reducing modal dispersion by up to three orders of magnitude. This makes graded-index multimode fibers preferred for data-center interconnects at 10-100 Gbps.

Mode Field Diameter and Coupling

In single-mode fibers, the mode field diameter (MFD) describes the effective beam width, which extends slightly beyond the physical core. Splice and connector losses depend sensitively on MFD mismatch. The Marcuse approximation provides an accurate estimate of MFD from V number, critical for designing low-loss fiber joints and couplers.

FAQ

What is the V number in optical fiber?

The V number (normalized frequency) determines how many modes a fiber can support. It equals pi times core diameter times numerical aperture, divided by wavelength. When V < 2.405, only the fundamental mode propagates (single-mode fiber).

What is the difference between single-mode and multimode fiber?

Single-mode fiber has a small core (8-10 um) and supports one mode, enabling long-distance transmission with minimal dispersion. Multimode fiber has a larger core (50-62.5 um) supporting hundreds of modes, suitable for short-distance links.

How does numerical aperture affect fiber performance?

Numerical aperture (NA) measures the light-gathering ability of the fiber. Higher NA accepts light at wider angles but increases modal dispersion in multimode fibers. Typical single-mode fibers have NA of 0.10-0.14.

What is modal dispersion?

Modal dispersion occurs when different modes travel at slightly different speeds through a multimode fiber, causing pulse broadening. Graded-index fibers reduce this by gradually varying the refractive index profile so that higher-order modes travel faster paths.

Sources

Embed

<iframe src="https://homo-deus.com/lab/photonics/optical-fiber-modes/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub