Modal noise

Modal noise is a fluctuation of received power in a fiber system that guides more than one mode. Coherent light in a multimode fiber leaves the core as a speckle pattern formed by the interference of the guided modes, and the pattern moves whenever the fiber is bent, stretched or heated. The total power is unchanged by that motion, but any element that passes only part of the pattern (an offset connector, a splice, a single-mode pigtail, a detector smaller than the core) converts it into intensity noise. With a 50 µm graded-index core, which guides about 340 modes at 850 nm, a 10 % mode-selective loss gives an rms power fluctuation of about 1.8 %, and a 50 % loss about 5.4 %.

Conditions for modal noise

Three conditions must hold together. The source must be coherent enough for the modes to interfere: its coherence time must exceed the spread of modal group delays over the fiber length. The fiber must be disturbed, so that the relative phases of the modes change during the measurement or the data stream. And the link must contain a mode-selective loss.

Coherence is usually the decisive factor. A step-index core with NA near 0.21 has a modal delay spread of about 49 ps per meter (see modal dispersion), so a 2 m jumper spreads the modes over 98 ps. A source with a linewidth below about 10 GHz, such as a single-mode VCSEL or a DFB laser with a coherence length of meters, produces fully developed speckle in that jumper. An 850 nm LED 40 nm wide has a coherence time near 0.06 ps; roughly 1600 independent speckle patterns are averaged over the 98 ps spread, reducing the contrast to about 2.5 % of its coherent value. A well-graded core is more prone to modal noise than a step-index one, because it equalizes the mode delays: an ideal profile spreads them by only 6.1 ps over 100 m, shorter than the coherence time of most lasers.

Size of the fluctuation

Treating the output as $M$ equally excited modes with random phases, the fraction of power passed by an element that accepts a fraction $\eta$ of the speckle fluctuates with a relative rms value

$$\frac{\sigma_P}{\langle P\rangle} \approx \sqrt{\frac{1-\eta}{\eta\,(M+1)}}.$$

For partially coherent light the result is multiplied by the speckle contrast. With $M = 340$ and $\eta = 0.9$ it gives 1.8 %, a signal-to-noise ratio of 34.9 dB; with $\eta = 0.5$ it gives 5.4 % and 25.3 dB. With only six modes and $\eta = 0.9$ the fluctuation is 13 %, about 18.0 dB. Few-mode operation is therefore the worst case.

That case occurs in single-mode fiber used below its cutoff wavelength. At 850 nm a standard single-mode fiber also guides the LP₁₁ group, and a two-mode beat between LP₀₁ and LP₁₁ meeting a splice or a single-mode component gives large, slow power swings as the fiber temperature drifts.

Observing and measuring it

In the lab, modal noise appears as power readings that change when a patch cord is touched, coiled differently or warmed with a hand. A controlled test shakes or heats a section of fiber while a power meter or a receiver with a known mode-selective element records the fluctuation; the excess noise lies at the low frequencies of the disturbance, typically hertz to kilohertz. Because the noise follows the disturbance, it is easily confused with relative intensity noise of the laser; the test is whether it disappears when the fiber is held still.

Remedies and pitfalls

The usual fixes act on one of the three conditions: a broadband or deliberately modulated source to shorten the coherence time; avoiding mode-selective elements by using well-aligned connectors and a detector larger than the core image; and mechanical isolation of the fiber. A mode scrambler makes the mode distribution repeatable but does not remove speckle.

Common pitfalls are assuming that multimode links use incoherent sources, when most short-reach links now use VCSELs, and splicing a short multimode or few-mode section in front of a single-mode component.

Common questions

Is modal noise the same as speckle?

Speckle is the spatial pattern; modal noise is the power fluctuation that results when that pattern moves and part of it is lost. A static speckle pattern with no mode-selective loss produces no modal noise.

Is modal noise the same as mode partition noise?

No. Mode partition noise comes from power shifting among the longitudinal modes of a laser combined with fiber dispersion. Modal noise comes from the transverse modes of the fiber and does not require a multi-longitudinal-mode laser.

References: R. E. Epworth, "The phenomenon of modal noise in analogue and digital optical fibre systems," Proceedings of the 4th European Conference on Optical Communication (Genoa, 1978); K. Petermann, Laser Diode Modulation and Noise (Kluwer, 1988); J. W. Goodman, Speckle Phenomena in Optics (Roberts and Company, 2007).