What actually limits optical reach

Three separate limits, three different shapes, and one model that will happily lie to you past a certain launch power.

Every amplifier costs you

An optical amplifier cannot distinguish signal from noise. It amplifies whatever arrives and adds its own amplified spontaneous emission on top. Power improves; signal-to-noise degrades. A chain of amplifiers is a chain of small, permanent reductions in quality.

The arithmetic has a shape worth internalising: doubling the number of spans costs exactly 3 dB of OSNR. Ten spans to twenty is 3 dB. Twenty to forty is another 3. Forty to eighty, another 3.

This is why long-haul reach is discussed as a budget being spent rather than a distance being covered, and why the answer to “can we add one more span” depends entirely on how many there already are. Adding an eleventh span to ten costs 0.41 dB; adding a second to one costs 3.

The first span is the expensive one

A noise figure one decibel worse costs one decibel at the far end, regardless of how many spans follow. A span two decibels lossier costs those two decibels permanently.

So the cheapest improvements are almost always at the front: a better amplifier, a cleaner connector, a shorter first span. Optimising span twelve of fourteen achieves the same decibel for considerably more effort.

Where the model stops being true

This is the part worth being explicit about, because the simplified OSNR formula is genuinely misleading past a point.

In the formula, every decibel of extra launch power buys a decibel of OSNR, without limit. Nothing in the arithmetic stops you entering +20 dBm and getting a wonderful answer.

Real fibre stops behaving linearly at high power. The refractive index of glass varies very slightly with light intensity, so an intense signal modulates its own phase — and its neighbours'. Those nonlinear effects grow rapidly with power while the noise benefit grows only linearly. The result is an optimum launch power, typically a few dBm per channel, beyond which adding power makes the system measurably worse.

A simplified model has no term for that, so it cannot show the turning point. Treat any figure much above a few dBm per channel as a number the model cannot support, and take the optimum from the vendor's planning tool, which knows the fibre type, the channel count and the modulation format.

Two kinds of spreading, two different shapes

Chromatic dispersion is linear and deterministic

Different wavelengths travel at slightly different speeds in glass. A pulse is never a single wavelength, so it spreads as it travels — and it spreads linearly with distance. Eighty kilometres of standard fibre accumulates about 1360 ps/nm; a hundred and sixty accumulates twice that.

Because it is deterministic it can be undone. Historically with dispersion-compensating fibre — a spool with the opposite sign, cancelling the accumulation at the cost of its own loss. In coherent systems, electronically at the receiver, which is why modern transponders tolerate accumulated dispersion that would have been impossible fifteen years ago.

Polarisation mode dispersion is neither

The two polarisation modes travel at slightly different speeds too. But the difference varies randomly along the fibre — with manufacturing variation, with stress, with how the cable was pulled — so contributions partly cancel rather than accumulating.

The result is that PMD grows with the square root of length. Quadrupling the distance only doubles the PMD. That also means shortening a route is a weak lever against it: halving the length reduces PMD by 29%, not 50%.

Worse, the figure is a statistical mean. Instantaneous differential group delay follows a Maxwellian distribution about it, and varies with temperature and physical disturbance. A link can briefly exceed a budget it comfortably meets on average.

This is why PMD problems present the way they do: intermittent errors that correlate with weather, with time of day, or with someone working near the cable route — rather than as steady, reproducible degradation. It is also why there is no fixed correction to apply, and why old fibre with a poor PMD coefficient sets a hard ceiling on the line rate it can carry.

Which limit binds

Which of the three stops you first depends on the system:

• Long amplified spans — OSNR is usually the binding limit, and the question is how many spans the budget allows.
• High rates on legacy fibre — PMD often binds, and it is the one that cannot be engineered around without replacing the fibre.
• Direct-detection systems — chromatic dispersion binds early, which is why compensation was ubiquitous before coherent detection.

Working out which one is closest to its limit is more useful than improving whichever is easiest to improve.

Frequently asked questions

Why does doubling the spans cost 3 dB?

Because noise from each amplifier adds, and doubling the number of contributions doubles the noise power — which is 3 dB. It also means adding one more span to ten costs 0.41 dB while adding a second to one costs 3, so the answer to “can we add a span” depends on how many there already are.

Why can I not just increase launch power?

Because glass stops behaving linearly at high intensity. Its refractive index varies slightly with power, so the signal modulates its own phase and its neighbours'. Those effects grow faster with power than the noise benefit does, so there is an optimum — typically a few dBm per channel — beyond which more power makes things worse. A simplified model has no term for that and will not show the turning point.

Where should I improve a chain first?

At the front. A noise figure one decibel worse costs a decibel at the far end regardless of how many spans follow, so a better first amplifier or a shorter first span buys the same improvement for less effort than optimising span twelve of fourteen.

Why does PMD grow as a square root?

Because the delay between polarisation modes varies randomly along the fibre, so contributions partly cancel rather than accumulate. Quadrupling the length doubles the PMD — and halving a route only reduces it by 29%, which makes a shorter path a weak lever.

Why can chromatic dispersion be compensated but not PMD?

Chromatic dispersion is deterministic and linear, so a fixed amount of opposite dispersion — or electronic compensation in a coherent receiver — cancels it exactly. PMD varies randomly with temperature and disturbance, so there is no fixed correction to apply.

Why do PMD problems come and go?

Because the calculated figure is a mean. Instantaneous delay follows a Maxwellian distribution about it and varies with temperature and physical disturbance, so a link can briefly exceed a budget it meets on average. That is why the symptoms correlate with weather and with work near the cable.

Which limit will stop me first?

It depends. Long amplified spans are usually OSNR-limited. High rates on legacy fibre are often PMD-limited, and that one cannot be engineered around without replacing the fibre. Direct-detection systems hit chromatic dispersion early, which is why compensation was universal before coherent detection.