Fibre Reach Lab
Four independent limits, only one of which is stopping your system — and which one it is changes with bit rate, drastically enough that a design optimised at one rate is optimised against the wrong wall at another.
1The route
Standard single-mode is around 0.25 dB/km and 17 ps/nm/km at 1550 nm. Modern fibre is under 0.1 ps/√km for PMD; cable installed before the mid-nineties can be several times worse, and that is the case where PMD becomes the wall.
2The system
3The four walls
4The same route, across bit rates
5The span length nobody builds
Derived from the OSNR expression rather than quoted as a rule: for a fixed total distance, OSNR is maximised at a span length of 10/(α·ln 10), which is around 20 km at typical attenuation. Real systems use four or five times that because amplifier sites cost money — a deliberate trade of optical performance for capital cost, and one worth making on purpose.
Why four limits and not one
A fibre link can be stopped by any of four independent things, and only one of them is doing the stopping at any moment. They do not scale together, they are fixed by different means, and improving the wrong one produces exactly nothing.
Loss is the one everyone starts with: transmit power minus receiver sensitivity, divided by attenuation. It is linear in distance and it is fixed by amplifiers or better optics.
OSNR replaces loss the moment amplifiers appear. Every amplifier adds noise, so signal-to-noise falls by 3 dB every time the span count doubles — permanently, because noise cannot be un-added. It is fixed by fewer or shorter spans, a better noise figure, or more launch power up to the nonlinear limit.
Chromatic dispersion is linear in distance and quadratic in bit rate. It is fixed by compensating fibre, or electronically at a coherent receiver — which is the change that made hundred-gigabit transport possible at all.
PMD grows as the square root of distance, which makes it forgiving over long routes and a weak lever: halving PMD needs a quarter of the route. It is fixed by replacing the cable, which is to say it is usually not fixed.
The inverse square law that catches people out
Dispersion tolerance falls with the square of the bit rate, because raising the rate both shortens the bit period and widens the signal's spectrum, and the two compound.
Ten to forty gigabits is four times the rate and one sixteenth of the tolerance. On standard fibre at 17 ps/nm/km, that takes an uncompensated reach of about 59 km down to under four. At a hundred gigabits it is a few hundred metres.
This is why direct detection ran out of road, and why coherent receivers — which undo dispersion in the electrical domain after detection — were not an incremental improvement but the thing that made the next generation exist.
Amplifiers fix loss and cost OSNR
The instinct when a link is loss-limited is to add an amplifier, and it works: optical power comes back. What comes with it is noise, and noise is permanent. Every amplifier in a chain adds its own spontaneous emission to a signal that already carries everything the previous ones added.
The arithmetic is unforgiving in a specific way: doubling the number of spans costs exactly 3 dB of OSNR. Ten spans to twenty is 3 dB; twenty to forty is another 3. Reach in an amplified system is a budget being spent, not a distance being covered.
What this does not do
It compares limits for one wavelength on one route. It does not model nonlinear effects, which set the upper bound on launch power and are the reason more power stops helping. It does not do Raman amplification, forward error correction coding gain, filter narrowing across a cascade of ROADMs, or the interaction between channels in a loaded system.
The dispersion tolerance is scaled from a stated reference point, and that reference depends on modulation format and on how much penalty is acceptable. Change the format and you change the reference, not the law.
Everything is calculated in your browser. Route lengths, equipment figures and system parameters are not uploaded.