One mode, one waveguide, three enemies

Single-mode fiber means the core is small enough (~8.2 µm against a 125 µm cladding) that only the fundamental LP₀₁ mode propagates at 1550 nm. Every higher-order mode is below cutoff and radiates away. That kills modal dispersion outright — which is why single-mode reaches hundreds of km and multimode reaches hundreds of metres. What's left to fight is attenuation, chromatic dispersion, and Kerr nonlinearity. The first two are linear and the DSP (digital signal processing) now erases the second one entirely. The third is the wall.

The core is a resonator, and a mode is a standing wave that fits

A step-index fiber is a cylindrical dielectric waveguide: core index n₁, cladding index n₂, with n₁ only 0.33% larger. Light bounces along by total internal reflection. But not every bounce angle survives — a mode has to be a self-consistent standing wave across the core, so only a discrete set of transverse patterns is allowed. Whether a given pattern is guided at all comes down to one number.

Think of it as a momentum budget. The medium fixes the magnitude of the wavevector at |k| = n₁k₀. You spend it between a transverse component k_t (wiggling across the core) and a longitudinal component β (actually going somewhere), and Pythagoras holds: kt² + β² = (n₁k₀)². A higher-order mode oscillates faster across the core, so it spends more on k_t and has less left for β. When β falls below n₂k₀, the cladding can support a travelling wave at that β — the field stops decaying outside the core and starts propagating outward instead. The mode is no longer bound. It radiates away over centimetres.

A wave has four independent knobs, and coherent detection reaches all of them

The field on the fiber is E(t) = A·cos(2πf·t + φ) in each of two orthogonal polarizations. So per polarization you have amplitude and phase; times two polarizations gives four real degrees of freedom per symbol interval. Direct detection — a photodiode — measures |E|². Squaring destroys φ and collapses both polarizations into one scalar. You get one dimension out of four, which is why 10G on-off keying was the ceiling for so long.

Coherent detection beats a local-oscillator laser against the incoming field in a 90° optical hybrid. The photodiodes then see the product of the two fields, so the beat term carries the incoming phase relative to the LO (local oscillator). Split by polarization first and you recover all four dimensions as four real electrical signals — I and Q, in X and Y. Those go straight to ADCs, and from that point on the light is just numbers.

Every extra bit per symbol costs about 3 dB, and 3 dB is half your reach

A constellation is the agreed dictionary of points in the I/Q plane. Noise turns each transmitted point into a fuzzy cloud at the receiver; you decode by nearest neighbour. Pack more points into the same power envelope and the gap between neighbours shrinks, so the same noise cloud starts overlapping the wrong decision region. Drag the OSNR (optical signal-to-noise ratio) slider down and watch the clusters merge. That single picture is the entire capacity-versus-reach argument in the optical industry.

Capacity and reach are the same budget spent two ways

Amplifiers set the ceiling. Each EDFA (erbium-doped fiber amplifier) adds amplified spontaneous emission, and ASE (amplified spontaneous emission) accumulates along the chain, so received OSNR falls roughly as 10log₁₀(N) in the number of spans. Required OSNR rises with constellation order. Where the falling curve crosses the rising threshold is your reach. Everything a transponder vendor does is an attempt to move one of those two curves.

Where the noise comes from, span by span

OSNR at the receiver, in the 0.1 nm reference bandwidth, for a chain of identical spans:

OSNR = 58 + P_ch − L_span − NF (noise figure) − 10·log₁₀(N)

The 58 is not magic: it is −10log₁₀(h·ν·Bref) in dBm for ν = 193.4 THz and B_ref = 12.5 GHz — the quantum noise floor of one reference slice. Everything else is bookkeeping: how much you launch, how much the glass eats, how much noise the amplifier stirs in, and how many times you repeat it.

The fiber's capacity did not grow as fast as the transponder's

The C-band is a fixed resource: about 4.8 THz between 1530 and 1565 nm. A signal occupies roughly its symbol rate in Hz — 95 Gbaud needs about a 100 GHz slot, and 200 Gbaud needs about 225 GHz. So when a new generation doubles baud rate to double per-wavelength capacity, it also doubles the spectrum each wavelength eats, and total fiber capacity barely moves.

What actually changed inside the box

Swapping a transponder buys you more capacity through four levers, and only four. Every generation is a different mix of them. Select a pair to compare and the chart decomposes the gain.

The whole path, client port to client port

Hover any stage. Note where the boundaries fall: the client domain is frames and OTN (optical transport network) containers, the DSP domain is numbers, and the optical domain is a modulated carrier. Almost everything interesting in the last fifteen years happened by moving work leftward out of the optical domain and into the DSP.

Glossary

Every abbreviation used anywhere in this document, including the ones that appear only as terse chart labels where there is no room to spell them out. Expanded on first use in the prose as well.