PE1-2.4 Power Launching & Receiver Operation

What this is and why it exists

Two things happen at the ends of a link that the fibre itself knows nothing about. Light has to get into the fibre, and the light arriving has to be turned into decisions about bits.

The first is a geometry problem and it loses more than people expect. The second ends in the most striking result of the subject: a floor on error rate that no engineering can beat.

The vocabulary

• Coupling efficiency — the fraction of the source's light that gets into the fibre and stays there.
• Area mismatch — the source emitting from a region larger than the fibre core.
• Angle mismatch — the source emitting over a wider cone than the fibre accepts.
• Front end — the first amplifier stage after the detector.
• High impedance front end — a large load resistor. Sensitive, and narrow in bandwidth.
• Transimpedance front end — an amplifier with feedback, converting current to voltage. Wider bandwidth.
• Thermal noise — noise from the receiver's own resistance and amplifier.
• Shot noise — noise from the random arrival of photons and the discreteness of charge.
• Probability of error — how often a bit is decided wrongly.
• Quantum limit — the best error rate possible with a perfect, noiseless receiver.

The mental model

Coupling first. Two mismatches cause the loss, and both are geometric.

If the source emits from an area larger than the fibre core, the light outside the core is lost, and no lens can fix it. If the source emits over a cone wider than the acceptance angle, everything outside that cone is lost too. An LED loses badly on both counts, which is why LED links use multimode fibre with its larger core and wider acceptance. A laser is directional and small, so it couples far better, and laser-to-single-mode coupling is still hard enough to be expensive.

The receiver has one job: decide, for each bit period, whether a one or a zero was sent. Everything else is about the noise that makes that decision uncertain.

Three noise sources compete. Thermal noise comes from the load resistance and the amplifier, and it does not depend on the signal. Shot noise comes from the randomness of photon arrivals and the discreteness of charge, and it grows with the signal. In an avalanche receiver, the multiplication adds its excess noise on top. Ranking these for a given design is how you decide what is worth improving. Improving an amplifier helps a thermal-noise-limited receiver and does nothing for a shot-noise-limited one.

The front end is the first real choice. A high impedance front end uses a large load resistor. That gives a large signal voltage and low thermal noise, so it is sensitive. Together with the detector capacitance it also gives a low bandwidth. A transimpedance front end uses feedback around an amplifier instead. The feedback holds the input near a fixed voltage, so the capacitance matters much less and the bandwidth is far wider. It is slightly noisier. Most practical receivers use the transimpedance arrangement for that reason.

Performance then becomes a calculation. Put the noise sources together. Work out how far apart the one and zero levels are, compared with the noise spread, then convert that into a probability of error. That number is what a link is specified by, and being able to run the calculation is the point of the topic.

The quantum limit is where it ends, and it is worth stating carefully. Imagine a receiver with no thermal noise, no amplifier noise, and perfect efficiency, counting individual photons. It can still make mistakes. Photon arrivals are random, so even when a one is transmitted there is a chance that no photon arrives at all during that bit period. If the receiver counts nothing, it decides zero, and it is wrong.

The probability of receiving nothing falls exponentially as the average number of photons per bit rises. So demanding a very low error rate sets a minimum average photon count per bit. For the error rates links are specified at, that works out at a few tens of photons.

That floor is a physical bound, not an engineering shortfall. Real receivers fall well short of it, and how far short tells you how much is left to win.

What you should now be able to explain or do

Explain the two geometric causes of coupling loss and why a laser couples better than an LED. Rank thermal, shot and excess noise for a given receiver and say what improving each would achieve. Compare high impedance and transimpedance front ends on sensitivity and bandwidth. Compute a probability of error from a signal-to-noise ratio. State the quantum limit and explain why it exists even for a perfect receiver.

Check yourself