Modulators

Each of the four lanes ends in a Mach–Zehnder modulator (MZM): the laser’s light is split into two arms, the lane’s voltage shifts the phase of one arm against the other, and the arms recombine. When they are in phase the light passes; when they are half a wavelength apart it cancels. The bit therefore becomes an optical field level, and it is fields, not powers, that the optical Fourier transform adds.

The modulator is biased at quadrature, half-way down the curve (bias 0.5 π rad paper), where the transfer is steepest and most nearly straight. A 1 swings the arms towards the top of the curve and a 0 towards the bottom, by the same amount each way.

The simulator models a push-pull MZM with an ideal cosine field transfer. Its peak power per lane is 43.6 µW illustrative and the drive swing is 0.22 π rad illustrative either side of quadrature; both are illustrative, chosen so that the worked example reproduces. Per-lane amplitude, phase and bias errors can be added (the calibration chapter uses them), but the curve itself is the textbook one.

With these values a 1 gives a field of 5.97 √µW and a 0 gives 2.81 √µW, out of a maximum of 6.6 √µW. The difference, d = 1.58 √µW, is what carries the information.

A 0 is not dark. At quadrature with this swing a 0 still passes 0.426 of the peak field (a 1 passes 0.905). Every lane therefore carries a steady carrier as well as its bit. After the optical Fourier transform the carriers of all four lanes add up in output 1 (the DC bin), which shows up at the receiver as a pedestal of 130 µA under a level step of 36.56 µA.

That pedestal costs range: DC-coupled, output 1 needs a span of 7.56 steps where the data alone needs four. It also costs a little noise, because the carrier’s power adds shot noise on output 1 (the receiver chapter). Calibration removes the pedestal by re-measuring the all-zeros response, and AC coupling removes it altogether (the DC-balance chapter).

The swing is a trade. A larger swing makes d bigger, so every level step is bigger against the receiver’s noise, and makes the carrier smaller; but it pushes both levels into the curved parts of the transfer, and a real driver delivers only so much voltage. Try the slider: at the illustrative default the extinction is modest, which is typical of a fast silicon modulator, and the model still closes the link with margin.

The model’s modulator is an ideal cosine. To trust its numbers for the real module one would need each lane’s measured transfer curve (its V_π, insertion loss and extinction), how the bias point drifts with temperature and time, the driver’s actual swing and bandwidth, and any amplitude or phase mismatch between the four lanes. Those feed straight into the per-lane amplitude and bias errors the simulator already supports.