4.3: Add-drop multiplexers

In wave division multiplexing (WDM), information is sent in parallel on different wavelengths. In general, we want to be able to be able to multiplex and demultiplex in a controlled way. One way to do this is with an add-drop multiplexer, as Illustrated in Figure \(\PageIndex{1}\). An add-drop takes advantage of the linearity and symmetry of most optical systems: if inport 1 takes 20 channels in and channel 3 is directed to outport 2, then channels 1,2,4-20 go to outport 1. That also means that if a signal on channel 3 is sent into inport 2, it will also appear on outport 1. Hence, we have simultaneously dropped channel 3 and added a new channel 3 to the multiplexed signal on outport 2.

Figure \(\PageIndex{1}\): conceptual diagram of an add/drop multiplexer designed to simultaneously drop and add channel \(x\). Channel \(x\) is separated from the the other channels at the left hand inport and redirected to the left hand outport. A new channel \(x\) is added via the right hand inport and combined with the remaining channels to exit at the right hand outport.

WDM channels can be as closely spaced as 12.5 GHz, however, it is much more common to use 50 and 100 GHz spacing. Given that the carrier frequency is about 195 THz, this means that an add-drop must have a frequency selectivity better than 0.05%, which cannot be achieved with something as coarse as an MZI. Instead, microring resonators (MRR) are used. The ring, pictured in Figure \(\PageIndex{2}\) is an optical resonator: light that is coupled in to the ring from the top waveguide must be a longitudinal mode of the resonator. As with a resonator consisting of two mirrors, the phase of the light must be an integer multiple of 2\(\pi\) after a round trip, which, in this case has a physical length of \(l = 2\pi r\), where \(r\) is the radius of the ring. However, the ring is also a waveguide with a refractive index \(n_{eff}\), so the resonance condition is satisfied when \(f = \frac{mc}{2\pi rn_{eff}}\), where \(m\) is an integer.

Figure \(\PageIndex{2}\): Microring resonator add/drop multiplexer. The ring waveguide diameter is such that channel \(x\) is resonant, allowing it to couple in from the left hand inport waveguide and out through the right hand outpot. Likewise the new channel \(x\) couples in from the right hand inport, and out through the right hand outport. The other channels are not resonant with the MRR and travel from the left hand inport to the right hand outport unaffected.

As with the optical resonators discussed earlier, the FSR of the MRR is a comb of possible frequencies that fall within the transparency range of the material used to fabricate the integrated optical circuit. An example of such a comb is shown in Figure \(\PageIndex{3}\) for a ring with a radius of 10 µm and \(n_{eff}=3\). Note that the spacing is between modes is very large (about 1.5 THz)

Figure \(\PageIndex{3}\): longitudinal modes of a 10 \(\mu\)m radius MRR in the C and L bands.

The parameters chosen for Figure \(\PageIndex{3}\) are reasonable for high-index materials like InP or silicon. However, for materials like silicon nitride, the radius of the MRR must be larger, leading to a smaller FSR. If we compare Figure \(\PageIndex{3}\) to the ITU grid spacing for 100 GHz DWDM (D = dense), then we expect 5 of the 80 channels to be resonant. Hence, a single MRR add-drop, as shown in Figure \(\PageIndex{4}\)a is insufficient to the purpose. There are two possible solutions, shown in Figures \(\PageIndex{4}\)b and \(\PageIndex{4}\)c. One solution is to take advantage of the fact that the drop port contains 5 channels with a separation of 1.5 THz, so a coarse filter, like an MZI or a directional coupler can be used to separate the desired channel from the five remaining channels.

Figure \(\PageIndex{4}\): A standard MRR add/drop multiplexer, but limited control over which channels are added or dropped. By first filtering the input with an MZI (b), a specific channel within the passband of the MZI can be chosen. However, this will also remove channels from outside the passband of the MZI from the outport of the MRR add/drop. Using two MRRs with different ring radii (c) allows the add/drop to be tuned such that only a single channel is dropped or added.

Alternatively, one can use two rings in place of a single ring. This works on the same principle as a DFB laser: each ring has a set of longitudinal modes, but, because the light couples from the waveguide to ring 1 to ring 2 and thence to a second waveguide, the light in the system as a whole must be a longitudinal model of both rings simultaneously. Thus, the FSR of the system becomes much larger, limiting the transmission to the drop port to a single channel, as shown in Figure \(\PageIndex{5}\).

Figure \(\PageIndex{5}\): longitudinal modes of MRRs with radii of 10 \(\mu\)m (fuchsia) and 12 \(\mu\)m (brown). There is only a single common mode for the two rings within the C and L bands. This can be more clearly seen in the longitudinal modes of the system (blue). Note the vertical scale is logarithmic and that the peak on the far right is outside the L band.

So far we have discussed the FSR of MRRs and how combining rings will lead to a greater FSR. However, another aspect is the bandwidth of the add-drop multiplexer. Consider that the data rate of a single channel might be as high as 40 Gb/s, meaning a bandwidth of at least 40 GHz is required. We saw with laser how the reflectivity of the mirrors also defined the bandwidth of the cavity. A MRR has no mirrors, but it does have a per-round-trip loss, and the waveguides that couple light in also couple light out, thus, the bandwidth of an MRR can be tuned to match the bandwidth of the communication system.

Exercise \(\PageIndex{1}\)

The code below allows you to calculate the transfer function of a two ring add-drop multiplexer. You can adjust the radii of the two rings, and the coupling between the rings and the waveguides. Tune (adjust the radii) the multiplexer so that it drops channel 18. How big a change in radii is required to drop channel 19? Zoom in on the next largest peak within the C or L band. What channel is closest? What is the relative cross talk from the chosen channel to channel 19?