# Frequency Comb-Based WDM Transmission Systems Enabling Joint Signal Processing
## 3 Receiver Comb Technologies
### Regeneration from Two Pilots  
As stated in Equation (1), the phase evolution of each comb carrier can be written in terms of the phase and timing-jitter noise. Thus, by knowing the phase evolution of two carriers, the phase evolution of any carrier can be found. If the phase evolution of the \(n\)th carrier, \(\phi_{n}(t)\), and \(m\)th carrier, \(\phi_{m}(t)\) is known, the phase evolution of the remaining carriers can be written as:  
\[\phi_{k}(t)=\phi_{n}(t)+\frac{k-n}{m-n}[\phi_{m}(t)-\phi_{n}(t)]. \tag{4}\]  
This property is of importance when aiming at utilizing the spectral coherence between the carriers provided by a frequency comb. From this equation, one can easily realize that in the ideal case by transmitting two unmodulated lines, e.g., two pilot tones, a frequency comb with the same individual phases as the transmitter carriers can be generated at the receiver side and therefore perform self-homodyne detection. We will refer to this technique as comb-regeneration for self-homodyne superchannel detection. We will here discuss several techniques, illustrated in Figure 5, that have already been demonstrated to regenerate a frequency comb. The first technique is injecting the two neighboring unmodulated lines and performing optical injection locking of a mode-locked laser, as shown in Figure 5a. This technique was already proposed in 2008 [89], although it was not shown that the quality of the regenerated frequency comb was sufficient to perform self-homodyne detection. More recently, we demonstrated that by having two unmodulated lines and using four-wave mixing [63; 64], a frequency comb can be all-optically regenerated. The main challenge of this technique is that the OSNR of the unmodulated lines must be sufficiently high to avoid undesired noise beating in the comb regeneration. Given that the pilot tones are co-transmitted with the data that are subject to the in-line amplifier noise, this can be a significant practical challenge. Therefore, optical filtering of these two unmodulated lines is of great importance. The first attempt to do this was based on optical injection-locked lasers [63], but achieving a filtering bandwidth below hundreds of MHz was still challenging with this technique. However, the filtering is critical to achieve successful comb regeneration. By exploiting the narrow bandwidth of Brillouin amplification, we demonstrated the first successful self-homodyne detection using a regenerated comb in [64]. While the Brillouin amplification  
Figure 5: Schematic of different methods for regenerating a frequency comb using (**a**) a mode-locked laser (MLL), (**b**) a parametric mixer (cascaded four-wave mixing) and (**c**) an electro-optic (EO) comb with external clock recovery. provided around 25 MHz of filtering, the noise added in this stage and the extinction ratio of the filtering (i.e., the gain of the amplifier) limited the number of regenerated carriers that could be used for self-homodyne detection to around 24 carriers. Another possible technique is the use of an electrical phase-locked loop (PLL) for retrieving the frequency separation among the carriers [65]. In this case, two neighboring carriers are beat in a photodiode, and the frequency separation is obtained and filtered by a PLL. The output of the PLL was then used to drive an EO comb. While this technique was demonstrated for an EO comb, it could also be implemented in any comb that uses an RF driving signal. In addition, this technique could be implemented for combs that can be seeded by two lines such as parametric combs or Kerr combs. In such a case, the two lines seeding the comb could be realized by a simple EO modulation stage. However, this technique will be limited by the bandwidth of the PLL, and PLL power consumption might become an issue. So far, we have mainly discussed techniques of adjacent pilot tones. Using non-adjacent tones is also viable, however at the expense of a more complex comb regeneration scheme.