# Frequency Comb-Based WDM Transmission Systems Enabling Joint Signal Processing
## 1 Introduction
### Optical Frequency Combs: A Background
#### 1.1.1 Technologies for Optical Frequency Comb Generation  
There is a vast range of laser technologies that qualifies as optical frequency comb generators. Each has different tradeoffs and can be engineered to meet different application-specific requirements. The first optical comb generators were based on the electro-optic modulation method [9; 10], often known as electro-optic frequency comb generators or simply electro-optic (EO) combs. In its most basic configuration, a continuous-wave (CW) laser is modulated by an electro-optic modulator. The modulator is itself driven by an external radio-frequency (RF) source. The modulation creates sidebands around the CW laser exactly spaced by the frequency of the RF source. Here, the frequency of the CW laser and the frequency of the RF source provide the two degrees of freedom of the comb generator. One common setup for an EO-comb is illustrated in Figure 2.  
Figure 1: A frequency comb in the frequency domain. The comb is fully characterized by the repetition rate \(f_{r}\), which defines the line spacing, and either the offset frequency from zero \(f_{0}\) or the central frequency \(f_{c}\). EO combs built with state-of-the-art, yet standard, telecommunication equipment feature high average power (\(\sim\)1-10 mW per line), a low optical linewidth (<100 kHz) and a smooth optical envelope [11; 12]. The RF source can be derived from high-performance RF oscillators, which translates into optical pulse trains with low timing jitter [13]. During the 1990s, there was a rapid development of ultrafast solid state mode-locked laser technology [14] and efficient nonlinear broadening mechanisms in photonic crystal fibers [15]. By the end of the decade, it became possible to implement the concept of self-referencing, whereby the two degrees of freedom of the comb could be locked to a common radio-frequency reference [16; 17]. However, modern light wave communications do not need combs with the frequency lines defined with such a level of accuracy. Instead, the lines need to display a high optical signal-to-noise ratio (OSNR) (>30 dB), a spacing in the order of 10-100 GHz, optical linewidths <100 kHz, a smooth spectral envelope and compatibility with fiber-optic components (ideally in a small and robust form factor). These demands, especially the line spacing, have challenged the use of more standard frequency comb generators used in frequency metrology applications, such as those based on erbium fiber mode-locked lasers, for applications in optical communications. Using combs as alternatives to discrete laser sources was explored based on nonlinearly broadened (so-called supercontinuum) pulses from mode-locked fiber lasers already in 1996 [18]. While enabling transmission records, those sources where not strict comb sources as the comb line separation was much smaller than the channel separation, and optical time-division multiplex filters were needed to increase the symbol rates. However, a few years later, it was recognized that optical frequency combs, particularly those based on EO comb technology, could be very attractive as WDM sources. This concept was originally explored with nonlinear broadened EO combs using on-off keying in [19]. The initial demonstrations involved a limited number of channels, but subsequent progress in highly nonlinear fibers enabled extending the concept to >1000 lines [20]. The aforementioned EO combs represent an excellent choice for exploring the possibilities of frequency combs as sources in WDM systems. The time-domain waveform emerging from an EO comb can be compressed to generate picosecond pulses [10], which can be used as the seed to generate additional bandwidth via nonlinear effects in an external waveguide (see, e.g., [21; 22]). By carefully shaping the pulses and the dispersion in the nonlinear medium, combs spanning the C + L light wave communication bands with high OSNR can be obtained [23]. The introduction of coherent technology in WDM systems imposed additional demands on the optical linewidth and OSNR for the comb lines.