# Impact of Chirp in High-Capacity Optical Metro Networks Employing Directly-Modulated VCSELs
## 3 Simulations  
As previously demonstrated, InP long-wavelength VCSELs can show different amount of chirp, depending on their design and fabrication. When analyzing the transmission performance of DM-VCSELs this parameter plays a critical role especially in the presence of filtering associated to wavelength multiplexers and demultiplexers present inside the WDM MAN, e.g., at the network nodes. It should be noted that the chirp interplay with CD can be neglected in case of COH-D exploitation, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Optical Source** & \(\alpha\) & \(\kappa\) \\ \hline Tunable VCSEL & 2.75 & \(8.3\times 10^{12}\) \\ Short-cavity VCSEL & 3.7 & \(1.52\times 10^{13}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measured chirp parameters of the two VCSEL sources. Figure 1: Experimental setup for chirp parameters measurement. Figure 2: Channel transfer functions obtained after 10-km (blue), 24-km (red) and 34-km (yellow) SSMF propagation for: (**a**) 8-GHz tunable VCSEL and (**b**) 20-GHz short-cavity VCSEL. where CD DSP compensation can be easily performed. Moreover, as DM is exploited, the transmitted signal is just intensity modulated, and a simplified coherent receiver can be used [15]: after I and Q components recovery and CD compensation the I and Q square moduli are performed and summed up in order to obtain the originally transmitted intensity signal. This approach avoids the use of phase and frequency recovery, reducing the complexity of the receiver DSP and also relaxing the constraints on VCSEL and local oscillator (LO) linewidths. As a drawback, this operation cancels the advantages in terms of bit error rate (BER) as a function of signal to noise ratio (SNR) of COH-D.  
Our simulations are obtained developing a modeling tool based on Matlab(tm) which includes all the transmitter, propagation, and receiver blocks. Specifically, the COH receiver exploits a 10-dBm per polarization LO with 100-kHz linewidth and has 25-GHz electrical bandwidth. The DM VCSEL is modeled considering both the intrinsic modulation properties and the extrinsic device parasitic components. The overall electrical modulation frequency response can be described by [16]:  
\[H(f)=H_{int}(f)\cdot H_{par}(f)=const.\frac{f_{R}^{2}}{f_{R}^{2}+j\frac{\gamma_{ r}}{2\pi}f-f^{2}}.\frac{1}{1+j\frac{f}{f_{p}}}, \tag{4}\]  
where \(f_{R}\) is the relaxation resonance frequency, \(\gamma\) is the intrinsic damping factor and \(f_{p}\) is the parasitic cut-off frequency. The simulations have been performed for three different chirp conditions, corresponding to the following three cases:  
1. a directly-modulated VCSEL with chirp parameters as the short-cavity device
2. a directly-modulated VCSEL with chirp parameters as the tunable device
3. a CW 500-kHz laser followed by an electro-absorption modulator (EAM) with \(\alpha=0.4\)  
For all the three cases, following [16] and Equation (4), the modulation frequency bandwidth is set to 18 GHz, although this bandwidth is now achieved only by the actual short-cavity devices. The VCSEL linewidth is 5 MHz, which is a suitable value for both long-wavelength VCSELs. The bias currents are set to 8 mA and 16 mA for case (1) and (2), respectively, while their modulation amplitudes are 8.5 mA and 26 mA respectively; thanks to the reduced amount of chirp, in fact, in the tunable VCSEL case, it is possible to exploit a higher modulation depth, allowing higher SNRs. The bias current and the modulation depth for case (3) are optimized in order to achieve an equivalent extinction ratio of 15 dB. The impact of optical filtering is evaluated using the transfer function of a 25-GHz channel spacing WSS, which shows a 21-GHz full width half maximum (FWHM) [9]. The propagation medium is a SSMF, with 0.25 dB/km attenuation and 17 ps/nm km dispersion at 1550 nm. Fiber spans of 35 km and 65 km are considered with the employment of Erbium-doped fiber amplifiers (EDFAs) with 6-dB noise figure (NF) to compensate for the transmission losses of each span.