## 2 Experiment Setup
### Single-Mode and Multimode VCSELs Comparison  
The SM-VCSEL is custom-designed and fabricated by Integrated Compound Semiconductor (ICS) from a GaAs/AlGaAs-based epitaxial structure supplied by the Compound Semiconductor Centre (CSC), whereas the MM-VCSEL is an off-the-shelf device (OPTEK OPV310). Measurements characterising both devices, including light-current-voltage (L-I-V) curves, magnitude responses and noise power spectral densities (PSDs), can be found in [21]. The L-I-V curves show that the SM-VCSEL exhibits higher dynamic resistance and emits lower optical power due to its smaller oxide aperture, which ensures single-mode  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Device/System** & **Module Description** & **Setup/Parameters** \\ \hline AWG & Keysight M8195A & BW = 23 GHz, SR = 60 CSA/s, 8-bit Res. DAC \\ \hline Photodetector & Newport 818-BB-45A & BW = 9 GHz, \(\varnothing\) 60 \(\mu\)m, \(\sim\)550 V/W Gain at 850 nm \\ \hline Optics Lens & Thorlabs ACL2520U & \(\varnothing\) 25 mm, Focal length = 20 mm \\ \hline Oscilloscope & Tektronix DPO71254C & BW = 12.5 GHz, SR = 50 CSA/s, 8-bit Res. ADC \\ \hline \hline \end{tabular} BW—Bandwidth, SR—Sampling Rate, and Res.—Resolution.  
\end{table}
Table 1: OWC system parameters.  
Figure 1: Illustration of experiment setup: (**a**) Photo of VCSEL-based OWC link. (**b**) Schematic for multilevel PAM.  
emission. To maintain eye-safe conditions, we drive the SM-VCSEL at approximately 2.2 mA, resulting in an optical power of around 0.7 mW (\(-\)1.47 dBm). Similarly, the MM-VCSEL is driven at about 5 mA to emit approximately 3 mW (4.7 dBm) of optical power. This ensures comparable bandwidths between the two VCSELs for meaningful performance comparisons. The measured \(-\)3 dB bandwidths of SM-VCSEL and MM-VCSEL are approximately 6.2 GHz and 6.4 GHz, respectively.  
We compare both VCSELs for the OWC link based on their measured noise power spectral densities (PSDs) at a received optical power (ROP) of approximately \(-\)1.75 dBm. The noise PSDs for the SM-VCSEL and MM-VCSEL average around \(-\)137 dB/Hz and \(-\)129 dB/Hz, respectively. In comparison, the OWC system with a ROP of \(-\)1.75 dBm has thermal and shot noises estimated at \(-\)146 dB/Hz and \(-\)151 dB/Hz, respectively. Therefore, the primary noise source for the OWC link is the relative intensity noise (RIN) from the VCSELs, as the noise PSDs from both VCSELs exceeds that of shot or thermal noise.  
We focus more on the eye-safe SM-VCSEL for PAM-\(M\) since it has a lesser RIN than the MM-VCSEL and offers a higher data rate for similar operating conditions [6; 21]. To illustrate the performance of the equalisers for the SM-VCSEL, we consider two setups with the SM-VCSEL-based OWC link as follows:  
* Setup-I: amplitude of 0.5 Vpp corresponding to \(\sim\)70% modulation index at 100 MHz, maximum ROP of \(-\)1.75 dBm;
* Setup-II: amplitude of 0.7 Vpp corresponding to \(\sim\)95% modulation index at 100 MHz, maximum ROP of \(-\)3.08 dBm.  
While Setup-II offers a higher SNR than Setup-I, it does so at the expense of higher non-linearity. This is demonstrated in Figure 2, which illustrates the non-linearity of the SM-VCSEL (with both setups) and the MM-VCSEL (with Setup-I) through their total harmonic distortion (THD). The THD indicates the level of additional harmonics per frequency, with higher THD signifying greater non-linear distortion from these harmonics [24]. The MM-VCSEL exhibits approximately 3.5 dB more THD than the SM-VCSEL with both VCSELs at \(\sim\)70% modulation index. Moreover, the SM-VCSEL has about 2.2 dB more THD when Setup-II is used instead of Setup-I.