# Microscope-Based Optical Frequency Comb Generator for 200 GHz Spaced WDM Data Transmission System
## 2 Methods
### Simulation of OFC Generation  
The OFC generation in a single family of fundamental modes is modeled numerically in the framework of the Lugiato-Lefever equation [1; 35]:  
\[t_{R}\frac{\partial E(t,\tau)}{\partial t}=\left[2\pi\,i\!k\!\sum_{k\geq 2} \frac{\beta_{k}}{k!}\!\left(\!i\frac{\partial}{\partial T}\!\right)^{k}+2\pi\,i \!R\gamma_{0}\!\int R(s)|E(t,\tau-s)|_{2}ds-\alpha-i\!\delta_{p}\right]E+\sqrt{ \theta}E_{p}, \tag{7}\]  
where \(E(t,\tau)\) is an electric field inside the resonator; \(T\) and \(t=N_{R}\cdot t_{R}\) are the fast and slow times; \(N_{R}\) is the number of a microresonator roundtrip; \(t_{R}=2\pi Rn_{\textit{eff}}\)/\(c\) is the roundtrip time; \(\delta_{p}\) is the phase detuning of the continuous wave (CW) pump field \(E_{p}\) from the nearest resonance; \(\theta\) is the coupling coefficient; \(\beta_{k}=\mathrm{d}^{k}\beta/\mathrm{d}\omega\) taken at the pump frequency \(\omega_{0}\) (we set \(\beta_{k}=0\) for \(k\geq 4\)); \(\beta(\omega)=n_{\textit{eff}}k_{0}\) is the propagation constant; \(\gamma_{0}\) is the nonlinear Kerr coefficient at \(\omega_{0}\); \(\alpha=(2\pi)^{2}R/(\mathcal{Q}\lambda_{p})\) is the loss coefficient including intrinsic and coupling losses; and \(\lambda_{p}\) is a pump wavelength. The response function is approximated by  
\[R(t)=(1-f_{R})\delta(t)+f_{R}h_{R}(t), \tag{8}\]  
where \(\delta(t)\) is the delta function; \(f_{R}=0.18\) is the fractional contribution of the delayed Raman response, and  
\[h_{R}(t)=\left(\tau_{1}^{-2}+\tau_{2}^{-2}\right)\!\tau_{1}\exp(-t/\tau_{2}) \sin(t/\tau_{1}), \tag{9}\]  
with constants \(\tau_{1}=12.2\) fs and \(\tau_{2}=32\) fs [35].  
We use a home-made software based on the split-step Fourier method [35] to simulate OFC generation numerically in the frame of Equation (7). We previously simulated DKS generation with similar software without the Raman nonlinearity [38; 39]. Although here, a more advanced version of the numerical code with allowance for the Raman nonlinearity is used.  
Simulation of Silica Microsphere OFC Generator-Based 4-Channel 200 GHz Spaced IM/DD WDM-PON Transmission System  
The purpose of our research model was to simulate the 4-channel 200 GHz spaced intensity modulation direct detection (IM/DD) WDM-PON data transmission system by the implementation of designed silica microsphere-based OFC generator as a portable light source. We evaluate the performance of such a communication system according to next-generation PON (NG-PON2) requirements for specified valid optical link distances of up to 60 km [40]. Therefore, we used \"VPI Photonics Design Suite\" software for the simulation of a 4-channel 10 Gbit/s per channel  
Figure 1: Schematic diagram of the whispering gallery modes (WGMs) for a microsphere at the initial temperature T\({}_{0}\) and heated by \(\Delta\)T.  
non-return-to-zero on-off keying (NRZ-OOK) modulated WDM-PON optical transmission system to show the implementation of an microsphere-based OFC generator providing a spectral and energy-efficient fiber optical telecommunication system solution.  
To achieve high precision of the measured results, it is crucial to provide the pseudo-random bit sequence (PRBS) with sufficient length, defined in VPI simulation scheme by using \"VPI photonics design suite\" simulation program modified built-in Wichman-Hill-Generator. Architecture and further simulation results of the above-described NRZ-OOK fiber optical communication system are presented in Section 3.3 of this article.