# Effect of Laser Parameters on Optical Stealth Transmission System Performance
## 2 Generation of Optical Stealth Carrier  
Based on gain-switched optical pulses, the configuration of optical stealth carrier generator is shown in Figure 1. The sine wave from local oscillator (LO) is launched into the DFB semiconductor laser. The gain-switched optical pulses are divided into different ports for encoding in the spectral domain. Each port is connected with an optical delay line to achieve time-domain encoding. The multiplexed signals are sent to a dispersion fiber span for temporal spreading. The transmitting power of stealth signal is controlled by a variable optical attenuator. The interaction between photons and carriers in the DFB laser can be modeled by the rate equations [11; 12; 13]. The dynamics of carrier density \(N(t)\) and complex electric field \(E(t)\) in the DFB laser can be expressed as  
\[ \begin{array}{c}\frac{dE(t)}{dt}=\frac{v_{2}a(N(t)-N_{1})FE(t)}{2[1+eE^{2}(t )]}-\frac{E(t)}{2\tau_{p}}+\frac{\Gamma gBN^{2}(t)}{2E(t)}+F_{E}\\ \frac{dN(t)}{dt}=\frac{I(t)}{eV}-\frac{v_{2}a(N(t)-N_{0})}{1+eE^{2}(t)}E^{2}(t )-\frac{N(t)}{\tau_{n}}+F_{N}\end{array}  \tag{1}\]  
where all the parameters have a unique meaning and some of them are listed in Table 1. In addition, \(I(t)\) is a time-varying injection current that contains the bias current \(I_{b}\) and sinusoidally varying current \(I_{m}\) from the LO. The Langevin noise sources \(F_{E}\) and \(F_{N}\) take into account spontaneous emission and spontaneous carrier recombination. The power of the gain-switched optical pulses is given by  
\[P(t)=\frac{E^{2}(t)V\eta_{0}\hbar v}{2\Gamma\tau_{p}} \tag{2}\]  
where \(\eta_{0}\) is the differential quantum efficiency, \(h\) is [PERSON]'s constant, and \(v\) is the unmodulated optical frequency. Therefore, the spectrum of the optical pulses can be expressed as \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Confinement factor (\(\Gamma\)) & 0.3 \\ Linear material gain coefficient (\(a\)) & \(3.3\times 10^{-20}\) m\({}^{2}\) \\ Spontaneous emission rate (\(\beta\)) & \(1\times 10^{-4}\) \\ Group velocity (\(v_{g}\)) & \(7.5\times 10^{7}\) ms\({}^{-1}\) \\ Electron charge (\(\epsilon\)) & \(1.6\times 10^{-19}\) C \\ Volume of the active region (\(V\)) & \(1.8\times 10^{-16}\) m\({}^{3}\) \\ Carrier density at transparency (\(N_{t}\)) & \(1.5\times 10^{24}\) m\({}^{-3}\) \\ Nonlinear gain compact factor (\(\epsilon\)) & \(3\times 10^{-23}\) m\({}^{3}\) \\ Photon lifetime (\(\tau_{p}\)) & \(3\times 10^{-12}\) s \\ Carrier life time at threshold (\(\tau_{n}\)) & \(2.1\times 10^{-9}\) s \\ Bimolecular recombination coefficient (\(B\)) & \(1.0\times 10^{-16}\) m\({}^{3}\) s\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Some parameter definitions and values in simulations. Figure 1: The generator of optical stealth carrier based on gain-switched optical pulses. LO, local oscillator; DFB, distributed feedback laser; WDM, wavelength division multiplexing; VOA, variable optical attenuator. \[\Omega=\Omega_{0}+FTShift(FFT\Big{|}\sqrt{P}\exp(j\phi(t)\Big{|})) \tag{3}\]  
where \(\Omega_{0}\) is the center angular frequency, FFT is fast Fourier transform, FFTshift shifts the outputs of FFT to the center of the spectrum, \(\phi\) is the instantaneous phase term. Further, the complex electric field of the gain-switched optical pulses based stealth carrier can be described as  
\[e_{d}(t)=e(t)\exp(-j\psi(\Omega)) \tag{4}\]  
where \(\psi\) is the phase delay induced by the chromatic dispersion of the dispersion fiber and \(e(t)\) can be written as  
\[e(t)=\sum_{i=1}^{m}\frac{1}{m}\sqrt{P}\exp(j\Omega_{i}(t-i\tau)+j\phi) \tag{5}\]  
where \(m\) is the number of ports, \(\Omega_{i}\) is the center angular frequency of \(i\)-th port, and \(\tau\) is the time-slot duration. The gain-switched optical pulses with the different bias currents are shown in Figure 2. The modulation frequency is 2.5 GHz and the modulation current is 0.2 A. In Figure 2a, the bias current varies from 0.04 to 0.24 A.