# Extended L-Band InAs/InP Quantum-Dash Laser in Millimeter-Wave Applications
## 3 Results and Discussion
### WL and SMF Transmission Performance Analysis
Consider the following two optical fields \(E_{0}\) and \(E_{2}\) of a dual-wavelength source, which are two optical carriers:  
\[E_{DWL}=E_{0}+E_{2} =A_{IL0}(1+\delta_{IL0}(t))\exp(j\omega_{IL0}t+\phi_{IL0}(t))+A_{IL2} (1+\delta_{IL2}(t))\exp(j\omega_{IL2}t+\phi_{IL2}(t)) \tag{1}\]  
where \(A_{ILn}\), \(\delta_{ILn}\), \(\omega_{ILn}=2\pi f_{ILn}=2\pi c/\lambda_{ILn}\), and \(\phi_{ILa}\) represent the amplitude, amplitude noise, angular frequency, and the phase noise of the SIL-based optical tones, respectively, with frequency, \(f_{ILn}\), and wavelength \(\lambda_{ILn}\) (\(n=0\) or \(2\)), and \(c\) is the speed of light [20; 30]. After the DSB modulation of these optical carriers (i.e., Equation (1)) in the MZM with a QPSK-modulated signal at an angular intermediate frequency \(\omega_{IF}=2\pi f_{IF}\), the output consists of optical carriers with their respective double sidebands, as shown in the right inset of Figure 3. This consists of spectral lines at angular frequencies \(\omega_{IL0}\), \(\omega_{IL0}-\omega_{IF}\), \(\omega_{IL0}+\omega_{IF}\), \(\omega_{IL2}\), \(\omega_{IL2}-\omega_{IF}\), and \(\omega_{IL2}+\omega_{IF}\). In the following, the beating of optical carriers with one sideband is considered in the PD after propagating through an SMF with length \(L\), as they correspond to the MMW beat tone of interest (i.e., 28 GHz). In particular, heterodyning of \(E_{0}\) with sideband \(\omega_{IL1}=\omega_{IL2}-\omega_{IF}\) that corresponds to the optical field \(E_{1}\) with phase (wavelength) \(\phi_{IL1}(\lambda_{IL1})\) and \(E_{2}\) with sideband \(\omega_{IL3}=\omega_{IL0}+\omega_{IF}\) corresponding to the optical field \(E_{3}\) with phase (wavelength) of \(\phi_{IL3}(\lambda_{IL3})\), is considered. Now, assuming identical amplitude as well as phase noise (i.e., \(\phi_{IL1}=\phi_{IL2}\) and \(\phi_{IL3}=\phi_{IL0}\)) variations of optical carriers and sidebands, and neglecting the second-order terms related to noise-to-noise beatings, the photodetected current can be represented as:  
\[ \begin{array}{l}I_{PD}(t)=\exp(-\alpha L)\Bigg{[}\sum\limits_{i=0,2}(I_{i}+ I_{i+1})+\sum\limits_{i=0,2}(I_{i}+I_{i+1})\sqrt{RIN(t)}\\ +2\sum\limits_{i=0,2}\sqrt{I_{1}I_{i+1}}\cos(\omega_{MMW}t-m\beta_{2}\omega_{ MMW}^{2}L+\big{(}\phi_{IL_{0}}(t)-\phi_{IL_{2}}(t,\tau_{i})\big{)})\end{array}  \tag{2}\]  
where \(I_{x}\) is the photodetected direct current (DC) of optical signal \(E_{x}\) (\(x=0\) to \(3\)), and \(RIN(t)\) corresponds to the relative intensity noise (RIN) of optical tones in the time domain [20; 30]; the second term represents the noise current of two optical carriers at a low frequency, while the third is the required MMW beat tone exhibiting the angular frequency and phase of \(\omega_{MMW}=\omega_{IL2}-\omega_{IF}-\omega_{IL0}\) and \(\phi_{IL_{0}}(t)-\phi_{IL_{2}}(t)\), respectively; the last term represents the noise current of the heterodyned two optical tones close to \(\omega_{MMW}\) and is responsible for increasing the intensity noise of the generated MMW beat-tone signal. Firstly, the relative optical power variation between the optical carrier and the sideband, which is typically inherent to DSB modulation, affects the RIN. Secondly, the amplitude noise of the two optical tones will also affect the generated MMW beat-tone quality by increasing the noise level of the signal [19; 20]. Moreover, in Equation (2), the second term in the argument of the cosine depicts a constant phase shift terms due to fiber dispersion, where \(\beta_{2}\) is the second-order fiber dispersion derivative, i.e., \(\beta_{2}=\partial^{2}\beta/\partial\omega^{2}=-D\lambda^{2}/2\pi c\), \(D\) is the fiber dispersion parameter, and \(m\) is a constant. This term, which assumes constant \(D\) and \(\lambda\) for both optical carrier and the sideband, creates a phase shift between them when propagating through fiber length \(L\). It is periodic in nature and results in the observation of peak powers and nulls in the MMW carrier power profile.