# A Pulse Shaping Based Optical Transmission System of 128 QAM for DWDM with N \(\times\) 904 Gbps
## 2 Pulse Shaping  
The processing procedure of a modulated photonic carrier with the modulation format of 128 QAM which is gotten by using Gaussian optical filtering on an optical shaping is given in Figure 1.  
The ultra-high-speed photonic carrier transmission with the modulation format of 128 QAM is achieved by using optical phase dual-arm modulation with four differential signals, which are converted by series-to-parallel. In order to make it easy to understand, one of the photonic carriers with 128 QAM based on optical phase dual-arm modulation is theoretically analyzed. The angular frequency of the continuous laser-carrier in the 128 QAM photonic transmitter is \(\omega_{0}\), and then, the continuous laser-carrier can be described by:  
\[E_{0}(t)=A_{0}exp(j\omega_{0}t) \tag{1}\]  
where \(A_{0}\) is the amplitude of the optical field output from the carrier-laser. \(E_{0}(t)\) is modulated by \(V_{s1}(t)\) and \(V_{s2}(t)\), which are output from 128 QAM sequence generator via the dual port Mach-Zehnder modulator (DPMZM) in the coherent 128 QAM photonic transmitter. The expression of the modulated signal output from the DPMZM can be further described by [16; 17]:  
\[E_{out}(t)=\frac{E_{0}(t)}{10^{(IL/20)}}\bigg{\{}\gamma\cdot\exp[\frac{j\pi V_ {s2}(t)}{V_{\pi RF}}+\frac{j\pi V_{bias2}}{V_{\pi DC}}]+[(1-\gamma)\cdot\exp[ \frac{j\pi V_{s1}(t)}{V_{\pi RF}}+\frac{j\pi V_{bias1}}{V_{\pi DC}}]\bigg{\}} \tag{2}\]  
Figure 1: Pulse shaping for a photonic carrier (GOF: Gaussian Optical Filter; QAM: Quadrature Amplitude Modulation). where \(E_{0}(t)\) is the output of the laser-wave; \(IL\) is the insertion loss; \(V_{s1}(t)\) and \(V_{s2}(t)\) are the input electrical voltages for the upper modulator arm and the lower modulator arm, respectively; \(V_{bias1}\) and \(V_{bias2}\) are the configurations for the bias voltage 1 and bias voltage 2 of the DPMZM; \(V_{\pi RF}\) is the switching modulation voltage; \(V_{\pi DC}\) is the switching bias voltage; \(\gamma\) is the optical power splitting ratio of the both Y-branch waveguides; and there is a definite functional relationship between \(\gamma\) and the extinction ratio [17]. The extinction ratio (ER) of the DPMZM is 20 dB; the parameters of \(V_{\pi RF}\) and \(V_{\pi DC}\) are configured as 3 V; the setting of \(IL\) is 5 dB; and the settings of \(V_{bias1}\) and \(V_{bias2}\) are 0 V.  
From [16; 17], and Equation (2), we can derive the following:  
\[E_{out}(t)=A_{C}\cdot\exp[j\omega_{0}t]+j\cdot B_{C}\cdot\exp[j\omega_{0}t] \tag{3}\]  
where \(A_{C}\) and \(B_{C}\) are the special constants, which can be described by:  
\[A_{C}=0.889A_{0}\cdot[\cos\frac{\pi V_{s2}(t)}{3}+\cos\frac{\pi V_{s1}(t)}{3}] B_{C}=0.889A_{0}\cdot[sin\frac{\pi V_{s2}(t)}{3}+sin\frac{\pi V_{s1}(t)}{3}] \tag{4}\]  
where \(V_{s1}(t)\) and \(V_{s2}(t)\) are two-channel electrical signals output from 128 QAM sequence generator; the numerical values of them are 0 or 1 at every moment, which can be regarded as constants. From Equation (3), by the method of the Bessel function expansion, we can see that a modulated photonic-carrier signal contains many photonic harmonic-waves, and the angular frequencies of the harmonic-waves are \(n\omega_{0}\) (\(n=0\), \(\pm 1\), \(\pm 2\), \(\pm 3\), \(\pm 4\), \(\pm 5\), and more). In other words, the angular frequency space of the adjacent harmonic-wave is \(\omega_{0}\). We can also see that the power of the central photonic harmonic-wave is maximum, and the powers of the others photonic harmonic-waves decrease gradually with the increase of \(n\), and each photonic harmonic-wave contains the same ultra-high-speed modulation information. Lastly, we can obtain the central photonic harmonic-wave from the output of the coherent 128 QAM photonic transmitter via an appropriate optical filtering, where the suitable filter is a Gaussian optical filter.