# DLI-Based DP-QPSK Reception Scheme for Short-Range Optical Communication
## 2 Structure and Basic Principle  
DP-QPSK is most commonly modulated at the transmitter through electro-optic modulators based on a Mach-Zehnder interferometer structure, which was first proposed by [PERSON] in 1891 and improved by [PERSON] in 1892 [23; 24]. Figure 1 gives the detailed structure of the DP-QPSK modulator and shows how it works. Figure 1: A diagram of the detailed structure of the dual-polarization quadrature phase-shift keying (DP-QPSK) modulator and how it works. DP-MZM: dual-parallel Mach–Zehnder modulator. \(\exp(j\beta L)\) is the phase shift due to the electrode length. The baseband signal to be modulated is applied to the electrode of the MZM. Each MZM is biased at the minimum transmission point and each DP-MZM is biased on one arm to introduce a 90\({}^{\circ}\) phase shift. A linearly polarized continuous-wave (CW) lightwave emitted from a laser diode (LD) is injected into a DP-QPSK modulator [25]. It was assumed that the optical signal at the input of the modulator was:  
\[E_{LD}(t)=\sqrt{P_{t}}\exp[j(\omega_{c}t+\varphi)], \tag{1}\]  
where \(P_{t}\) is the optical power, \(\omega_{c}\) is the optical frequency, and \(\varphi\) is the initial phase. A DP-QPSK modulator mainly consists of four Mach-Zehnder modulators (MZM) and a 90\({}^{\circ}\) polarization rotator. Every two MZMs are connected in parallel or in series to form a DP-MZM. The transfer equation of an MZM biased at the minimum transmission point is [25; 26]:  
\[E_{\text{MZM}}(t)=jE_{in}(t)\ \exp(j\beta L)\cos[\pi\frac{V_{1}(t)\ -\ V_{2}(t)}{2V_{\pi}}], \tag{2}\]  
where \(E_{in}(t)\) is the input signal into the MZM, \(\beta\) is the modulation coefficient of the MZM, \(L\) is the length of the electrode, \(V_{\pi}\) is the half-wave voltage of the MZM, and \(V_{1}(t)\) and \(V_{2}(t)\) are the drive voltages of the MZM. In Figure 1, \(\varphi_{lQ}=\pi\frac{V_{1}(t)-V_{2}(t)}{2V_{\pi}}\), which is the baseband signal to be modulated. Each DP-MZM is biased on one arm to introduce a 90\({}^{\circ}\) phase shift. Hence, the output of the DP-MZM is:  
\[ \begin{array}{ll}E(t)&=jE_{LD}(t)\exp(j\beta L)[\cos(\varphi_{l}t)+\cos( \varphi_{Q}t)\exp(j\pi/2)]\\ &\triangleq jE_{LD}(t)\exp(j\beta L)\exp(j\Phi),\end{array}  \tag{3}\]  
where \(\Phi\) is the modulated phase. Then, one of the DP-MZM output signals is applied to a polarizer and the two DP-MZM outputs give the two orthogonal polarization states. The output DP-QPSK signal can be written as follows:  
\[E_{s}(t)=\left[ \begin{array}{c}jE_{LD}(t)\ \exp(j\beta L)\ \exp(j\Phi_{ \parallel})\\ jE_{LD}(t)\ \exp(j\beta L)\ \exp(j\Phi_{\perp})\end{array} \right]. \tag{4}\]  
The optical signal from the transmitter is transmitted through a fiber-optic link and reaches the receiver for demodulation. The structure of a DLI-based DP-QPSK receiver is schematically shown in Figure 2. A DP-QPSK demodulator is mainly composed of two DP-DLIs and four pairs of balanced photodiodes. Each DP-DLI consists of two Mach-Zehnder DLIs and every DLI is traditionally tuned with an exact one-symbol-period differential delay on one arm and a +45\({}^{\circ}\) (-45\({}^{\circ}\)) phase shift on the other, which is the most efficient configuration in back-to-back systems [27; 28]. Figure 2: A schematic diagram of the structure of a delay-line interferometer (DLI)-based DP-QPSK receiver. OS: optical signal; DPC: dynamic polarization alignment controller; PBS: polarization beam splitter; LPF: low-pass filter; CDR: clock data recovery. The input optical signal is separated through a dynamic polarization alignment controller (DPC) and a polarization beam splitter (PBS) into two signals with mutually orthogonal polarization states, realizing polarization demultiplexing. The separated single-polarized signals are then injected into a DP-DLI each, which converts the phase-difference information into intensity information in the optical domain. Finally, signals containing the intensity information are directly detected through balanced photodiodes and high-frequency noise is eliminated after filtering.