## 2 Principles  
In Figure 1, we present the schematic diagram of the proposed analog-digital combined high-secure optical communication system. The encryption module is made up of two encrypting portions: digital and analog. The unified 3D chaotic system generates chaotic signals for the analog-digital combined encryption. In the analog part, \(\mathbf{x}\) chaotic signal is generated by the corresponding circuit of the chaotic system to encrypt the phase. In the digital part, the \(\mathbf{y}\) and \(\mathbf{z}\) sequences of the chaotic system are generated by MATLAB to encrypt the data in the time and frequency domain. At the receiver, the PM is demodulated by using chaotic circuit to generate chaotic signal, which is opposite to the \(\mathbf{x}\) chaotic signal. Then, the digital signal processing (DSP) performs the opposite operation with the transmitter to decrypt in the digital domain. Employing the following 3D chaotic system to generate a chaotic signal to encrypt the original data:  
\[\left\{ \begin{array}{l}\dot{\mathbf{x}}=\mathbf{y}\\ \dot{\mathbf{y}}=\mathbf{z}\\ \dot{\mathbf{z}}=-\mathbf{a}\mathbf{z}+\mathbf{b}\text{sgn}(\mathbf{x})-\mathbf{x}-\mathbf{y}\end{array} \right. \tag{1}\]  
Figure 1: Schematic diagram of the proposed encryption scheme. when \(\mathbf{a}=0.6\), \(\mathbf{b}=1\), and \((\mathbf{x}_{1},\mathbf{y}_{1},\mathbf{z}_{1})=(0,\,0,\,1)\), the system (1) is in a chaotic orbit, as shown in Figure 2.  
We designed the chaotic circuit corresponding to the chaotic system to implement the encryption on the hardware. The proposed scheme utilizes the chaotic signal generated by the chaotic circuit to drive the PM to encrypt rather than the optical carrier, and the transmission capacity is no longer limited by the bandwidth of the chaotic signal. The chaotic circuit has the characteristics of small size, low cost and high sensitivity. Its size is only 10 cm \(\times\) 5 cm. The circuit is composed of three channels, which are integrated according to the state variables \(\mathbf{x}\), \(\mathbf{y}\), and \(\mathbf{z}\), respectively. The circuit schematic of system (1) was designed as shown in Figure 3. The construction of the corresponding chaotic circuit can be represented as:  
\[\left\{ \begin{array}{l}\dot{\mathbf{x}}=\frac{1}{R_{1}C_{1}}\mathbf{y}\\ \dot{\mathbf{y}}=\frac{1}{R_{2}C_{2}}\mathbf{z}\\ \dot{\mathbf{z}}=-\frac{1}{R_{7}C_{3}}\mathbf{z}+\frac{1}{R_{8}C_{3}}\text{sgn}(\mathbf{x} )-\frac{1}{R_{5}C_{3}}\mathbf{x}-\frac{1}{R_{6}C_{3}}\mathbf{y}\end{array} \right. \tag{2}\]  
Figure 3: Chaotic circuit schematic diagram. Figure 2: Phase trajectory diagram of the chaotic system. (**a**) the phase trajectory of \(\mathbf{x}\)-\(\mathbf{y}\), (**b**) the phase trajectory of \(\mathbf{z}\)-\(\mathbf{x}\), (**c**) the phase trajectory of \(\mathbf{z}\)-\(\mathbf{y}\), and (**d**) the phase trajectory of \(\mathbf{x}\)-\(\mathbf{y}\)-\(\mathbf{z}\). The chaotic circuit completes the computing of integral, addition, subtraction and nonlinear operations. The supply voltage of the circuit is \(\pm 13.5\) V. The corresponding circuit components can be selected as:  
\[\left\{ \begin{array}{l}\text{C}_{1}=\text{C}_{2}=\text{C}_{3}=100\text{ nF},\,R_{1}=16.6\text{ K}\Omega\\ R_{2}=R_{3}=R_{4}=R_{5}=R_{6}=R_{7}=R_{8}=R_{9}=R_{10}=R_{13}=R_{14}=10\text{ K}\Omega\\ R_{11}=13.5\text{ K}\Omega,\,R_{12}=1\text{ K}\Omega\end{array} \right. \tag{3}\]  
The type specification of operational amplifier is LM741 CN. The physical equipment of the analog circuit is shown in Figure 4a. The phase trajectory of the analog circuit in the oscilloscope shows in Figure 4b,c. Figure 4b is the phase trajectory of \(\mathbf{x}\)-\(\mathbf{y}\), and Figure 4c is the phase trajectory of \(\mathbf{y}\)-\(\mathbf{z}\). The outputs waveform of the physical circuit is consistent with the simulation outputs. The temporal waveform of the generated chaotic signal \(\mathbf{x}\) is shown in Figure 4d. Figure 4e shows the spectrum of the generated chaotic signal \(\mathbf{x}\).