# Chaotic Optical Communication with Wavelength-Hopping Technology Based on Tunable Lasers
## 3 Numerical Simulation and Analyses  
We now further analyze the security of the wavelength-hopping chaotic communication system in detail. Considering the performance of chaotic communication systems [23], and based on our system, the parameters of the numerical simulation are shown as follows: emitter power \(P_{T}=5\) mW, mask efficiency \(\alpha=0.2\), time delay mismatch \(\Delta T=1\) ps, strength feedback mismatch rate \(\Delta\beta/\beta=0.004\), offset phase mismatch \(\Delta\phi=0.02\) rad, high cutoff response time mismatch rate \(\Delta\tau/\tau=0.02\), and the distance of optical fiber transmission channel is 30 km. For the photodetector, we took a typical photodetector as an example, and its spectral response is given in the product manual (the spectral response between 1530 nm and 1600 nm is shown in Figure 2b). Figure 2a shows the BER of [PERSON] and [PERSON] under different emitter wavelengths (from 1530 nm to 1600 nm, C band and L band) based on this PD. It can be seen that the BER remains below \(10^{-7}\) when the laser wavelength of the emitter is synchronized with that of the receiver. When the wavelength of the receiver remains at 1550 nm, with an increase of the wavelength of the emitter, the BER first decreases; it reaches its lowest value when the wavelength of the emitter is also 1550 nm, and then it increases soon after. The BER reaches up to \(10^{-2}\) when the wavelength of the emitter is 1600 nm. It is always higher than \(10^{-6}\) when the wavelength of the emitter ranges from 1570 nm to 1600 nm and is higher than \(10^{-3}\) in the range of 1585 nm to 1600 nm. Since the wavelength of this chaotic system is hopping, the wavelength control of the three tunable lasers in the emitter and receiver is of particularly note. As shown in Figure 1, there is an optical fiber transmission channel between the emitter and receiver, which is tens or even hundreds of kilometers long in practical communication. The time when the signal transmits in the feedback loop can be written as \(t\), and the time when the optical signal transmits in the optical fiber channel can be written as \(\Delta t\). Thus, after the split by the coupler of the emitter, a part of the signal applies to the MZ modulator of the emitter and generates a chaotic signal, which takes the time \(t\), and the wavelength of the chaotic signal  
Figure 2: (**a**) BER of Bob (wavelength match) and Eve (wavelength mismatch) under different wavelengths of the emitter. (**b**) Spectral response of a typical photodetector from 1530 nm to 1600 nm. can be written as \(\lambda_{1}\). Similarly, another part of the signal applies to the MZ modulator of the receiver and generates a chaotic signal, which takes the time \(t+\Delta t\), and the wavelength of the chaotic signal can be written as \(\lambda_{2}\). Since the chaotic signal generated by the emitter also takes the time \(\Delta t\) to transmit to the receiver, it is possible to recover the message by subtracting the two input signals of the power combiner if \(\lambda_{1}=\lambda_{2}\). The wavelength-switching sequence of the three tunable lasers is shown in Figure 3. In terms of LD1, in order to make the message signal and the chaotic carrier signal not be separated in the optical fiber transmission channel, the wavelength-switching moment and sequence of LD1 should be synchronous with that of LD2. For LD2 and LD3, their wavelength-switching sequences and time intervals should be controlled uniform, and the wavelength switching of LD3 should have a time delay \(\Delta t\) relative to LD2. The value \(\Delta t\) can be expressed as  
\[\Delta t=L/c \tag{7}\]  
where \(L\) is the distance of the optical fiber transmission channel and \(c\) is the speed of light in the fiber. Figure 4 shows the BER of this system when the wavelength switching of LD3 has a time delay or no time delay relative to that of LD2. The tunable time of the tunable lasers we chose is 350 ms/5 nm, and in this period, the message stops transmitting because of the unstable wavelength.