# Chaotic Optical Communication with Wavelength-Hopping Technology Based on Tunable Lasers
## 3 Numerical Simulation and Analyses
We assume that the working time of the lasers in each wavelength is 350 ms and that the optical fiber transmission channel is 30 km long; thus, the time delay of LD3 is 0.1 ms. In the case of not considering the time delay, in the first 0.1 ms, since the signal of the receiver achieves the power combiner when the signal of the emitter is transmitting in the channel, the value of the BER is 1. Between 0.1 ms and 0.35 s, even though the time delay is not considered, the wavelength of the two input signals of the power combiner is the same, and the BER is not affected. Within the 0.1 ms after 0.35 s, LD3 has worked for 0.35 s and is in a state where it is unable to switch wavelengths. However, there is the signal emitter by LD2 with input to the power combiner during this time, and the value of BER is 1. In the following period, the BER changes periodically according to this rule. This shows that when designing the system, it is necessary to consider the time delay of the laser LD3. Figure 3: Wavelength-switching sequence of the three tunable lasers. We assume that the signal transmission rate is 1 Gb/s, and after the same time interval, the wavelength hops from \(\lambda\)1 to \(\lambda\)2, \(\lambda\)3, and \(\lambda\)15, and then returns to \(\lambda\)1. The switching sequence of LD3 has a time delay \(\Delta t\) compared to LD1 and LD2. Additionally, the wavelength tuning time is not shown in the figure. We set the wavelength of the tunable laser of the transmitter to switch once every 5 nm from 1530 nm to 1600 nm, for a total of 15 wavelengths, which is a period. The tunable laser wavelength switching time of the 5 nm interval is 350 ms, and we set the working time of each wavelength to 350 ms; each period is then 11.2 s. The wavelength switching of LD3 is set as mentioned above, and the laser wavelength of the eavesdropper is assumed constant, always at 1550 nm. In Figure 5a, the BER always stays below \(10^{-7}\) and remains almost unchanged during authorized communication between [PERSON] and [PERSON]. For [PERSON], since the wavelength of the tunable laser in the emitter is constant during the working time, the BER is constant during this period. When the wavelength of the emitter is switched, the BER also hops with it. The BER of [PERSON] changes periodically with the periodic hopping of the wavelength of the emitter. It decreases at first and then increases, reaching the maximum at the end of the period. In addition, we use the average BER to show the BER of [PERSON] within the previous time. After a few seconds, with the increase in the BER of [PERSON], the average BER also increases and remains at a relatively high value. The value of the average BER of [PERSON] in one period is 2.6 \(\times\)\(10^{-3}\), which is five orders of magnitude higher than the BER of [PERSON]. Due to the lack of forward error correction (FEC) technology in our transmitting subsystem of the chaotic optical communication system, the BER of systems must be less than \(10^{-6}\). Therefore, [PERSON] can transmit communication normally and [PERSON] cannot. In addition, in order to study the worst-case scenario, we conduct a numerical analysis and evaluation based on the assumption that [PERSON] knows the key to our chaotic communication system accurately except for the wavelength hopping. In fact, the BER of [PERSON] will be much worse than in the case described here because [PERSON] cannot accurately master our key parameters. Figure 4: BERs under wavelength match. (**a**) Without considering the time delay of the wavelength-switching sequence of LD3. (**b**) Considering the time delay of the wavelength-switching sequence of LD3, and 0 s represents the time of LD3 after time delay. The time when tunable lasers work in each wavelength is 350 ms, and the tuning time of tunable lasers is also 350 ms. The working time of the three tunable lasers is shown at the top of the figure.