# Chaotic Optical Communication with Wavelength-Hopping Technology Based on Tunable Lasers
## 2 Principle  
The wavelength-hopping chaotic communication scheme proposed in this paper is represented in Figure 1. Based on the electro-optical feedback structure [6], the optical intensity chaos is generated, and the chaotic synchronization is realized by using the emitter (Alice) and receiver (Bob) with the same structure and parameters. In this system, a driver drives the tunable laser diode 1 (LD1), and LD1 is directly modulated by a digital message m(t). Initially, the optical signal c1(t) emitted by the tunable laser diode 2 (LD2) passes though Mach-Zehnder electro-optical modulator 1 (MZM1). Then it is split into two branches by fiber coupler 1. One output c1(t)/2 of coupler 1 in the emitter is transmitted to the receiver directly, and when the signal is applied to Mach-Zehnder electro-optical modulator 2 (MZM2) in the receiver, the output of MZM2 can be written as c2(t). The other output c1(t)/2 of coupler 1 is fed back to MZM1 through photodiode 1 (PD1) and amplifier 1, and the output of MZM1 can be also written as c2(t). Then c2(t) arrives at coupler 1 again. At the same time, a digital message m(t), which comes from LD1, also arrives at coupler 1. Then, through fiber coupler 1, the signal composed of c2(t) and m(t) is transmitted to the receiver. Finally, in the receiver, the first signal composed of c2(t) and the second signal composed of c2(t) and m(t) are detected by photodiode 3 (PD3) and photodiode 4 (PD4). Then, the two branches of the signal are converted into electrical signals, and the message signal can be found by subtraction. The decoded message is analyzed by a BER analyzer. The erbium-doped fiber amplifier (EDFA) is used to compensate for the loss in the optical fiber  
Figure 1: Wavelength-hopping chaotic laser communication system. LD1, LD2, and LD3 are tunable lasers. transmission channel and the beam-splitting loss of the coupler at the receiver, to ensure that the optical power into the feedback loop of the emitter and the receiver is equal. Different from the chaotic optical fiber communication systems in previous works, tunable lasers are used in this system in both the emitter and the receiver. The wavelength of tunable lasers is kept a secret key between Alice and Bob. In the process of communication, a pseudo-random sequence generator controls the selection circuit of the laser wavelength, so the wavelengths of the lasers in the emitter and the receiver hop within a certain range synchronously and at pseudo-random. For a chaotic system, nonlinear dynamics are very important [22]. In a chaotic communication system, the BER is mainly affected by the mismatch noise, and in our system, the root mean square amplitude of the mismatch noise is affected by the wavelength. Based on Ref. [23], considering the effect of the wavelength, \(<\!\!n_{\lambda}\!^{2}\!>\) can be approximated as  
\[\langle\!n_{\lambda}\!^{2}\!\rangle\approx\frac{1}{2}K_{\lambda}\!^{2}\Bigg{[} \langle\varepsilon^{2}\rangle+(\Delta\phi)^{2}+\frac{1}{4}\bigg{(}\frac{ \Delta K_{\lambda}}{K_{\lambda}}\bigg{)}^{2}\Bigg{]}, \tag{1}\]  
where \(\Delta\phi\) is the mismatch offset phase, \(\Delta K_{\lambda}\) is the mismatch of detection and can be given as \(\Delta K_{\lambda}=K_{\lambda}\!^{\prime}-K_{\lambda}\). \(K_{\lambda}\), and \(K_{\lambda}\!^{\prime}\) can be expressed as  
\[K_{\lambda}=\frac{1}{4}P_{T}g_{EDFA}\alpha_{T}R_{\lambda}g_{APD}, \tag{2}\]  
\[K^{\prime}_{\lambda}=P_{T}\!^{\prime}R_{\lambda}\!^{\prime}g_{APD}\!^{\prime} \tag{3}\]  
where \(P_{T}\) and \(P_{T}\!^{\prime}\) are the optical power of the emitter laser and the receiver laser, respectively, and \(g_{APD}\) and \(g^{\prime}_{APD}\) are the gain of PD3 and PD4, respectively. The gain of the EDFA is \(g_{EDFA}\), and \(\alpha_{T}\) is the loss in the transmission line. In order to realize the parameter match, \(g_{EDFA}\alpha_{T}/4=1\) is used. The response of PD3 and PD4 are given as \(R_{\lambda}\) and \(R_{\lambda}\!^{\prime}\), and they are the function of \(\lambda\) and \(\lambda^{\prime}\), respectively.