Multiplexed Chaos-Based Communications with ...

INPE – National Institute for Space Research São José dos Campos – SP – Brazil – July 26-30, 2010

Multiplexed Chaos-Based Communications with Semicondutor Lasers D. Rontani1,2,3 , D.S. Citrin1,2 , A. Locquet2,1 , M. Sciamanna3,2,1 1

Georgia Institute of Technology, School of Electrical and Computer Engineering, 777 Atlantic Drive NW, Atlanta GA 30332-0250, USA 2 UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2-3 Rue Marconi, 57070 Metz, France 3 Supélec, OPTEL and LMOPS EA 4423, 2 Rue Edouard Belin, 57070 Metz, France

keywords: Applications of Nonlinear Sciences, Chaotic Dynamics, Communication with Chaos, Optoelectronic and Granular Matter, Synchronization. 1. INTRODUCTION Optical chaos cryptography is a promising alternative to conventional mathematical techniques for the enhancement of privacy of transmission at the physical layer of communication networks [1, 2]. Two legitimate users, Alice (the emitter) and Bob (the receiver), are willing to securely exchange data on a public communication channel wiretapped by Eve (an eavesdropper). When chaotic optical devices, such as semiconductor lasers, are considered, Alice usually realizes the encryption by mixing her random data with the chaotic fluctuation generated by her laser. The signal produced is then sent into a communication channel. At the receiver end, Bob has a physical twin of Alice’s laser (theoretically, internal and operational parameters are identical). When the chaotic laser are properly coupled [3] Bob’s laser synchronizes on the deterministic chaotic fluctuations generated by Alice’s laser only. That is why Bob retrieves the concealed data by performing a substraction. The problem becomes, however, more difficult when multiple users want to securely transmit their message on a single communication channel. Conventional optical communications are using either timeor wavelength-division multiplexing (TDM or WDM) as a criterion to separate multiple signals transmitted in a single channel. Chaos encryption has been already applied on the top of conventional WDM approaches using multimode lasers [4, 5] or multiple monomode lasers operating at largely detuned frequencies [6]. In this abstract, we propose a new theoretic architecture to ensure chaos multiplexing with a spectral efficiency of optical fields generated by several semiconductor lasers with identical free-running frequencies. 2. THEORY AND MODEL FOR MULTIPLEXED SYNCHRONIZATION Our architecture is illustrated in Fig. 1. For the sake of illustration and simplification, we have considered the case

of two pairs of lasers. The architecture has multiple arms, and variable attenuators to control and constrain the time delays and injection (coupling) strengths. In the external optical feedback, shared between the various Alices, there is a multiplexed optical field ET , which results from the sum of all the Alices’ optical fields with specific time delays and coupling strengths. This field drives the dynamics of the various Alices’ lasers, and its expression is given in the second line of Eq. (1). The architecture is modeled within the frame-

Figure 1 – Architecture for the multiplexing of several chaotic optical fields. LD: laser diodes, VA1,2 : variable attenuators, OI: optical isolator, M and Mf : mirrors, BS: beam splitter, ET multiplexed optical field

work of Lang-Kobayashi equations [7] by using monomode semiconductor lasers. It reads dEka 1 a = (1 + iαka ) (Gak − 1/τpk )Eka + Fka dt 2 n X a/a ¡ ¢ a a a −iω0j τjk +i∆ωjk t a a + ηjk e Ej t − τjk , (1) j=1

dEkb dt

= +

¢ 1¡ b 1 + iαkb (Gbk − 1/τpk )Ekb + Fkb 2 n X a/b ¡ ¢ s b b −iω0j τjk +i∆ωjk t a b ηjk e Ej t − τjk , (2) j=1

dNka,b

=

¯ ¯ ¯ a,b ¯2 a,b a,b Jka,b − γsk Nk − Ga,b E ¯ k k ¯ ,

(3) dt where the subscript k denotes the kth users pair and superscripts a, b Alice’s or Bob’s variables, respectively, Eka,b =

a,b

|Eka,b |eiφk is the slowly varying complex electric field, Nka,b a,b a,b the carrier number, Ga,b k , τpk the photon lifetime, αk is the

a,b linewidth enhancement factor, γsk is the carrier decay rate, a,b a,b Jk is the pumping current density, ω0k is the free-running a c laser frequency. The delays τjk (τjk ) are the flight time between Alicej and Alicek and Alicej and Bobk , respectively. a The same notations are used for the injection strength ηjk a/a

b and ηjk , and the frequency detuning ∆ωjk

a a − ω0k = ω0j

a/b

b a and ∆ωjk = ω0j − ω0k . The spontaneous emission noise q is modeled by Langevin sources Fka,b = 2βka,b Nka,b ξka,b

with βsp the spontaneous emission rate and ξka,b independent Gaussian white noises with unitary variance. The geometry and coupling strengths are adjusted in such a way that each pair Alicek /Bobk can exhibit complete chaos a synchronization, when the injection rates are identical ηjk = b ηjk , and assuming that no parameter mismatch, no frequency detuning, and no noise exist in a given pair of users. Similarly to the single emitter/single receiver case [3], each pair of users has different anticipation times ∆τk (k = 1, . . . , n). 3. NUMERICAL SIMULATIONS A numerical simulation (Fig. 2) shows that under the aforementioned conditions two pairs of semiconductor lasers a a ) = ω02 (n=2) with identical free-running pulsations (ω01 can generate separable chaotic optical fields although their spectral overlap is very important. Complete synchronization between the two users of a given pair is used to realize the separation of the different chaotic carriers. We observe it in Fig. 2(a1)-(a4), and it occurs with different anticipation times: ∆τ1 = 9 ns and ∆τ2 = 11 ns. However, the cloudy trajectories in Fig. 2(a2)-(a3) implies that the optical fields produced by each pair of users (Alicek /Bobk ) are strongly uncorrelated.

4. CONCLUSION This abstract shows the possibility to transmit multiple chaotic optical fields on a single optic channel. The separation of each channel is ensured by the chaos synchronization between each pair of users. This allows to multiplex multiple optical signals with overlapping optical spectra, hence improving the spectral efficiency when compared to chaotic wavelength division multiplexing [4–6]. Consequently, this architecture constitutes a first step toward the multiplexed transmission of multiple data streams using optical chaos encryption. References [1] G.D. Van Wiggeren and R. Roy, “Communication with chaotic lasers”, Science, vol. 279, pp. 1198-1200, 1998. [2] A. Argyris, D. Syvridis, L. Larger,V. Annovazzi-Lodi, P. Colet, I. Fisher, J. GarciaOjalvo, C.R. Mirasso, L. Pesquera and K.A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links”, Nature, vol. 438, pp. 343-346, 2005. [3] A. Locquet, C.Masoller, and C.R. Mirasso, "Synchronization regimes of optical-feedbackinduced chaos in unidirectionally coupled semiconductor lasers", Phys. Rev. E, vol. 65, pp. 056205, 2002. [4] J.K. White and J.V. Moloney, "Multichannel communication using an infinite dimensional spatiotemporal chaotic system", Phys. Rev. A, vol. 59, pp. 2422-2426, 1999. [5] M.W Lee and K.A. Shore, "Two-mode chaos synchronisation using a multi-mode externalcavity laser diode and two single-mode laser diodes", IEEE J. Lightwave Technol., vol. 23, pp. 1068-1073, 2005. [6] T. Matsuura, A. Uchida, and S. Yoshimori, "Chaotic wavelength division multiplexing for optical communication", Opt. Lett., vol. 29, pp. 2731-2733, 2004. [7] R. Lang and K. Kobayashi, "External optical feedback effects on a semiconductor injection laser properties", IEEE J. Quantum. Electron., vol. 16, pp. 347-355, 1980.

Figure 2 – Synchronization diagrams in the plane of the intena,b a b sity of Alice and Bob: (I1,2 (t − ∆τ1,2 ), I1,2 (t)) with I1,2 = a,b 2 |E1,2 | ).