IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 37, NO. 3, MARCH 2001 337 Synchronized Chaotic Mode Hopping in DBR Lasers with Delayed Opto-Electric Feedback Yun Liu, Peter Davis, and Tahito Aida Abstract—We propose and demonstrate a scheme for gener- ating synchronized chaotic mode hopping in two wavelength-tun- able lasers. Chaotic mode hopping resulting in large hops in wave- length is induced by delayed feedback of an electrical signal pro- portional to the intensity of the laser output which passes through an optical filter. Mode hopping among up to 11 modes was exper- imentally observed and optical signals in each wavelength band show a different on–off modulation time series. Analysis of the time series indicates high dimensionality. By using a unidirectional cou- pling method that injects part of the output of one laser into an- other, we can synchronize the chaotic mode hopping of two sepa- rate lasers and obtain synchronized chaotic on–off modulation pat- terns in multiple corresponding wavelength bands. The robustness of the synchronization with respect to the parameter mismatch and the effects of the coupling strength are investigated. The chaotic mode hopping dynamics and synchronization are well described with a numerical model that includes the characteristics of the laser tuning and the filter transmission. A multiplexed data transmis- sion scheme using chaotic carriers is proposed and experiments demonstrate that multiple messages can be simultaneously recov- ered when chaos synchronization is achieved. Index Terms—Chaos, synchronization, mode hopping, optical communications, secure data transmission, spread-spectrum. I. INTRODUCTION C HAOS synchronization, or synchronization of chaotic os- cillators, provides a means to copy chaos, that is, to gen- erate identical chaotic oscillations in different sites, by coupling the oscillators with suitable link signals [1], [2]. The topic of chaos synchronization has received considerable attention be- cause of possible relevance to secure and robust communica- tions [2], [3] and signal processing in biological systems [4], [5]. In the context of communication, an information signal con- taining a message is transmitted using a chaotic signal as a broad-band carrier. A key problem is the synchronization of a driven oscillator in a remote receiver by injecting a signal sent from a master oscillator in a transmitter. This is important when applying chaos to both secure communications and spec- trum-spread systems where chaotic oscillations are used to mask or multiplex information in signals. Owing to its high dimension and high bandwidth, laser chaos has been of particular interest in recent research on chaos syn- chronization and related secure communications using chaos [6]–[14]. Most of the laser chaos systems studied so far have been implemented using a delayed-feedback configuration due Manuscript received March 14, 2000; revised October 17, 2000. The authors are with the ATR Adaptive Communications Research Labora- tories, Kyoto 619-0288, Japan. Publisher Item Identifier S 0018-9197(01)01619-0. to the simplicity of implementation and feasibility of gener- ating high dimensional dynamics [15]. In achieving synchro- nization of laser chaos in delayed-feedback systems, a unidi- rectional coupling scheme has been widely employed. Abar- banel and Kennel [16] numerically demonstrated the synchro- nization of two Ikeda type ring cavities via the unidirectional coupling. Recent experiments by Van Wiggeren and Roy [9] and Goedgebuer et al. [10] demonstrated the excellent perfor- mance of secure optical data transmission based on chaos syn- chronization using a particular unidirectional coupling method, i.e., the open-loop receiver scheme, which was first proposed by Volkovskii and Rulkov [17] in electronic systems. Another attractive aspect of laser chaos is the possibility of generating signals with multiple wavelengths. This is potentially useful for communications systems using wave- length-hopping spread spectrum [18] or systems combining spread spectrum with wavelength multiplexing [19]. Chaotic variation of wavelength has been observed and studied in a number of different laser systems. Liu and Ohtsubo [20] demonstrated chaotic oscillations in a laser diode with feed- back from a Twyman–Green interferometer which nonlinearly converts wavelength variation to injection current of the laser diode itself. In their experiments, attention was given to inten- sity variations and the accompanying wavelength oscillations were limited to a few tens of gigahertz corresponding to a subnanometer order. Recently, Larger et al. [21] proposed a chaotic wavelength oscillation system that consists of a wavelength-tunable laser and a birefringent plate between crossed polarizers to generate a feedback signal which is a nonlinear function of lasing wavelength. The variation range of the wavelength is extended to a few subnanometers but is still within the continuous tuning range of a single mode of the laser. They further demonstrated synchronized chaotic oscillation in two similar lasers using the unidirectional coupling scheme [10]. In our previous work [22], we reported the synchronization of chaotic mode hopping among multiple longitudinal modes in two wavelength-tunable distributed Bragg reflector (DBR) lasers. This paper extends the previous work and presents detailed discussions, both experimentally and numerically, on mode-hopping dynamics, its synchronization, and applications to secure data transmission. This paper is organized as follows. In the next section, we describe the setup of the experimental system which mainly consists of a wavelength-tunable DBR laser, an optical wavelength filter, and delayed opto-electric feedback. Characteristics of some key elements including the tuning characteristics of the light source and the optical filter transmission function are described with experimental 0018–9197/01$10.00 © 2001 IEEE