IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 51, NO. 9, SEPTEMBER 2015 2400309 Simultaneous Suppression of Time-Delay Signature in Intensity and Phase of Dual-Channel Chaos Communication Amr Elsonbaty, Salem F. Hegazy, and Salah S. A. Obayya, Senior Member, IEEE Abstract—In this paper, we propose a novel dual-channel opti- cal chaos system with a time-delay (TD) feature simultaneously suppressed in all observables, i.e., in both intensity and phase. A hybrid optical and electro-optic feedback for a single vertical- cavity surface-emitting laser (VCSEL) is verified to induce simul- taneous TD suppression for the polarization-resolved components of the chaotic output. A comprehensive mathematical model is developed to incorporate the optical and electro-optic time delays into the rate equations of the VCSEL. The suppression of TD signature is then examined by means of autocorrelation function and delayed mutual information. The results show that the output chaotic signal has the TD feature well eliminated in both the intensity and phase over certain regions of parameter space identified using the peak signal to mean ratio technique. The independent evolution of the two orthogonal VCSEL modes renders the polarization-resolved output modes appropriate for the enhanced dual-channel chaos applications. To the best of our knowledge, this is the first time that a dual-channel chaos communication system is reported with simultaneous suppression of the TD feature in all the transmitted observables. Index Terms—Vertical-cavity surface-emitting laser (VCSEL), optical feedback, time delay (TD) suppression, dual-channel chaos communication. I. I NTRODUCTION T HE optical chaos generated by a semiconductor laser (SL) subject to a delayed feedback has attracted considerable interest during the last two decades [1]–[3]. Its broadband spectrum, extreme sensitivity to initial conditions, and ability to establish synchronization between two remote systems make it the preferred candidate to physically obscure and encode mutual information signals in both time and frequency domains [4]–[9]. These features evoke further vital applica- tions as ultra-fast physical random bit generation [10]–[12], Manuscript received May 13, 2015; revised July 9, 2015; accepted July 27, 2015. Date of publication August 7, 2015; date of current version August 26, 2015. A. Elsonbaty is with the Centre for Photonics and Smart Materials, Zewail City of Science and Technology, Giza 12588, Egypt, and also with the Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt (e-mail: aturkey@zewailcity.edu.eg). S. F. Hegazy is with the National Institute of Laser Enhanced Sciences, Cairo University, Giza 12613, Egypt, and also with the Centre for Photonics and Smart Materials, Zewail City of Science and Technology, Giza 12588, Egypt (e-mail: shegazy@zewailcity.edu.eg). S. S. A. Obayya is with the Centre for Photonics and Smart Materi- als, Zewail City of Science and Technology, Giza 12588, Egypt (e-mail: sobayya@zewailcity.edu.eg). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JQE.2015.2466176 chaotic radar [13], chaotic lidar [14], and optoelectronic logic gates [15]. High dimensional chaos generators are required to increase the complexity of chaotic attractor, hence to boost the security of chaos-based communication. Optical high-dimensional chaos can be generated by introducing one or more time delay (TD) terms into the rate equations describing the system or, from a physical point of view, by “actualizing” all-optical [16]–[18] and/or electro-optic [19], [20] feedbacks. However, the security of chaos encryption is not guaranteed only by the high dimensionality of the chaos [21] (Actually, the higher dimensionality does not in general lead to signifi- cantly more unpredictability [22], [23]), but also by prevent- ing critical information about the chaos system from being leaked through the chaotic carrier. Along with the SL intrinsic parameters such as central wavelength and threshold current, the value of TD is considered one of the primary secret keys of the chaos system. An eavesdropper who could recognize the TD signature is, at least in principle, readily capable to reconstruct the chaotic system [24]–[27]. On the other hand, obvious TD signature directly diminishes the statistical per- formance of the random bit generation [10] as well as reduces the signal-to-noise ratio of the chaotic radar system [14]. Numerous schemes of all-optical feedback have been verified to effectively suppress TD signature in intensity time series. Among these schemes are all-optical feedback operating in short-external-cavity regime [28], double variable- polarization feedback [1], [3], double unbalanced optical feedbacks [29], [30], and distributed feedbacks [31]. However, as demonstrated by Nguimdo et al. [32], the TD information entirely hidden in the intensity time series can be still available in the phase time series. This breakthrough renders achieving effective suppression of TD signature more challenging. Recently, there have been some trials to simultaneously suppress TD information in all transmitted observables, i.e., both the intensity and phase. In a more recent paper [33], Nguimdo et al suggested some scenarios leading to simul- taneous TD suppression by making use of semiconductor ring laser with a cross-feedback configuration. Also it has been shown that the chaos from two SLs with dual-path injection [34] as well as three SLs in a cascade scheme [35] exhibit simultaneous TD concealment for appropriate injection strength and frequency detuning. Relative to conventional edge-emitting SLs, vertical-cavity surface-emitting lasers (VCSELs) have a number of beneficial 0018-9197 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.