We study dynamics of chaos in dual port erbium-doped fiber ring laser (EDFRL). The laser consists of

two erbium-doped fibers, intracavity filters at 1549.30 nm, isolators, and couplers. At both ports, the laser

transitions into the chaotic regime for pump currents greater than 100 mA via period doubling route. We

calculate the Lyapunov exponents using Rosenstein’s algorithm. We obtain positive values for the largest

Lyapunov exponent (≈0.2) for embedding dimensions 5, 7, 9 and 11 indicating chaos. We compute the

power spectrum of the photocurrents at the output ports of the laser. We observe a bandwidth of ≈ 25

GHz at both ports. This ultra wideband nature of chaos obtained has potential applications in high speed

random number generation and communication

Jain, Ankita

Krishnamurthy, Pradeep Kumar

Landais, Pascal

Mirg, Shubham

Pandey, Akash

Applied Optics

English

We study dynamics of chaos in dual port erbium-doped fiber ring laser (EDFRL). The laser consists of
two erbium-doped fibers, intracavity filters at 1549.30 nm, isolators, and couplers. At both ports, the laser
transitions into the chaotic regime for pump currents greater than 100 mA via period doubling route. We
calculate the Lyapunov exponents using Rosenstein’s algorithm. We obtain positive values for the largest
Lyapunov exponent (≈0.2) for embedding dimensions 5, 7, 9 and 11 indicating chaos. We compute the
power spectrum of the photocurrents at the output ports of the laser. We observe a bandwidth of ≈ 25
GHz at both ports. This ultra wideband nature of chaos obtained has potential applications in high speed
random number generation and communication

Irish Universities

Experimental demonstration of 25 GHz wideband
chaos in symmetric dual port EDFRL

DCU Online Research Access Service

Research Article Applied Optics 1Experimental demonstration of 25 GHz widebandchaos in symmetric dual port EDFRLSHUBHAM MIRG1, ANKITA JAIN2, AKASH PANDEY2, PRADEEP KUMAR K.1,2,*, AND PASCAL LANDAIS31Department of Electrical Engineering, IIT Kanpur, Kanpur-208016, India2Center for Laser and Photonics, IIT Kanpur, Kanpur-208016, India3School of Electronic Engineering, Dublin City University, Dublin-9, Ireland*Corresponding author: pradeepk@iitk.ac.inCompiled July 27, 2017We study dynamics of chaos in dual port erbium-doped fiber ring laser (EDFRL). The laser consists oftwo erbium-doped fibers, intracavity filters at 1549.30 nm, isolators, and couplers. At both ports, the lasertransitions into the chaotic regime for pump currents greater than 100 mA via period doubling route. Wecalculate the Lyapunov exponents using Rosenstein’s algorithm. We obtain positive values for the largestLyapunov exponent (≈0.2) for embedding dimensions 5, 7, 9 and 11 indicating chaos. We compute thepower spectrum of the photocurrents at the output ports of the laser. We observe a bandwidth of ≈ 25GHz at both ports. This ultra wideband nature of chaos obtained has potential applications in high speedrandom number generation and communication. © 2017 Optical Society of AmericaOCIS codes: (140.1540) Chaos; (140.3560) Lasers, ring; (140.3500) Lasers, erbium.http://dx.doi.org/10.1364/ao.XX.XXXXXX1. INTRODUCTIONChaotic systems are deterministic but exhibit extreme sensitiv-ity to perturbations in initial conditions [1]. These systems arecharacterized by a broad bandwidth and rapidly dropping auto-correlation and these exhibit a ‘noise-like’ long-term behaviour[2]. Thus, the ability of chaos to mask signals makes it suitablefor secure communications [3]. Chaotic systems can also be usedas sources of physical randomness since at a macroscopic levelthese systems behave randomly [4]. Chaos based random num-ber generators have been successfully demonstrated [5]. Whilespeed of random number generation and data rates of chaoticcommunication, using electronic circuits, are limited by chaosbandwidth in the range of few MHz, optical chaos compara-tively has a much higher bandwidth and thus have garneredconsiderable attention for high speed random number genera-tion and secure communication [5–8]. Optical chaos is seen inboth semiconductor and fiber laser. Various techniques suchas external optical feedback, optical injection, loss modulationexist that can be implemented to obtain chaos in semiconductorlasers [9]. The underlying principle of all the above techniquesis to add instability to laser through which chaos is obtained ei-ther via period doubling or quasi periodic or intermittent route.Several GHz of chaos bandwidth has been demonstrated withsemiconductor lasers [10].Optical chaos in erbium-doped ring fiber lasers (EDFRL) hasbeen numerically as well as experimentally demonstrated to ex-hibit rich chaotic behaviour [11–14]. To study chaotic behaviourin EDFRL, the laser is modelled as a three level class B laser ow-ing to its fast decay time of polarization variables [11]. Chaos inEDFRL is obtained by either of the following three techniques ora combination of them: pump modulation [12], loss modulation[15] and loop nonlinearities [11]. Pump and loss modulationgenerated chaotic waveform bandwidths are limited to MHzrange due to relaxation oscillation time of fiber laser. Numericalmodelling of EDFRL suggests chaos generation due to nonlinearKerr effect and chaotic bandwidth to be at least several GHz[11, 13]. Experimental demonstration of the generation of chaosin EDFRL using nonlinear Kerr effect yielded a bandwidth of 2GHz [14].In this paper, we demonstrate experimentally large chaoticbandwidth in EDFRL. A near symmetric EDFRL structure withdual port output is employed. As pump currents are increased,well above the threshold, chaotic output is observed at bothoutput ports with similar bandwidth. We employ Rosenstein’salgorithm to obtain divergence curves and estimate the largestLaypunov exponent (LLE) [16]. Positive LLE values are ob-tained at different embedding dimensions indicating presenceof chaos. The presence of chaos is further verified by calculatingpower spectrum, autocorrelation, and phase portraits. Finally,we report a chaos bandwidth of 25 GHz from both ports simulta-neously. To the best of our knowledge, this is the largest reportedbandwidth of chaos in EDFRL.The rest of the paper is organized as follows. In section 2Research Article Applied Optics 2we discuss our experimental setup to generate chaos in EDFRL.In Section 3, we discuss the results of chaos generation in bothports of EDFRL. We describe the various properties of the outputsignals and indicate the distinction between chaotic and non-chaotic regimes. We conclude by summarizing our work in4.2. EXPERIMENTAL SETUPFig. 1 shows our experimental setup of the dual port near sym-metric erbium-doped fiber ring laser (EDFRL) to generate chaos.The setup is near symmetric with each side consisting of erbium-doped fiber (EDF) of approximately 7 m length, an optical isola-tor, optical bandpass filter (BPF), and a 3 dB coupler to extractoptical signals from the laser. Two 980 nm laser diodes are usedto pump the EDFs. Single mode fiber (SMF) patch chords areused to connect optical components of the laser. An optical iso-lator ensures unidirectional operation of laser. The bandpassfilter is has a central wavelength of 1549.30 nm and fixes thelasing wavelength of EDFRL. The two outputs from ports 1 and2 are converted to photocurrents and measured using a real-timeoscilloscope at 50 GSa/s, for pump currents in the range of 70 to200 mA. The pump currents are adjusted to obtain near equalpowers at the two output ports.Fig. 1. Experimental setup of dual port near symmetricerbium-doped fiber ring laser to generate chaos. Output fromports 1 and 2 is monitored using real time oscilloscope withsampling rate of 50 GSa/s.As various electric fields circulate inside the fiber cavity, theyare phase modulated due to the nonlinear Kerr effect. Increas-ing pump current to 100 mA increases the optical power in-side cavity and leads to increase in nonlinear phase shift. Thismodulation provides the perturbation required by the laser forgeneration of chaos via period doubling route [11].3. RESULTS AND DISCUSSIONAs we increase the pump current, of both EDFs simultaneously,the laser starts lasing at approximately 70 mA. On further in-creasing the pump currents to about 100 mA, the laser startsbifurcating towards chaotic regime via period doubling. Finallyat around 200 mA, the laser is in the chaotic region. The pho-tocurrents at the laser outputs are recorded by the real-time oscil-loscope and processed using Rosenstein’s algorithm to estimatethe LLE [16]. Rosenstein’s algorithm works by reconstructingattractor dynamics and calculating the average separation ofnearest neighbours as the system evolves. The divergence oftrajectories have exponential dependence on Lyapunov expo-nents of the system, with LLE dominating the growth initially[16]. In the chaotic region with positive LLE, the initial rise inlogarithmic plots of divergence curves will be linear with slopedetermined by LLE. Fig. 2 shows natural logarithm of diver-gence trajectories at various pump currents and for differentembedding dimension (m) of 5, 7, 9, and 11. When pump cur-rents at pumps 1 and 2 are 70 and 72 mA respectively, EDFRLis just at the threshold of lasing. In Figs. 2(a) and (b), we ob-serve that divergence curves do not rise linearly. This is due tothe negative Lyapunov exponents at play, indicating absence ofchaotic dynamics of the laser at these pump current levels. Onfurther increasing the pump currents to 98 and 94 mA at pumps1 and 2, the electric fields start interfering due to Kerr effect. InFigs. 2(c) and (d) we see divergence curves are still not linearinitially but are much smoother than previous pump currents.This stage is identified as the transition region between chaotic0 10 20-6-5-4Port 1 m=5m=7m=9m=110 10 20-6-5-4Port 20 10 20ln(divergence)-5-4-3-20 10 20ln(divergence)-5-4-3-2Sampling units0 10 20-6-5-4-3Sampling units0 10 20-6-5-4-3d)b)a)c)e) f)Fig. 2. Natural logairthm of divergence plotted at variousembedding dimensions (m). Curves plotted for a), b)- Pumpcurrents 70 and 72 mA c), d)- Pump currents 98 and 94 mA e),f)- Pump currents 200 and 196 mA.and non-chaotic. However, as we increase the pump currentswell above the lasing threshold, 200 and 196 mA for pumps 1and 2 respectively, the laser transitions into the chaotic regimeas seen in Figs. 2(e) and (f). In the chaotic region, we observe aninitial linear rise in divergence curves with the slope determinedby LLE. However as the system evolves further, other Lyapunovexponents cause the divergence curves to become flat. Table 1shows the calculated value of LLE exponents for different valueof m, all positive and indicative of chaos.In Fig. 3, we plot the power spectrum of photocurrents ob-tained at both output ports of the laser. In Fig. 4, we plot thepower spectrum on an expanded frequency axis. Discrete spec-Research Article Applied Optics 3Table 1. Largest Lyapunov exponent (LLE) calculated fromthe slope of divergence curve for Port 1 from Fig. 2(e) andPort 2 from Fig. 2(f)Port 1 Port 2m LLE (slope) m LLE (slope)5 0.2313 5 0.23037 0.2167 7 0.21729 0.1906 9 0.191111 0.1658 11 0.1655tral lines are observed in Figs. 3(a) and (b), for pump currents 70and 72 mA at pumps 1 and 2. For similar pump currents in Figs.4(a) and (b), we observe the first peak to be at 90 MHz for bothports and rest of the peaks at the harmonics. The output signalsof both ports show periodicity in this region with fundamentalfrequency of 90 MHz. As the laser goes through the transitionregion, the power spectrum in Figs. 3(c) and (d), additionalfrequencies are generated with 15 and 45 MHz fundamentalharmonic for ports 1 and 2. This can be observed in Figs. 4(c)and (d). 0 10 20 -100-50Port 2 0 10 20 -120-100-80-60Port 1SignalNoise 0 10 20Power (dB)-120-100-80-60  0 10 20Power (dB)-120-100-80-60 Frequency (GHz)0 10 20 -120-100-80 Frequency (GHz)0 10 20 -120-100-80 e)c)a)f)d)b)70 mA98 mA200 mA72 mA94 mA196 mAFig. 3. Power spectrum for output of ports 1 and 2 for differentpump currents (blue). For comparison we also plot powerspectrum of electronic noise (orange) alone.This clearly suggests that the laser bifurcation to chaos viathe period doubling route. Increasing pump currents further,drives the laser into chaotic region. We plot the power spectrumfor this region in Figs. 3(e) and (f), at pump currents of 196 and200 mA. Due to the laser being chaotic, the discrete spectral linesvanish, as seen in Figs. 4(e) and (f), and a flat power spectrumis obtained with a bandwidth of approximately 25 GHz (two-sided) as shown in Figs. 3(e) and (f). Another set of distinctharmonics peaks with a fundamental frequency of 6.3 GHz areobserved in all regions of Fig. 3, irrespective of pump currents.These peaks arise from the amplifier resonances and cannot be0 1 2-100-50Port 10 1 2-100-50Port 20 1 2Power (dB)-80-70-600 1 2Power (dB)-80-70-60Frequency(GHz)0 1 2-90-80Frequency(GHz)0 1 2-90-80a)c)e)d)f)b)70 mA94 mA98 mA72 mA200 mA 196 mAFig. 4. Power spectrum plot with expanded frequency axis.Signals at both ports show the discrete spectral lines at variouspump currents.Time (ns)0 0.5 1 1.5 210-410-21000 0.5 1 1.5 2Autocorrelation10-410-21000 0.5 1 1.5 210-410-2100a)c)b)Fig. 5. Autocorrelation of output signal at port 1 for three dif-ferent regions at different pump currents a) Non-Chaotic, b)Transition, c) ChaoticResearch Article Applied Optics 4Voltage (V)-0.02 -0.01 0 0.01 0.02Voltage (V)-0.02-0.0100.010.020.03Port 1Voltage (V)-0.02 -0.01 0 0.01 0.02Voltage (V)-0.02-0.0100.010.020.03Port 2Fig. 6. Phase portrait for ports 1 and 2 and pump currents of200 and 196 mA at pumps 1 and 2, respectively.eliminated.In Fig. 5, we plot autocorrelation of the output signal fromport 1. The output signal is correlated with the delayed versionof itself and normalized. Autocorrelation is an important pa-rameter for random number generation as it provides an insightto the ability of setup to behave randomly. In the non-chaoticregime, the autocorrelation does not drop significantly as seenin Figs. 5(a) and (b). However, operating the laser in the chaoticregion leads to a rapid drop in the value of autocorrelation toalmost 10−3 in Fig. 5(c). The signal from output port 2 has asimilar drop in the value of autocorrelation.Finally, we plot phase portraits in Fig. 6. Phase portraits rep-resent trajectories of dynamical systems pertaining to differentinitial conditions in the phase space. We reconstruct the phaseportrait using method of delays [16]. A uniform spread in thephase space without any fixed trajectory lines in Fig. 6, is againindicative of chaos.4. CONCLUSIONSIn summary, we have shown that by using a near symmetricdual port EDFRL setup, ultra high bandwidth chaos can begenerated. Increasing pump currents to ≈100 mA, the laser isset on a period doubling route to chaos due to nonlinearities.Chaotic dynamics in the laser are seen at pump currents of≈200 mA. This is verified by calculating LLE using Rosenstein’salgorithm. We obtain positive LLE values of around 0.2 forvarious embedding dimensions, indicating chaos in the system.Further, when pump currents are increased from threshold, at≈70 mA, to ≈100 mA, the fundamental frequency in powerspectrum reduces by half, hence confirming that the laser takesthe period doubling route to chaos. On further increasing pumpcurrents, flat power spectrum with no distinct spectral linesand an almost immediate drop in autocorrelation is observed,due to the onset of chaotic regime. A clear transition from non-chaotic to chaotic region is observed in divergence curves, powerspectrum and autocorrelation plots.The rapid drop in autocorrelation shows the setup is suitablefor high speed random number generation. The dual port outputfurther enables us to use the difference method to remove thebias from the random numbers generated [17]. Finally, bothports indicate simultaneous presence of chaos and have similarbandwidths of 25 GHz, the largest seen in EDFRL to best of ourknowledge.5. ACKNOWLEDGEMENTWe acknowledge Marie Curie International Research Staff Ex-change Scheme Fellowship, 7th European Community Frame-work Programme, under Grant 318941 for supporting travel ofPradeep Kumar K. and Ankita Jain.REFERENCES1. S. H. Strogatz, Nonlinear dynamics and chaos: with applications tophysics, biology, chemistry, and engineering (Westview press, 2014).2. M. P. Kennedy and G. Kolumbán, “Digital communications using chaos,”Signal Processing 80, 1307 – 1320 (2000).3. G. D. VanWiggeren and R. Roy, “Communication with chaotic lasers,”Science 279, 1198–1200 (1998).4. T. Stojanovski and L. Kocarev, “Chaos-based random numbergenerators-part i: analysis [cryptography],” IEEE Transactions on Cir-cuits and Systems I: Fundamental Theory and Applications 48, 281–288(2001).5. T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random numbergenerators. part ii: practical realization,” IEEE Transactions on Circuitsand Systems I: Fundamental Theory and Applications 48, 382–385(2001).6. K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, “Synchronizationof lorenz-based chaotic circuits with applications to communications,”IEEE Transactions on Circuits and Systems II: Analog and Digital SignalProcessing 40, 626–633 (1993).7. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi et al., “Chaos-basedcommunications at high bit rates using commercial fibre-optic links,”Nature 438, 343 (2005).8. K. Ugajin, Y. Terashima, K. Iwakawa, A. Uchida, T. Harayama,K. 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Experimental demonstration of 25 GHz wideband

chaos in symmetric dual port EDFRL

Shubham Mirg

Ankita Jain

Akash Pandey

Pradeep Kumar Krishnamurthy

Pascal Landais

Crossref

Experimental demonstration of 125  GHz wideband chaos in symmetric dual-port EDFRL

http://doras.dcu.ie/24225/1/chaos_shubham.pdf

Experimental demonstration of 25 GHz wideband chaos in symmetric dual port EDFRL

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Irish Universities

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