Special Issue Selected papers inspired by the Semiconductor and Integrated Optoelectronics (SIOE 2008) Conference ISSN

Published in IET Optoelectronics Received on 28th April 2008 Revised on 28th July 2008 Special Issue Selected papers inspired by the Semiconductor and Integrated Optoelectronics (SIOE 2008) Conference ISSN 1751-8768 Synchronisation and chaos in a laser diode driven by a resonant tunnelling diode B. Romeira 1 J.M.L. Figueiredo 1 T.J. Slight 2 L. Wang 2 E. Wasige 2 C.N. Ironside 2 J.M. Quintana 3 M.J. Avedillo 3 1 Centro de Electrónica, Optoelectrónica e Telecomunicaçoes (CEOT), Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal 2 Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8LT, UK 3 Instituto de Microelectrónica de Sevilla, IMSE-CNM, Universidad de Sevilla, Seville 41012, Spain E-mail: bmromeira@ualg.pt Abstract: The authors report on a hybrid integration of a resonant tunnelling diode laser diode driver configuration that can operate as a self-oscillating circuit, and when externally perturbed shows regions of frequency division and frequency multiplication, quasi-periodic and chaotic oscillations, both in the optical and electrical outputs. The authors also demonstrate that this optoelectronic circuit is well described as a Liénard s oscillator. The synchronisation capabilities of the circuit have potentially novel functions for optical communications systems including clock recovery, clock division and data encryption. 1 Introduction Resonant tunnelling diodes (RTDs) have attracted a lot of attention because of their strong nonlinear current voltage (I V ) characteristic, wide bandwidth, negative differential resistance (NDR) region and inherent high-frequency operation at room temperature [1]. Negative resistance elements are important components in oscillator circuits and form the basis of many other nonlinear devices. A circuit consisting of such nonlinear elements often shows complex dynamic behaviour that includes the appearance of deterministic chaos [2, 3]. Previously, work on optoelectronic integrated circuits (OEICs) has shown that it is possible to monolithically integrate a RTD with an optical waveguide electroabsorption modulator [4], and an RTD with a laser diode (RTD-LD) [5]. This paper presents a hybrid optoelectronic integrated circuit (HOEIC) consisting of an RTD driving an optical communication LD, which can produce electrical and optical outputs including self-sustained oscillation, frequency division (synchronisation) and chaotic behaviour (unsynchronised signals). The circuit preserves the nonlinear dynamical behaviour of the RTD, increasing the LD functionality with several potential advantages such as low modulating voltage, ultra-high-speed operation and significant reduction in the complexity of chaotic optical carrier generators needed in optical communication systems [6]. In optical communication systems, these operation modes have promising applications including clock recovery, clock division and data encryption. 2 Circuit description and operation Fig. 1 shows the schematic diagram of the RTD-LD hybrid OEIC. A shunt capacitor (1 mf) was used to decouple the DC from the AC circuit. DC voltage and the RF signal were supplied to the circuit s input through a bias tee (wideband: 10 4200 MHz). The RTD detailed structure is described in [4]. The LD was an optical communication laser fabricated by Compound Semiconductor Technologies Global Ltd; it has a threshold current of 6 ma, bandwidth of 20 GHz, and operates at around 1550 nm with an average output power of 5 mw. The circuit electrical output was taken across the RTD-LD series; the laser optical IET Optoelectron., 2008, Vol. 2, No. 6, pp. 211 215 211 & The Institution of Engineering and Technology 2008

Figure 1 Schematic of the experimental RTD-LD hybrid OEIC output was coupled to a lensed optical fibre and detected by a 45 GHz IR New Focus photo-detector. When DC biased in the NDR region, the experimental circuit represented by Fig. 1 produces self-sustained electrical oscillations at a frequency around 500 MHz, determined mainly by the microstrip line and wire bonding inductance and RTD-LD capacitance, which is approximately equal to the RTD capacitance. The LD optical output is modulated by the current oscillations induced by the RTD switching, producing an optical output with the same harmonic content of the electrical oscillations. Recently, preliminary work shows that a similar circuit using an improved layout can operate at a higher oscillation frequency because of the reduction of inductance as a result of a shorter bond wire length 1 2 mm (down from 5 mm). This circuit configuration shows self-sustained oscillations at around 2.1 GHz, an indication that with fully integrated versions much higher operating frequencies in the region of 10 Gbits or higher can be expected data rates more appropriate for present day optical communication systems. When a sinusoidal excitation is applied, the RTD-LD circuit can produce a series of electrical and optical outputs: synchronised oscillations (sub-harmonic frequency division and harmonics of the injected signal frequency multiplication), and unsynchronised oscillations (quasiperiodic and chaotic oscillations). Again, the LD current is constrained by the electrical properties of the RTD and the nonlinearity of the RTD-LD circuit can produce optical outputs showing period-adding bifurcation in a sequence of synchronised and unsynchronised signals at low driving AC voltages, turning into chaotic signals at higher driving voltages. Figure 2 Equivalent lumped RTD-LD circuit oscillator 3 Theory and numerical model The nonlinear dynamic behaviour of the RTD-LD circuit configuration presented in Fig. 1 can be analysed using the equivalent lumped circuit shown in Fig. 2, because the shunt capacitor used for DC bias stabilisation acts as a short circuit at the frequencies under consideration. We assume the LD operation is above the threshold current, being represented by its small signal equivalent circuit, that is, a drop voltage with a series resistance. The estimated RTD- LD equivalent capacitance C presented in Fig. 2 can be approximated by the RTD capacitance because the laser capacitance is much larger than the RTD intrinsic capacitance. In Fig. 2, R represents the equivalent resistance due to the series resistances of the devices (RTD and LD) and the impedance of the measuring instruments, and L is the inductance because of the wire bonding and the microstrip transmission line. From the lengths of the transmission line and bond wires, the estimated equivalent inductance is 8 nh. 3.1 Electrical model For purposes of analysis and simulation, the RTD-LD series overall I V characteristic was modelled using an adaptation of the physics-based description of the RTD voltage dependent current source F(V ) given in [7]. The currentvoltage equation is " # F(V ) ¼ A ln 1 þ eq(b Cþn 1 V (t))=k B T 1 þ e q(b C n 1 V (t)=k B T p 2 þ C n 1 V (t) tan 1 D þ H e n 2 ev (t)=k B T 1 The parameters q and k B are the unit electric charge and the Boltzmann constant, respectively. Fig. 3 shows the experimental I V characteristic of the RTD-LD and the fitting given by (1). The fitting parameters are A ¼ 6.60 10 23, B ¼ 0.07, C ¼ 0.2346, D ¼ 0.0104, H ¼ 1.411 10 23, n 1 ¼ 0.1252, n 2 ¼ 0.0181 and T ¼ 300 K. For a given DC bias voltage, V DC, the voltage across the RTD-LD series, V(t), can be obtained considering the circuit of Fig. 2. From Kirchhof f s rules (using Faraday s law), it can be described by the following two first-order (1) 212 IET Optoelectron., 2008, Vol. 2, No. 6, pp. 211 215 & The Institution of Engineering and Technology 2008

densities _N (t) ¼ I(t) N (t) S(t) g qq t 0 N (t) N 0 1 þ 1S(t) S(t) _S(t) ¼ g 0 N (t) N 0 1 þ 1S(t) S(t) bn (t) þ t p t (5) Figure 3 Experimental and modelled DC I V characteristics for the RTD-LD oscillator coupled differential equations _V (t) ¼ 1 I (t) F(V ) C ½ Š _I(t) ¼ 1 L V DC RI (t) V (t) þ V AC sin 2pf in t The system represented by (2) is a two-dimensional system subjected to a time-dependent signal and therefore is nonautonomous, and is referred as one of the generalised nonlinear Liénard systems [8], subjected to a periodic driving force. After some algebra, we find that the system (2) is equivalent to the following second-order differential equation (2) V (t) þ H(V ) _V (t) þ G(V ) ¼ V AC sin (2pf in t) (3) For the equivalent lumped circuit presented in Fig. 2, H(V ) and G(V ) are given by H (V ) ¼ R L þ 1 C _ F(V ) G(V ) ¼ V ðtþ LC þ R LC F(V ) V DC LC where G(V ) is a nonlinear force, and H (V ) _V (t) and V AC sin(2pf in t) are the damping factor and the externally applied driving signal, respectively. In the next section, we compare the numerical simulation with the experimental results. In the simulation, we assume the following circuit parameters C ¼ 5.5 pf, L ¼ 8.0 nh, R ¼ 1.0 V and V DC ¼ 1.84 V (corresponding circuit selfsustained oscillation around 500 MHz). 3.2 Optical model The LD optical output was modelled using the LD single mode rate equations for the electron N(t) and photon S(t) (4) where I(t) is the current through the LD given by Liénard s model in (2); q the electron charge; q the active region volume; t and t p the spontaneous electron and photon lifetimes, respectively; b the spontaneous emission factor; g 0 the gain coefficient; N 0 the minimum electron density required to obtain a positive gain; and 1 the value for the nonlinear gain compression factor [9, 10]. In the next section, the laser dynamics is modelled employing the typical parameters of semiconductor LDs [9, 10], with adjustments to fit with the experimental results: q ¼ 6.75 10 211 cm 3, t ¼ 0.8 ns, t p ¼ 1.2 ps, b ¼ 4 10 22, g 0 ¼ 10 26 cm 3 /s, N 0 ¼ 10 18 cm 23 and 1 ¼ 10 217 cm 3. 4 Synchronisation and chaos The hybrid optoelectronic integrated RTD-LD (RTD-LD HOEIC) circuit outputs various types of signal patterns including frequency division and multiplication, quasiperiodic and chaotic oscillations, when driven by an external sinusoidal signal. We have observed both experimentally and numerically that as the frequency of the applied signal, f in, is varied, a stable period-n (n ¼ 1, 2,...) is obtained, followed by an unsynchronised region, then a stable period-(n þ 1), followed by unsynchronised signals and so on. This behaviour is known as period-adding bifurcation, where windows of consecutive regions showing synchronisation (frequency division) are separated by windows of unsynchronised signals (quasiperiodic or chaotic behaviour) [2]. Figs. 4a and 4b show the experimental and numerical results of frequency division by 2 and 5, respectively, in the laser optical output induced by low driving AC voltages. The synchronised regions were obtained experimentally, DC biasing the RTD-LD circuit in the NDR region at around 1.8 V and varying the frequency of the injected signal from 0.1 to 3 GHz, using driving amplitudes as low as 100 mv. Frequency division regions for AC amplitudes of V AC ¼ 100 and V AC ¼ 150 mv were observed, following the period-adding sequence at up to a frequency division by 6. The numerical output compares well with the experimental electrical and optical outputs, which indicates the operation of the optical communication RTD-LDbased driver circuit is well described by Liénard s oscillator theory. Frequency division was also observed changing the AC amplitude or, alternatively, changing the DC bias voltage, IET Optoelectron., 2008, Vol. 2, No. 6, pp. 211 215 213 & The Institution of Engineering and Technology 2008

As mentioned, period-adding bifurcation occurs in the electrical and optical domains in a sequence of quasi-periodic (unlocked) and synchronised (locked) oscillations, as observed experimentally. Bifurcation diagrams of the forced Liénard s oscillator can be used to investigate the dynamical behaviour of the RTD-LD circuit. The calculated bifurcation diagram map presented in Fig. 5 shows the amplitudes of the output voltage oscillations, V(t), as a function of the excitation frequency, f in, for a driving signal amplitude of V AC ¼ 150 mv. The observed frequency division by 2 and 5, shown in Fig. 4, iswellpredictedbytheliénard s model as shown in the diagram of Fig. 5 at around 0.9 and 2.5 GHz, respectively. Figure 4 Optical synchronisation in the laser output a Frequency division by 2 in time domain and model when V AC ¼ 150 mv and f in ¼ 0.9 GHz b RF spectrum of the laser output showing frequency division by 5 and model when V AC ¼ 150 mv and f in ¼ 2.5 GHz When the system is not synchronised, either quasiperiodic oscillations or chaotically signals are produced. In the quasi-periodic regions, depending on parameter conditions, chaotic behaviour in both the electrical and optical outputs is expected. A transition from the quasiperiodic to chaotic output can be achieved increasing the driving signal amplitude. Fig. 6a presents the RF spectrum of a quasi-periodic signal in the optical laser output of the RTD-LD circuit that self-oscillates at around 2.1 GHz, when driven by an RF sinusoidal signal at 2.2 GHz with 2 dbm of power. When the bias voltage is increased from 1.806 to 1.809 V, the optical signal becomes chaotic with a clear broadband peak near the input frequency (Fig. 6b). keeping in both cases the input AC signal frequency fixed. Since the bifurcation phenomenon appears in limited frequency regions, this RTD-LD circuit can be regarded as an optoelectronic dynamic frequency divider. Figure 5 Period-adding bifurcation sequence and calculated bifurcation diagram for V AC ¼ 150 mv a Period-adding bifurcation sequence b Calculated bifurcation diagram for V AC ¼ 150 mv Figure 6 RF spectra of optical laser outputs when the RTD- LD is driven by an RF signal at 2.2 GHz a Quasi-periodic signal when the DC bias is 1.806 V b Chaotic signal when the DC bias is 1.809 V 214 IET Optoelectron., 2008, Vol. 2, No. 6, pp. 211 215 & The Institution of Engineering and Technology 2008

This broad peak structure of continuous finite (random) components is a characteristic of chaotic behaviour and does not appear in the quasi-periodic oscillations. The same chaotic signal is observed in the RF spectrum of the electrical output, a clear indication that the chaotic signals are generated because of the RTD nonlinear behaviour that modulates the current flowing through the LD and, consequently, modulates its optical output. The process of chaos generation using RTD-LD circuits is physically different from that in semiconductor lasers externally modulated [11]. In RTD-LD circuits, chaotic signals are generated electrically exclusively because of the nonlinearity of the RTD device. Since the LD optical output mimics the electrical signal, the circuit optical output shows the features of the circuit electrical output. 5 Conclusion We have demonstrated that a hybrid optoelectronic integrated RTD-LD circuit can output various types of signal patterns including frequency division and multiplication, quasiperiodic and chaotic oscillations, when an external sinusoidal signal is applied. The synchronisation operation was investigated theoretically and experimentally. The subharmonic locking can be used for dynamic frequency division with a selectable dividing ratio. Observation of the optical chaotic signals in the RF spectrum was also shown, demonstrating the capability of the RTD-LD circuit to operate as an optical chaotic generator. We also have shown that the electrical and optical operation of this nonautonomous RTD-LD oscillator circuit can be described by Liénard s oscillator theory. A full study of the system dynamics is under way and will facilitate the prediction of the chaotic operation of the RTD-LD optoelectronic circuit in more detail. 6 Acknowledgments We thank Wyn Meredith of Compound Semiconductor Technologies Global Ltd for providing the laser diode. B. Romeira and J. M. L. Figueiredo were supported by the Centro de Electrónica, Optoelectrónica e Telecomunicações and the Fundação para a Ciência e a Tecnologia, Portugal. B. Romeira acknowledges the support of the Fundação Calouste Gulbenkian, Portugal. 7 References [1] BROWN E., SÖDERSTRÖM J., PARKER C., MAHONEY L., MOLVAR K., MCGILL T.: Oscillations up to 712 GHz in InAl/AlSb resonant-tunnelling diodes, Appl. Phys. Lett., 1991, 58, (20), pp. 2291 293 [2] MAEZAWA K., KAWANO Y., OHNO Y., KISHIMOTO S., MIZUTANI T.: Direct observation of high-frequency chaos signals from the resonant tunneling chaos generator, Jpn. J. Appl. Phys., 2004, 43, (8A), pp. 5235 5238 [3] ZHOU S., SWEENY M., XU J., BEROLO O.: Chaotic behaviour of quantum resonant tunnelling diodes, Physica D, 1991, 52, (2 and 3), pp. 544 550 [4] FIGUEIREDO J., STANLEYC., IRONSIDE C.: Electric field switching in a resonant tunneling diode electroabsorption modulator, IEEE J. Quantum Electron., 2001, 37, (12), pp. 1547 1552 [5] SLIGHT T., IRONSIDE C.: Investigation into the integration of a resonant tunnelling diode and an optical communications laser: Model and experiment, IEEE J. Quantum Electron., 2007, 43, (7), pp. 580 597 [6] VAN WIGGEREN G., ROY R.: Communication with chaotic lasers, Science, 1998, 279, (5354), pp. 1198 1200 [7] SCHULMAN J., SANTOS H., CHOW D.: Physics-basedRTD current-voltage equation, IEEE Electron Device Lett., 1996, 17, (5), pp. 220 222 [8] FIGUEIREDO R.: Existence and uniqueness results for Liénard s equation, IEEE Trans. Circuit Theory, 1970, CT-17, pp. 313 321 [9] MENA P., KANG S., DETEMPLE T.: Rate-equation-based laser models with a single solution regime, IEEE J. Lightwave Technol., 1997, 15, (4), pp. 717 730 [10] TSOU B., PULFREY D.: A versatile spice model for quantum well lasers, IEEE J. Quantum Electron., 1997, 33, (2), pp. 246 254 [11] WALKER R.P., REES P., PIERCE I., SPENCER P.S., ROBERTS G.W.: Analysis of chaos generated by a modulated selfpulsating laser diode, IEE Proc., Optoelectron., 2005, 33, (2), pp. 90 96 IET Optoelectron., 2008, Vol. 2, No. 6, pp. 211 215 215 & The Institution of Engineering and Technology 2008