1436 ieee journal of quantum electronics, vol. 45, no. …w3.ualg.pt/~jlongras/ari2009-2.pdf ·...

1436 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 45, NO. 11, NOVEMBER 2009

Nonlinear Dynamics of Resonant TunnelingOptoelectronic Circuits forWireless/Optical Interfaces

Bruno Romeira, Student Member, IEEE, José M. L. Figueiredo, Thomas James Slight, Liquan Wang,Edward Wasige, Member, IEEE, Charles N. Ironside, Senior Member, IEEE, Anthony E. Kelly, and Richard Green

Abstract—We report on experimental and modeling resultson the nonlinear dynamics of a resonant-tunneling-diode-based(RTD) optoelectronic circuits that can be used as the basis ofa wireless/optical interface for wireless access networks. TheRTD-based circuits are optoelectronic integrated circuits thathave negative differential resistance and act as optoelectronicvoltage-controlled oscillators. These circuits display many ofthe features of classic nonlinear dynamics, including chaos andsynchronization. These highly nonlinear oscillators behaves asinjection-locked oscillators that can be synchronized by a smallinjection signal of either wireless or optical origin, and thus, cantransfer phase encoded information from wireless to the opticaldomain or the optical to the wireless domain.

Index Terms—Chaos, injection locking, integrated opto-electronics, microwave oscillators, nonlinear systems, opticalreceivers, radio broadcasting, resonant tunneling diodes (RTDs),semiconductor lasers.

I. INTRODUCTION

H IGH data rates mobile access networks are emerging asthe primary choice for many communication systems

users [1], [2]. The radio-over-fiber (RoF) systems are one ofthe promising schemes for the future broad-band wireless com-munication systems such as mobile communications, hotspots,and suburban areas [1]–[3]. Compared with the conventionalhigh-frequency wireless or coaxial links, RoF systems showmany advantages such as low-cost, high-performance, hugebandwidth, and long-distance transmission. Such is the demandthat so-called picocellular access [4], with wireless cells offew meters range, is being considered as a highly promisingroute for delivering high-bandwidth mobile access. Since a

Manuscript received April 08, 2009; revised June 22, 2009. Current versionpublished November 06, 2009. This work was supported in part by the Fundaçãopara a Ciência e a Tecnologia under Grant SFRH/BD/43433/2008, the FundaçãoCalouste Gulbenkian, Portugal, and the Research Networks-Treaty of WindsorProgramme 2008/09-U32, Portugal.

B. Romeira and J. M. L. Figueiredo are with the Centro de Electrónica, Opto-electrónica e Telecomunicações, Universidade do Algarve, 8005-139 Faro, Por-tugal (e-mail: [email protected]; [email protected]).

T. J. Slight, L. Wang, E. Wasige, C. N. Ironside, A. E. Kelly, andR. Green are with the Department of Electronics and Electrical En-gineering, University of Glasgow, Glasgow G12 8LT, U.K. (e-mail:tslight@ elec.gla.ac.uk; [email protected]; [email protected];[email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JQE.2009.2028084

typical RoF picocellular network will require hundreds ofmicrowave/photonic interface circuits, high-performance pic-ocellular systems have a great challenge ahead in order tointegrate microwave and optical functions on the same chip asa mean of delivering low-cost and highly reliable interfaces.

In recent developments on a hybrid optoelectronic integratedcircuit (OEIC) consisting of a laser diode (LD) driven by aresonant tunneling diode (RTD) oscillator, the RTD-LD OEIC,we have demonstrated the circuit is capable of behaving non-linearly, with RTD-LD optical output emulating RTD nonlinearcharacteristics, which gives rise to a variety of additionaloptoelectronic operation modes, including optoelectronicvoltage-controlled oscillator (OVCO) [5], injection locking,period-adding [6], and chaotic carriers generation [7], withpotential applications in optical chaotic communications [8].(Previous work showed that it is possible to monolithicallyintegrate an RTD with a LD [9]). In this paper, we discussthe nonlinear dynamics operation of a new RTD-LD pho-tonic–microwave circuit where the RTD has incorporated aphotoconductive region, the RTD-LD optoelectronic oscillator,acting both as microwave–photonic and photonic–microwaveconverters. The results also show that when connected toa patch antenna the new RTD-LD circuits can act as wire-less/optical (W-O) and optical/wireless (O-W) interfaces. Inthe context of this paper what we regard as a wireless signalis the typical signal used in digital communication systems,such as global system mobile (GSM), and it is an RF signal ina frequency range 0.5–10 GHz that can be broadcasted withantenna around a few meters range, and for this application, itis usually digitally encoded using phase-shift keying (PSK).

The RTD-LD W-O interface uses synchronization of an os-cillator to convert RF signals into optical subcarriers. In thepresence of a low-power RF signal emitted by an antenna theRTD-LD synchronizes to the RF signal, locking the phase ofthe laser optical subcarrier to the phase of the RF signal. TheRTD-LD O-W interface uses optical injection locking to syn-chronize the RTD oscillator to convert optical subcarriers intoRF signals that can be broadcasted by wireless systems. Thesesynchronization capabilities can be used in digital communi-cation to translate phase-shift-keyed-modulated RF signals intooptical subcarriers and conversely. Due to the negative differen-tial resistance (NDR) amplification effect the RTD-LD respondsboth to very low-power injected RF signals and to optical sub-carriers. This is a novel concept that has the advantage of beinga simple way to integrate microwave and optical functions on

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ROMEIRA et al.: NONLINEAR DYNAMICS OF RESONANT TUNNELING OPTOELECTRONIC CIRCUITS FOR WIRELESS/OPTICAL INTERFACES 1437

Fig. 1. Schematic of the RTD-LD W/O interface for microwave-to-optical con-version. Also shown is the optical injection port (OW) used to the optical-to-electrical conversion.

a single OEIC chip, rather than having separate monolithic mi-crowave integrated circuit (MMIC) chips [10] and optical chips.

In broad terms, the approach that we discuss in this paperis similar to the classic injection-locked oscillator (ILO) tech-niques (see, for example, [11]–[14]) that are routinely employedin digital wireless communications systems. However, here, weapply nonlinear dynamical theory to a unique optoelectronicILO that has the potential to be integrated in a single chip. Suchchips represent a highly promising route to producing low-cost,compact, robust, and reliable microwave/optical interface de-vices for the next generation of wireless access networks.

The paper is organized as follows. Section II describes themicrowave–photonic interface and the characterization exper-imental setup. Section III is devoted to the RTD-LD nonlineardynamics analysis using the optoelectronic circuit numericalmodel that consists of a Liénard’s driven system coupled tosingle-mode LD rate equations. In Section IV, the experimentalresults are presented, discussed, and compared with the circuitoptoelectronic model predictions. The conclusions are pre-sented in Section V.

II. MICROWAVE–PHOTONIC OSCILLATOR

RTDs are nanoelectronic devices easily integrated with pho-tonic components, such as LDs, modulators, and photodetec-tors, due to their simple structure and small size, enhancingsubstantially their modulation/detection performances [9], [15].The optoelectronic interfaces for wireless access networks dis-cussed here take advantage of the RTD’s strong nonlinear cur-rent–voltage – characteristic that shows wide-bandwidthNDR at room temperature. Among other effects, the NDR cangive rise to electrical amplification, which in the presence ofa resonant circuit can produce ultrafast signals up to terahertz(THz) frequencies [16], picosecond switching induced by low-voltage signals [17], locking to signals with frequency close thecircuit natural frequency or one of its sub/harmonics [18], [19],and generation of high-dimensional broad-band chaos [20].

The microwave–photonics interface, schematically shown inFig. 1, is formed by connecting a patch antenna to a hybridcircuit consisting of an RTD containing a photoconductive re-gion [optical waveguide (OW)] and an LD mounted in seriesdirectly onto the surface of a printed circuit board [5], [6]. Anoptical fiber is used to couple light to the circuit optical injec-tion port (the RTD photoconductive region). The RTD-LD cir-cuit dc bias is supplied via a high-bandwidth bias tee. A shunt

Fig. 2. �–� characteristics of the individual and integrated components, RTD,LD, and RTD-LD, respectively. Also included is the plot of the physics-basedanalytic voltage-dependent current source function � �� used to emulate thenonlinear �–� characteristic of the RTD.

capacitor and a shunt resistor are connected in parallel withthe RTD-LD in order to impose a low-frequency cutoff and toavoid spurious oscillations caused by the dc-bias circuitry, re-spectively. An Agilent E8257D RF signal generator connectedto a patch antenna was used to generate RF signals. With ap-propriate antenna configuration and/or light coupling the NDRamplification effect makes possible to phase-lock the RTD-LDto both very low-power RF broadcasted signals and to moderatepower optical subcarrier signals without the need of externalamplification.

The RTD was fabricated from InGaAlAs/InP RTD epi-ma-terial that was first used in the work described in [15]. Briefly,its structure consists of two 2-nm-thick AlAs barriers separatedby a 6-nm-wide InGaAs quantum well, embedded in a 1- m-thick InGaAlAs OW core. The RTD-OW devices used havepeak currents around 50 mA and peak-to-valley current ratios(PVCRs) as high as 3 (see Fig. 2), with valley-to-peak voltageand peak-to-valley current differences, and

, around 0.6 V and up to 34 mA, respec-tively. The LD was a continuous wave (CW) source fabricatedby Compound Semiconductor Technologies Global Ltd., with athreshold current 17 mA at the voltage 1.8 V (seeFig. 2), an efficiency around 0.85 mW/mA, and 50 pF para-sitic capacitance. When connected in series with the RTD-OW,the LD shifts the RTD current peak region to higher voltage byabout 1.8 V, with a slight reduction of the NDR width, as shownin Fig. 2.

The RTD-LD oscillator operates as follows. Without externalperturbation, dc biasing the circuit in the NDR region (seeFig. 2), it operates as an autonomous self-sustaining OVCO[5], [6], producing electrical relaxation oscillations that aretransferred to the laser optical output. By tuning the RTD-LDquiescent point across the NDR region from the peak to thevalley, the circuit natural oscillation frequency changes fromaround 560 MHz up to 1.0 GHz, as shown in Fig. 3. Moreover,in the presence of injected signals (optical or RF), the RTD-LDoptoelectronic oscillator undergoes a variety of dynamicaloperation modes, including locked and unlocked regimes, de-pending on the frequency and power of the injected signals. In



Fig. 3. Experimental RTD-LD electrical/optical free-running oscillation fre-quency as function of dc-bias voltage.

Sections III and IV, we analyze numerically and experimentallythe nonlinear dynamics of RTD-LD optoelectronic oscillatorinduced by both RF and optical signals.

III. LIÉNARD’S DRIVEN OSCILLATOR

In a previous publication [5], we showed how the RTD-LDoscillator can be represented as a Liénard’s oscillator and howthat gives considerable insight into the operation of the circuit.In this section, we go over the Liénard’s driven oscillator repre-sentation introduced in [7], with particular regard to the featuresrelevant to its operation as a driven optoelectronic ILO.

For purposes of analysis and simulation, the RTD is modeledas a capacitance in parallel with a voltage dependent currentsource [21]. The modeled RTD – characteristic (seeFig. 2) is represented by the function

(1)

with fitting parameters A, V,V, V, A, ,

and . The parameters and are the electriccharge and the Boltzmann constant, respectively.

The electrical behavior of the RTD-LD optoelectronic oscil-lator can be described using the small-signal equivalent lumpedcircuit shown in Fig. 4 [7], since the shunt capacitor–resistorused for dc-bias stabilization acts as a short circuit at the fre-quencies under consideration. Because the bias operating pointis well above the LD threshold current, the LD is replaced byits small-signal equivalent circuit, i.e., the drop voltage( 1.8 V) and the series resistance . Since the capacitanceof the LD is much larger than the RTD device intrinsic capac-itance [22], the capacitance presented in Fig. 4 correspondsto the RTD capacitance. In Fig. 4, represents the equivalentresistance due to the devices’ (RTD and LD) series resistancesand the 50 impedance of the measuring instruments, and isthe inductance due to wire bonding and PCB microstrip trans-mission line. From the transmission line and bond wires lengths,we estimate an equivalent inductance around 6 nH.

Fig. 4. Electrical small-signal equivalent lumped circuit of the RTD-LD opto-electronic oscillator. The circuit parameters used in the numerical analysis were� � �� , � � �� nH, and � � �� pF.

Considering the circuit of Fig. 4, the current throughthe RTD-LD series can be obtained from Kirchhoff’s rules(using Faraday’s law). The electrical behavior of the RTD-LDoscillator driven by a wireless carrier signal is well describedby the following two first-order nonlinear coupled differentialequations:

(2)

(3)

where is the wireless carriersignal and is the carrier phase function. Equations (2) and(3) correspond to a kind of driven oscillator known as a Liénardsystem under external injection.

The optoelectronic dynamics of the circuit is modeled usingsingle-mode LD rate equations with the current flowing throughthe LD corresponding to the dc-bias current plus the oscillatorycurrent given by the Liénard’s driven system (2), (3). For nu-merical purposes, we make use of the normalized carrier den-sity and the normalized photon density ,where and is thethreshold carrier density, to obtain the normalized single-moderate equations

(4)

(5)

where and are two dimensionless pa-rameters, and is the LD threshold current.Table I summarizes the LD physical parameters used in the nu-merical simulations.

We have numerically analyzed the RTD-LD optoelectronicnonlinear dynamics over a range of RF signal parameters, in-cluding frequency and power (or the equivalent voltage ampli-tude), and circuit dc-bias voltage. A simple way to map theRTD-LD modes of operation is to obtain the system bifurcationdiagrams. The bifurcation maps were constructed by calculatingthe time series of a given system variable, such as the voltage,current, or photon density, and plotting the corresponding peakheights as a function of a given circuit control parameter, which,



TABLE IDESCRIPTION OF THE STANDARD LASER RATE EQUATIONS PARAMETERS AND

THE TYPICAL VALUES USED IN THE NUMERICAL SIMULATION

Fig. 5. Numerical bifurcation map showing maxima of normalized photon den-sity with the normalized bias voltage at fixed broadcasted carrier frequency� � � GHz with power corresponding to the equivalent voltage amplitudes(a) � � �� and (b) � � �� .

in our case, were the broadcasted frequency, the signal power (orequivalent voltage amplitude) and the circuit dc-bias voltage.For each of these control parameters, the corresponding bifur-cation map was obtained. In order to avoid transients, the first50 periods of the RTD-LD dynamics were neglected.

The influence of dc-bias voltage on the dynamics of theRTD-LD system is summarized in Fig. 5, which shows photondensity bifurcation diagrams with the dc bias as a controlparameter, for two input power equivalent voltage carrieramplitude values, (a) 0.15 V and (b) 0.25 V, both at 3 GHz. Inorder to compare the results with experimental data, we defineda dc-bias-voltage-normalized parameter ,where is the dc RTD-LD peak voltage, in this case 2.9 V,and is the RTD quiescent voltage. The maps show that underthese operating conditions the system oscillates for dc-biasvoltage from 3.0 to 3.59 V.

For certain injected signal amplitudes, the optoelectronic ex-tended Liénard system can produce waveforms whose periodsare exactly times the injected RF carrier period , withan integer. A period- sequence corresponds to a mode of oper-ation where the circuit synchronizes to the injected signal (thewaveforms’ period satisfy the relation ). For the conditionsindicated in Fig. 5, we can expect the RTD-LD will have twowide dc-bias voltage regions corresponding to and .The period reduction from to with the dc bias is

Fig. 6. Numerical bifurcation map showing maxima of normalized photondensity with the normalized broadcasted frequency with signal power corre-sponding to the equivalent voltage � � �� .

mainly due to the increase of the circuit natural frequency, in ac-cordance to the experimental behavior demonstrated in Fig. 3.

To the right of the locking window there is anextended region of nonperiodic behavior with intermediatevery narrow branches of locking regions. From the analysis ofFig. 5(a) and (b), we can conclude that increasing the injectedsignal power enlarges the locking windows (regions where agenerated waveform period satisfies the relation ), whichcorresponds to larger tuning range . Increasing injectedpower also makes high-order -sequence periodicity windowsmore discernible, as is the case of the period-7 region inFig. 5(b).

A bifurcation map of the photon density with the normalizedcarrier frequency as a control parameter, is shown in Fig. 6,where (with and being the carrier and oscil-lator natural frequencies, respectively), for normalized dc bias

and carrier amplitude 0.15 V. Under the operatingconditions of Fig. 6, the system undergoes in a period addingsequence with locking windows corresponding to 1, 2, 3,and 4. This nonlinear dynamical behavior is a characteristic ofRTD oscillators [18] and is similar to other NDR oscillator sys-tems, such as the forced van der Pol oscillator [23]. The bifur-cation diagrams of Figs. 5 and 6 give clear indications the LDdynamics is determined by the RTD-induced oscillation charac-teristics, since the laser output shows the same dynamic statesof the RTD-induced oscillatory current.

IV. EXPERIMENTAL RESULTS AND DISCUSSION

In what follows, we present the experimental results of theoperation regimes of the RTD-LD optoelectronic circuit actingas a microwave-to-photonics interface and include preliminaryresults on optical injection locking, showing RTD-OW opera-tion as an optical-to-microwave interface.

A. Free-Running Relaxation Oscillations

As mentioned, when dc biased in the NDR region and withoutexternal excitation, the RTD-LD optoelectronic circuit operatesas a self-sustained relaxation oscillator undergoing repetitive



switching between two dc stable points that are below and abovethe NDR region [24], [25], with the laser optical output fol-lowing the circuit oscillation, with the corresponding RF spectraof both signals showing frequencies up to the tenth harmonic,confirming the observed optical pulses widths [5], [6].

The RTD-LD free-running oscillation frequency is deter-mined to a first approximation by the circuit resonator (tankcircuit, see Fig. 4) frequency GHz. Theoscillation frequency depends also on the RTD nonlinearimpedance, which is a function of the dc-bias voltage [5]. Asshown in Fig. 3, the circuit oscillation frequency does not varymonotonically with bias voltage: tuning the dc bias from 2.95to 3.45 V changes the circuit natural oscillation frequencyfrom 560 MHz oscillations up to 1.0 GHz (3.35 V), decreasingslightly below 1 GHz for higher voltage values. The RTD-LDOVCO capabilities can be used in systems where frequencyreuse is needed, and opens out the possibility of using theRTD-LD circuits in a wide range of applications, as discussedin the next sections.

B. Injection Locking

Injection-locking experiments were performed using the cir-cuit setup shown in Fig. 1. In the presence of an RF broadcastedsignal, the RTD-LD oscillator phase-locks to the RF signal whenits frequency is close to free-running frequency, with the LDoutput power being modulated by an amplified version of theRF signal.

The photon density bifurcation map with the frequency ofthe RF signal as control parameter (see Fig. 6), presents a seriesof frequency bands where the circuit produces waveformswhose period are exactly times the injected RF carrier period

. We have experimentally analyzed these frequency lockingregions. Fig. 7 shows the measured RF power spectra of photo-detected LD optical outputs produced in the frequency bandcorresponding to period-1 , due to free-running oscil-lation operation around 600 MHz, curve (a), and phase-lockedoperation induced by 41 and 26 dBm RF power levels atthe reception patch antenna plane, curve (b) and curve (c),respectively. (The RF-broadcasted power level on the receiverantenna plane was measured connecting the patch antennadirectly to the RF analyzer; during the experiments describedhere, the transmitter and receiver antennas were 2 m apart.)

The curve (a) of Fig. 7 indicates the LD optical output dueto relaxation oscillation operation produces a broad frequencyline centered at 600 MHz, with a gradual decrease of the spec-tral power density as we move away from the peak. On the con-trary, in the presence of a 41 dBm RF signal, the RTD-LDproduces an optical output with a much sharper line spectrum,curve (b), a clear indication the RTD oscillation is phase-lockedto the RF signal detected by the patch antenna. The locking tothe 26 dBm RF signal occurs with an appreciable noise reduc-tion, as shown in curve (c). The comparison of spectrum (c) ofFig. 7 with the spectrum of the signal produced by the generatorshows the LD optical subcarrier has the same spectral charac-teristics as the injected RF signal. The 26 dBm signal leads tophase noise reduction by more than 40 dB at 10 kHz offset, when

Fig. 7. Photodetected RTD-LD optical outputs showing phase-locking andphase noise reduction. (a) Free-running oscillation at around 600 MHz. RFphase-locking due to injected broadcasted signals with 600 MHz carrier fre-quency: injected power levels (b) �41 dBm and (c) �26 dBm. The resolutionand video bandwidths of spectrum analyzer are 1 kHz.

compared to the free-running oscillations phase noise. These re-sults demonstrate that the optical subcarrier has the same spec-tral quality as the broadcasted RF signal, with significant im-provement over free-running oscillation. It is worth mentioningthat we have observed frequency-locking operation for powerlevels as low as 50 dBm. This is a significant result, if we takein consideration that the RTD and LD, and the circuits were notoptimized for this operation.

As verified in the numerically simulations (see Section III),the regions where locking occurs are determined by the fre-quency of the RF signal and circuit dc-bias voltage. Underthe condition of injection around 26 dBm, the normalizedlocking bandwidth was measured to be approximately0.3% MHz , with the LD optical output notchanging appreciable within this locking range. The injec-tion-locking operation of the RTD-LD oscillator circuit followsthe behavior observed in other negative-resistance oscillatorsin the small-signal limit [25], usually quantified using Adlerequation [26]

(6)

where is the free-running power, is the injected power,and is the cold cavity bandwidth. Equation (6) is onlyvalid in the small-signal limit, i.e., when . FromFig. 7, we estimate a cold cavity bandwidth of around 12 MHz.

Since the RTD-LD can operate as an ILO that locks onto thephase of the injected signal, the information encoded on thephase of the broadcasted RF signal can be transferred to the op-tical output subcarrier. The ILO is an example of the synchro-nization of a nonlinear system to a weak signal. Fig. 8 comparesthe RF spectrum of a phase-modulated RF signal with corre-sponding RF spectrum of the detected RTD-LD optical output,showing the RF signal information content is transferred to theoptical subcarrier. The phase synchronization presented herecan have applications in the next generation wireless access net-works that employ PSK modulation, the digital version of phasemodulation.



Fig. 8. (a) RF spectrum of a 600 MHz broadcasted electrical phase-modulatedsignal with 1 MHz subcarrier signal and phase shift of 180 degrees. (b) Photo-detected RF spectrum of optical output phase-locked to free-running oscilla-tions around 600 MHz and showing 1 MHz sidebands resulting from phasemodulation.

As mentioned earlier (see Fig. 6), the RTD-LD circuitproduces waveforms whose periods are exactly times theinjected RF carrier period . We have experimentally con-firmed locking to broadcasted signals with frequencies aroundsecond, third, and fourth harmonics of the circuit free-runningfrequency. The LD optical power followed the dynamic be-havior presented in Figs. 5 and 6 where the dividing ratio isdetermined adjusting the dc-bias voltage or the injected signalfrequency. We have also confirmed the nonlinear dynamicssequence of period-5 and period-4 shown in Fig. 5, inducedby changing the dc bias from 2.95 to 3.45 V. Fig. 9 shows thecorresponding measured RF photodetected power spectra andwaveform of period-4 when a 3 GHz RF signal was injected(frequency division by 4).

The synchronization sequences of period- observed experi-mentally are summarized in the Arnold tongues map of Fig. 10.Arnold tongues correspond to phase-locking regions in param-eter space where a system responds synchronizing to an externalstimulus. The Arnold tongues reveal the regions of frequencyand RF power equivalent amplitudes that cause synchronization.We have observed the dividing ratio increases with frequencywith locking ranges up to tens of megahertz at RF powers closeto the free-running power.

C. Optical Injection Locking

As mentioned in Section I, the RTD structure employed in thiswork was designed to operate as a low-voltage electroabsorption

Fig. 9. (a) Experimental spectra of the photodetected LD optical output whenoperating as a free-running oscillator and dc biased at 3.073 V �� and when frequency locked to fourth harmonic of a injected 3 GHz RF signal.(b) Corresponding time series of frequency division by 4. Inset in grey color isschematically represented the time series of the 3 GHz injected carrier signal.

Fig. 10. Experimental Arnold tongues showing frequency-division operationfor dc-bias voltage 3.023 V, with the RF power � ranging from �19 to�3 dBm. Each dividing ratio � is represented by a tongue limited by dottedlines, inset schematically in color, corresponds to the RTD-LD locking regions.

modulator (for more details see [15]), consisting of a ridge op-tical waveguide with 1- m-thick InGaAlAs core incorporatinga double-barrier quantum well. The optical waveguide is essen-tially a ridge waveguide single mode in the growth direction forwavelength around 1550 nm. It allows endfire light couplingand, at the same time, gives a short path for the photogeneratedcarrier to be quickly removed from the absorption region bythe electric field across the waveguide core generated by the



dc bias that is perpendicular to the light guiding direction. TheInGaAlAs waveguide core acts as a photoconductive region forlight with energy close to the core bandgap energy and provideslight confinement along the double-barrier quantum-well planeincreasing the interaction length between the waveguide deple-tion region and the optical field (augmenting the light absorp-tion, and hence, the photogenerated current). The absorption ofa modulated optical signal gives rise to photogenerated currentthat can be used to tune, frequency modulate, and injection lockthe RTD self-sustained oscillations.

The RTD-OW acting as a optical-to-microwave converterworks as follows: modulated light incident on the photoconduc-tive region produces photocharges that reduces the RTD seriesresistance, leading to peak and valley voltages red shifts, givingrise to photodetection with responsivity in the order of few tensof amperes per watt [27]. Moreover, when biased in the NDRregion, certain modulated optical signals induce photogeneratedcurrents that are able to control the RTD free-running oscil-lations, producing electrical signals that emulate the opticalsubcarrier. Since the incident light changes the NDR regionprofile, the RTD current flow dynamics is then controlled bythe incident optical power, making several nonlinear modes ofoperation possible. This RTD-OW when integrated with an LD,as discussed previously, makes possible the implementationof an optoelectronic voltage controlled oscillator with bothelectrical- and optical injection ports, that adds to the electrical-and optical output ports of the simple RTD-LD circuit. In suchoptoelectronic oscillator, the electrical- and optical-output sig-nals can be controlled by both electrical- and optical-injectedsignals.

We now present preliminary results on optical-to-microwaveconversion due to synchronization of RTD oscillations to an op-tical subcarrier. The RTD oscillator capture range and the lownoise capabilities are discussed. The light source employed wasa Photonetics Tunics tunable LD with emitting wavelength inthe range 1460–1600 nm, which can be directly modulated up to1 GHz. In some of the experiments, the Photonetics laser outputwas amplified using an erbium-doped fiber amplifier (EDFA),and then launched into the RTD waveguide using a standardlensed single-mode fiber. The variable dc bias was applied viaa bias T (45 MHz–26.5 GHz) connected to a high-frequencyprobe to contact the RTD CPW transmission line.

First, we analyzed the RTD-OW response to optical modu-lated signals as function of the dc bias (see Fig. 11). The RTDelectrical response to the optical injected signal was character-ized using a high-bandwidth spectrum analyzer and an oscil-loscope. Since we are also interested in optical-to-microwaveinterfaces for wireless networks, the generated electrical sig-nals were fed directly to a patch antenna making part of theRTD circuit and broadcasted in a range of a few meters to bedetected by an identical patch antenna connected to the oscil-loscope or to the RF spectrum analyzer. It is worth mentionthat no amplification was used to strengthen the RTD-WO gen-erated RF signal prior to the broadcasting. Fig. 11(a) presentsthe RF injection-locking capture level of light modulated sinu-soidally at 1 GHz, for both peak and valley voltage polariza-tions, and , respectively. The capture level increases up to10 dB at the wavelength 1550 nm. Fig. 11(b) shows RF power of

Fig. 11. (a) Photodetected RF power as function of wavelength with dc-biasvoltage as parameter for a CW optical signal modulated at 1 GHz and 500 mV.(b) Photodetected signal due to 1550 nm CW optical signal modulated at 1 GHzwhen the RTD-OW is dc biased in the peak �� and valley �� regions.

photodetected optical signals of wavelength 1550 nm modulatedat 1 GHz for dc bias at the peak and the valley regions showingapproximately 9 dB gain in the transition from the peak to thevalley region (the results were limited by the available laser fre-quency modulation bandwidth and modulation depth).

We also have observed that when the RTD-OW is operatingin the NDR region the RTD oscillation can be locked to op-tical subcarrier signals. The RF power used to modulated theLD at microwave frequencies, giving a certain optical signalmodulation depth, and the optical injected power were varied toinvestigate the optical locking phenomena. We confirmed pre-vious results that the RTD oscillations follows the frequencyand the phase of the photodetected RF subcarrier. A notice-able locking phenomenon with significant noise reduction ap-peared at RF modulation powers as low as 100 mV. The lightcoupled to the RTD-OW was estimated to be less than 1 mW(corresponding to less than 10% of the input optical signal),because of the low overlap between the waveguide modes andthe optical fiber mode. Fig. 12 shows the measured spectrumof free-running oscillation operation around 600 MHz and thecorresponding spectrum due to optical injection-locking of a op-tical signal RF modulated at 600 MHz using a 400 mV ampli-tude voltage waveform. The noise levels of the synchronized



Fig. 12. RTD-OW free-running oscillation and locking to a 1530 nm opticalsignal modulated by an RF signal with 600 MHz and 400 mV.

signal compares with the noise figures of the signal used to mod-ulate the Photonetics LD.

The RTD-OW output power allows direct RF broadcastingof phase-locked signals connecting an RTD-OW to a patch an-tenna, without the need of external pre-amplification. Under theearlier operating conditions, the phase noise of the RTD elec-trical oscillations locked to the optical injected signal is reducedby up to 25 dB at a 100 kHz offset, when compared with thefree-running oscillations. Recent results in a similar experimentwith higher modulation frequencies indicate the RTD-OW canwork as a high-speed optical-to-RF converter, taking advantageof the optical waveguide design.

D. Chaos Dynamics

The earlier results demonstrate regular oscillation dynamicsand noise reduction properties of the RTD-LD/RTD-OW oscil-lator induced by injected RF/optical signals. We now presentexperimental results of the RTD-LD optoelectronic oscillatorchaotic capabilities. The RTD-LD shows a long-period behaviorthat includes the generation of nonperiodic waveforms, such asquasi-periodic signals, and in certain situations, namely tran-sitions between periodic- and nonperiodic signals, the wave-forms can evolve into chaotic patterns. The alternation betweenregions of regular and chaotic dynamics is known as intermit-tency [28]. We have observed intermittency near tangent bi-furcation windows of regular dynamics. In these intermittencytransitions a simple periodic orbit is replaced and turns into achaotic orbit, with the stable trajectory either becoming unstableor being destroyed, which gives rise to nonperiodic signals aspredicted numerically (see Figs. 5 and 6).

Fig. 13 presents the spectra of the photodetected LD opticaloutputs corresponding to quasi-periodic and chaotic signals dueto intermittency regions found between the windows of period-5and period-4 shown in Fig. 5. In Fig. 13(a), the spectrum of aquasi-periodic signal with high-frequency content correspondsto a first region of intermittency after period-5. A slight in-crease of the bias voltage, maintaining the carrier frequencyand amplitude, moves the system to a second region of inter-mittency [see Fig. 13(b)], where chaotic signals are produced.

Fig. 13. Spectra of the photodetected LD optical output of unlocked signalsdue to an injected wireless signal with 3 GHz and 16 dBm. (a) Quasi-periodicoutput and (b) chaotic output. The comparison between (a) and (b) shows a clearincrease of the signal background level in the spectrum of the chaotic signal,superior to 10 dBm in the 500 MHz to 2.3 GHz region.

Fig. 13(b) shows the typically features of a chaotic phenomena:broad-band spectrum and the rise of the spectrum backgroundlevel.

V. CONCLUSION

We have presented numerically and experimentally thesynchronized and desynchronized operations of RTD-LDbased microwave/photonics interfaces. The RTD oscillatorcapabilities are used to drive the LD making it possible tooperate as a optoelectronic voltage-controlled oscillator. Theinjection-locking and frequency-division regimes of operationwere presented and discussed, showing the locking leads toa considerable reduction of the oscillator phase noise evenfor low-power injected signals, meaning the RTD-LD can actas an injection-locking oscillator that can be used to transferbroadcasted RF signal phase information to an optical sub-carrier. The unsynchronized behavior includes the productionof quasi-periodic and chaotic signals. The results presentedconfirm that the RTD-LD optical behavior is determined by theRTD nonlinear characteristics, and that the circuit optoelec-tronic model based on the Liénard’s driven system approachdescribes the RTD-LD nonlinear dynamics quite well under RFinjection.



In another experiment using the optical waveguide incorpo-rating an RTD, optical injection was observed and the photode-tection characteristics of the RTD-OW device were character-ized. The RTD-OW is capable to lock to optical subcarrier sig-nals in telecommunication windows, and due to RTD intrinsicgain, the photodetected phase-locked signals can be directlybroadcasted, without the need of preamplification, in a rangeof a few meters with potential applications as an optical–RF in-terface for RoF systems.

The small size of the circuit and the low-power broadcastsignal levels needed for RF to optical conversion anticipate thenonlinear dynamics of RTD waveguide-based circuits can haveapplications in the next generation of wireless communicationsand wireless access networks as low-cost and high-reliabilitymicrowave–photonic interfaces due to the single-chip-platformcapability, low power consumption, and intrinsic RTD electricalgain. The unsynchronized operation may be used in chaotic dataencoding schemes in both optical and RoF chaos transmission.

ACKNOWLEDGMENT

The authors would like to thank W. Meredith of CompoundSemiconductor Technologies Global Ltd., for providing thelaser diodes.

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Bruno Romeira (S’08) received the Diploma degreein physics and chemistry from the Universidade doAlgarve, Faro, Portugal, in 2006. He is currentlyworking toward the Ph.D. degree in optoelectronicintegrated circuits incorporating resonant tunnelingdevices from the Centro de Electrónica, Optoelec-trónica e Telecomunicações (CEOT), Faro, Portugal.

From 2006 to 2008, he was with the CEOT, Faro,Portugal, where he was engaged in optoelectronicdevices containing low-dimensional quantum struc-tures. His current research interests include nonlinear

dynamics of electronic/optoelectronic circuits and the numerical simulation,design, and characterization of optoelectronic circuits containing resonanttunneling diodes for communication systems.



José M. L. Figueiredo received the B.Sc. degreein physics (optics and electronics) in 1991, and theMSc. degree in optoelectronics and lasers in 1995,both from the University of Porto, Portugal.

From 1995 to 1999, he was with the Department ofPhysics at the University of Porto and the Departmentof Electronics and Electrical Engineering at the Uni-versity of Glasgow, U.K., as a Ph.D. student workingon the optoelectronic properties of resonant tunnelingdiodes, receiving the Ph.D. degree in physics from theUniversity of Porto in 2000. He is with the Physics

Department at the University of the Algarve since 1999. His research interestsinclude the design and characterization of electronic and optoelectronic devicesand circuits incorporating low-dimensional quantum structures.

Thomas James Slight received the B.Eng. degree in physics and electronicengineering and the Ph.D. degree in electronic engineering from the Universityof Glasgow, Glasgow, U.K., in 2002 and 2006, respectively.

He is currently with the Department of Electronics and Electrical En-gineering, University of Glasgow. His current research interests includeoptoelectronic integrated circuits utilizing resonant tunneling diodes and shortwavelength quantum cascade lasers for gas sensing.

Liquan Wang was born in China in 1981. He re-ceived the M.Sc. degree in electronics and electricalengineering in 2006 from the University of Glasgow,Glasgow, U.K., where he is currently working towardthe Ph.D. degree in the reliable design of microwaveand millimeter-wave oscillators using tunnelingdiodes and resonant tunneling diodes (RTDs).

His current research interests include under-standing RTD-driven laser diode circuits andassociated applications.

Edward Wasige (S’97–M’02) received the B.Sc.(Eng.) degree in electrical engineering from theUniversity of Nairobi, Nairobi, Kenya, in 1988,the M.Sc. (Eng.) degree in microelectronic systemsand telecommunications from the University ofLiverpool, Liverpool, U.K., in 1990, and the Dr.-Ing.degree in electrical engineering from the Universityof Kassel, Kassel, Germany, in 1999.

During 1990–1993 and 1999–2001, he was en-gaged in teaching electronics and communicationsengineering courses at Moi University, Eldoret,

Kenya. From May 2001 to August 2002, he was a United Nations Educational,Scientific and Cultural Organization Postdoctoral Fellow at the Technion-IsraelInstitute of Technology, Haifa, Israel. In September 2002, he joined theUniversity of Glasgow, Glasgow, U.K. His current research interests includethe reliable design of resonant tunneling diode microwave and millimeter-waveoscillators, and the development of new types of gallium nitride-based hetero-junction FETs for power electronics and microwave applications.

Charles N. Ironside (M’87–SM’05) has beenin the Department of Electronics and ElectricalEngineering, University of Glasgow, Glasgow,U.K., since 1984. He has been engaged in a varietyof optoelectronic projects that include, ultrafastall-optical switching in semiconductor waveguides,monolithic mode-locked semiconductor lasers,broad-band semiconductor lasers, quantum-cascadelasers, and optoelectronic integrated chip (OEIC)devices, which concentrated on the integration ofresonant tunnelling diodes with electroabsorption

modulators and semiconductor lasers.

Anthony E. Kelly received the B.Sc., M.Sc., andPh.D. degrees from the University of Strathclyde,Glasgow, U.K.

He was with British Telecom Laboratories andCorning. He is also a cofounder of Kamelian Ltd.,and Amphotonix Ltd., Glasgow, U.K. He is cur-rently with the University of Glasgow, Glasgow.His current research interests include the use ofsemiconductor optical amplifiers for PONs, opticalburst switching, and ultrafast optical switching. Hehas authored or coauthored more than 100 journal

and conference papers on a range of optoelectronic devices and systems andholds a number of patents.

Richard Green received the M.Phys. and Ph.D. degrees in material and op-tical properties of mid-infrared quantum cascade lasers from the University ofSheffield, Sheffield, U.K.

For three years, he was a Postdoctoral Fellow at the Scuola NormaleSuperiore, Pisa, Italy, studying the dynamical characteristics of terahertzquantum cascade lasers. Since 2008, he has been with the University ofGlasgow, Glasgow, U.K. His current research interests include time-resolvedmeasurements of optoelectronic materials and devices.


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