dynamic-range enhancement and linearization in electrooptically modulated coherent optical links

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 11, NOVEMBER 2007 3289

Dynamic-Range Enhancement and Linearization inElectrooptically Modulated Coherent Optical Links

Yu-Chueh Hung, Bartosz Bortnik, and Harold R. Fetterman, Fellow, IEEE

Abstract—We present a general analysis of various electrooptic-modulation configurations on the system performance of a co-herent analog optical link. We evaluate the dependence of themodulation scheme of the optical modulator and its propertieson the system dynamic range and linearity. Linearization of acoherent optical link based on extending the length of a direc-tional-coupler modulator is also described, illustrating the uniqueconsiderations when linearizing a coherent link. System-level mod-eling of an analog coherent optical link under different modulationconfigurations is presented.

Index Terms—Coherent detection, electrooptic modulation,linearized modulator, suppressed-carrier modulation.

I. INTRODUCTION

R ECENT advances in millimeter-wave generation and dis-tribution via photonic techniques have sparked signifi-

cant interest due to several promising applications, such aswireless-access networks [1], [2], antenna remoting [3], etc.The advantages of utilizing optical methods are many, suchas extending the link bandwidth, simplifying the electronichardware, and reducing the weight and size of the system.There are several architectures that have been proposed forfiber–radio millimeter-wave wireless-access systems, includ-ing optical self-heterodyning, external-modulation techniques[4]–[6]. These advances are trying to meet the demand of uti-lizing higher operating frequencies in commercial and militarysystems.

To date, implementations of optical analog communicationsystems are mainly in the direct-detection mode of operation.However, the RF output characteristics at the detection sideare determined differently by various system parameters ifa coherent link is implemented instead. Coherent links canattain high dynamic range due to a finer control of the noisefloor and an enhanced sensitivity [7]. Therefore, the impact ofvarious modulation scenarios on the system performance of ananalog coherent optical link needs to be addressed. Nonlinear

Manuscript received February 23, 2007; revised June 12, 2007.Y.-C. Hung was with the Department of Electrical Engineering, University

of California at Los Angeles, Los Angeles, CA 90095 USA. She is nowwith the Department of Optoelectronics, University of Duisburg–Essen, 47057Duisburg, Germany (e-mail: [email protected]).

B. Bortnik is with the Millimeter Wave and Optoelectronics Laboratory,Department of Electrical Engineering, University of California, Los Angeles,CA 90095 USA.

H. R. Fetterman is with the Department of Electrical Engineering, Universityof California, Los Angeles, CA 90095 USA.

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

Digital Object Identifier 10.1109/JLT.2007.907747

Fig. 1. Diagram of a coherent optical link as discussed in this paper. Theoptical carrier with an angular frequency ωo is modulated by an RF signal and iscombined with an optical LO with an angular frequency ωL by a 3-dB coupler.The mixing field is detected by a balanced photodetector.

distortion in radio-over-fiber systems with single-sideband sub-carrier modulations has been theoretically investigated recently[8]. Several schemes have also been proposed to reduce thenonlinearity of a coherent system at the receiver side [9],[10]. However, linearization considerations of a modulator ina coherent link have not yet been reviewed.

In this paper, we present design considerations and lin-earization techniques when using electrooptic modulation inan optical coherent-detection system, as shown in Fig. 1.We will mainly focus on the electrooptic modulation with aMach–Zehnder modulator (MZM) and a directional-couplermodulator. It will be shown below that a directional-couplermodulator is better suited at increasing the dynamic rangein coherent optical links. In this paper, specific designs of adirectional-coupler modulator that has significantly more lin-earity in a coherent system will be presented.

A coherent system refers to a configuration where an extraoptical carrier, commonly a local oscillator (LO), is utilizedand mixed with the optical signal in the optical domain beforephotodetection, such as in optical heterodyning or homodyning.Note that this definition also includes situations where an extraoptical tone is added on the transmission side, as opposed to thedetection side. Although many published systems, like thoseaforementioned, are not specifically described as employingcoherent detection, the dynamic-range and linearization con-siderations discussed here can also be applied in these systemsdue to their utilization of extra optical tones. This is particu-larly relevant in systems where several optical-to-electrical andelectrical-to-optical conversion and mixing stages are involvedin data transmission in radio-over-fiber applications.

This paper is structured as follows. In Section II, the uniqueconsiderations of electrooptic modulation on dynamic rangeand its effect in a coherent links will be addressed. Then,

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3290 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 25, NO. 11, NOVEMBER 2007

Fig. 2. Hypothetical examples to illustrate the resulting RF-power spectrumproduced by two phase choices of the inserted third tone for both the homodyneand heterodyne cases. For the homodyne case, the phase of the LO willaffect the signal detected, as shown in the electrical spectrum, whereas inthe heterodyne case, all optical components will be revealed in the electricalspectrum with a heterodyned intermediate frequency shift of ωIF.

electrooptic-modulation characteristics based on these uniqueconsiderations will be presented with MZMs described inSection III and with directional-coupler modulators describedin Section IV. In order to evaluate the system performance withdifferent types of modulators and modulation schemes, systemmodeling is done by simulating a coherent optical link aspresented in Section V, and the numerical results are presentedin Section VI. A brief discussion and a conclusion are given inSections VII and VIII, respectively.

II. DYNAMIC RANGE IN COHERENT OPTICAL LINKS

In order to appreciate the unique considerations of elec-trooptic modulation and its effect on the dynamic range ina coherent link, let us first consider the correspondence ofthe optical spectrum on the RF output. Fig. 2 shows sev-eral possible output RF-power spectra when a third opticaltone, namely, from an LO, with an angular frequency ωL,a phase θL, and an electric-field amplitude EL, is combinedwith an optical spectrum formed by suppressed-carrier double-sideband modulation, with a suppressed-carrier frequency ofωo = ((ωa + ω−a)/2). The output RF-power spectrum resultsfrom the beating of the LO with each of the sidebands at(ωL ± ωa), with the upper and lower sideband frequencies ofω±a. Each sideband has a corresponding phase of θ±a andelectric-field amplitude of Ea. Considering only in-band RFfrequencies, the photodetector current corresponds to

i(t) ∝ ELEa cos [(ωa − ωL)t+ (θa − θL)]

+ ELEa cos [(ωL − ω−a)t+ (θL − θ−a)] . (1)

Fig. 2 illustrates the resulting RF-power spectrum producedby the two phase choices of the inserted third tone for both thehomodyne and heterodyne cases. For the homodyne case, theLO frequency ωL is equal to the original carrier frequency, i.e.,ωL = ωo, leaving both cos terms in (1) with the same angular

frequency. In the first instance, the local-oscillator phase is setto θL = 0◦, and hence, we see that there are no photodetectedRF frequencies. However, when the carrier phase is set toθL = 90◦, the two terms in (1) add constructively, and a fre-quency term at ωa − ωL is observed in the RF-power spectrumafter photodetection. Thus, tight control of the phase of the LO,in this case, is necessary to ensure high dynamic range. Thishypothetical example illustrates the importance of phase whenconsidering the design of a linear analog link in the homodyneconfiguration. In addition, most direct-detection schemes alsooperate in this manner, where the phase of the optical frequencytones is critical in determining the detected RF signal. The useof phase relationships to cancel the RF intermodulation tones isa common mechanism in many published linearization direct-detection schemes [11] and can also be exploited in a homodynesystem. Since a homodyne system is difficult to implement inpractice, we only emphasize our discussions on direct detectionand heterodyne systems in the following sections.

In the heterodyne case, the inserted optical tone from theLO does not equal the original carrier frequency, i.e., ωL �=((ωa + ω−a)/2). In this instance, (1) reduces to two terms withdifferent angular frequencies. Thus, the RF spectrum containstwo RF tones. We see that, unlike the homodyne case, thephase of the optical tones is irrelevant in the production ofthe detected RF-power spectrum. Hence, when designing alinearized heterodyne link, great emphasis must be taken tominimize the amplitude of the intermodulation tones in theoptical domain, since they entirely determine the spurious tonesin the RF spectrum. This stands in contrast to the homodynelink, as aforementioned, and in sharp contrast to many types ofproposed optical linearization schemes in direct-detection sys-tems, which rely on the cancellation of intermodulation beatingtones by control of the phase relationships between tones inthe optical spectrum. To illustrate this unique design emphasisin a heterodyne-detection link, we give an example and thesystem results of a linearized directional-coupler modulator inSection IV, where the intermodulation tones have been entirelyeliminated in the optical domain.

In order to quantify the impact of the intermodulation dis-tortion on the system linearity, the spur-free dynamic range(SFDR) is used as one important figure of merit [12]. The SFDRis defined as the signal-to-noise ratio when the intermodulationdistortion is above the noise level. The SFDR is determined,namely, by the power of the fundamental, the intermodulationdistortion power level, and the noise floor, as shown in Fig. 3.Typically, in direct detection, the optical carrier is the maincontribution of the dc photocurrent that results in the noise ofthe system. However, in a coherent system, the signal levelsof the sideband and the optical carrier, which are externallycontrolled, can be optimized such that a higher fundamentalpower is possible without increasing the noise floor. For in-stance, suppressed-carrier modulation in a coherent system hasbeen demonstrated to improve the SFDR of the link [13], [14].For this reason, in this paper we will only focus on utilizingsuppressed-carrier operation in a coherent system.

In addition to utilizing suppressed-carrier operation in acoherent analog system, the SFDR can also be enhancedby minimizing the intermodulation distortion of the optical

HUNG et al.: DYNAMIC-RANGE ENHANCEMENT AND LINEARIZATION IN COHERENT OPTICAL LINKS 3291

Fig. 3. Diagram of SFDR of an analog optical link. The SFDR is determinedby the power of the fundamental, the intermodulation distortion, and thenoise floor.

modulator. The directional-coupler modulator contains aninherent spectral asymmetry, which is apparent from its asym-metric transfer function, making it a likely candidate forlinearization by altering its optical spectrum. This will bediscussed in great detail in Section IV.

III. MZM IN COHERENT OPTICAL LINK

The MZM has been the prominent type of electroopticmodulator used in high-speed communication links due toits simple structure, low driving voltage, and good extinctionratio. A Mach–Zehnder can also be used in a coherent system;however, special considerations need to be taken into accountto maximize the link linearity. The SFDR of an optical link isdetermined by the fundamental power level, the intermodula-tion distortion power level, and the noise floor. The fundamentalpower, which is typically determined by the optical carrierpower in direct-detection links, is strongly affected by differ-ent modulation-configuration mechanisms in coherent opticallinks. This, in turn, makes an impact on the system dynamicrange, since the noise level is no longer determined by theoriginal optical carrier. The following discussion lists somemajor considerations of electrooptic modulation and how thesefactors affect the dynamic range of the system in a coherentoptical link.

A. Electrooptic Modulation

First, we will give an overview of dual-frequencyelectrooptic-phase modulation in order to examine the linear-ity of an interferometer-based optical modulator, such as anMZM. The MZM will then be discussed in various modulationconfigurations.

1) Phase Modulation: Electrooptic-phase modulation hasfully been described in the literature [15]. It is normally ex-pressed as

Epm(t) = E0ejωotejφ(V ) (2)

where ωo is the angular frequency of the optical carrier, φ(V )is the modulated optical phase, which is a function of appliedvoltages in an electrooptic modulation. If the modulation is a

sinusoidal function, the modulated electric field is expressedas the following and can be expanded in terms of Besselfunctions [15]:

Epm(t) =E0ejωotejφbej∆(sinω1t)

=E0ejωotejφb

(∑m

Jm(∆)ejmω1t

)(3)

where φb is the phase shift due to a bias voltage. ∆ is themodulation depth, which is defined as

∆ = πV

Vπpm(4)

where V is the modulation voltage and is equal to√

2RMPm,where RM is the modulator impedance and Pm is the RF inputpower. Vπpm is the voltage required in order to introduce aphase shift of π in a phase modulator. The use of (4) ensuresa well-defined modulation depth in different modulation con-figurations. For instance, if the MZM is driven with a push–pullconfiguration, the Vπ of this modulator will be half of Vπpm.

If the modulator is driven by a two-tone signal with angularfrequencies ω1 and ω2 assuming that the modulation depth ∆ isthe same at both frequencies, φ(V ) can be expressed as

φ(V ) = ∆(sinω1t+ sinω2t). (5)

The mathematical expansion of the phase modulation by a two-tone signal can be described as

Epm(t) =E0ejωotejφbej∆(sinω1t+sinω2t)

=E0ejωotejφb

(∑m

Jm(∆)ejmω1t

)

×(∑

n

Jn(∆)ejnω2t

). (6)

Note that a pure phase modulator cannot produce intensitymodulation. One sideband of the odd order has the same phaseas the carrier, while the other sideband has a π phase shift.Therefore, the beating of the odd-order terms, including thefundamental signals, with the carrier will be canceled at thedetector. In order to recover the odd-order signals, the phaseof the optical carrier needs to be changed. This can be done byadding another optical carrier with a different phase. This alsoexplains how the detected odd-order signals vary with respectto the bias change in a single-drive MZM (SDMZ).

2) Push–Pull MZM (PPMZ): The output of a PPMZ is theinterference of two phase modulators. The electric field at theoutput of a PPMZ can be expressed as

EPPMZ(t) =12E0e

jωot(ejφbejφ(V ) + e−jφ(V )

). (7)

Note that, in this case, the voltage required to introduce a phaseshift of π between the two arms is Vπpm/2. For a push–pull op-eration, one of the phase-modulated arms is reversed in polarity,


Fig. 4. Diagrams of an SDMZ and a PPMZ. With a laser input at a carrierfrequency ωo, the output optical spectra are depicted for each modulatorconfiguration when the modulators are operated as carrier suppressed. Thereis a carrier residue in a single-drive configuration, whereas the carrier cancompletely be canceled in a push–pull configuration. In addition, the opticalsideband amplitude in a push–pull configuration is twice as that of a single-drive configuration.

which results in phase reversal of the odd-order component butnot the even components and the carrier. This is due to one ofthe properties of the Bessel function, as shown in the following:

Jn(−∆) = (−1)nJ(∆). (8)

Modulating with a two-tone signal, as described in (5), thephases of the sidebands are either zero or π without bias. Ifa bias voltage is applied to the upper arm, which corresponds toa phase shift of all the modulated components, the addition ofthe sidebands can vary depending on the modulation bias. In theultimate case where φb is π, the odd-order sidebands can add upconstructively while the carrier and the even-order sidebandswill add destructively. This corresponds to a double-sidebandsuppressed-carrier modulation (DSB-SC), as depicted in Fig. 4.Note that, in this case, the amplitudes of the odd sidebandsare maximized, since the sidebands of both phase modulatorsare added in phase. However, no fundamental signal will bedetected in a direct-detection scheme because there is no opticalcarrier. Therefore, the advantage of doubling the amplitude ofthe sideband in DSB-SC can be utilized in a coherent systemdue to use of an external carrier.

An optical filter can be placed after the MZM to selectone sideband to generate a single-sideband suppressed-carriermodulation (SSB-SC). The optical filter also filters out anyresidue carrier, although, in an ideal PPMZ, the carrier shouldcompletely be canceled out.

3) SDMZ: In an SDMZ, the voltage required to introduce aphase shift of π between two arms is Vπpm, i.e., Vπ = Vπpm.The output field of an SDMZ can be expressed as

ESDMZ(t) =12E0e

jωot(ejφbejφ(V ) + 1

). (9)

The output of an SDMZ is the interference of a phase modu-lator with the optical carrier. In this configuration, the carriercannot completely be suppressed but has a residue amplitudeof (1/2)(1 − J0(∆)) of an optical electric field, as shownin Fig. 4.

B. Direct Detection Versus Coherent Detection

In a direct-detection system, the modulator must be biasedat the quadrature for maximum fundamental power. In thesingle-drive case, the carrier from the non phase-modulated armbeats with the optical sidebands from the modulated arm at thephotodetector. In a push–pull case, the sidebands and carriercombine from both arms, such that they are each a squareroot of two larger than the single-drive case. In comparisonto a single-drive modulator, the beating of the carrier with thesidebands from a quadrature-bias push–pull modulator resultsin an increase of the electric current by a factor of two and,hence, the detected RF power by a factor of four.

In a heterodyne link, where suppressed carrier is used, theSDMZ has sidebands of the same height as the direct-detectionsingle-drive case, since only sidebands are produced by oneof the arms. It is important to note that since some of thecarrier is converted to sideband power in the modulated arm,and hence, it is not possible to fully eliminate the carrier by de-structive interference between the two arms. When a push–pullmodulator is used, the suppressed-carrier operation causes thesideband power from both arms to add entirely constructivelyand produce optical sidebands that are two times greater thanthe single-drive case, hence yielding an RF signal that is fourtimes greater in power. In the homodyne link, the push–pullmodulator once again produces four times greater RF powerthan the single-drive modulator. It is interesting to note that, dueto the contribution of both sidebands, the homodyne push–pullmodulator creates an electrical current that is a factor of fourlarger than a heterodyne single-drive modulator, yielding eighttimes (9 dB) more in RF power, assuming the same LO is usedin both cases.

IV. DIRECTIONAL-COUPLER MODULATORS IN

COHERENT OPTICAL LINKS

The operation mechanism of a directional coupler is basedon the coupling effects between two waveguides describedby couple-mode theory. There are fundamental distinctionsbetween a directional-coupler modulator as compared tothe phase-modulator-based modulators described previously.The unique characteristics of a directional-coupler modula-tor that allow enhanced linearity in coherent links will bediscussed in great detail in this section. The general reviewof a directional-coupler modulator will be presented, and itscharacteristics in different modulation configurations will beelaborated.

The directional-coupler modulator is, in general, categorizedinto two types: the two by two (2 × 2) and the one by two(1 × 2) directional coupler, as shown in Fig. 5. The analyticalexpressions of a directional-coupler modulator have been welldeveloped in the literature [16]. For arbitrary input R(0) and


Fig. 5. Diagram of a 2 × 2 and 1 × 2 directional-coupler modulator. Eachoutput port is denoted as either the R port or the S port.

S(0) of a codirectional coupler, its corresponding output R(z)and S(z) after length z is [15], [17]

R(z) = eiδz

((cos√κ2 + δ2z − i

δ sin√κ2 + δ2√

κ2 + δ2

)R(0)

− iκ√

κ2 + δ2sin√κ2 + δ2zS(0)

)

S(z) = e−iδz

(−iκ

∗ sin√κ2 + δ2z√

κ2 + δ2R(0)

+

(cos√κ2+δ2z+i

δ sin√κ2+δ2√

κ2+δ2

)S(0)

)

(10)

where κ is the coupling coefficient, and δ is the velocitymismatch produced by the driving electrical signal. For thisanalysis, we further define parameters s and φ(V ), which is thenormalized coupling length and the cumulative phase mismatchintroduced by a voltage, respectively

κz =π

2s (11)

δz =φ(V ). (12)

The analysis of this paper is focused on the linearity character-istics, and therefore, a two-tone signal is applied into (10) toevaluate the intermodulation distortion of the system

φ(V ) =12

(φb + ∆(sin(ω1t) + sin(ω2t))) (13)

where φb is the phase mismatch introduced by a dc voltage, and∆ is the modulation depth.

Most of the discussions to date of directional-coupler modu-lators emphasize the characteristics of the total system transferfunction after photodetection [18], [19]. However, as discussedin Section II, the detected signals will strongly be affected bythe detection scheme. Therefore, it is necessary to examinethe components of the electric field in the optical domain.

Assuming that an input electric field of Eoejωot is applied to

the modulator, an optical LO is introduced and defined as

EL(t) = ELej(ωLt+φL) (14)

where ωL and φL are the angular frequency and the opticalphase of the LO, respectively. A power ratio r between the inputoptical power and the LO power is defined as

r =|EL|2|Eo|2

. (15)

Note that a suppressed-carrier modulation is assumed inthis paper, where an optical filter is involved to filter out theoptical carrier. This assumption is made in order to exempt theexcess-noise contribution from the original carrier such thatthe comparison in dynamic range with a suppressed-carrierMZM discussed in the previous section can be evaluated withthe same photocurrent. Although an extra filter increases thecomplexity in system implementation, a suppressed-carrier op-eration is generally preferred in a coherent optical link since thenoise level can be externally controlled without affecting thesignal level, which has been discussed in a previous section asone of the schemes to enhance the dynamic range of a coherentlink. For either a 2 × 2 or 1 × 2 directional-coupler modulator,the output characteristics will be further described in detail,depending on the mixing frequency and the power ratio, asshown as follows.

A. 2 × 2 Directional-Coupler Modulator

For a 2 × 2 directional-coupler modulator, optical light isnormally launched into one of the input ports, for example,the R port. After one coupling length, the light will totallybe coupled into the cross port, i.e., S port. In this analysis,we assume that the input optical light is launched from the Rport only, i.e., R(0) = Eoe

jωot and S(0) = 0. To evaluate theoutput performance after the photodetection process in variousfrequency-mixing scenarios, an LO defined in (14) is utilizedto combine with the output electric field of the modulator. De-pending on the mixing frequency and the power ratio, the outputcharacteristics after the photodetection process are described asfollows.

1) ωo = ωL; r = 0 (Direct Detection): In this case, there isno LO involved, and the output field is directly detected withoutmixing with an extra field, which represents the direct-detectionconfiguration. Considering a conventional design with one cou-pling length, s = 1, the output amplitude is a sinc function withrespect to a dc bias. If a two-tone signal, as described in (13),is applied to the modulator, the amplitudes of the fundamentaland the third-order intermodulation distortion are found bynumerically computing the Fourier transform

Ie(ωm) =2T

∣∣∣∣∣∣T∫

0

|R(z)|2 ejwmtdt

∣∣∣∣∣∣ (16)

and observing the fundamental and intermodulation amplitudesat ω = ω1,2 and ω = 2ω1,2 − ω1,2. Fig. 6(b) shows the result


Fig. 6. Amplitudes of the fundamental and the third-order intermodulation with respect to bias in direct detection of an (a) MZM and (b) 2 × 2 directional-couplermodulator with s = 1, where s is the normalized coupling length.

as a function of the bias normalized by one switching voltage.Due to the symmetry caused by the square in (16) and since|R(z)|2 + |S(z)|2 = 1, either the R or the S port could bemonitored, yielding similar results. Unlike an MZM where thefundamental and the third-order intermodulation level behavein a synchronized manner, as shown in Fig. 6(a), these twolevels of a directional coupler are diminished under differentbias conditions. This characteristic makes it possible to biasthe directional coupler in a way such that the third-order in-termodulation is eliminated while the fundamental signals stillremain. As shown in Fig. 6(b), a directional-coupler modulatoris normally biased at 0.4394Vs for maximum fundamentalsignal [20], where Vs is one switching voltage. The third-orderintermodulation level is eliminated at a different bias conditionat 0.7955Vs [20], and it is noticed that the correspondingfundamental signal is lower. The system gains a maximumdynamic range in a direct-detection system at this bias pointat the expense of a lower RF gain. This is due to a morecomplicated linearization scheme, which normally results inpower penalty. The amount of RF gain decrease in a linearizedphotonic link depends on the linearization schemes that areimplemented [20].

2) ωo �= ωL, r �= 0 (Heterodyne): In this case, the fre-quency of the LO is different than the original optical carrier,which represents a heterodyne scheme. As aforementioned inSection II, linearization in this case requires only the dimin-ishing of the amplitude of the intermodulation component inthe optical spectrum, since the electrical spectrum is essentiallya frequency-shifted version of the optical spectrum. This isdepicted in Fig. 7. Instead of beating at baseband in the pho-todetection, the modulated sidebands are now centered at theheterodyned angular frequency ωIF = (ωo − ωL). We assumethat the modulation and optical LO frequencies are carefullychosen such that there is no overlap among the componentsin the RF band of interest. The amplitudes of the detectedcomponents are totally independent of the phase of the LO.However, they do depend on the structure of the device, suchas the number of coupling lengths and the biasing point. Weapply a two-tone signal described in (13) to the modulator andperform a 2-D scan with respect to coupling lengths and bias.The bias is normalized by one switching voltage Vs and is

Fig. 7. Linearization mechanism in heterodyne links. The upper part depicts atypical optical spectrum after modulation. In heterodyne links, the linearizationrequires diminishing the amplitude of the intermodulation component in theoptical spectrum, as depicted in the lower part.

denoted as φbn. Fig. 8 shows the amplitudes at the fundamentaland the intermodulation frequencies of ω = ωo ± ω1,2 and ω =ωo ± (2ω1,2 − ω2,1), respectively, of the R and the S portsfound by obtaining the amplitude spectrum of the electric-fieldoutput for the R (and S) using

Io(ωm) =2T

∣∣∣∣∣∣T∫

0

R(z)ejwmtdt

∣∣∣∣∣∣ (17)

in contrast to (16) in the direct-detection case shown previously.The amplitude variations are symmetric along the axis ofφbn = 0, but the amplitude variations are different in both portswith respect to coupling lengths and bias. This is due to adifferent electric-field representation of the output ports R(z)and S(z), which are apparent in (10) when S(0) = 0.

In a heterodyne situation where all the optical componentsare detected or an optical single-sideband situation where only


Fig. 8. Amplitudes at the fundamental and the third-order intermodulation optical frequencies of the R port and S port in a 2 × 2 directional-coupler modulatorwith respect to coupling length and normalized bias.

Fig. 9. Amplitudes at the fundamental and the third-order intermodulationoptical frequencies of the R port in a 2 × 2 directional-coupler modulator withrespect to coupling lengths when the bias is zero.

one sideband beats with the carrier at the photodetector, theintermodulation distortion level will be determined by the com-ponent at ω = ωo ± (2ω1,2 − ω2,1) in the optical domain. Aftermixing with an LO with an angular frequency ωL, the intermod-ulation distortion will be revealed at the heterodyned frequency(ωo − ωL) ± (2ω1,2 − ω2,1). In order to obtain a high dynamicrange, a lower level of the intermodulation is preferred. Itis observed that along the axis of φbn = 0, the amplitude ofthis intermodulation component reaches a minimum at certaincoupling lengths. Therefore, we monitor the amplitude varia-tions at the fundamental and the third-order intermodulation inFigs. 9 and 10 along this axis to examine the characteristics

Fig. 10. Amplitudes at the fundamental and the third-order intermodulationoptical frequencies at of the S port in a 2 × 2 directional-coupler modulatorwith respect to coupling lengths when the bias is zero.

of these components for the R and S ports, respectively. Asshown, the amplitudes vary with respect to coupling length,and again, we can see certain points where the third-orderintermodulation component is eliminated while the fundamen-tal still remains. Note that this is a unique characteristic ofa directional-coupler modulator, since in an MZM, the vari-ations of fundamental and intermodulation are synchronized,as discussed previously and shown in Fig. 6(a). This propertycan be exploited to implement a linearization scheme in aheterodyne coherent system, where the modulator is designedto yield intermodulation suppression. For example, when thecoupling length s is tailored to be 2.37, the intermodulation


Fig. 11. Fundamental and the third-order intermodulation distortion of a 1 × 2directional-coupler modulator with respect to bias in direct detection. The biasis normalized to one switching voltage.

component from the S(z) port will totally be suppressed. As forR(z), the intermodulation suppression is at s = 2.98. The third-order intermodulation suppression implies an enhancement indynamic range. A numerical analysis of the dynamic rangeof a coherent system with such device will be provided inSection VI.

B. 1 × 2 Directional-Coupler Modulator

For a 1 × 2 directional-coupler modulator, the input port is aY -fed junction, and the optical power is equally distributed intoboth coupler arms, i.e., R(0) = S(0) = 1/

√2E0e

jωot in (10).The analytical expressions of the electric fields in both armsare the same in a 1 × 2 directional-coupler modulator. Similarto the previous analysis, the output characteristics depend onthe mixing frequency and the power ratio.

1) ωo = ωL, r = 0 (Direct Detection): In direct detection,a 1 × 2 directional-coupler modulator is normally designedat s = 1/

√2 for maximum extinction ratio. Fig. 11 shows the

amplitudes of the fundamental and the third-order intermodu-lation with respect to the bias point in a conventional 1 × 2directional coupler with s = 1/

√2. The modulator is normally

biased at zero for maximum fundamental signal. For a highdynamic range, the modulator is biased at 0.4214Vs with asmaller RF gain, since the corresponding fundamental is lowerthan that under the optimum operating point.

2) ωo �= ωL, r �= 0 (Heterodyne): A 2-D analysis, similar tothe 2 × 2 case utilizing (17), is given in Fig. 12. In a 1 × 2directional-coupler modulator, R(0) = S(0) = 1/

√2E0e

jωot

in (10), and therefore, the electric-field representations ofboth R and S output ports are the same at zero bias, whichcan be observed in the figure. The amplitude variations areasymmetric along φbn = 0 axis but the variations betweenthe R and S ports have mirror symmetry along this sameaxis, which can be observed from the electric-field repre-sentations, where |R(z, δ)| = |S(z,−δ)|. Fig. 13 shows theamplitude variation at ωo ± ω1,2 and (ωo ± (2ω1,2 − ω2,1))of the R port along φbn = 0.527Vs. At this bias point, thesuppression of the third-order intermodulation distortion occurswhen s = 2.4.

V. LINK MODEL

In order to evaluate the system performances with variousmodulator configurations, as discussed in the previous sections,a coherent optical link, as shown in Fig. 1, is numericallysimulated. A laser sends an optical carrier with power Po of100 mW at an angular frequency ωo into a modulator. Themodulator is characterized by the modulator impedance RM

and a switching voltage. The modulator is driven by an RFsignal, and the modulated optical carrier is combined with anLO, which has an optical power PL of 3 mW and an angularfrequency ωL. The mixed signal is detected by a photodetectorwith responsivity ηD and load impedance RD. The ratio of theLO and the carrier power is denoted as r, as defined in (15).The parameters used in modeling this optical link are listed inTable I. We assume a 0-dB optical loss not only for calculationsimplicity but as a practical implementation choice since theoptical loss can be compensated by the optical amplifier (notethat, as discussed in Section I, the introduction of an opticalLO is for analysis purposes, and the analysis results are alsoapplicable to situations where an extra optical tone is added onthe transmission side, as opposed to the detection side).

At the receiving end, an LO signal is combined with themodulated electric field by a 3-dB coupler. A balanced detectoris utilized in the modeling and is also a preferred choice as thereceiver. The LO intensity noise produced in each detector isin phase and, therefore, can be suppressed by subtracting thetwo photocurrents. Furthermore, the balanced detector makesuse of both coupler outputs, and therefore, the signal loss fromthe coupler can be compensated.

RF gain of the system is defined as the ratio of out-put RF power at the modulation frequency and modulatedRF power. The input modulation power can be expressed asPin = (V 2/2RM ). The gain can be derived as

G =Pout

Pin. (18)

The output noise is

Nout = B(GkT0 + fRkT + 2eIdcRD) (19)

where kT0 is the thermal noise energy at 290 K, fR is thereceiver-noise figure, Idc is the dc photocurrent at the receiver,and B is the noise bandwidth. Note that the laser relativeintensity noise (RIN) is not included, since an optimized linkis assumed with a balanced photodetector. This implies that,with an LO power of 3 mW and a rejection of RIN more than20 dB, an LO RIN of −165 dB/Hz or smaller is assumed inorder to make it negligible [21].

The system dynamic range due to third-order nonlinearity isdefined as

DR =(

IPn

Nout

)n−1n

(20)

where IPn is the n-order intercept point. For the linearizedmodulators, the dynamic range is defined as the fundamental-to-noise ratio when the intermodulation level equals the systemnoise.


Fig. 12. Amplitudes at the fundamental and the third-order intermodulation optical frequencies of the R arm in a 1 × 2 directional-coupler modulator withrespect to coupling length and bias.

Fig. 13. Amplitudes at the fundamental and the third-order intermodulationoptical frequencies of the R port in a 1 × 2 directional-coupler modulator withrespect to the number of coupling lengths when bias is 0.527Vs. The minimumIMD3 occurs when s = 2.3719.

The numerical algorithm is similar to the approach thatwas utilized by Farwell and Chang [22]. The frequencies arecarefully chosen such that there is no aliasing in those signalbands of interest. The simulation results of this algorithm arenumerically compared with other published systems [20] andhave been verified to be consistent.

In this simulation, it is assumed that the switching voltagerequired, for an SDMZ, is the same as that of a 1 × 2directional-coupler modulator with one coupling length, whichis 6 V. Since some modulation configurations are performedin a heterodyne scheme, where a switching voltage is hard todefine, we will assume that an input voltage will correspond tothe same amount of total accumulated phase mismatch, i.e., ∆is the same for the same input voltage in (13).

TABLE IOPTICAL-LINK PARAMETERS

VI. RESULTS

Based on the system parameters listed in Table I,we performed numerical simulations on both the MZMand directional-coupler modulators with various modulationschemes and modulator configurations that are discussed inthe previous sections. MZMs are analyzed as either SSB orDSB and as either single-drive or push–pull operation. Fordirectional-coupler modulators, optimized operations and de-vice parameters that yield the maximum dynamic range are pre-sented for both 2 × 2 and 1 × 2 directional-coupler modulators.The system performances are summarized in Table II.

The first case is a single sideband and SDMZ withsuppressed-carrier operation. The dynamic range is 116 dBfor a 1-Hz noise bandwidth, and the RF gain is −12.9 dB.Since only the single sideband remains after filtering, the linkperformance is the same for both ωo = ωL and ωo �= ωL. If aPPMZ is utilized, the sideband amplitude increases by a factorof two, and therefore, the RF gain increases by a factor of four,i.e., 6 dB. The dynamic range increases by a factor of two thirdsin decibels, as shown in Table II. The system performance is thesame for a DSB-SC SDMZ with ωL = ωo and a π/2 phase ofthe LO for maximum power. An extra 4-dB improvement in


TABLE IILINK CHARACTERISTICS VERSUS MODULATION SCHEMES

dynamic range can be obtained, if a DSB-SC PPMZ is utilizedwith ωo = ωL.

A larger dynamic range can be obtained when utilizinga directional-coupler modulator, since the intermodulation iseliminated with specific modulator configurations and modu-lation schemes. Fig. 14 shows the dynamic range of the systemwith respect to the tuning of the coupling length of a 2 × 2directional coupler where the outputs R(z) and S(z) are com-bined with ωo �= ωL. As shown, the dynamic range can beimproved as compared to an MZM in an SSB-SC configura-tion by carefully tuning the coupling length s. For the outputS(z), the SFDR enhancement occurs within a range starting ats = 2.33 up to s = 2.55 with a maximum at s = 2.3719, in-creasing the SFDR by 20 dB, as compared to an SSB-SC MZM.The R(z) port has a smaller fundamental amplitude at the cou-pling length, where the intermodulation power is eliminated.Nonetheless, the SFDR enhancement occurs within a rangefrom s = 2.98 to s = 2.988 with a maximum at s = 2.9833,where a more modest, but still significant, SFDR increase of12 dB exists for the R(z) port. The amount of SFDR enhance-ment decreases in R(z) port due to a smaller amplitude of thefundamental signal, which is also shown in the system gain inthe table. For both cases, the maximum SFDR occurs at thethird-order elimination point in Figs. 9 and 10. This is a designexample of a 2 × 2 linearized directional-coupler modulator forcompletely suppressing the third-order intermodulation distor-tion in the optical spectrum. For a 1 × 2 directional-couplermodulator, Fig. 12 indicates that a completely suppressionof the third-order intermodulation distortion occurs when thebias is 0.527Vs and the coupling length s is 2.4. The SFDRenhancement occurs within s = 2.31−2.55 with a maximumat s = 2.4 when fixing the bias at 0.527Vs and increasing theSFDR by 20 dB. Note that the linearization schemes introducedhere for heterodyne detection are based on different consider-ations, as compared to those linearization schemes that weredeveloped in direct detection. They are particularly relevant, asdescribed in Section II, to be utilized in systems where severaloptical-to-electrical and electrical-to-optical conversion andfrequency-mixing stages are involved in data transmission inradio-over-fiber applications.

Experimental verification of this analytical model has beendemonstrated recently with a suppressed-carrier MZM in a

Fig. 14. Computed SFDR of a heterodyne system for the R and S ports in a2 × 2 directional-coupler modulator with respect to the coupling length. Thepeak of the SFDR happens at the coupling length where the minimum amplitudeof the third-order intermodulation elimination occurs in Figs. 9 and 10.

heterodyned link [23]. While the experimental dynamic rangepresented in [23] was restricted by component limitations,the experimental results are consistent with the above simula-tions when the experimental system parameters are taken intoaccount.

VII. DISCUSSION

In general, a directional-coupler modulator can achievehigher SFDR in a coherent analog optical link. This is in con-trast to a conventional MZM, which cannot be further linearizedin the coherent links presented in this paper by changing thedevice structure. A directional-coupler modulator, on the otherhand, provides more degrees of freedom in terms of deviceconfigurations to suppress the intermodulation product. A num-ber of design and implementation issues for directional-couplermodulators were discussed in the literature, such as fabricationtolerances [19] and operation bandwidth [24], [25]. The formerissue can normally be solved by introducing a second sectioninto the directional-coupler modulator [19], whereas the latterissue can be solved by applying an extra dc bias [24]. Althoughthese discussions are mainly in the regime of direct detection,these techniques for tailoring the performance of directional-coupler modulators can also be applied in a coherent opticallink. Linearity performance will also vary with respect tooperational wavelength, which can be considered as a variationin coupling length. Therefore, Fig. 14 can provide a designguideline where the sensitivity of dynamic range is shown withrespect to the coupling length of the device.

Directional-coupler modulators have successfully been fab-ricated with various materials such as GaAs [26], [27], lithiumniobate [28], [29], and polymers [30], [31]. Among all, elec-trooptic polymer is particularly promising for making suchdevices whenever coupling length tuning is the major lineariza-tion mechanism. Recently, we have demonstrated a linearizedpolymer-based directional-coupler modulator where linearized


performance is realized by trimming the device length and thecoupling coefficient [31]. By UV photobleaching in polymerwhere the amount of refractive index change of the polymerdepends on UV exposure time, the coupling coefficient κ and,hence, the coupling length of a directional-coupler modulatorcan easily be tuned. By exposing UV light to a polymer-baseddirectional-coupler modulator for different periods of time, atwo-section directional-coupler modulator with enhanced lin-earity has recently been made [32]. Electrooptic polymer hasalso been identified as an attractive candidate for making high-speed devices [33] because of its numerous advantages suchas high electrooptic coefficient, low-velocity mismatch, andease of fabrication. The ease of fabrication of such polymerdevices, coupled with their high-speed performance, makesthe implementation of a highly linear coherent optical linka promising technology for millimeter-wave transmission andwireless-access systems.

VIII. CONCLUSION

In this paper, the unique considerations for dynamic-rangeenhancement of an electrooptically modulated coherent opticallink are presented when using MZMs and directional-couplermodulators. It is shown that the RF gain, and hence the SFDR,can effectively be increased by optimizing the operation condi-tions of an MZM operated with suppressed carrier. To furtherincrease the SFDR of a coherent optical link by incorporat-ing a linearized modulator, different design criteria must betaken into account due to its unique characteristics as com-pared to direct detection. By tailoring the coupling length ofa directional-coupler modulator, the intermodulation distortioncan effectively be suppressed for a coherent optical link and,therefore, the SFDR can be enhanced. Numerical modelingshows that an SFDR of 140 dB for a 1-Hz noise bandwidth, andfull suppression of the intermodulation is possible by properdesign of a directional-coupler modulator for a coherent link.The results presented here can be applied to increase systemperformance in radio-over-fiber applications, where coherentprocesses, such as frequency conversion or signal mixing, arealready involved.

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[33] B. Bortnik, Y.-C. Hung, H. Tazawa, B.-J. Seo, J. Luo, A. K.-Y. Jen,W. H. Steier, and H. R. Fetterman, “Electrooptic polymer ring resonatormodulation up to 165 GHz,” IEEE J. Sel. Topics Quantum Electron.,vol. 13, no. 1, pp. 104–110, Jan./Feb. 2007.

Yu-Chueh Hung received the B.S. degree in elec-trical engineering from National Taiwan University,Taipei, Taiwan, R.O.C., in 2001 and the M.S. andPh.D. degrees from the Department of ElectricalEngineering, University of California at Los Angelesin 2003 and 2007, respectively.

She is currently a Researcher with the Departmentof Optoelectronics, University of Duisburg–Essen,Duisburg, Germany. Her research topics includelinearized analog links, microwave/millimeter-waveoptoelectronics, and polymer photonics.

Dr. Hung is a member of the IEEE Lasers and Electro-Optics Society.

Bartosz Bortnik received the B.S. degree in en-gineering physics and the M.S. and Ph.D. degreesin electrical engineering from the University ofCalifornia, Los Angeles (UCLA) in 2001, 2004, and2007, respectively.

During the summer of 2001, he was with theNorthrop Grumman Corporation (formerly TRWSpace Technologies), Redondo Beach, CA, wherehe implemented new techniques for analyzing directdigital frequency synthesizers. He is currently withthe Millimeter Wave and Optoelectronics Labora-

tory, Department of Electrical Engineering, UCLA, working on high-speedmicrowave photonic systems.

Dr. Bortnik is a member of the IEEE Lasers and Electro-Optics Society andEta Kappa Nu.

Harold R. Fetterman (SM’81–F’90) received the B.A. degree (with honors)from Brandeis University, Waltham, MA, in 1962 and the Ph.D. degree inphysics from Cornell University, Ithaca, NY, in 1968.

In 1969, he was with Lincoln Laboratory, Lexington, MA, where his initialresearch concentrated on the use of submillimeter sources. In 1982, he joinedthe Electrical Engineering Department, University of California at Los Angeles,where he is currently a Professor and where he has also served as the firstDirector of the Center for High Frequency Electronics. Currently, he hasprograms that investigate new millimeter-wave device concepts and novelmeans of high-frequency testing using laser techniques. He has concentratedon combining high-frequency structures and systems with optical devices.

dynamic-range enhancement and linearization in electrooptically modulated coherent optical links

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