signal and noise conversions in rf-modulated optical links

1302 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 52, NO. 4, APRIL 2004

Signal and Noise Conversions inRF-Modulated Optical Links

Mohammad Reza Salehi, Student Member, IEEE, Yannis Le Guennec, and Beatrice Cabon, Member, IEEE

Abstract—The power spectral density of the optical intensity inRF modulated optical links is investigated theoretically and exper-imentally in interferometric systems with a good agreement. Theinfluence of the Henry factor of directly modulated distributedfeedback laser diodes is shown on the conversion of phase noise intointensity noise for the first time.

Index Terms—Direct modulation, distributed feedback (DFB)laser, intensity noise, interferometric systems, microwavephotonics mixing, optical links, phase noise.

I. INTRODUCTION

THE semiconductor laser is one of the most important lightsources in fiber-optical and integrated optical systems [1].

This is due to its high efficiency, simplicity of modulation, andcompact size. Distributed feedback (DFB) lasers are fast be-coming the transmitters of choice in most optical communica-tion systems today. In optical communication systems, manytypes of impairments (e.g., noises) are added to the signal [2],[3]. These impairments result in a fluctuation to the signal. Thus,the statistical properties of the signal are changed and, therefore,they can degrade the system performance.

Laser phase noise results from fluctuations in the differencebetween the phases of two identical waves separated in time.The phase noise is very important in designing optical-fibercommunication systems. The dynamic range of many opticalsignal-processing and sensing devices incorporating two-beaminterferometers, such as Mach–Zehnder (MZ), can be limited byrandom phase fluctuations of the optical source emission field[4], [5].

The analysis of the fluctuations of the optical power is es-sential to understanding the degradation of the phase noise ofthe optical link. Quality of the transported information is cru-cial as, for instance, the close-to-carrier phase noise of a localoscillator (LO). The phase noise of the LO must be preserved tomatch the requirements during signal processing and analysis,e.g., in radar applications.

Several authors have considered the effects of phase-to-inten-sity noise conversion on noisy light without modulation [3]–[7].We, and other authors, have considered optical processing ofmicrowave subcarriers with conversion of frequency modula-tion (FM) into intensity modulation (IM). Optical carriers are

Manuscript received October 2, 2003.The authors are with the Institut de Microelectronique, Electromagnétisme et

Photonique, UMR CNRS 5130 Centre National de la Recherche Scientifique,Ecole Nationale Supérieure d’Electronique et Radioélectricité de Grenoble,38016 Grenoble Cédex, France (e-mail: [email protected]; [email protected];[email protected]).

Digital Object Identifier 10.1109/TMTT.2004.825733

then modulated by interferometers like MZ modulators [8], [9].However, the conversion of FM noise (due to chirp of diodes)into intensity noise in these interferometric systems has neverbeen considered before.

The problem addressed here concerns the phase-to-intensitynoise conversion process in microwave optical links. It occurswhenever self-delayed interference exist either due to the inser-tion of an optical cavity or an interferometric structure like anunbalanced MZ interferometer.

In previous studies, we have considered this system formicrowave-photonics signal processing. We demonstrated thatan passive unbalanced Mach–Zehnder (UMZ) can generatefrequency conversion of analog microwave subcarriers with orwithout digital modulation [9], [10], where a directly modu-lated laser diode (LD) with a large chirp is used for FM-to-IMconversion at the output of the MZ. The higher the chirp, thehigher the FM index is and the larger the mixing conversiongain is. In this paper, we consider the conversion of FM noiseand the influence of .

Section II presents phase-to-intensity noise conversion withthe MZ interferometer without modulation of the LD. Section IIIdeals with FM-to-intensity noise conversion with direct modula-tion of an LD, and the effect of the laser chirp coefficient . Dif-ferent frequency-modulation index values are investigatedand their effects on the noise power spectra are demonstrated.Both white noise and noise are considered. The objective isto characterize noise in analog RF modulated optical links underdirect modulation. Investigations are made on both experimentaland theoretical points-of-view.

It is shown that the low-frequency noise is reduced by aproper choice of the FM index . Section IV presents anexample of signal processing using a UMZ. Section V showsexperimental results and excellent agreement with theory.

II. CONVERSION OF PHASE-TO-INTENSITY NOISE IN AN

INTERFEROMETER WITHOUT MODULATION

In this case, the input optical field into the interferometer is

where is the field amplitude, is the center angular opticalfrequency, is the constant phase of laser, and is theinstantaneous phase representing the laser phase noise.

The schematic diagram of a fiber-optic system using an UMZis shown in Fig. 1 with a delay between the two arms

, is the effective index of the fiber, is the light ve-locity, and is the length difference.

0018-9480/04$20.00 © 2004 IEEE

SALEHI et al.: SIGNAL AND NOISE CONVERSIONS IN RF-MODULATED OPTICAL LINKS 1303

Fig. 1. Fiber-optic MZ. DFB: DFB laser. PD: photodetector.

All modeling data obtained here are related to an experi-mental DFB laser emitting at 1550 nm that has been used incombination with the UMZ for signal-processing purposes [9].

The light intensity , detected by the optical receiverplaced at the output of the interferometer of delay betweenthe two arms, is expressed as

The interference term is

(1)

Equation (1) can be written as

where is the average optical intensity and the phase-noise variable is defined as

The noise power spectral density (NPSD) can be calculatedfrom the normalized Fourier transform of the autocorrelationfunction of the interference term . The autocor-relation function is

At quadrature operation of the interferometer, can bewritten as [5]

where represents the spectrum of the instantaneous fre-quency fluctuation (FM-noise spectrum). The FM noise consistsof a white noise component and a noise component

. We have

Fig. 2. Microwave-photonics signal-processing system.

where and are constants, , is the co-herence time, , is the laser linewidth that canbe expressed as , is the linewidthpredicted by the well-known Schawlow–Townes formula [11],and is the linewidth enhancement factor introduced by Henry[12] (also called the chirp factor) to explain the experimentalvalues reported by Fleming and Mooradian [13] , which canbe written as

where is the group velocity of the light in the active medium,is the lasing photon energy, is the spontaneous emission

factor [14], is the loss, and is the output power per facet,where is the gain, , is the coherencetime of noise. The NPSD can be written as

(2)

where is the Fourier transform.Simulation results fit experimental measurements very well

as will be shown in Section V. Constants and have beenextracted from fitting our experimental data, as shown in Sec-tion V. We have then obtained

Hz Hz

which leads to s.

III. INFLUENCE OF CHIRP ON INTENSITY NOISE IN MICROWAVE

MODULATED INTERFEROMETRIC SYSTEMS

The schematic diagram of a microwave-photonics signal-pro-cessing system with consideration to the direct modulation of alaser is shown in Fig. 2.

The optical field at the input of the interferometer has bothamplitude and FMs. It is expressed as

where is the field amplitude, is the IM index, is the FMindex (due to the LD chirp), is the modulation frequency(microwave range), is the constant phase of the laser, and

is the instantaneous phase and represents the laser phasenoise.

Under small sinusoidal signal modulation, and are cor-related by [15]

(3)


where is a characteristic angular frequency depending on theLD and on its bias point. When is high enough, but lowerthan , is approximated to

(4)

Our experimental DFB LD has a resonant frequencyaround 7 GHz at a bias point of 35 mA, a threshold current

mA, a slope efficiency mW/mA, and .In the case of a fixed IM index, and GHzfor our experimental laser. Above this frequency, is constantand equals one. The effects of large FM with large have beenexplored by investigating different modulation frequencies

since decreases with [see (3)] [16].The interference term can be written as

(5)

At quadrature operation of the interferometer, the autocorre-lation function of can be written as

(6)

(see the Appendix ).The NPSD can be calculated as

(7)

These NPSDs under various and [ , ,and in (3)] are shown in Figs. 3 and 4 for the previousvalues of , , and . This value of makes thecomparison with experimental data of Section V feasible.

The modulation will shift the low-frequency noise spectrumto harmonics of the modulation frequency . For greater sim-plicity, the noise power is shown around . Figs. 3 and 4

Fig. 3. Normalized NPSD in the incoherent regime (� = 6:61� ). (a) � = 2,f = 800 MHz. (b) � = 28, f = 50 MHz. (c) � = 140, f = 10 MHz.

Fig. 4. Normalized NPSD in the incoherent regime (� = 6:61� ). (a) � =2, f = 800:028 MHz. (b) � = 14, f = 100:001 MHz. (c) � = 28,f = 50:003 MHz.

demonstrate that the variations in the NPSD with frequency de-pend strongly on . The close to carrier phase noise is reducedby a proper choice of (which depends on both and ).

In Section IV, we show that we have interest in increasing theFM index for the purpose of better frequency mixing of analogmicrowave subcarriers [9]. It is shown here that we also haveinterest in having a large for noise reduction in interferometricsystems with direct modulation.

IV. EXAMPLE OF SIGNAL PROCESSING: OPTICAL

MICROWAVE MIXING USING

UMZ INTERFEROMETER

Microwave mixing is frequency conversion of the RF signalby using an LO. In optical broad-band links, microwave mixingcan be generated all optically; this avoids electrical-to-opticalconversion loss. Mixing is always generated by exploiting anonlinearity. The nonlinearity in optical processing is based onthe sinusoidal function of output optical power at the output ofthe interferometer.


In the case of this paper, mixing is generated by an originalmethod detailed in [17] and [18]. The two frequencies and

directly modulate a DFB LD, which is followed by a pas-sive UMZ.

Direct modulation of the LD induces FM of the light. Theoptical power at the output of the interferometer is also a sinu-soïdal function of the optical frequency.

Indeed, if we neglect the IM, the optical field emitted by theLD can be written as

(8)

where is the amplitude of the optical field, and andare the FM index at frequency and .

This optical field contains all the harmonics and intermodu-lation products of the input signals. However, the interferometeracts as a linear filter on this optical field and can consequentlysuppress some spectral components. Under the two conditionsstated hereafter, the optical power at the output of the UMZ,calculated from the coherent beating of the optical field, has theform

(9)

where is the insertion loss of the interferometer including thecoupling and propagation loss.

Better mixing is obtained under these two conditions. Thefirst condition concerns specific relations between input fre-quencies values and the free spectral range (FSR) of the inter-ferometer [18]

(10a)

The second one concerns the transmission regime, which hasto be maximum or minimum

(10b)

with representing the LD optical frequency.This condition is fulfilled by changing biasing current of the

LD and by thermal control of both the LD and the glass substrateof the MZ.

Supposing that the LO power is chosen in order to maximizethe mixing power and that the RF power is low, the power de-tected at the mixing frequencies after quadratic photodetectioncan then be written as [18]

(11)

where relates to optical/electrical conversion and isthe optical IM index that can be measured by a photodetector(PD) placed directly at the output of the LD.

Fig. 5. Schematic experimental setup. TC: temperature controller.PCS: precision current source. SG: microwave synthesizer. DFB: DFB laser.I: isolator. D: divisor. AOM: acoustooptic modulator. PD: photodetector.SA: spectrum analyzer.

Fig. 6. Spectrum at the output of the UMZ.

Here, we assumed that, at , the intensity and FM indexare related by

From (11), logically, the greater is, the more efficient theFM response due to the chirp of the LD is, and the more efficientthe mixing power.

V. EXPRIMENTAL RESULTS

This shows experimental results for both purposes of signalprocessing and noise reduction. The experimental setup isshown in Fig. 5.

The measurement setup is basically an MZ interferometer.The laser examined is a DFB laser with a wavelength of1550 nm. An isolator is used in order to prevent any disturbingreflection back to the laser.

A. Signal Processing: Example of Frequency Conversion

The two signals RF and LO are applied by the two differentmicrowave synthesizers, which directly modulate the DFB LD.Fig. 6 shows the detected microwave spectrum at the output ofthe UMZ at a maximum of transmission. Input signals are theLO signal at GHz and a binary phase-shift keying(BPSK) signal modulating an RF signal at GHz.These frequency values respect (10a) with GHz.

In Fig. 6, it is shown that the subcarrier of the digital signal iseffectively converted at GHz and


Fig. 7. Normalized NPSD in the coherence regime and without modulation.Measurements and calculations are compared (without modulation).

Fig. 8. Normalized NPSD in the coherence regime and without modulation.Measurements and calculations are compared (without modulation).

GHz. An efficient mixing process is demonstrated because theDFB laser has an enhancement factor of approximately fivedespite the fact that the two input RF and LO signals do notrespect (10a) well, which explains why harmonics of arenot well rejected.

B. Noise Conversion With and Without Modulation

In this experiment, we have introduced an acoustooptic mod-ulator (AOM) in order to shift the beat note frequency around40 MHz instead of zero because measuring around isdifficult by a spectrum analyzer. First, we do not have any RFsignal from the microwave synthesizer (SG), and the DFB LD isnot modulated. The measured spectra are shown in Figs. 7 and 8for the case of the coherent regime m .Fig. 8 is a zoom of Fig. 7. Simulation data with

Hz and Hz are plotted with measurement curves.As can be shown, a very good agreement is obtained betweensimulation and experiment.

Direct RF modulation of the LD driving current is thenapplied. Both FM and IM exist. The measurements ofFigs. 9 and 10 show the influence of the modulation index

on noise power for the incoherent regime (

Fig. 9. Measured NPSD in the incoherent regime (� = 6:61� ), Span =10 MHz, and RBW = 10 kHz. (a) � = 2, f = 800:028 MHz. (b) � =9:38, f 150:011 MHz. (c) � = 14, f = 100:001 MHz. (d) � = 28,f = 50:003 MHz (with modulation).

Fig. 10. Measured NPSD in the incoherent regime (� = 6:61� ), Span =2 MHz and RBW = 10 kHz. (a) � = 2, f = 800:028MHz. (b) � = 9:38,f = 150:011MHz. (c) � = 14, f = 100:001MHz. (d) � = 28, f =50:003MHZ (with modulation).

and m). The microwave synthesizer SG de-livers a microwave signal at four different frequencies, i.e.,

and MHz, in order tohave four different values of according to (3). The modulationindex is fixed at . It is shown that the higher is,the lower the NPSD is. This confirm the simulation results ofFigs. 3 and 4.

VI. CONCLUSION

In this paper, we have presented theoretical calculations andexperimental results on optical microwave signal processing andon conversion of FM noise to intensity noise in an RF-opticallink that use an UMZ interferometer and a directly modulatedDFB LD. The calculations are valid for any regime of interfer-ence, coherent and incoherent.

We have also shown that FM of the optical field can be ex-ploited to generate microwave mixing by using an unbalancedinterferometer and a directly modulated LD. We take advantageof the conversion of FM of the LD into IM at the interferometeroutput. We have shown that a digital BPSK signal can be trans-mitted with up/down conversion of the microwave sub-carrier,and that the greater FM is, the more efficient the mixing power.

In this paper, the influence of FM on intensity noise conver-sion is demonstrated, and it is shown that the linewidth enhance-ment factor has a strong influence on the noise power measuredat the output of the unbalanced MZ interferometer.

A proper choice of the FM and of the subsequent FM mod-ulation index can reduce the noise conversion in self-delayedinterferometers. It has been shown that the greater FM is, thelower the noise spectral density is at the output of the interfer-ometer. Experimental confirmations are shown in this paper.


We can then conclude that FM modulation of a DFB LD al-lows better mixing power, as well as reduced noise at the inter-ferometer output.

The simulations shown here of NPSDs can be used to estimatethe laser phase-noise performance and dynamic range of opticaltwo-beam interferometer systems. These can be applied in op-tical radar signal processing where signal integrity is mandatory.

APPENDIX

The autocorrelation function is

(12)By using (5) and (12), and

, we obtain

(13)

The variations of term

are on a much bigger scale than those due to the term involvingas follows:

For this reason, the term including will be neglected.Also, by using

, can be written as

(14)

By using , (14) can be written as

(15)

By using a calculation of [19], we have

(16)

Also, we have

(17)

Equation (17) can be written as

(18)

We have

(19)


By using (18) and (19), we obtain

(20)

From (20), and using , we have

(21)

By using (16) and (21), we obtain

(22)

The fast PD used follows the fast variations of the signal, butcannot follow the variations of the phase of noise because thevariations of the phase of noise are very fast. Therefore, it isnecessary to consider the average only in part of the phase. From(15) and (22) (also the terms including , , and areneglected), the autocorrelation function can then be writtenas

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[8] J. Marti, F. Ramos, V. Polo, J. M. Fuster, and J. L. Corral, “Mil-limeter-wave signal generation and harmonic upconversion throughPM-IM conversion in chirped fiber grating,” Fiber Integrated Opt., vol.19, pp. 187–198, 2000.

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[10] Y. L. Guennec, B. Cabon, and G. Maury, “Conversions of the microwavesubcarriers of digital signals in optical links,” presented at the IEEELEOS Conf., San Diego, CA, Nov. 2001.

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[15] K. Petermann, Laser Diode Modulation and Noise. Tokyo, Japan:Tokyo Univ. Press, 1991.

[16] M. R. Salehi, B. Cabon, and Y. Leguennec, “Influence of chirp effectof DFB laser in phase-to-intensity noise conversion in RF-modulatedoptical links,” in IEEE MTT-S Int. Microwave Symp. Dig., June 8–13,2003, pp. 1371–1374.

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Mohammad Reza Salehi (S’02) was born inTehran, Iran. He received the B.Sc. degree inelectrical engineering from the Amirkabir Universityof Technology (Tehran Polytechnique), Tehran, Iran,in 1991, the M.Sc. degree in electrical engineeringfrom Shiraz University, Shiraz, Iran, in 1995, andis currently working toward the Ph.D. degree inoptics–opto-electronics–opto-microwaves at theInstitute of Microelectronics, Electromagnetism andPhotonics (IMEP) Laboratory, Grenoble, France.

His research interests include opto-electronics, mi-crowave photonics, quantum electronics, and optical systems.


Yannis Le Guennec was born in Le Havre, France,on May 20, 1977. He received the Engineer degreefrom the Grenoble National School for Physics,Grenoble, France, in 2000, and the Ph.D. degreefrom the National Polytechnics Institute of Grenoble(INPG), Grenoble, France, in 2003.

His research interests include microwave pho-tonics and digital signals.

Beatrice Cabon (S’93–M’95) received the Ph.D.degree in microelectronics from the Institut NationalPolytechnique de Grenoble (INPG), Grenoble,France, in 1986.

From 1986 to 1989, she held a post-doctoralposition with the National Center of Telecommu-nications, Grenoble, France. In 1989, she joinedthe INPG, where she is currently a Professor withthe Ecole Nationale Supérieure d’Electronique etRadioélectricité de Grenoble (ENSERG), NationalEngineering School in electronics/INPG. She

is Director of the RF–Microwave–Microwave/Photonics Research Group,Institute of Microelectronics, Electromagnetism, and Photonics (IMEP) ofthe INPG–Centre National de la Recherche Scientifique (CNRS). She hascontributed to over 180 technical publications in these areas. She edited fourbooks on microwave photonics and has authored several book chapters. Herresearch interests include microwave photonics, photonic microwave signalprocessing, and optical links for high bit-rate signals.

Prof. Cabon is a member of the IEEE Lasers and Electro-Optics Society(IEEE LEOS) and the IEEE Microwave Theory and Techniques Society (IEEEMTT-S). She is a member of the Technical Committee on Microwave Photonicsof the IEEE Microwave Theory and Techniques Society (IEEE MTT-S), IEEEMTT-3. She is member of the Technical Program Committee (TPC) of the IEEEInternational Topical Meeting on Microwave Photonics and the InternationalMicrocoll Conference. She was an expert for auditions for the European Com-mission for the programs ACTS and COPERNICUS in 1997. She was an expertfor auditions and evaluations for the program Information Society Technologies(IST) of the European Commission in 2002 and 2003. She was coordinator of thetwo European projects PROCOPE (1993–1996) and BALATON (1994–1997).She was the organizer of the international summer school on optics/microwavesinteractions (OMW) (1998–2000), which is funded by the Training MobilityResearch (TMR) Program of the European Commission and the IEEE MTT-S.Since 1999, she has been coordinator at the national French level of the Op-tics and Microwaves Club of the French Optical Society S.F.O. She is currentlycoordinator of a network of excellence IST-2001-32786 “NEFERTITI” on Mi-crowave Photonics with 28 European organizations from nine countries, whichis a project of the IST program funded by the European Commission.

signal and noise conversions in rf-modulated optical links

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