signal and noise conversions in rf-modulated optical links
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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
AbstractThe 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 TermsDirect modulation, distributed feedback (DFB)laser, intensity noise, interferometric systems, microwavephotonics mixing, optical links, phase noise.
THE semiconductor laser is one of the most important lightsources in fiber-optical and integrated optical systems .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 ,. 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 MachZehnder (MZ), can be limited byrandom phase fluctuations of the optical source emission field, .
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 .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, Electromagntisme et
Photonique, UMR CNRS 5130 Centre National de la Recherche Scientifique,Ecole Nationale Suprieure dElectronique et Radiolectricit de Grenoble,38016 Grenoble Cdex, France (e-mail: firstname.lastname@example.org; email@example.com;firstname.lastname@example.org).
Digital Object Identifier 10.1109/TMTT.2004.825733
then modulated by interferometers like MZ modulators , .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 MachZehnder (UMZ) can generatefrequency conversion of analog microwave subcarriers with orwithout digital modulation , , 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 ANINTERFEROMETER 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 .
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
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 
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 SchawlowTownes formula ,and is the linewidth enhancement factor introduced by Henry (also called the chirp factor) to explain the experimentalvalues reported by Fleming and Mooradian  , 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 , 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
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
which leads to s.
III. INFLUENCE OF CHIRP ON INTENSITY NOISE IN MICROWAVEMODULATED 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 
1304 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 52, NO. 4, APRIL 2004
where is a characteristic angular frequency depending on theLD and on its bias point. When is high enough, but lowerthan , is approximated to
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)] .The interference term can be written as
At quadrature operation of the interferometer, the autocorre-lation function of can be written as
(see the Appendix ).The NPSD can be calculated as
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 = 800MHz. (b) = 28, f = 50MHz. (c) = 140, f = 10MHz.
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 )