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A model for optimization of the performance of frequency-Modulated DFB semiconductor laser

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A model for optimization of the performance of frequency-Modulated DFB semiconductor laser
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  IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 41, NO. 4, APRIL 2005 473 A Model for Optimization of the Performance of Frequency-Modulated DFB Semiconductor Laser Xiaobo Xie, Jacob Khurgin, Fow-Sen Choa  , Senior Member, IEEE  , Xiuqin Yu, Jianxin Cai, Jingzhou Yan,Xiaoming Ji, Yonglin Gu, Yun Fang, Yang Sun, Guoyun Ru  , Student Member, IEEE  , and Zhibao Chen  Abstract— We have developed a model of frequency modulateddistributed feedback laser with intracavity phase modulator andhave shown that it can operate in two different regimes, only oneof which has good frequency-modulated (FM) response. We haveidentifiedthecombinationofthelaserparametersthatforceslaserto operate in high FM efficiency regime. The results of our initialexperiments support these conclusions.  Index Terms— Frequency modulation (FM), semiconductorlasers. I. I NTRODUCTION F REQUENCY-modulated (FM) semiconductor lasers havebeen regarded as promising source for optical communi-cation links [1] and microwave photonics systems [2]. For the semiconductor lasers, FM leads to the chirp-free operation andthe dynamic range larger than attainable with intensity modula-tion.AnumberofschemesforFMofsemiconductorlasershavebeen successfully implemented [3]. The most basic FM laserimplementation would be a Fabry–Perot laser with an intra-cavity index modulator, but this configuration suffers from theproblemofmultimodeoscillationand,therefore,notsuitableforthe FM operation. Composite cavity lasers [4] do achieve singlemode operation, yet are very difficult to fabricate with a highdegree of reproducibility. For this reason, the distributed Braggreflector (DBR) [5] and distributed feedback (DFB) [6] lasers have become the devices of choice for FM operation. WhileDBR and DFB structures are closely related, when it comes toFM operation, the DFB laser has a significant advantage: sincethe distributed reflector provides both gain and reflection, thephase-modulating section can occupy a relatively larger frac-tion of the cavity leading to higher FM efficiency.One frequently used technique of operating the DFB laser inan FM mode consists of modulating the density of injected in- jection carriers either within the main gain section or within aseparate dedicated passive section, usually referred as “phasesection” [7]. Although the index changes (and thus FM effi-ciency) attained by modulating the free carrierdensity are large, Manuscript received September 1, 2004; revised December 22, 2004. Thiswork was supported by the Defense Advanced Research Projects Agency underthe FLICS Project.X. Xie was with the Johns Hopkins University, Baltimore, MD 21218 USA.He is now with Science Systems & Applications Inc., Lanhan, MD 20706 USA(e-mail: xiexb@pha.jhu.edu).J. Khurgin is with Johns Hopkins University, Baltimore, MD 21218 USA.F.-S. Choa, X. Yu, J. Cai, J. Yan, X. Ji, Y. Gu, Y. Fang, Y. Sun, G. Ru,and Z. Chen are with the University of Maryland at Baltimore County, Balti-more, MD 21250 USA.Digital Object Identifier 10.1109/JQE.2005.844070 this method is not free from drawbacks. In a laser with a sepa-rate phase section the long lifetime of injected carriers limitedthe high frequency response to a few hundred megahertz. If thegain section itself is modulated the carrier lifetime is shortenedby stimulated emission and the bandwidth approaches tens of gigahertz. But the frequency modulation in this scheme is in-evitably accompanied by the spurious intensity modulation. Inaddition this configuration suffers from FM thermal dip whenoperated at lower frequencies [8].Toavoidtheaforementionedproblems,anothertechniquehasbeen successfully used [9]. The phase section consists of theelectrooptic modulator in which the index change is caused bythe electric field. Since no carriers are present the bandwidth islimitedbytheusualcombinationofRCconstantandtransittime[1] and for a small modulator can reach into tens of GHz. Fur-thermore, absence of the injected carriers usually means lowerinsertion loss. The most suitable phase modulator in this con-figuration is the quantum-confined Stark effect (QCSE) modu-lator operated well below the exciton peak [10]. Such devicescan provide strong index modulation, relatively low insertionloss and high speed [11], [12]. Furthermore, since the only dif- ference between the QCSE modulator and the gain section isslightly higher absorption edge in the former, both sections canbe grown simultaneously using selective growth epitaxy [13].As mentioned above, DFB structure is introduced in the FMlaser to assure that the device operates at a single longitudinalmode, i.e., has high side-mode suppression ratio (SMSR).Making the distributed feedback strong usually attains this goalbut in the process it also “locks” the operating frequency andmakes changing it difficult. Both the frequency sweep and FMefficiency suffer as a result. Clearly, the sets of parameters thatlead to high SMSR, low threshold, and high FM efficiencyare not the same. The objective of this paper is to provide aguideline for designing the DFB FM laser with the best combi-nation of the aforementioned characteristics. This guideline isdeveloped following rigorous theoretical analysis of the DFBlaser and subsequent computer simulations.II. B ASIC  E QUATIONS AND  D ERIVATION OF  FM E FFICIENCY AtypicalDFBFMlaserdesignisshowninFig.1andconsistsof the DFB gain section and phase section of length andrespectively with the cleaved facets of reflectivities and .There is also a small reflectivity at the plane of interface be-tween the gain and phase sections. The DFB gain section [14] ischaracterized by the grating period , grating’s coupling coeffi-cient , refractive index , and the gain coefficient , the latter 0018-9197/$20.00 © 2005 IEEE  474 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 41, NO. 4, APRIL 2005 Fig. 1. Schematic drawing of a DFB FM laser with phase modulatormodulated by applied RF voltages. being a function of the cavity electron density . The mod-ulator section is characterized by the effective index that isvariedbytheappliedreversedbiasvoltage ,andbytheabsorp-tion coefficient that is unfortunately also varied with appliedvoltage. This phenomenon, as shown further along, leads to theundesirableeffectofspuriousintensitymodulation[15].Aswillbecome clear further in this work, it is that extinction loss in thephase section that can become the key factor determining FMefficiency.In our model, we combine the round trip loss in the phasesection with the transmission loss at the facet and define aseffective reflectivity of the phase section. The oscillation condi-tion for the laser follows from the fact that the round trip overthelasercavityshouldleavethecomplexamplitudeofthesignalunchanged(1)where(2)(3)are the reflectivities in the section interface plane for the lightpropagating respectively to the left and right. In (3), isso-called confinement factors [16] in modulator section andin (2) is the phase delay when looking from the modulator side.The effective DFB grating reflection and transmission in thepresence of gain are [16](4)(5)where is effective detuning and. One can now differentiate (1) and split it into theamplitude and phase equations with the help of (2) and (3).(6)and(7)where is the frequency of laser oscillating mode.Equation (6) describesspurious intensitymodulation that canbe minimized by operating away from the exciton peak in highqualityquantumwells (QWs).Inrecent work [12],largechangeof refractive index V has been re-ported with negligible change in absorption. The chirp factorof has been measured. Large chirpfactor in the modulation section combined with the large differ-ential gain in the DFB section lets us neglect the spurious mod-ulation of current density and decouple (6) and (7) to obtain theexpression for the FM efficiency(8)where is defined as effective length of DFB structure(9)III. P RELIMINARY  A NALYSIS It is clear from (8) that the FM efficiency is directly pro-portional to the ratio of modulator length to the effective lasercavity length. The most straightforward path leading to higherefficiency is by increasing the phase section length, yet it alsoincreases the insertion loss and reduces the free spectral range(FSR) of the cavity. Smaller FSR not only makes single longitu-dinal mode lasing more difficult to achieve, but also reduces themaximum frequency swing. Clearly the best way of achievinghighFMefficiencyliesinoptimizationofDFBpartthatcanpro-duce a combination of low threshold and small effective length.This should involve not just optimizing the grating strength andlength but also position of the oscillating frequency of the laserrelative to the Bragg frequency of the DFB.Theneedforoptimizationbecomesevidentonceoneanalyzesthe DFB dispersion curves presented in Fig. 2. Fig. 2(a) showsthe dependence of the amplitude of DFB reflectivity on thedetuning from the center, or Bragg frequency,(normalized with respect to the total DFB section length )at different values of coupling strength and gain coefficient.Fig. 2(b) shows the same dependence for the effective lengthof the DFB section (also normalized with respect to ).According to Fig. 2(a) amplitude of the DFB reflec-tivity (i.e., overall DFB section gain) grows with increase of thegain coefficient and rises dramatically at the edges of gratingreflection spectrum, where the lasing modes of pure (i.e., withno additional phase shift) DFB lasers are known to be located[17]. Unfortunately, according to Fig. 2(b), the effective lengthexperiences sharp rise in precisely the same frequencyrange. The increase in , that can be intuitively understoodfrom the Kramers–Kronig relation between gain and dispersion[18], becomes more dramatic for stronger (higher ) gratings.Thus, operating close to the pure DFB mode frequencies willalways result in the poor FM efficiency. The minimum of ef-fective length (i.e., the region of high FM efficiency) is located  XIE  et al. : A MODEL FOR OPTIMIZATION OF THE PERFORMANCE OF FREQUENCY-MODULATED DFB SEMICONDUCTOR LASER 475 Fig. 2. (a) DFB section reflectivity versus frequency. (b) Ratio of effectivelength to the grating length versus frequency at different grating couplingstrength      0.5 or 2.5 and gain      0 and 0.5. near the Bragg frequency that can never be a lasing mode forthe pure DFB laser [14]. Thus, in a good FM laser the phasesection must provide phase shift that would “pull” the operatingfrequency closer to the Bragg frequency. Simply adjusting theoptical length of the phase section [ in (3)] is not sufficientto assure the shift of the lasing frequency away from the pureDFB mode—the effective facet reflectivity must be madeadequately high.One can reason along the following lines. If the effective re-flectivity is low, which can be either due to low facet re-flectivity or, more likely, due to large loss in the phase section,it is most advantageous (i.e., results in the lowest threshold)for the laser to have the majority of its photons confined in-side the DFB section. The frequency of this mode, which weshall refer to as “quasi-DFB” (QDFB), stays largely unaffectedby the index variations in the phase section and the FM effi-ciency is low. However, as the effective facet reflectivity in-creases and becomes comparable to the grating strength, morephotons tend to penetrate into the phase section to take advan-tage of stronger feedback. Now the oscillating frequency can beaffectedbyindexchangesinthephasesection.ThishighFM-ef-ficiency mode can be thought of as a mode in a DBR laser [19]with gain inside the reflector itself, and we shall refer to it as an“active DBR” (ADBR) mode. One can always “force” the laserto operate in theADBR modeby reducing the coupling strength, but going too far along this path may make the threshold toohigh—thus a careful optimization process is needed.IV. N UMERICAL  M ODELING To gain an insight of the main factors affecting FM efficiencyatfirstweshallconsiderthemostbasicDFBFMlaserhavingnoreflectivity at the boundaries of the DFB region .This configuration does in fact closely resembles the one en-countered in practical DFB-FM laser since the DFB-phase in-terface has inherently low reflectivity and the DFB facet reflec-tivity should be low for efficient out coupling of radiation.As discussed before, we consider as an effective reflec-tivity that includes the loss of modulator section and could betunedeitherbycoatingopticallayeronfacetorapplyingvoltageon the top of modulator.Firstweturnourattentiontotheissueoftuningthefrequencyof the FM laser toward the Bragg frequency. In the ordinarysingle-mode DFB this is accomplished by a 90-degree-phaseshift near the center of DFB structure[14]. In the composite FMlaser, one can achieve the required shift by applying dc bias tothe phase section, thus changing its effective dc phase shift .To understand how that shift is accomplished, one should notethat according to (1) when the laser operates in a continuous-wave(CW)modebothrealandimaginarypartsoffunctionare equal to zero. The plots of and asfunction of frequency are shown in Fig. 3 for four different laserconfigurations. The coupling strength of the DFB section in allcases is assumed to be , and the effective reflectivityisequalto0inthecaseFig.3(a)andequalto0.8inthecasesof Fig. 3(b)–(d). In the calculation, we chose both the gratingand modulator length equal to 300 m. To obtain the curves wehave varied the tuning frequency and increased gain until thefirst point where the real and imaginary part of is zerocomes out.The two curves in Fig. 3(a) have obvious characteristicsof a pure DFB laser—two degenerate modes at the edges of high reflectivity region of the grating. When the feedback [20]is introduced in Figs. 3(b)–(d), this degeneracygets broken by the additional phase delay . The degree towhich the degeneracy is broken increases with increase inand reaches its maximum at (Fig. 3(d)),and at this point the frequency of the lasing mode becomesexactly equal to the Bragg frequency. This result is, of course,not surprising and can be simply understood as phase sectionproviding the necessary shift to compensate for the 90 shiftintroduced by grating operating at the Bragg frequency asfollows from (4).Numerical analysis done so far confirms the fact that by bi-asing the phase section one can always obtain a nondegeneratemode at the Bragg frequency, but it does not ensure that thismode has the lowest threshold of all possible modes and is actu-ally the oscillating one. To locate the lasing mode we have usedthesearchstrategydescribedin[21]toobtaincomplexsolutionsof (1). In this method, a 3 3 grid covering a narrow region inthe complex phase-gain plane is used to obtain trial solutions of (1). If a minimum value of is detected at the center of grid, the size of the grid gets shrunk before the next iteration isperformed. Otherwise, the center of grid is moved toward theminimum point. We used initial values given by the Fig. 3 inorder to avoid local minima.As a result of the search, for each value of the phase shiftand effective reflectivity of the phase section one can findthe frequency and gain coefficient at the threshold. We use twohorizontal scales for the frequency—the lower scale is normal-ized to the grating length, and the upper scale provides an ex-ample for a grating length of 300 m. These values are plottedin Fig. 4 in a family of curves, one for each value of . Twosolid squares in Fig. 4 correspond to the locations and threshold  476 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 41, NO. 4, APRIL 2005 Fig. 3. Real and imaginary parts of    0     . (a) Pure DFB laser. (b) DFB FM laser with phase modulator at different phase shift      . (c)    . (d)        . gain coefficients of the pure DFB laser and thus serve as impor-tant reference points.Clearly, depending on the value of there exists two dif-ferent regimes of oscillation. At high there exists only onemodehavingrelativelylowthresholdgaincoefficientandwhosefrequency can be varied around the Bragg frequency withinlarge limits by changing the phase delay in the phase section.This is precisely the desired ADBR mode that we described inSection III.For smaller effective reflectivities, however, there exist twogroups of relatively high threshold solutions whose frequenciesare localized near the pure DFB frequencies and whose tuningrange is relativelynarrow. These are of course theQDFB modesthat one must try to avoid, thus it is important to determine thecritical effective reflectivity at which the transition from theADBR to QDFB mode takes place.In the example of Fig. 4, for the coupling strengththe critical reflectivity was found to be as shownby solid triangles in the figure. At this value of , the oscil-lation takes place simultaneously at three different modes—oneADBRandtwoQDFBmodes.Ofcourse,thecriticalreflectivityis a function of grating coupling strength and we shall explorethisdependenceinthenextsection.Priortodoingthis,however,we shall investigate the FM efficiency and SMSR at differenteffective modulator facet reflectivities for the same grating cou-pling strength.In Fig. 5 the FM efficiency calculated according to (8) isplottedversustheoperatingcenterfrequencyfordifferentvaluesof effective reflectivity . In these calculations, the gratinglength and the modulator length are assumed to be equal, the Fig. 4. Lasing thresholds and operating frequencies of the two-section FMlasers.TwodegeneratemodesofthepureDFBlaserwithsamecouplingstrengthare also shown. The upper frequency scale assumes grating length of 300    m. grating coupling strength, as before, is , the effectiveindex change is V [12], and the modu-latorconfinementfactoris .Itshouldbenotedthatbyoperatingcloser totheexcitonic peak theeffectiveindexchangeand thus FM efficiency can be easily enhanced by as much asan order of magnitude, but only at the expense of having spu-rious IM. In this paper, however, we are not concerned with the  XIE  et al. : A MODEL FOR OPTIMIZATION OF THE PERFORMANCE OF FREQUENCY-MODULATED DFB SEMICONDUCTOR LASER 477 Fig. 5. FM efficiency     GHzV   at different lasing frequency andfacet reflectivities as the modulator length varies. “material”componentoftheFMefficiencyandconcentrateonlyon the comparative FM efficiencies of different laser designs.These comparative results will not be affected if the absoluteFM efficiency is scaled up or down by choosing different oper-ating wavelength.As expected, the FM curves split into two families—for, i.e., in the ADBR mode both FM efficiency andFM range are relatively large, while for , i.e., in theQDFB mode the operating frequency remains “pinned” andboth FM efficiency and FM range are significantly smaller.At the same time, within each family, the curves for differents lay very close to each other, indicating that once the laseris forced to operate in a given mode its FM efficiency almostremains unaffected by the effective reflectivity of the externalcavity. The FM efficiency however does depend on the valueof the center frequency—thus the response of FM laser has anonlinear component that limits its dynamic range [22]. Fortu-nately, when the phase section is prebiased to operate at exactlythe Bragg frequency the FM efficiency changes are symmetric,thus only the odd order nonlinearities will be present in theresponse.In Fig. 6, the SMSR—a function of operating center fre-quency—is plotted for the same set of parameters as in theprevious figure. The SMSR is evaluated according to [16, Eqs.(3.75) and (3.77)], where we assume a typical laser operatingcurrent around 3.3 times threshold current. Solid curves in thefigure represent the SMSR of the FM laser operating in anADBR regime, while the dashed curves represent the SMSRwhen the laser is in the QDFB regime. As one can see, theSMSR reaches its maximal values in the middle of either of two operating ranges and decreases near the boundary betweentwo operating ranges, i.e., close to the point of mode hopping.The relations between the SMSR and the effective reflectivityexhibit opposite trends in two operating modes. In theADBR regime the SMSR improves with increase of , Fig. 6. SMSR versus operating frequencies of the two-section FM laser atdifferent facet reflectivities and modulator lengths. while in the QDFB regime the SMSR actually gets worse asgrows. The SMSR reaches its minimum near the criticaleffective reflectivity, i.e., near the mode hopping. This is easyto understand since it is well known that both DFR and DFBlasers are capable of single-mode oscillation and having theeffective reflectivity either much larger or much lower than thecritical one will ensure that the two-section FM laser is solidlyin one of these modes.V. L IMITATIONS AND  T RADEOFFS Numerical results presented in Figs. 4–6 indicate that a com-bination of low threshold, high FM efficiency and SMSR in thetwo-sectionFMlaseroccurswhenitoperatessquarelyintheac-tive DBR mode and has relatively long phasesection. Long phase section, however, is expected to have highlossthusreducingtheeffectivereflectivity .Topreventlaserfrom switching into the QDFB mode the grating strength willthen have to be reduced and that will increase the threshold.Thus, necessary tradeoffs will have to be made.These tradeoffs and critical roles played by the effective re-flectivityisevidentfromFig.7.Fourvariablesareplottedversusthe DFB coupling strength. One is the critical reflectivity andtheotherthreearethemainFMcharacteristics:frequencysweeprange , FM efficiency, and the threshold gain . [To avoidcrowdingtheaxesthefirsttwocurvesareplottedinFig.7(a)andtwo others in Fig. 7(b)]. As in the previous graphs, the FM pa-rameters are given both in units of grating FSR and in ab-soluteunitsfor m.Theeffectivereflectivityatwhichthese characteristics are calculated for each coupling strength istaken to be slightly above the critical reflectivity for this cou-pling strength .At first glance, it appears that the way to better FM laser liesin increasing the DFB coupling strength since threshold is re-duced while the FM range and efficiency are increased, as thecoupling gets stronger. However, increasing the DFB strength
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