PTL- z/zl/ Self-Sustained Ultrafast Pulsation in Coupled VCSELs C.Z. Ning* Computational Quantum Optoelectronics, NASA Ames Research Center Mail Stop T27A-1, Moffett Field, CA 9,1035-1000 Abstract High frequency, narrow-band self-pulsating operation is demonstrated in two coupled vertical-cavity surface-emitting lasers (VCSELs). The coupled VCSELs provide an ideal source for high-repetition rate (over 40 GHz), sinusoidal-like modulated laser source with Gaussian-like near- and far-field profiles. We also show that the frequency of the modulation can be tuned by the inter-VCSEL separation or by DC-bias level. Index terms: surface-emitting lasers; optical modulation; millimeter wave modulation; self-pulsing lasers; ultrafast optics. *email: [email protected] High repetition-rate optical signal generationis important for a numberof applications [1], including narrow-banddata transmissions[2], high bit-rate optical time-devisionmul- tiplexing (OTDM) technologyfor telecommunications[3-5], and millimeter-waveoptics [6]. Due to typical long carrier lifetime in a standard diode laser, wheredirect current modu- lation is limited to modulation frequencyof up to 20GHz, other meansof generationhave to be pursuedfor higherfrequencysources. Typically suchlasersourcesare provided by multi-sectionedge-emittinglasers,suchasself-pulsatingDFB lasers[7]or otherpassiveand active Q-switching lasers.It is well-knownthat vertical-cavity surface-emittinglasers(VC- SELs) havemany advantagesoveredge-emitting lasers,similar high modulation frequency VCSEL sourcesshouldbeof great interestsfor the abovementionedapplications. In arecentpaper[8],weshowedthat, byputting twoVCSELsin closeproximity, ultrafast directional beamswitchingcan be achieved due to inter-VCSEL coupling. In this paper, we further explore this coupled VCSEL system for the purpose of generating narrow-band high- repetition optical signal. To demonstrate this scheme, we performed a.numerical simulation. Our numerical simulation shows that this coupled VCSEL system is ideal for producing Gaussian-like near- and far-field profiles that are modulated in a sinusoidal fashion at a repetition rate over 40 GHz. Furthermore the repetition rate can be tuned by adjusting inter- VCSEL separation or DC-bias level. We believe that such VCSELs sources are potentially useful to replace similar edge-emitting sources in some of the applications mentioned at the beginning. Our simulation begins with the effective Bloch equations(EBEs) [9], which have been used recently to simulate transverse mode dynamics in VCSELs [10]. The model consists of three coupled equations describing diffraction of laser field, carrier diffusion in the transverse plane, and optical gain and refractive index dynamics represented by an effective polarization Pl: ng OE i 2 iKF c 0t- = _--_V±E- RE + 2-_0eb(P0 + P1), (1) -O-F&1- = ...........+......i[ao- _I(N)]] P, - ieogb_i-_-(f)E .................. (2) o.'¢ (z,y) - V±D.vVIN - _tnN + + Ot e .LF + z_-[(P0 + P,)*E - (Po + P1)E*] (3) where P0 = eoebXo(N)E. The variables and parameters are defined as follows: E is the slowly time-varying complex amplitude of the laser field and N is the 2D carrier density. Po and P1 are complex polarizations of the semiconductor medium induced by the laser field. ng and nb are group and phase refractive index of the unexcited semiconductor, c is the speed of light and _0 is the dielectric constant, all of the vacuum. K : 2zcnb/A is the optical wave-vector in the medium, where A is the wavelength. 7,_ is the carrier decay rate. _ is the loss due to cavity transmission and background absorption. It is related to the corresponding decay rate _ through _ = _ng/c. The value of _ is taken as 0.52 per picosecond. The V± represents spatial derivatives with respect to x and y, which are transverse to the propagation direction. 80 is the detuning between the reference and bandgap frequencies. The diffusion constant is taken as D,v = 20cm2/s and the carrier decay constant is ,assumed a value of one inverse nanosecond. The cavity length L is one half of the wavelength. Gain confinement is represented by the space-dependent current profile J(x, y), which also defines locations of VCSELs. The rest of parameters and the construction of the model equations are given in detail elsewhere [8,9]. The numerical scheme has been described in the past [8,10]. As an example, the sim- ulation is performed for gain-guided VCSELs of 5.6 microns in diameter with edge-to-edge separation of 0.6, 0.8, Or 1.0 microns. Fig.1 shows snapshots of laser near- (bottom) and far-field (top) intensity profiles for the case of 0.8 micron separation, where a cross-section of the intensity profile along the x-axis (or 0,-axis) is shown. The two profiles are repre- sentative of the coupled VCSEL Case considered in this paper. The VCSELs are DC-biased equally and slightly above the threshold of the individual lasers. If the two lasers operate independently without coupling, both are stable at their fundamental mode. However, the mutual proximity gives rise to the oscillatory behavior due to gain coupling, as indicated by ........................................................................ the density profile in the bottom part. The two profiles show moments in time when one 3 of the lobesdominates. In general,the situation is somewherebetweenthe cases shown. Therefore, when either near or far field measurements ate made with respect to one of the two lobes, one observes a fundamental-mode-like lobe with its intensity oscillating in time. The frequency of this oscillation is around 42 GHz for this specific case, as we will discuss in more detail in the following. In short, what we have is a Gaussian-like near or far field lobe whose intensity oscillates at over 40 GHz. To study the effects of inter-VCSEL separation, we considered three values for the edge- to-edge separation. The bottom part of Fig.2 shows power spectra for these cases, where near-field intensity from one of the lasers is taken. As we pointed out [8], the spectral response becomes diminished, if the total output from both lasers are taken due to spatial averaging. As we see in the figure, the peak frequencies decrease from 45, 41.5, to 38 GHz as we increase the separation from 0.6, 0.8 to 1.0 #m. This is easy to understand. As we pointed out, the oscillation is due to inter-VCSEL coupling. As the separation increases, the coupling strength decreases, and thus the oscillation frequency..This property gives us an important design flexibility to tune modulation frequency by adjusting the inter-VCSEL separation. However, it seems unlikely to increase the coupling any further by decreasing the separation much smaller than 0.6. Additional coupling mechanisms, such as antiguiding coupling as demonstrated recently for VCSEL arrays [11,12], are needed to increase the coupling strength further if higher frequency modulation is desired. Another factor affecting the modulation response is the DC bias level. In the upper part of Fig.2, we compare power spectra at two DC bias levels. The dashed curve corresponds to the near-threshold case as in Fig.1. The solid curve is the power spectrum at bias level 50 percent higher. As a result, the peak frequency shifts by 1 GHz. The reason for this shift is again the increase of coupling between the two lasers due to increased overlap between the two carrier density profiles. In the cases studied so far, both lasers are DC-biased. The oscillation behavior described above is an example of self-pulsating behavior, seen in lasers with saturable absorber, also known as passive Q-switching. In the following, we consider the effects of current modulation on the pulsating behavior..-ksanexample,weconsiderthe casein Fig.l., but nowwith an extra .-kCbiasto oneof the lasers.Wevary the AC modulation frequencyfrom 1GHzto 50 GHzasindicatedby the squaresignsin Fig.3, wherethe responseoflaserintensity ofoneof the lasersasa function of modulation frequencyis shown.The sinusoidalAC amplitude is 1percentof the DC level. Thereareafew featuresworth mentioning! First, the little peak at 3.5GHz is the well-knownrelaxationoscillation (RO) frequencyof the individual lasers. The peakaround 12GHz is what webelieveto be the RO frequencyof the joint system. This needsto beelaboratedin somedetail: The systemwestudy hereissomewherebetween acaseof two independentlasersandacaseof onebig laserformedby mergingthe two. As aresult, both the individuality andthecollectivity showup in the spectralresponse.Dueto the reducedabsorptionin the overlaparea,the bigjoint laseriseffectivelypumpedfarther awayfrom its thresholdandthushaslargerrelaxation oscillationfrequency.A third feature ofthe responsecurveis the highestpeakaround42GHz,which ismorethan 15dB stronger than the responsearound RO frequency.This peakcorrespondsto the self-pulsation (SP) frequency. The nearand far-field of eachindividual laserschangeat this frequency. The two sidebandsaround the highest peak correspondto beatingsbetweenthe SP and RO frequencies. It is known that frequencylockingoccursif aself-pulsatinglaseris modulated with an AC currents. This is demonstratedin Fig.4, wherewe plot time seriesof the integrated intensity overboth lasers(upper trace with smaller amplitude) and thoseof the intensity of oneof lasers(lower trace with large amplitude). All the parametersarethe sameasin Fig.l, except that the DC biasis increasedby 50percentand a AC modulating current is addedwith an amplitude that is 30 percentof the DC level. In all three casesshownin Fig.4(a), (b), and(c), wechoosetostart from thesameinitial conditions,theonly difference bctweenthemis themodulation frequency.Without modulation (a),weseeboth tracesshow strong modulation at the relaxationoscillation frequencyaround 5 GHzin addition to the SP frequencyat 42.5GHz. In Fig.(b) where wemodulate at 45GHz, the slowmodulation around 5GHz is somewhatdiminished, but the small modulation still persists. However, when we apply a modulation at the SP frequency as in Fig.(c), the slow modulation at RO frequencydiesout very quickly within 1 ns. The systemis quickly lockedto the SP frequency,with asinusoidal-liketemporal waveform. In summary, we havedemonstrateda new approachto generateultrafast modulation at a rate muchhigher than the typical RO limited frequency. Weinvestigatedthe effects of inter-VCSEL separationand the DC biason the generationof suchsources.The study indicatesseveralwaysto tune themodulation frequencyandto maximizeit whennecessary. The ultrafast sourceswe proposedherehavea few advantagesover existing sources. As VCSELs,suchsourceshaveautomatically allthe advantagesofregularVCSELs. In addition, the individual laserintensity showsa Gaussian-likedistribution for both the nearfield and farfield. Finally the temporal waveformofmodulation pattern issinusoidal.Webelievethat suchVCSELsourcesareimportant for manyof the applicationsmentionedat the begirming of the paper. ACKNOWLEDGMENT The authorthanksPeterGoorjianfor thecomputercodethat wasusedforthesimulation ofthis work. 6 FIGURE CAPTIONS Fig.l: Snapshots of the near- (bottom) and far- (top) field intensity at two different moments in time showing the Gaussian-like lobes in both near and far fields. Dotted line at the bottom shows an example of the carrier density profile. Both lasers are DC biased slightly above threshold. Fig.2 Power spectra of one of two lasers under DC bias showing comparison between different DC bias levels (top) and different inter-VCSEL distances (bottom). Fig.3 Modulation response under sinusoidal modulation with amplitude 1 percent of the DC bias which is slightly above threshold. The inter-VCSEL separation is 0.8 microns. Inset shows an expanded view of the lower frequency range around the relaxation oscillation frequency. Fig.4 Time traces of the total intensity (upper trace in each figure with small amplitude) and that of the intensity of one of the two lasers (lower trace with large amplitude) for three modulation frequencies 0 GHz (a), 45 GHz (b), and 42.5 GHz (c). :Intensity of individual VCSELs shows a sinusoidal-like temporal waveform at the SP frequency. 7 [1] T. Hoshida, H. Liu, M.Tsuchiya, Y. Ogawa, T. Kamiya, "Subharmonic hybrid mode-locking of a monolithic semiconductor laser", IEEE J. Selected Topics in Quant. Electron., 2, 514(1996) [2] R. Nagarajan, S. Levy, A. Mar, and J. Bowers, "Resonantly enhanced semiconductor lasers for efficient transmission of millimeter wave modulated light", IEEE Photon. Tech. Lett., 5, 4(1993) [3] R. Barry et al, "All-Optical Network Consortium-Ultrafast TDM Networks", IEEE J. Selected Areas in Communications. 14, 999(1996) [4] D.M. Spirit, A Ellis, and P. Barnsley, "Optical Time Devision Multiplexing: Systems and Networks", IEEE Communications Mag., December, 56(1994) [5] U.Feiste, D. As, and A. Ehrhardt, "18 GHz All-Optical Frequency Locking and Clock Recovery Using a Self-Pulsating Two-Section DFB-Lasers",IEEE Photon. Tech: Lett., 6, 106(1994) [6] A. Daryoush, "Optical synchronization of millimeter-wave oscillators for distributed architec- tures", IEEE Trans. Microwave Tech., 38, 467(1990) [7] M. Moehrle, U. Feiste, J. Hoerer, R. Molt, and B. Sartorius, " Gigahertz Self-Pulsations in 1.5 #m Wavelength Multisection DFB Lasers", IEEE Photon. Tech. Lett., 4, 976(1992) [8] C.Z. Ning and P. Goorjian, "Ultrafast directional beam switching in coupled VCSELs', (sub- mitted to Applied Physics Letters) [9] C.Z. Ning, R.A. Indik, J.V. Moloney, "Effective Bloch Equations for Semiconductor Lasers and Amplifiers", IEEE J. Quant. Electr., 33, pp. 1543-1550, (1997) [I0] C.Z. Ning and P.M. Goorjian, in Feature Issue on "Spatial and Polarization Dynamics of Semiconductor Lasers",eds. G.P.Agrawal, C.Z. Ning, and M. San Miguel, J. Opt. Soc. Am., - BI6, 2072(1999) .................................... 8 [i1] D.K. Serkland,K.D. Choquette,G.R.Hadley,K.M. Geib,andA. Allerman, "Two-element phased array of antiguided vertical-cavity lasers", Appl. Phys. Lett., 75, 3754(1999) [12] D. Zhou and L.J. Mawst, "Two-dimensional phased-locked antiguided vertical-cavity surface- emitting laser arrays", Appl. Phys. Lett., 7'/, 2307(2000) 9 Near-Field Intensity Far-Field Intensity ,o_o_ , _i 011"-_ ''I_''1C,O _ 01 _t',.{. ° ' ' ' ° ' ' _" © ° :: t "--I" ,", I _ I , ! , ! , "--i" ! I ! I I / 0 0 _J