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4:15pm - 4:30pmSL8.3 Theory of enhanced AM -modulation bandwidth in Push-pull DFB lasersD. D. Marcenac, M.C.Nowel1 and J. E. CarrollUniversity Engineering Department, Trumpington Street, Cambridge CB2 lPZ, UK

Abstract:Push-pull modulation of a two contact, uniform DFB laser enables AM modulation bandwidl iswell beyond the conventional electron-photon resonance limit for single contact deviccs. Asmall signal analytic theory for this AM response is given.Introduction: Laser sources with small, or even negative, chirp, and high amplitude-niodul*I 1 onbandwidths are necessary for high-speed, long distance optical fibre telecommunication I inks .Directly modulated single contact DFB lasers are convenient sources for opticalcommunications, but suffer both from substantial chirping due to a non-zero l inewidllienhancement factor, and from a modulation bandwidth limited by the electron-photonresonance. The use of DFB lasers with external or integrated modulators is a natural way toreduce th e chirp over conventional, directly modulated DFBs. Another way is to use multi-contact DFB lasers in a push-pull modulation scheme: the total drive current to the dcvicc i skept constant, but amplitude modulation is provided by increasing the current into one end of t h cdevice, while simultaneously decreasing the drive current into the other end. As shown in FigurcI , transmission of a digital I could achieved with currents, say, (11,12)=(20,40)mA, whilc a0 requires (I 1,12)=(40,20)mA. The amplitude modulation is caused by a longitudinaldisplacement of optical power within the laser, due to the bending of the Bragg stopband underinhomogeneous current injection. As demonstrated experimentally [11, the symmetry of thcdevice means that both the I and 0 tates have the same wavelength, hence that chirp isreduced. Another striking property of push-pull modulation is the enhanced AM modulationbandwidth predicted by time domain dynamic modelling [2], the theory for which is presentedhere.

-u7nJl-=nJI1 + I2 + Iragg stopband

Figure 1 : (a) Push-pull modulation scheme; (b ) Displacement of the optical power by th e shifted Braggstopbands.Small signal AM rcsponsc: The AM response of conventionally modulated laser diodes i scharacterized by a resonance at the laser relaxation oscillation frequency, beyond which thcresponse drops at a rate of 20dB/decade. The relaxation oscillation frequency increases with thesquare root of the optical power. For push-pull modulation of a uniform DFB with 2nd order

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grating, the AM response is dramatically different, as shown in Figure 2(a). Indeed, simulationsusing a large signal travelling wave time domain model [3] reveal that: (A) a first cut-off appearsat frequency Fc, beyond which the response drops by lOdB/decade, which is followed (B )by aresonance at FR,and a subsequent 30dB/decade roll-off. FRdoes not vary with optical power, butis a function of the laser structure, whle Fc increases linearly with optical power.

IOo Frequency(Gk) 10(a)

3 d . FR=50GHzmcvznw06,+

10 Frequency (G k ) lo(b)Figure 2: (a) Magnitude of AM response for low and high bias drive currents D; (b) Response of opticalpower displacement over difference in carrier density in the two sections.Figure 2(b) shows the response of the difference in optical power in both halves of the laser AP,over the difference in mean carrier density AN in both sections of the laser: this response isindependent of optical power, and features a resonance at frequency FR, followed by a20dB/decade fall-off. The frequency FR depends on the laser structure, and is equal to theseparation between the (-1), lasing mode and the (-2) side mode. Since FRgoverns the ultimatemodulation speed of the laser, shorter cavities and weaker gratings, which result in a largermode spacing, are beneficial for ultra-fast modulation. Once the simple response of Fig. 2(b) isestablished for a given structure, an analytic theory for the full AM response of figure 2(a) iseasily derived, from rate equations linking the difference in carrier density AN, the difference inoptical power AP, and the difference in current injection AI=I1-12 in both sections.Summary: An analytic formula for the AM modulation response of push-pull DFB lasers isderived. Its predictions are that at high powers, the modulation bandwidth is limited by aresonance FR,dependent on the laser structure, and equal to the spacing between the lasingmode, and its closest side mode. This ultimate modulation bandwidth is typically between 20and 100 GHz for common DFB devices. At lower powers, a cut-off frequency Fc limits themodulation bandwidth. Fc increases linearly with optical power, and is larger in a laser withhigh linewidth enhancement factor, where a small difference in carrier density AN is moreeffective at displacing the optical power from the center of the device.References:[11 M.C.Nowel1, L.M.Zhang, J.E.Carrol1 and M.J.Fice. IEEE Photon. Tech. Lett. 5:1368-1371,1993.[2] M.C.Nowel1, L.M.Zhang, and J.E.Carrol1, Paper CWJ1, Proc. CLEO 94, Anaheim, CA,1994.[3] C.F.Tsang, D.D.Marcenac, J.E.Carrol1 and L.M.Zhang. IEE Proc Part-J. 141:11-17, 1994.

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