IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 10, NO. 12, DECEMBER 1998 1709 Spectral Shift and Broadening of DFB Lasers Under Direct Modulation Avi Zadok, Hamutal Shalom, Moshe Tur, Fellow, IEEE, W. D. Cornwell, and Ivan Andonovic, Senior Member, IEEE Abstract—The spectrum of DFB lasers, directly modulated at 144 and 622 Mb/s, is found to be considerably wider than the modulating random sequence rate. The broadening, which may be as high as ten times the data bandwidth, is accounted for by frequency changes (chirp) along each bit, incorporating a recently observed short time constant on the order of 10–20 ns. These changes will also introduce a few gigahertz spectral shifts as a function of the bit rate. Index Terms—Distributed-feedback lasers, optical communication, optical modulation/demodulation. I. INTRODUCTION T HE PRESENCE of dispersion in optical fibers requires the transmitting laser to have the narrowest possible optical spectrum under modulation conditions. However, even the most currently used single frequency source, the distributedfeedback (DFB) laser is spectrally broadened by direct modulation. Three main mechanisms are involved: 1) transient chirp, associated with the relaxation oscillations following a sudden current change , ; 2) adiabatic chirp, introduced by the effect of the injection current on the refractive index of the cavity –; and 3) a more slowly evolving thermal chirp, where the junction temperature affects both the refractive index and the cavity length, thus changing the optical frequency , . While the adiabatic chirp follows the instantaneous injection current, the thermal chirp maintains correspondence with the active region temperature. The various chirp mechanisms broaden the laser spectrum significantly beyond the original laser linewidth and the modulation bandwidth. Transient chirp could greatly increase the linewidth when modulation rates reach several gigabits per second , , though modern DFB’s display very little transient chirp at subgigahertz-per-second rates. Broadening due to adiabatic chirp would be dominant in many modulation schemes , . However, in digital modulation systems with high extinction ratios, its effect is negligible since “zero” bits carry almost no light, and the entire signal is characterized by a single current level. Commonly stated values for time constants associated with thermal chirp range from 150 ns to several milliseconds , –, suggesting that the optical spectrum of a digitally Manuscript received June 26, 1998. A. Zadok, H. Shalom, and M. Tur are with the Faculty of Engineering, Tel-Aviv University, Tel-Aviv, Israel. W. D. Cornwell and I. Andonovic is with the Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1XW, Scotland, U.K. Publisher Item Identifier S 1041-1135(98)08760-6. modulated laser at rates of several hundred megabits-persecond would be of the same order as the data rate, and will not be influenced by thermal chirp. In a recent experiment, however, chirp of five different DFB lasers was characterized using a high-resolution Mach–Zender interferometer, indicating for the first time the existence of much shorter chirp time constants, of the order of 10–20 ns . Such a short time constant may lead to considerable spectral broadening of directly modulated lasers, at bit rates as high as 622 Mb/s. Chirp also causes a shift of the central optical frequency, as a function of the bit rate. This letter examines the effect of the short time constant on the spectrum of a DFB laser, directly modulated by a random bit sequence. Section II presents simulation results, Section III displays the experimental results, and concluding remarks are given in Section IV. II. THEORY AND SIMULATION The impulse response of the thermal chirp is often stated different time constants, associated with the in terms of various elements of the laser structure , ,  (1) The step response of the thermal chirp would be of the same form. The instantaneous optical frequency of the laser can be obtained by applying an th-order digital filter, equivalent to (1), to the input current waveform. This procedure was taken ns and for a MQW laser that is best described by ns, with respective frequency shifts GHz/mA and GHz/mA. Fig. 1 shows the resulting instantaneous frequency for a 32-bit sequence at three different modulation rates: 5, 100, and 622 Mb/s. Zero bits are assumed to carry no light, and the modulation current is 20 mA. Fig. 1 suggests that thermal-like chirp should have two effects on the spectrum of a DFB laser under random-sequence will direct modulation. 1) The central optical frequency change with the bit rate. When the bit duration is longer than the chirp time constants, the optical frequency moves , resulting in a red shift of the toward average frequency. On the other hand, for bit rates much , no frequency shift is expected. 2) Chirp faster than broadens the spectrum of the modulated laser as the bit rate slows down. Since the frequency shift associated with the short 1041–1135/98$10.00 1998 IEEE 1710 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 10, NO. 12, DECEMBER 1998 TABLE I EXPERIMENTALLY DETERMINED IMPULSE RESPONSE PARAMETERS FOR THE CHIRP OF THE TWO TESTED LASERS Fig. 1. Simulated instantaneous optical frequency of a DFB laser along a direct modulation sequence, at bit rates of 5 Mb/s (dashed curve), 100 Mb/s (dotted curve) and 622 Mb/s (solid curve). The modulating sequence is displayed at the bottom of the figure. Modulation amplitude is 20 mA. (a) Fig. 2. Simulated optical spectrum for PRBS direct modulation, at bit rates of 100 Mb/s (dashed curve), 300 Mb/s (dotted curve), and 640 Mb/s (solid curve). Modulation current is 32 mA. time constants of 10–20 ns is on the order of 200 MHz/mA , chirp induced by a modulation current of 10–40 mA should dominate the spectral linewidth even when the bit rate is several hundred megabits per second. In order to calculate the resulting optical spectrum we express the complex field of the directly modulated laser as (2) is determined by the input modulation where the power is expressed as an integral sequence, and the phase calculated using (1). of the instantaneous frequency Phase noise and phase discontinuities when the laser is turned off are neglected. Therefore, the power spectral density of (2) incorporates the combined effect of both chirp and data sequence, and produces the overall optical spectrum induced by the specific direct modulation sequence. The obtained spectral density can be perceived as a convolution of the data AM spectrum and a related chirp induced FM term, and the overall linewidth is approximately the sum of the data rate and the width of chirp distribution. (b) Fig. 3. Simulated (solid curves) and experimental (dotted curves) spectra of DFB lasers, PRBS direct modulation. (a) DFB 1, 10 mA, 144 Mb/s. (b) DFB 2, 32 mA, 622 Mb/s. Spectral shifting and broadening is demonstrated in Fig. 2, where the optical spectrum of the same laser is simulated for a pseudorandom bit sequence (PRBS). The bit rates are 100, 300, and 600 Mb/s and the modulation current is 32 mA. The full-width at half-maximum (FWHM) is 4.8, 3.1, and 2.4 GHz, respectively, significantly broader than the data spectrum in all three cases. The optical spectrum is broadened and shifted by 1.4 GHz as the bit rate slows down from 600 to 100 Mb/s. The existence of short time constants suggests, therefore, that the spectrum of directly modulated lasers is both shifted and broadened by the nonadiabatic chirp, even for bit rates of several hundred megabits per second. ZADOK et al.: SPECTRAL SHIFT AND BROADENING OF DFB LASERS UNDER DIRECT MODULATION III. EXPERIMENT The spectrum of two directly modulated DFB lasers was measured under PRBS current modulation, using a scanning Fabry–Perot interferometer. The impulse responses of the tested lasers were previously determined experimentally in terms of (1) , and the response parameters are summarized in Table I. The two lasers were tested using two similar experimental setups. Due to equipment limitations, measurements over a wide range of bit rates could not be performed at either experiment. Fig. 3(a) shows the simulated and experimental spectra for Laser 1, at a bit rate of 144 Mb/s and modulation current of 10 mA. High-resolution interferometric measurements of the optical frequency verified the absence of transient chirp (the pulse rise and fall times were 2 ns). The effect of the nonsquare pulse shape on the resulting chirp was simulated and found to be negligible. The measured FWHM of 1.4 GHz is in very good agreement with the predicted value of 1.2 GHz, while the spectral width of the data sequence is of the order of only 70 MHz. Fig. 3(b) refers to Laser 2, the one used for Figs. 1 and 2, at 622 Mb/s and 32 mA modulation. Once again, the measured FWHM of 1.85 GHz agrees reasonably well with the simulated value of 2.4 GHz, although the overall spectrum is not as broad as expected. The obtained width is approximately three times larger than the data rate. Both experiments indicate that the spectral width of a DFB laser under direct modulation is dominated by thermal-like chirp, and is much broader than the data bandwidth even at bit rates up to 622 Mb/s. IV. CONCLUSION The existence of thermal-like chirp with a 10–20 ns short time constant is shown to be responsible for a significant spectral broadening of DFB lasers under direct digital modulation. This resulting optical spectrum is broader that the data bandwidth for bit rates of up to several hundred Mb/s. The whole output spectrum is also expected to shift by several gigahertz as a function of the bit rate. While this broadening has negligible effect on applications dominated by adiabatic chirp, such as frequency modulation in coherent communication , , –, it may greatly affect the performance of direct detection communication systems , . 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