APPLIED PHYSICS LETTERS
VOLUME 78, NUMBER 26
25 JUNE 2001
Fast modulation scheme for a two laterally coupled laser diode array G. Carpintero,a) H. Lamela, and M. Leone´s Grupo de Optoelectro´nica y Tecnologı´a La´ser, Universidad Carlos III de Madrid, Avenue de la Universidad, 30. 28911 Legane´s, Madrid, Spain
C. Simmendinger and O. Hess Theoretical Quantum Electronics, Institute for Technical Physics, DLR, D-70569 Stuttgart, Germany
共Received 29 November 2000; accepted for publication 20 April 2001兲 The present letter reports a modulation scheme that takes advantage of the unique characteristics of a two laterally coupled laser diode 共also known as twin stripe array兲 to overcome the limit on the modulation imposed by the laser’s relaxation oscillation frequency. Through the use of the rate equation description of the device we uncover the device dynamics behind the modulation scheme generating 35 ps 共full width at half maximum兲 laser pulses at 8 Gb/s modulation rate. Our scheme relies on the fast dynamics of the phase difference, controlled by means of the current injection on each stripe. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1378806兴
As light sources for optical fiber communications, semiconductor lasers present the unique ability to directly modulate their output by changing the device current. Therefore, the dynamic response of these lasers to current modulation has been extensively studied, with special attention to the small-signal modulation bandwidth, shown to be limited by the existence of a relaxation oscillation 共RO兲 frequency. Improved laser diodes achieve RO frequencies within the 20 GHz range.1 Further increases of the bandwidth in semiconductor lasers are expected from new structures, on which new modulation schemes can be applied. Among the structures of interest, we can point out multisection distributed feedback lasers and two laterally coupled laser diodes 共also known as twin stripe arrays兲. While in the first small signal bandwidths of 30 GHz have been demonstrated,2 a substantial improvement of the small-signal bandwidth was predicted under out-of-phase modulation of the twin stripe.3,4 However, optical fiber communications require short pulse generation at high repetition rates, which concern the large signal response of the device. Even though the small-signal bandwidth is considered as a reliable indicator of the large signal response, this can be complex due to the nonlinear properties of the device, limiting the maximum modulation frequencies. The present study describes a modulation scheme that takes advantage of the twin stripe dynamics to generate ultrashort intensity pulses at high repetition rates. The scheme is based upon the fast response of the phase difference between the fields in each stripe. We can briefly describe the twin stripe array as two laser diodes whose active regions are placed side by side with evanescent field coupling between them. As a result of the coupling, the device achieves a common global behavior, where just two spatial patterns are possible. Each pattern, or operating mode, provides for its own constant phase difference between the fields in the lasing stripes. A common approach to the device dynamics is to describe it through a set of rate equations.2,4 After a proper normalization, the set of a兲
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ordinary differential equations that account for the dynamics of the device are dn x ⫽ j x ⫺n x ⫺ 共 n x ⫺n t 兲 a 2x , d
共1a兲
with x⫽1,2,
冋
册
冋
册
da 1 A ⫽T 共 n 1 ⫺n th兲 a 1 ⫹k r a 2 cos共 兲 ⫺k i a 2 sin共 兲 , d 2 共1b兲 A da 2 ⫽T 共 n 2 ⫺n th兲 a 2 ⫹k r a 1 cos共 兲 ⫹k i a 1 sin共 兲 , d 2 共1c兲
冋
冉
冊
A a1 a2 d ⫽T ␣ 共 n 2 ⫺n 1 兲 ⫺k r ⫹ sin共 兲 d 2 a2 a1 ⫹k i
冉
冊
册
a1 a2 ⫺ cos共 兲 , a2 a1
共1d兲
where n 1 , n 2 , a 1 , and a 2 are, respectively, the carrier densities and field amplitudes within each stripe, the phase difference between the fields 共defined as 1 ⫺ 2 兲 and is the normalized time 共t⫽ n , with n ⫽2.4 ns兲. We assume that the stripes are independently addressable, being the normalized injection current in each stripe j 1 and j 2 . The other normalized parameters are the transparency level n t , the threshold carrier density n th , the linewidth enhancement factor ␣, the linear gain coefficient A, and the ratio between carrier lifetime over photon lifetime T. The complex coupling constant k⫽k r ⫹ik i models the evanescent coupling between emitters. Using standard values for the laser parameters 共as those in Ref. 4兲, we obtain T⬃1010, providing accuracy to the model even in the case that no carrier diffusion is included.5 Under symmetric bias current injection on both stripes ( j 1 ⫽ j 2 ), the system of equations has two steady-state solutions that correspond to the two possible modes of operation of a twin stripe laser array.3,5 One is the in-phase solution, for which a 1 ⫽a 2 ⫽a 0 , n 1 ⫽n 2 ⫽n 0 , and ⫽2 m 共with m an integer兲, while the other is the out-ofphase solution, for which a 1 ⫽a 2 ⫽a , n 1 ⫽n 2 ⫽n , and ⫽(2m⫹1) 共with m an integer兲. The scheme to generate
0003-6951/2001/78(26)/4097/3/$18.00 4097 © 2001 American Institute of Physics Downloaded 25 Jun 2001 to 129.247.143.154. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp
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Appl. Phys. Lett., Vol. 78, No. 26, 25 June 2001
optical pulses relies on two major properties of the device operating modes: 共a兲 one out of the two modes is preferred, and 共b兲 there exists a mechanism by which one can force the twin stripe array to leave the preferred mode of emission. To understand the origin of the mode preference, we must first realize that under a symmetric current injection 共where the equilibrium points predict equal carrier and field amplitudes on both stripes兲, the phase difference rate equation reduces to
冉
冊
a1 a2 d ⫽⫺Tk r ⫹ sin共 兲 . d a2 a1
共2兲
Equation 共2兲 provides opposite signs to the phase derivative for each operating mode, thus only one of them is stable against perturbations. The out-of-phase mode will be regained after a perturbation is applied as long as k r ⬍0, since the sign of the derivative in Eq. 共2兲 opposes that of the perturbation. Using this type of reasoning, one concludes that Eq. 共2兲 forces a lock on ⫽0 when k r ⬎0 and a lock on ⫽ when k r ⬍0. Previous analysis indicated that the twin stripe prefers the out-of-phase mode,3,5 in agreement with the experimental observations where a two-lobed far-field pattern is observed.6 For this reason, from this point we will assume k r ⬍0. Under this condition, and assuming symmetric current injection, a lock on ⫽ is achieved. Therefore, if the fields from each stripe are coherently combined 共as it happens when one detects on axis兲, these add up destructively and a null intensity at the output would then be collected. Note that so far only symmetric current injection was considered. On the other hand, the right-hand side of Eq. 共1d兲 shows that the phase difference exhibits carrier dependence. Therefore, the phase difference can be forced to leave the equilibrium value under symmetric injection by a nonsymmetric one, increasing when j 1 ⬍ j 2 and decreasing if j 1 ⬎ j 2 . As soon as the phase difference leaves the symmetric equilibrium value ( ⫽ ), the interference is not completely
FIG. 1. Time evolution of the phase difference between the emitters. For the sake of clarity, the current pattern has been introduced in the top of the figure, with a solid line for stripe S 1 and a dotted line for stripe S 2 .
destructive, leading to a nonzero output intensity, which is maximum as passes through 0. When the current returns again to its initial symmetric condition, the locking mechanism forces the system to a ⫽(2n⫹1) phase difference, where the interference is destructive. It is worth noting that the pulses are generated by a change in the phase difference, a variable that from the rate equation description we observe that evolves at the photon time scale. From this fact, we expect that this device can be used to generate short intensity pulses. This scheme has been verified by numerical integration of the twin stripe laser array model. The coupling constant has been shown to be one of the most critical parameters as it determines the stability of the device.3,5,7 In our normalized notation, where this constant is normalized by the photon lifetime 共2.5 ps兲, we used k r ⫽⫺0.09 and k i ⫽⫺0.08 for the real and imaginary parts, respectively. The signs of the coupling constant have been chosen to set the lock on the
FIG. 2. Optical intensity obtained when the fields between the two stripes are coherently combined. The change of the phase induced by the current produces pulses in the optical output. The inset represents the eye diagram when a pseudorandom pattern is applied at a 10 Gb ps rate.
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Carpintero et al.
Appl. Phys. Lett., Vol. 78, No. 26, 25 June 2001
FIG. 3. Pulses generated under two different (k r ,k i ) pairs: the dotted trace corresponds to (k r ,k i )⫽(⫺0.08,⫺0.09) and the thin trace to (k r ,k i ) ⫽(⫺0.05,⫺0.2).
out-of-phase solution. The device is biased, applying to each stripe equal currents at twice the threshold level. From the previous discussion, this symmetric current injection sets the device into its out-of-phase mode 共with the initial phase difference at ⫽ 兲. Over this rest point we now apply a train of pulses in the current, increasing the current in stripe 1 while at the same time the current injected in stripe 2 is decreased by the same amount, thus producing a temporarily asymmetric injection. Figure 1 represents the time evolution of the phase difference in response to such a current pulse train. It can be appreciated in Fig. 1 that while equal injection currents are applied to both emitters, the phase remains locked on a ⫽(2n⫹1) value, where destructive interference between the fields in the stripes is produced. When the current is pulsed, breaking the symmetry in the injection, the phase difference is no longer locked. As the asymmetry is produced by setting j 1 ⬎ j 2 , the phase difference decreases. The resulting pulses from the deviation of the phase from the destructive value can be appreciated in Fig. 2. The full width at half maximum 共FWHM兲 is 35 ps, while the repetition rate of the applied pulses is 8 GHz. The inset in Fig. 2 represents the device response, in the form of an eye diagram, to a pseudorandom sequence at 10 Gb/s rate, to demonstrate the potential use in fiber-optic communications.
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Previous studies demonstrated that the coupling constant determines the stability of the device.3,5 We now show that it also has a direct influence on the pulse generation. The uppermost trace in Fig. 3 presents the current on stripe 1, showing the applied current step. The response of the phase difference and combined intensity to the current pulse is given for two coupling pairs of values (k r ,k i ). While the dotted trace denotes the values used above, 共⫺0.09, ⫺0.08兲, the thin trace is the response for 共⫺0.05, ⫺0.2兲, with a reduction of the FWHM to 30 ps. This reduction is achieved at the expense of moving the system eigenvalues on the complex plane, thus changing the damping rates. This can be observed on the different extent on which the phase is affected by the current as well as on the ringing frequency, which is directly related to the coupling.3 In conclusion, this letter presents the basis for a modulation scheme for a two laterally coupled 共twin stripe兲 laser array. This technique produces short optical pulses, taking advantage of the fast dynamics of the phase difference between the emitters. Two mechanisms are involved: 共a兲 locking of the phase under symmetric current injection and 共b兲 forcing phase changes by asymmetric injection, both with time scales related to T. This study opens the way for the possible applications of these devices as part of the theoretical tasks under the frame of the FALCON European Network 共Contract No. ERB 4061 PL97-0131兲, where device fabrication and experimental characterization tasks are also being developed. We acknowledge support by the European Commissions TMR program through the Fast Lasers Collaboration Network project 共FALCON兲. 1
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