Pattern dependence in high-speed Q-modulated distributed feedback laser Hongli Zhu, Yimin Xia, and Jian-Jun He* State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou 310027, China *[email protected]
Abstract: We investigate the pattern dependence in high speed Q-modulated distributed feedback laser based on its complete physical structure and material properties. The structure parameters of the gain section as well as the modulation and phase sections are all taken into account in the simulations based on an integrated traveling wave model. Using this model, we show that an example Q-modulated DFB laser can achieve an extinction ratio of 6.8dB with a jitter of 4.7ps and a peak intensity fluctuation of less than 15% for 40Gbps RZ modulation signal. The simulation method is proved very useful for the complex laser structure design and high speed performance optimization, as well as for providing physical insight of the operation mechanism. ©2015 Optical Society of America OCIS codes: (140.5960) Semiconductor lasers; (250.5300) Photonic integrated circuits.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
M. Marciniak, “Next generation networking in transparent optical networks-Challenges and opportunities,” Proc. 8th Int. Conf. Laser Fiber-Optical Networks Modeling, 76–79 (2006). K. Takagi, S. Shirai, Y. Tasuoka, C. Watatani, T. Ota, T. Aoyagi, and E. Omura, “120oC 10 Gb/s uncooled direct modulated 1.3um AlGaInAs MQW DFB laser diodes,” IEEE Photon. Technol. Lett. 16(11), 2415–2417 (2004). C. W. Chow, C. S. Wong, and H. K. Tsang, “Reduction of amplitude transients and BER of direct modulation laser using birefringent fiber loop,” IEEE Photon. Technol. Lett. 17(3), 693–695 (2005). M. Suzuki, Y. Noda, H. Tanaka, S. Akiba, Y. Kushiro, and H. Isshiki, “Monolithic integration of InGaAsP/InP distributed feedback laser and electroabsorption modulator by vapor phase epitaxy,” J. Lightwave Technol. 5(9), 1277–1285 (1987). J.-J. He, “Proposal for Q-modulated semiconductor laser,” IEEE Photon. Technol. Lett. 19(5), 285–287 (2007). D. Liu, L. Wang, and J.-J. He, “Rate equation analysis of high speed Q-modulated semiconductor laser,” J. Lightwave Technol. 28(21), 3128–3135 (2010). P. Vankwikelberge, G. Morthier, and R. Baets, “CLADISS-A longitudinal multimode model for the analysis of the static dynamic and stochastic behavior of diode laser with distributed feedback,” IEEE J. Quantum Electron. 26(10), 1728–1741 (1990). L. M. Zhang, J. E. Carroll, and C. Tsang, “Dynamic response of the gain coupled DFB laser,” IEEE J. Quantum Electron. 29(6), 1722–1727 (1993). J. E. Carroll, J. Whiteaway, and D. Plumb, Distributed Feedback Semiconductor Lasers (IET, 1998). X. Li, A. D. Sadovnikov, W. P. Huang, and T. Makino, “A physics-based three-dimensional model for distributed feedback laser diodes,” IEEE J. Quantum Electron. 34(9), 1545–1553 (1993). J. Zhi, H. Zhu, D. Liu, L. Wang, and J.-J. He, “Travelling wave analysis on high-speed performance of Qmodulated distributed feedback laser,” Opt. Express 20(3), 2277–2289 (2012). G. P. Li, T. Makino, and H. Lu, “Simulation and interpretation of longitudinal-mode behavior in partly gaincoupled InGaAsP/InP multi-quantum-well DFB lasers,” IEEE Photon. Technol. Lett. 5(4), 386–389 (1993). X. Li, Optoelectronic Devices: Design, Modeling, and Simulation (Cambridge University Press, 2009). D. F. Gallagher, “Design and simulation of widely tunable lasers using a time domain travelling wave model,” Proc. SPIE 5722, 465–476 (2005). D. F. G. Gallagher, Optoelectronic Devices: Advanced Simulation and Analysis (Springer, 2005).
1. Introduction High-speed, low-chirp, low power consumption semiconductor lasers and modulators are important components for next generation optical networks [1]. Although directly modulated laser (DML) is widely used for its simplicity [2, 3], it has limitation on modulation speed and wavelength chirp. An external Mach-Zehnder modulator (MZM) based on LiNbO3 has
#235454 - $15.00 USD © 2015 OSA
Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11887
excellent performance in high speed modulation with low chirp, but it is difficult to be integrated with lasers in the same chip. Electro-absorption modulator (EAM) is convenient to be integrated with a semiconductor laser, but it has a compromise on bandwidth and chirp [4]. Besides, MZM and EAM both have inherent energy loss for the dissipation or absorption of light in the OFF state. A novel structure of semiconductor distributed feedback (DFB) laser based on Q-modulation mechanism was recently proposed, which has advantages of highspeed, low-chirp and low power consumption [5]. Compared to directly modulated lasers, the Q-modulated laser (QML) has a stronger relaxation oscillation, which can produce a stronger pattern dependence. Therefore, the optimization of the structural parameters and operation conditions is very important to reduce the pattern dependent effects, particularly the ON state signal fluctuations and time jitters. An accurate theoretical model and analysis on the high speed performance of the complex Qmodulated distributed feedback laser are therefore needed. The high speed performance of the QML has been modeled and simulated by rate equation analysis [6]. However, the rate equation analysis is a zero-dimension approximation which completely ignores the light traveling time in the laser structure. It therefore cannot produce accurate results at high bit rate. Traveling wave method has been widely used for the time and longitudinal dimension analysis in DFB lasers [7–10]. However, the models have only been established for the analysis of single section DFB laser with a uniform grating. The Q-modulated DFB laser comprises three sections separated by deeply etched trenches: the gain, the Q-modulator and the phase sections [5]. The theoretical formulation and modeling in such a non-periodical structure using the traveling wave method become very complex. To simplify the modeling, the previous traveling wave analysis for the QML only considers the light traveling time in the gain section, while the reflectivity change caused by the absorption change in the modulation section is considered instantaneous [11]. This simplification cannot take into account the time delay caused by the wave traveling in the phase and modulation sections of the QML. Since the delay caused by the traveling time in the modulation and phase sections can affect the response speed and pattern dependent modulation properties, a physical model that considers the full device structure and material parameters are needed to provide more accurate and reliable simulation of the device performance. In this paper, we present a physical model of the QML based on the whole laser structure and material properties for the performance simulation. The theoretical model is first described in detail in Section 2. The simulation results for an example design of the QML are presented and discussed in Section 3. The pattern dependent properties of the QML are analyzed, both in terms of the ON state signal fluctuation and time jitter. Finally the conclusions are drawn in Section 4. 2. Laser structure and theoretical model The device structure of a Q-modulated DFB laser is schematically shown in Fig. 1. It consists of three sections. On the right hand side, a gain section with a forward bias is used to provide a suitable optical gain for lasing. On the left hand side, a modulation section with a reverse bias electrode, placed between two deep etched trenches, is used to change the back reflectivity of the DFB, leading to a change of the Q value and the threshold current of the laser. Between the two sections, a phase section is used to adjust the reflective phase at the section interface X, as seen from the gain section, to form a constructive interference with the distributed feedback mechanism. The grating is etched on the active layer to form a partially gain-coupled DFB for a stable single longitudinal mode lasing [12]. Although the gratings in the phase and modulation sections are unnecessary, it is convenient to embed a uniform grating in the whole structure for fabrication simplicity. The deep etched trench-1 near the phase section is filled with silicon nitride, a commonly used high index dielectric material with a refractive index of 2.0, so as to enhance the variation of the back reflectivity, which results in a large modulation depth and high extinction ratio (ER). The whole structure, including not only the gain section, but also the phase and modulation sections, is simulated by the following method based on the traveling wave model.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11888
Fig. 1. Schematic structure of the Q-modulated DFB laser
The optical wave in the DFB structure can be written as: E ( z , t ) = F ( z , t )e− j β0 z + R( z , t )e j β0 z e jω0t
(1)
where β 0 is the effective propagation constant, ω0 is the angular frequency, F ( z , t ) and R ( z , t ) are the forward and backward waves propagating along the longitudinal z direction, respectively. According to the coupled mode theory, the propagating waves satisfy the following equations [13]: 1 ∂ ∂ 1 1 + F ( z , t ) = Γg ( z , t ) − α ( z ) + jδ + jk0 ΓΔn( z , t ) F ( z , t ) + jκ R ( z , t ) + sF 2 2 vg ∂t ∂z (2)
1 ∂ ∂ 1 1 − R ( z , t ) = Γg ( z , t ) − α ( z ) + jδ + jk0 ΓΔn( z , t ) R ( z , t ) + jκ F ( z , t ) + sR 2 2 vg ∂t ∂z (3)
where vg is the group velocity, Γ is the confinement factor, g ( z , t ) is the optical gain defined by Eq. (4), Δn( z , t ) is the variation of refractive index defined by Eq. (5), α ( z ) is the waveguide loss, δ is the detuning factor defined by Eq. (7), k0 is the wave vector in vacuum, κ is the coupling coefficient defined by Eq. (8), sF and sR are the spontaneous noises coupled into the forward and backward waves, respectively [14, 15]. Considering the wavelength dependence and saturation, the optical gain spectrum can be modeled by a Lorentian curve: g ( z, t ) =
g N [ N ( z , t ) − N tr ] 1 + ε P( z, t )
1 1 + τ p (ω − ω p ) 2 2
(4)
where g N is the differential gain, N is the carrier density defined by Eq. (6), N tr is the transparent carrier density, ε is the gain compression coefficient, P is the photon density, 2
2
and P = F + R , τ p is the curvature of the gain peak [15], ω p is the angular frequency of the gain peak.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11889
For different types of bias in the gain, phase and modulation sections, the variation of the refractive index can be written as: α H λ0 − 4π g N [ N ( z , t ) − N ( z , 0)] , for forward bias Δn( z , t ) = − α H λ0 [α (V ) − α (0) ] , for reverse bias loss loss 4π
(5)
where α H is the line enhancement factor, λ0 is the reference wavelength in vacuum, α loss (0) and α loss (V ) are the waveguide losses at reverse bias voltages of 0 and V. Additionally, with the consideration of the lateral diffusion, the carrier density can be written as ∂N ( z , x, t ) I ∂ 2 N ( z, x, t ) (6) = − AN ( z, x, t ) − BN 2 ( z , x, t ) − CN 3 ( z , x, t ) − vg g ( z , t ) P ( z , t ) − DN ∂t eVg ∂2 x
where I is the injection current, e is the electron charge, Vg is the volume of active region, DN is the lateral diffusion coefficient of carrier, A, B, and C are the nonradiative recombination coefficient, bimolecular recombination coefficient, and auger recombination coefficient, respectively. The detuning factor is expressed as:
δ = β0 −
π Λ
(7)
where Λ is the pitch of the grating. The coupling coefficient κ of the DFB can be written as:
κ=
k 0 Δn G g −j c 2 2
(8)
where Gc is the gain coupling coefficient, and g is the average gain of the grating section. In order to solve the wave equations, we also need the boundary conditions as follows F i ( z ', t ) T11i T12i F i ( z , t ) i = i i i R ( z ', t ) T21 T22 R ( z , t )
(9)
where F i ( z ', t ) and B i ( z ', t ) denote the forward and backward waves at the left hand side of the interface i, F i ( z, t ) and Bi ( z, t ) denote the forward and backward waves at the right hand side of the interface i, with i being a letter corresponding to the section interfaces A, B, C, D, E, and X. T jki represent the transfer matrix of the interface i, and can be obtained from the scattering matrix
T=
1 1 S 21 S11
− S22 − det S
(10)
where the scattering matrix S is a set of reflective and refractive coefficients at each boundary interface, and can be calculated as shown in Table 1.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11890
Table 1. Scattering matrix elements for boundary conditions at each interface ( n fill is the refractive index of the filling medium in trench-1) Interface
S11 = − S22
S12 = S21 = 1 − S112
A
rf
1 − rf2
B
( n fill − neff ) / (n fill + neff )
2 n fill neff / (n fill + neff )
C
( neff − n fill ) / (neff + n fill )
2 neff n fill / (neff + n fill )
D
(1 − neff ) / (1 + neff )
2 neff / (1 + neff )
E
(neff − 1) / ( neff + 1)
2 neff / (neff + 1)
X
0
1
Then, the output power and frequency chirp at the interface A can be obtained as follow: F = Pout
dwvg hc0 Γλ Δf =
F ( z A , t ) 2 − R( z A , t ) 2
(11)
1 ∂Φ F ( z A , t ) ∂t 2π
(12)
Where h is the Planck constant, c0 is the speed of light in vacuum, d and w are the thickness and width of the active layer, and Φ F is the phase of the forward wave. Applying the above traveling wave equations and boundary conditions to the whole laser structure, we can obtain the wave solutions in time domain. By discretizing the differential equations into difference equations, numerical simulations can be performed by computer. 3. Numerical simulation results and discussions
The parameters for the example laser structure are given in Table 2. Table 2. Parameters used in the numerical simulations. Symb ol
Parameter
Value
Symbol
Parameter
Value
λ0
Center wavelength
1552(nm)
h
Planck constant
6.63e-34(Js)
Λ
Grating pitch Effective index of grating Effective index of filling medium Length of gain waveguide Length of phase waveguide Length of modulator waveguide Width of deep etched trench-1 Width of deep etched trench-2 Width of waveguide
241.2(nm) 3.2174 2.0
c0 e A
3e8(ms−1) 1.6e-19(C) 1e8(s−1)
1000 Λ
B
25( μm )
C
101λ0 / 4neff
gN
Light speed in vacuum Electron charge Nonradiative recombination coefficient Bimolecular recombination coefficient Auger recombination coefficient Differential gain coefficient
1.65e-16(cm2)
5λ0 / 4n fill
Ntr
Transparent carrier density
1e18(cm−3)
3λ0 / 4
β sp
2e-5
2.5( μm )
K
Spontaneous coupling coefficient Peterman’s coefficient Nonlinear gain coefficient Linewidth enhancement factor Absorption coefficient at reverse bias 0(ON state)
9e-17(cm3) 3
Absorption coefficient at reverse bias V (OFF state)
2000(cm−1)
neff nfill Lg Lp Lm Wtr1 Wtr2 w
Γ
Confinement factor Thickness of active layer
0.15 44(nm)
ε αH
rf
Reflective coefficient of facet-A
1e-3
α loss (0)
vg
Group velocity
c0/neff
α loss (V )
d
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1e-10(cm3s−1) 7e-29(cm6s−1)
1
0(cm−1)
Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11891
The widths of the two deep etched trenches are designed with an odd integer multiple of quarter wavelength to facilitate the fabrication. The width of trench-2 is 1.16 micron, which is 3 times of quarter wavelength in air. Trench-1 is filled with high refractive index medium (silicon nitride) for increasing the reflectivity change. Its width is designed to be 0.97 micron, which is 5 times of the quarter wavelength in silicon nitride. In the main example, the length of the modulator wave guide is about 12.19 micron, which is about 101 times of the quarter wavelength in the waveguide. They form an anti-resonant cavity as a rear reflector of the laser, which is the key feature of the Q-modulated DFB laser. Figure 2 gives the reflectivity and reflective phase of the rear reflector calculated by the traveling wave method. Considering a center wavelength of 1552nm, the modulator has two states: ON state when its absorption coefficient is 0, and OFF state when its absorption coefficient is 2000cm−1. The reflectivity changes from 0.82 to 0.27, and the reflective phase changes from 8.9 degree to 9.0 degree. These results are consistent with the results of the previous work by using the transfer matrix method [5,6].
Fig. 2. Reflectivity (a) and reflective phase (b) of the rear reflector calculated by the traveling wave method.
Since both the DFB grating and the rear reflector provide feedbacks to the laser cavity, a phase section is needed to adjust the phase to produce a constructive interference between the two feedback mechanisms. The phase section can therefore influence the threshold current. In the previous work [5, 7],the phase section was simplified by a phase value, which cannot take into account the propagation time in the phase section, and is therefore not suitable for more accurate physical modeling of the Q-modulated DFB laser. In order to be able to adjust the phase over the full range between 0 and 2π, the phase section needs to have a certain length so that the required current injection is not too large. We have chosen the length to be 25μm in our design example. Figure 3 shows the relationship between the reflective phase change at the interface-X and the injection current of the phase section. We can see that a variation of 360°of the reflective phase can be achieved with a phase section current variation from 0 to 90 mA. The phase variations are almost identical for the ON and OFF modulator states.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11892
Fig. 3. Reflective phase variation at the interface-X versus the phase section current.
Figure 4 shows the threshold current of the gain section versus the phase section current for both the ON and OFF modulator states. We can see that a maximum threshold difference occurs when the phase section current is about 6mA. This condition also produces the lowest threshold at the ON state and highest threshold for the OFF state. In principle, under this optimal bias condition of the phase section, by setting the gain section current to 80mA, which is the threshold current corresponding to the modulator OFF state, the laser can be switched off with a high extinction ratio. However, as we will see from the dynamic simulation below, this gain section current value is not the optimal operating point when the pattern-dependent signal fluctuations and the time jitter are considered.
Fig. 4. Threshold current of the gain section versus the phase section current.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11893
For the dynamic simulations, we apply a 40Gbps return-to-zero (RZ) voltage signal to the modulator section, leading to a variation of absorption coefficient between 0 and 2000 cm−1.The input reverse-biased signal is shown in Fig. 5(a). The Q-modulated output power is first simulated with the gain section current biased at 80mA, as shown in Fig. 5(b).The extinction ratio (ER) is calculated by the ratio between the average ON state peak power to the average OFF state minimum power, and is about 10.2dB in this case. Although the ER is high, there is a strong pattern dependence which results in large ON state power fluctuations. The peak fluctuation is calculated by the ratio between the standard deviation of ON state peak power to the average ON state peak power, and is about 35% in this case. By increasing the gain section current to 140mA, the ON state power fluctuation is significantly reduced to 15%, although the ER is also reduced to 6.8dB, as shown in Fig. 5(c).
Fig. 5. Input 40Gbps RZ signal (a),output power at gain section current of 80mA(b) and output power at gain section current of 140mA (c).The phase section current is set at6mA.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11894
In Figs. 5(b) and 5(c), we have also plotted the variation of the average carrier density in the gain section. We can see that when a signal “1” pulse is emitted, the carrier density drops. When there are consecutive “0”s, the carrier density keeps increasing. This indicates that during the OFF period, the energy from the continuous current injection in the gain section is stored in the laser cavity as excited-state electron-hole pairs. The energy is then released during the ON periods. Unlike external modulators such as electro-absorption modulators and Mach-Zehnder modulators where the light is first emitted then absorbed or dissipated in the OFF state, the QML emits no or little light but store the energy in the OFF state. It is therefore much more energy efficient. On the other hand, as we can see from Fig. 5(c), the variation of the carrier density is only a small fraction of the time averaged carrier density (less than 10%), the wavelength chirp caused by carrier density variation is much smaller compared to directly modulated laser. The eye diagrams have also been simulated for different gain section currents from 80mA to 150 mA, as shown in Fig. 6. Although the ER is high when the gain section current is 80mA, the jitter, the overshoot and undershoot of output power in the eye diagram are rather poor as shown in Fig. 6(a). The jitter is about 11.4ps, which is caused by the pattern dependent time delay of the output power with respect to the input signal. The averaged output power levels in both the ON and OFF states are shown as a red dash lines in each graph of Fig. 6. As the gain section current increases, the OFF state output power increases, which causes the ER to decrease. At the same time, the ON state output power increases, and the rise and fall times decrease, which result in lower pattern dependent ON state output power fluctuation, as well as smaller jitter. Table 3 gives the variations of the ER, peak power and jitter with the gain section current. The variation of the ER and jitter are plotted in Fig. 7. Clearly, there is a compromise between the ER and the jitter. The decrease of the jitter and peak fluctuation becomes saturated at the gain section current of 140mA. Therefore, this appears to be an optimal point for overall performance. The extinction ratio is 6.8dB and the jitter is 4.7ps, while the peak fluctuation is about 15%.
Fig. 6. Eye diagrams for different gain section currents of 80mA (a), 90mA (b), 100mA (c), 110mA (d), 120mA (e), 130mA (f), 140mA (g), 150mA (h)
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11895
Table 3. Extinction ratio, peak fluctuation and jitter versus the gain section current. Gain current (mA) Jitter (ps) Peak fluctuation ER(dB)
80
90
100
110
120
130
140
150
11.4 35%
9.6 30%
6.4 23%
5.6 18%
4.9 16%
4.8 16%
4.7 15%
4.7 15%
10.2
8.7
8.1
7.9
7.4
7.1
6.8
6.6
Fig. 7. Variation of the ER and jitter versus the gain section current.
We have also considered the cases where the modulator length is increased to about 25μm, 50μm and 100μm, to analyze the effect of the modulator length on the high speed performance while the product αL of the absorption and length is kept constant. The increased length reduces the requirement on the absorption coefficient in the OFF state, and also reduces the effect of the absorption saturation. Figure 8 shows the variation of the extinction ratio with the modulator length when the gain section current is 130mA. The ER decreases from 7.1dB to 6.4dB when the modulator length increases from 12μm to 100μm. For modulator length up to 100μm, the quality of the eye diagrams remains almost the same.
Fig. 8. Variation of the ER with modulator length.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11896
4. Conclusions
In conclusion, we have investigated the pattern dependence of a complex Q-modulated DFB laser under high-speed modulation based on an integrated traveling wave analysis with full device structure and material properties. The high speed performance of the QML is simulated with the consideration of time delays caused by the wave traveling in the modulation and phase sections, as well as in the gain section. The simulation method is proved very useful for the QML structure design and performance optimization, as well as for providing physical insight of the operation mechanism. Through an example device structure, we have shown that 40Gbps RZ modulation can be achieved with well open eye diagrams. The gain section current needs to be biased well above the OFF state threshold to achieve good performance. An extinction ratio of 6.8dB with a low jitter of 4.7ps and low peak fluctuation of 15% were obtained, which are sufficient for many applications. Little degradation is observed when the modulator length is increased to 100μm. Unlike external modulators such as electro-absorption modulators and Mach-Zehnder modulators where the light is first emitted then absorbed or dissipated in the OFF state, the QML emits no or little light in the OFF state and stores the energy in the form of increased carrier density to be released in the ON state. It is therefore much more energy efficient. This advantage, combined with the ability of high speed modulation, makes it an excellent candidate for optical interconnects in high-performance computers and data center networks. Acknowledgements
This work was supported by the National Natural Science Foundation of China (grant No. 61377038) and the National High-Tech R&D Program of China (grant No. 2013AA014401).
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11897
Abstract: We investigate the pattern dependence in high speed Q-modulated distributed feedback laser based on its complete physical structure and material properties. The structure parameters of the gain section as well as the modulation and phase sections are all taken into account in the simulations based on an integrated traveling wave model. Using this model, we show that an example Q-modulated DFB laser can achieve an extinction ratio of 6.8dB with a jitter of 4.7ps and a peak intensity fluctuation of less than 15% for 40Gbps RZ modulation signal. The simulation method is proved very useful for the complex laser structure design and high speed performance optimization, as well as for providing physical insight of the operation mechanism. ©2015 Optical Society of America OCIS codes: (140.5960) Semiconductor lasers; (250.5300) Photonic integrated circuits.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
M. Marciniak, “Next generation networking in transparent optical networks-Challenges and opportunities,” Proc. 8th Int. Conf. Laser Fiber-Optical Networks Modeling, 76–79 (2006). K. Takagi, S. Shirai, Y. Tasuoka, C. Watatani, T. Ota, T. Aoyagi, and E. Omura, “120oC 10 Gb/s uncooled direct modulated 1.3um AlGaInAs MQW DFB laser diodes,” IEEE Photon. Technol. Lett. 16(11), 2415–2417 (2004). C. W. Chow, C. S. Wong, and H. K. Tsang, “Reduction of amplitude transients and BER of direct modulation laser using birefringent fiber loop,” IEEE Photon. Technol. Lett. 17(3), 693–695 (2005). M. Suzuki, Y. Noda, H. Tanaka, S. Akiba, Y. Kushiro, and H. Isshiki, “Monolithic integration of InGaAsP/InP distributed feedback laser and electroabsorption modulator by vapor phase epitaxy,” J. Lightwave Technol. 5(9), 1277–1285 (1987). J.-J. He, “Proposal for Q-modulated semiconductor laser,” IEEE Photon. Technol. Lett. 19(5), 285–287 (2007). D. Liu, L. Wang, and J.-J. He, “Rate equation analysis of high speed Q-modulated semiconductor laser,” J. Lightwave Technol. 28(21), 3128–3135 (2010). P. Vankwikelberge, G. Morthier, and R. Baets, “CLADISS-A longitudinal multimode model for the analysis of the static dynamic and stochastic behavior of diode laser with distributed feedback,” IEEE J. Quantum Electron. 26(10), 1728–1741 (1990). L. M. Zhang, J. E. Carroll, and C. Tsang, “Dynamic response of the gain coupled DFB laser,” IEEE J. Quantum Electron. 29(6), 1722–1727 (1993). J. E. Carroll, J. Whiteaway, and D. Plumb, Distributed Feedback Semiconductor Lasers (IET, 1998). X. Li, A. D. Sadovnikov, W. P. Huang, and T. Makino, “A physics-based three-dimensional model for distributed feedback laser diodes,” IEEE J. Quantum Electron. 34(9), 1545–1553 (1993). J. Zhi, H. Zhu, D. Liu, L. Wang, and J.-J. He, “Travelling wave analysis on high-speed performance of Qmodulated distributed feedback laser,” Opt. Express 20(3), 2277–2289 (2012). G. P. Li, T. Makino, and H. Lu, “Simulation and interpretation of longitudinal-mode behavior in partly gaincoupled InGaAsP/InP multi-quantum-well DFB lasers,” IEEE Photon. Technol. Lett. 5(4), 386–389 (1993). X. Li, Optoelectronic Devices: Design, Modeling, and Simulation (Cambridge University Press, 2009). D. F. Gallagher, “Design and simulation of widely tunable lasers using a time domain travelling wave model,” Proc. SPIE 5722, 465–476 (2005). D. F. G. Gallagher, Optoelectronic Devices: Advanced Simulation and Analysis (Springer, 2005).
1. Introduction High-speed, low-chirp, low power consumption semiconductor lasers and modulators are important components for next generation optical networks [1]. Although directly modulated laser (DML) is widely used for its simplicity [2, 3], it has limitation on modulation speed and wavelength chirp. An external Mach-Zehnder modulator (MZM) based on LiNbO3 has
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11887
excellent performance in high speed modulation with low chirp, but it is difficult to be integrated with lasers in the same chip. Electro-absorption modulator (EAM) is convenient to be integrated with a semiconductor laser, but it has a compromise on bandwidth and chirp [4]. Besides, MZM and EAM both have inherent energy loss for the dissipation or absorption of light in the OFF state. A novel structure of semiconductor distributed feedback (DFB) laser based on Q-modulation mechanism was recently proposed, which has advantages of highspeed, low-chirp and low power consumption [5]. Compared to directly modulated lasers, the Q-modulated laser (QML) has a stronger relaxation oscillation, which can produce a stronger pattern dependence. Therefore, the optimization of the structural parameters and operation conditions is very important to reduce the pattern dependent effects, particularly the ON state signal fluctuations and time jitters. An accurate theoretical model and analysis on the high speed performance of the complex Qmodulated distributed feedback laser are therefore needed. The high speed performance of the QML has been modeled and simulated by rate equation analysis [6]. However, the rate equation analysis is a zero-dimension approximation which completely ignores the light traveling time in the laser structure. It therefore cannot produce accurate results at high bit rate. Traveling wave method has been widely used for the time and longitudinal dimension analysis in DFB lasers [7–10]. However, the models have only been established for the analysis of single section DFB laser with a uniform grating. The Q-modulated DFB laser comprises three sections separated by deeply etched trenches: the gain, the Q-modulator and the phase sections [5]. The theoretical formulation and modeling in such a non-periodical structure using the traveling wave method become very complex. To simplify the modeling, the previous traveling wave analysis for the QML only considers the light traveling time in the gain section, while the reflectivity change caused by the absorption change in the modulation section is considered instantaneous [11]. This simplification cannot take into account the time delay caused by the wave traveling in the phase and modulation sections of the QML. Since the delay caused by the traveling time in the modulation and phase sections can affect the response speed and pattern dependent modulation properties, a physical model that considers the full device structure and material parameters are needed to provide more accurate and reliable simulation of the device performance. In this paper, we present a physical model of the QML based on the whole laser structure and material properties for the performance simulation. The theoretical model is first described in detail in Section 2. The simulation results for an example design of the QML are presented and discussed in Section 3. The pattern dependent properties of the QML are analyzed, both in terms of the ON state signal fluctuation and time jitter. Finally the conclusions are drawn in Section 4. 2. Laser structure and theoretical model The device structure of a Q-modulated DFB laser is schematically shown in Fig. 1. It consists of three sections. On the right hand side, a gain section with a forward bias is used to provide a suitable optical gain for lasing. On the left hand side, a modulation section with a reverse bias electrode, placed between two deep etched trenches, is used to change the back reflectivity of the DFB, leading to a change of the Q value and the threshold current of the laser. Between the two sections, a phase section is used to adjust the reflective phase at the section interface X, as seen from the gain section, to form a constructive interference with the distributed feedback mechanism. The grating is etched on the active layer to form a partially gain-coupled DFB for a stable single longitudinal mode lasing [12]. Although the gratings in the phase and modulation sections are unnecessary, it is convenient to embed a uniform grating in the whole structure for fabrication simplicity. The deep etched trench-1 near the phase section is filled with silicon nitride, a commonly used high index dielectric material with a refractive index of 2.0, so as to enhance the variation of the back reflectivity, which results in a large modulation depth and high extinction ratio (ER). The whole structure, including not only the gain section, but also the phase and modulation sections, is simulated by the following method based on the traveling wave model.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11888
Fig. 1. Schematic structure of the Q-modulated DFB laser
The optical wave in the DFB structure can be written as: E ( z , t ) = F ( z , t )e− j β0 z + R( z , t )e j β0 z e jω0t
(1)
where β 0 is the effective propagation constant, ω0 is the angular frequency, F ( z , t ) and R ( z , t ) are the forward and backward waves propagating along the longitudinal z direction, respectively. According to the coupled mode theory, the propagating waves satisfy the following equations [13]: 1 ∂ ∂ 1 1 + F ( z , t ) = Γg ( z , t ) − α ( z ) + jδ + jk0 ΓΔn( z , t ) F ( z , t ) + jκ R ( z , t ) + sF 2 2 vg ∂t ∂z (2)
1 ∂ ∂ 1 1 − R ( z , t ) = Γg ( z , t ) − α ( z ) + jδ + jk0 ΓΔn( z , t ) R ( z , t ) + jκ F ( z , t ) + sR 2 2 vg ∂t ∂z (3)
where vg is the group velocity, Γ is the confinement factor, g ( z , t ) is the optical gain defined by Eq. (4), Δn( z , t ) is the variation of refractive index defined by Eq. (5), α ( z ) is the waveguide loss, δ is the detuning factor defined by Eq. (7), k0 is the wave vector in vacuum, κ is the coupling coefficient defined by Eq. (8), sF and sR are the spontaneous noises coupled into the forward and backward waves, respectively [14, 15]. Considering the wavelength dependence and saturation, the optical gain spectrum can be modeled by a Lorentian curve: g ( z, t ) =
g N [ N ( z , t ) − N tr ] 1 + ε P( z, t )
1 1 + τ p (ω − ω p ) 2 2
(4)
where g N is the differential gain, N is the carrier density defined by Eq. (6), N tr is the transparent carrier density, ε is the gain compression coefficient, P is the photon density, 2
2
and P = F + R , τ p is the curvature of the gain peak [15], ω p is the angular frequency of the gain peak.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11889
For different types of bias in the gain, phase and modulation sections, the variation of the refractive index can be written as: α H λ0 − 4π g N [ N ( z , t ) − N ( z , 0)] , for forward bias Δn( z , t ) = − α H λ0 [α (V ) − α (0) ] , for reverse bias loss loss 4π
(5)
where α H is the line enhancement factor, λ0 is the reference wavelength in vacuum, α loss (0) and α loss (V ) are the waveguide losses at reverse bias voltages of 0 and V. Additionally, with the consideration of the lateral diffusion, the carrier density can be written as ∂N ( z , x, t ) I ∂ 2 N ( z, x, t ) (6) = − AN ( z, x, t ) − BN 2 ( z , x, t ) − CN 3 ( z , x, t ) − vg g ( z , t ) P ( z , t ) − DN ∂t eVg ∂2 x
where I is the injection current, e is the electron charge, Vg is the volume of active region, DN is the lateral diffusion coefficient of carrier, A, B, and C are the nonradiative recombination coefficient, bimolecular recombination coefficient, and auger recombination coefficient, respectively. The detuning factor is expressed as:
δ = β0 −
π Λ
(7)
where Λ is the pitch of the grating. The coupling coefficient κ of the DFB can be written as:
κ=
k 0 Δn G g −j c 2 2
(8)
where Gc is the gain coupling coefficient, and g is the average gain of the grating section. In order to solve the wave equations, we also need the boundary conditions as follows F i ( z ', t ) T11i T12i F i ( z , t ) i = i i i R ( z ', t ) T21 T22 R ( z , t )
(9)
where F i ( z ', t ) and B i ( z ', t ) denote the forward and backward waves at the left hand side of the interface i, F i ( z, t ) and Bi ( z, t ) denote the forward and backward waves at the right hand side of the interface i, with i being a letter corresponding to the section interfaces A, B, C, D, E, and X. T jki represent the transfer matrix of the interface i, and can be obtained from the scattering matrix
T=
1 1 S 21 S11
− S22 − det S
(10)
where the scattering matrix S is a set of reflective and refractive coefficients at each boundary interface, and can be calculated as shown in Table 1.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11890
Table 1. Scattering matrix elements for boundary conditions at each interface ( n fill is the refractive index of the filling medium in trench-1) Interface
S11 = − S22
S12 = S21 = 1 − S112
A
rf
1 − rf2
B
( n fill − neff ) / (n fill + neff )
2 n fill neff / (n fill + neff )
C
( neff − n fill ) / (neff + n fill )
2 neff n fill / (neff + n fill )
D
(1 − neff ) / (1 + neff )
2 neff / (1 + neff )
E
(neff − 1) / ( neff + 1)
2 neff / (neff + 1)
X
0
1
Then, the output power and frequency chirp at the interface A can be obtained as follow: F = Pout
dwvg hc0 Γλ Δf =
F ( z A , t ) 2 − R( z A , t ) 2
(11)
1 ∂Φ F ( z A , t ) ∂t 2π
(12)
Where h is the Planck constant, c0 is the speed of light in vacuum, d and w are the thickness and width of the active layer, and Φ F is the phase of the forward wave. Applying the above traveling wave equations and boundary conditions to the whole laser structure, we can obtain the wave solutions in time domain. By discretizing the differential equations into difference equations, numerical simulations can be performed by computer. 3. Numerical simulation results and discussions
The parameters for the example laser structure are given in Table 2. Table 2. Parameters used in the numerical simulations. Symb ol
Parameter
Value
Symbol
Parameter
Value
λ0
Center wavelength
1552(nm)
h
Planck constant
6.63e-34(Js)
Λ
Grating pitch Effective index of grating Effective index of filling medium Length of gain waveguide Length of phase waveguide Length of modulator waveguide Width of deep etched trench-1 Width of deep etched trench-2 Width of waveguide
241.2(nm) 3.2174 2.0
c0 e A
3e8(ms−1) 1.6e-19(C) 1e8(s−1)
1000 Λ
B
25( μm )
C
101λ0 / 4neff
gN
Light speed in vacuum Electron charge Nonradiative recombination coefficient Bimolecular recombination coefficient Auger recombination coefficient Differential gain coefficient
1.65e-16(cm2)
5λ0 / 4n fill
Ntr
Transparent carrier density
1e18(cm−3)
3λ0 / 4
β sp
2e-5
2.5( μm )
K
Spontaneous coupling coefficient Peterman’s coefficient Nonlinear gain coefficient Linewidth enhancement factor Absorption coefficient at reverse bias 0(ON state)
9e-17(cm3) 3
Absorption coefficient at reverse bias V (OFF state)
2000(cm−1)
neff nfill Lg Lp Lm Wtr1 Wtr2 w
Γ
Confinement factor Thickness of active layer
0.15 44(nm)
ε αH
rf
Reflective coefficient of facet-A
1e-3
α loss (0)
vg
Group velocity
c0/neff
α loss (V )
d
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1e-10(cm3s−1) 7e-29(cm6s−1)
1
0(cm−1)
Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11891
The widths of the two deep etched trenches are designed with an odd integer multiple of quarter wavelength to facilitate the fabrication. The width of trench-2 is 1.16 micron, which is 3 times of quarter wavelength in air. Trench-1 is filled with high refractive index medium (silicon nitride) for increasing the reflectivity change. Its width is designed to be 0.97 micron, which is 5 times of the quarter wavelength in silicon nitride. In the main example, the length of the modulator wave guide is about 12.19 micron, which is about 101 times of the quarter wavelength in the waveguide. They form an anti-resonant cavity as a rear reflector of the laser, which is the key feature of the Q-modulated DFB laser. Figure 2 gives the reflectivity and reflective phase of the rear reflector calculated by the traveling wave method. Considering a center wavelength of 1552nm, the modulator has two states: ON state when its absorption coefficient is 0, and OFF state when its absorption coefficient is 2000cm−1. The reflectivity changes from 0.82 to 0.27, and the reflective phase changes from 8.9 degree to 9.0 degree. These results are consistent with the results of the previous work by using the transfer matrix method [5,6].
Fig. 2. Reflectivity (a) and reflective phase (b) of the rear reflector calculated by the traveling wave method.
Since both the DFB grating and the rear reflector provide feedbacks to the laser cavity, a phase section is needed to adjust the phase to produce a constructive interference between the two feedback mechanisms. The phase section can therefore influence the threshold current. In the previous work [5, 7],the phase section was simplified by a phase value, which cannot take into account the propagation time in the phase section, and is therefore not suitable for more accurate physical modeling of the Q-modulated DFB laser. In order to be able to adjust the phase over the full range between 0 and 2π, the phase section needs to have a certain length so that the required current injection is not too large. We have chosen the length to be 25μm in our design example. Figure 3 shows the relationship between the reflective phase change at the interface-X and the injection current of the phase section. We can see that a variation of 360°of the reflective phase can be achieved with a phase section current variation from 0 to 90 mA. The phase variations are almost identical for the ON and OFF modulator states.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11892
Fig. 3. Reflective phase variation at the interface-X versus the phase section current.
Figure 4 shows the threshold current of the gain section versus the phase section current for both the ON and OFF modulator states. We can see that a maximum threshold difference occurs when the phase section current is about 6mA. This condition also produces the lowest threshold at the ON state and highest threshold for the OFF state. In principle, under this optimal bias condition of the phase section, by setting the gain section current to 80mA, which is the threshold current corresponding to the modulator OFF state, the laser can be switched off with a high extinction ratio. However, as we will see from the dynamic simulation below, this gain section current value is not the optimal operating point when the pattern-dependent signal fluctuations and the time jitter are considered.
Fig. 4. Threshold current of the gain section versus the phase section current.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11893
For the dynamic simulations, we apply a 40Gbps return-to-zero (RZ) voltage signal to the modulator section, leading to a variation of absorption coefficient between 0 and 2000 cm−1.The input reverse-biased signal is shown in Fig. 5(a). The Q-modulated output power is first simulated with the gain section current biased at 80mA, as shown in Fig. 5(b).The extinction ratio (ER) is calculated by the ratio between the average ON state peak power to the average OFF state minimum power, and is about 10.2dB in this case. Although the ER is high, there is a strong pattern dependence which results in large ON state power fluctuations. The peak fluctuation is calculated by the ratio between the standard deviation of ON state peak power to the average ON state peak power, and is about 35% in this case. By increasing the gain section current to 140mA, the ON state power fluctuation is significantly reduced to 15%, although the ER is also reduced to 6.8dB, as shown in Fig. 5(c).
Fig. 5. Input 40Gbps RZ signal (a),output power at gain section current of 80mA(b) and output power at gain section current of 140mA (c).The phase section current is set at6mA.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11894
In Figs. 5(b) and 5(c), we have also plotted the variation of the average carrier density in the gain section. We can see that when a signal “1” pulse is emitted, the carrier density drops. When there are consecutive “0”s, the carrier density keeps increasing. This indicates that during the OFF period, the energy from the continuous current injection in the gain section is stored in the laser cavity as excited-state electron-hole pairs. The energy is then released during the ON periods. Unlike external modulators such as electro-absorption modulators and Mach-Zehnder modulators where the light is first emitted then absorbed or dissipated in the OFF state, the QML emits no or little light but store the energy in the OFF state. It is therefore much more energy efficient. On the other hand, as we can see from Fig. 5(c), the variation of the carrier density is only a small fraction of the time averaged carrier density (less than 10%), the wavelength chirp caused by carrier density variation is much smaller compared to directly modulated laser. The eye diagrams have also been simulated for different gain section currents from 80mA to 150 mA, as shown in Fig. 6. Although the ER is high when the gain section current is 80mA, the jitter, the overshoot and undershoot of output power in the eye diagram are rather poor as shown in Fig. 6(a). The jitter is about 11.4ps, which is caused by the pattern dependent time delay of the output power with respect to the input signal. The averaged output power levels in both the ON and OFF states are shown as a red dash lines in each graph of Fig. 6. As the gain section current increases, the OFF state output power increases, which causes the ER to decrease. At the same time, the ON state output power increases, and the rise and fall times decrease, which result in lower pattern dependent ON state output power fluctuation, as well as smaller jitter. Table 3 gives the variations of the ER, peak power and jitter with the gain section current. The variation of the ER and jitter are plotted in Fig. 7. Clearly, there is a compromise between the ER and the jitter. The decrease of the jitter and peak fluctuation becomes saturated at the gain section current of 140mA. Therefore, this appears to be an optimal point for overall performance. The extinction ratio is 6.8dB and the jitter is 4.7ps, while the peak fluctuation is about 15%.
Fig. 6. Eye diagrams for different gain section currents of 80mA (a), 90mA (b), 100mA (c), 110mA (d), 120mA (e), 130mA (f), 140mA (g), 150mA (h)
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11895
Table 3. Extinction ratio, peak fluctuation and jitter versus the gain section current. Gain current (mA) Jitter (ps) Peak fluctuation ER(dB)
80
90
100
110
120
130
140
150
11.4 35%
9.6 30%
6.4 23%
5.6 18%
4.9 16%
4.8 16%
4.7 15%
4.7 15%
10.2
8.7
8.1
7.9
7.4
7.1
6.8
6.6
Fig. 7. Variation of the ER and jitter versus the gain section current.
We have also considered the cases where the modulator length is increased to about 25μm, 50μm and 100μm, to analyze the effect of the modulator length on the high speed performance while the product αL of the absorption and length is kept constant. The increased length reduces the requirement on the absorption coefficient in the OFF state, and also reduces the effect of the absorption saturation. Figure 8 shows the variation of the extinction ratio with the modulator length when the gain section current is 130mA. The ER decreases from 7.1dB to 6.4dB when the modulator length increases from 12μm to 100μm. For modulator length up to 100μm, the quality of the eye diagrams remains almost the same.
Fig. 8. Variation of the ER with modulator length.
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11896
4. Conclusions
In conclusion, we have investigated the pattern dependence of a complex Q-modulated DFB laser under high-speed modulation based on an integrated traveling wave analysis with full device structure and material properties. The high speed performance of the QML is simulated with the consideration of time delays caused by the wave traveling in the modulation and phase sections, as well as in the gain section. The simulation method is proved very useful for the QML structure design and performance optimization, as well as for providing physical insight of the operation mechanism. Through an example device structure, we have shown that 40Gbps RZ modulation can be achieved with well open eye diagrams. The gain section current needs to be biased well above the OFF state threshold to achieve good performance. An extinction ratio of 6.8dB with a low jitter of 4.7ps and low peak fluctuation of 15% were obtained, which are sufficient for many applications. Little degradation is observed when the modulator length is increased to 100μm. Unlike external modulators such as electro-absorption modulators and Mach-Zehnder modulators where the light is first emitted then absorbed or dissipated in the OFF state, the QML emits no or little light in the OFF state and stores the energy in the form of increased carrier density to be released in the ON state. It is therefore much more energy efficient. This advantage, combined with the ability of high speed modulation, makes it an excellent candidate for optical interconnects in high-performance computers and data center networks. Acknowledgements
This work was supported by the National Natural Science Foundation of China (grant No. 61377038) and the National High-Tech R&D Program of China (grant No. 2013AA014401).
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Received 2 Mar 2015; revised 21 Apr 2015; accepted 22 Apr 2015; published 27 Apr 2015 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011887 | OPTICS EXPRESS 11897
