Static and dynamic analysis of side-mode suppression of widely tunable sampled grating DBR (SG-DBR) lasers

Optics Communications 282 (2009) 81–87

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Optics Communications journal homepage: www.elsevier.com/locate/optcom

Static and dynamic analysis of side-mode suppression of widely tunable sampled grating DBR (SG-DBR) lasers Kai Shi a,c,*, Yonglin Yu a, Ruikang Zhang b, Wen Liu a,b, Liam P. Barry c a

Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan, Hubei, China Accelink Technologies Co. Wuhan, Hubei, China c Research Institute for Network and Communications Engineering, School of Electronic Engineering, DCU, Dublin 9, Ireland b

a r t i c l e

i n f o

Article history: Received 25 June 2008 Received in revised form 15 September 2008 Accepted 19 September 2008

Keywords: Dependence of gain on wavelength Side-mode suppression Tunable lasers Wavelength switching

a b s t r a c t Side-mode suppression is an important issue for widely tunable laser design and applications. In this paper, we have developed a relatively simple algorithm to analyze side-mode suppression of widely tunable sampled grating distributed Bragg reflector (SG-DBR) lasers by using the Transfer Matrix Method (TMM) in combination with multimode rate equations. The dependence of gain spectrum on wavelength is also included in this model, and its effects on tuning characteristics of the devices are investigated for the first time. Static tuning characteristics and dynamic behaviors of wavelength switching are simulated. Results agree well with the experimental results reported. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction Widely tunable lasers are becoming a critical technology in agile optical networks for exploiting the full capacity of optical communications and realizing dynamic reconfiguration of networks [1–3]. Various monolithically integrated devices based on distributed Bragg reflector (DBR) have been presented, including grating-assisted co-directional coupler with sampling grating reflector (GCSR) lasers, sampled grating distributed Bragg reflector (SG-DBR) lasers, super-structure grating DBR (SSG-DBR) lasers, and digital super-mode DBR (DS-DBR) lasers [1,2]. These devices exhibit high performance with wide wavelength tuning range (>60 nm), high side-mode suppression ratio (SMSR > 30 dB), and high output power (>10 dBm). Moreover, these devices have fast wavelength switching capability (switching time in a few ten nanoseconds). Therefore, the interest in the devices is enhanced by their potential applications, such as optical packet switching (OPS) and optical burst switching (OBS) [4–7]. Several theoretical studies have been performed on widely tunable DBR lasers. A time-domain large-signal model was presented for widely tunable DBR lasers with periodically sampled and chirped gratings, and tuning characteristics and amplitude modu-

* Corresponding author. Address: Research Institute for Network and Communications Engineering, School of Electronic Engineering, DCU, Dublin 9, Ireland. Tel.: +353 1 7005884; fax: +353 1 7005508. E-mail address: [email protected] (K. Shi). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.09.069

lation response were simulated [8]. A dynamic model based on the Transfer Matrix Method (TMM), was developed for widely tunable GCSR lasers to study wavelength and output power properties [9]. In addition, using the TMM approach, static tuning performances were simulated for widely tunable digital super-mode DBR (DS-DBR) laser [10]. Recently, we reported some simulated results for a new structure, i.e. digital concatenated grating DBR (DCDBR) laser [11]. Side-mode suppression is an important issue for widely tunable laser design and applications [1,2]. Tuning range and accessible wavelength channels are limited by the wavelength range that the device can reach with high side-mode suppression ratio (SMSR). In other words, the devices must operate at a stable single mode condition for each wavelength channel within the tuning range. In practical design, fabrication and operation, any unfavorable factors could change stable single mode condition, resulting in mode-hopping due to side-mode gain enhancement [12,13]. Degradation of SMSR under dynamic operation was also observed experimentally [14]. In this paper, we extend the TMM to analyze side-mode suppression of widely tunable SG-DBR lasers. Static tuning characteristics and wavelength switching dynamics are simulated in combination with multimode rate equations, also taking into account dependence of gain on wavelength. Results of SMSR as well as lasing wavelength, output power, and threshold current over a wide tuning range are presented. It is shown that gain curve characteristics play an important role in the design of such devices. Dynamic SMSR during wavelength switching is also simulated. This

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work will be helpful for optimization of design and operation of such devices.

To analyze side-mode suppression, we combine TMM with the multimode rate equations. Here we consider the main mode (with subscript m) and the strongest side mode (with subscript s),

2. Model theory

dP m ¼ 0 ¼ Rspm þ Pm v g ðgðxm ; Nath Þ  am Þ dt dP s ¼ 0 ¼ Rsps þ Ps v g ðgðxs ; Nath Þ  as Þ dt dN a ðtÞ Ia  RðN ath Þ ¼0¼ dt eV a   Ps Pm  v g gðxs ; N ath Þ þ gðxm ; Nath Þ ; Va Va

The Transfer Matrix Method (TMM) method was first proposed by Björk and Nilsson [15]. The basis of the method is to divide the laser longitudinally into a number of sections and in each section the structural and material parameters are assumed to be homogenous. Each section is then described by a 2-by-2 complex transfer matrix which represents the relation between forward and backward propagating waves. The one-dimensional laser structure is described with effective index methods [16]. Fig. 1 shows our process of calculating the over all transfer matrix for the SG-DBR laser structure. r1 and r2 are the amplitudes of the two reflectivities of the equivalent cavity and can be derived from transfer matrices of particular sections as shown in Fig. 1.

ð1Þ ð2Þ

ð3Þ

where x is the specific angular optical frequency and a is the total loss of each mode. These two parameters are the first root (main mode) and second root (strongest side mode) of the lasing condition in TMM. P is the photon number in the active region. Rsp = nsptgg(x, Nath) represents the spontaneous emission contribution, where the

Fig. 1. The process of calculating the over all transfer matrix of the whole structure of SG-DBR lasers.

K. Shi et al. / Optics Communications 282 (2009) 81–87

83

spontaneous emission coefficient nsp is taken as wavelength-independent for simplicity. tg is the group velocity. Ia is the current to the active section and Va is the volume of the active section. The spontaneous recombination rate R(Nath) is described as

RðNÞ ¼ AN þ BN2 þ CN3 ;

ð4Þ

and A, B, C account for the nonradiative linear, the radiative bimolecular, and nonradiative Auger recombination, respectively. When the laser is operated at threshold current, the photon number can be omitted and the threshold current can be obtained from (3), taking Pm, Ps = 0 as

Ith ¼ eV a RðN ath Þ:

ð5Þ

From (2), the photon number of the side mode can be written as

Ps ¼ 

Rsps

v g ðgðxs ; Nath Þ  as Þ

:

ð6Þ

When the laser is lasing at the main mode wavelength, the difference between g(xm, Nath) and am is supposed to be zero. By putting (5) and (6) into (3), the main mode photon number can be obtained as

Pm ¼

Ia Ith ev g

 gðxs ; Nath ÞPs gðxm ; Nath Þ

:

ð7Þ

Then the front sampled grating output power can be derived from (6) and (7) as

Poutf ¼ hxi v g agf ðxi ÞP i ; i

ð8Þ

where  h is Plank’s constant, and the subscript i represents modes, for the main mode i = m, for the side mode i = s. The front sampled grating loss agf is calculated from

agf ðxi Þ ¼

1 1 ln : Lactive r 1 ðxi Þ

ð9Þ

The angular optical frequency xi is included because different wavelength will get different reflectivity in the comb-like spectrum as shown in Fig. 2a. Then the side-mode suppression ratio can be easily get from the definition as

SMSR ¼ 10 lg

Poutf m Poutf s

:

ð10Þ

With static tuning curves calculated by the method above, the dynamic analysis of the switching can be carried out. Detailed descriptions will be presented in Section 4. 3. Dependence of gain spectrum on wavelength The dependence of gain on wavelength is not normally considered necessary for narrow tunable lasers. However, for widely tunable devices, wavelength-independent gain can be assumed only when the reflector spectrum bandwidth is smaller than the gain spectrum bandwidth. Fig. 2 gives an explanation for the gain roll-off effects on SMSR and thus the maximum tuning range. The amplitude of roundtrip gain can be written as

g round ¼ r1 r 2 egnet Lactive ;

Fig. 2. (a) Field reflectivity spectrum at two facets shown in (b) Roundtrip gain (solid blue line) and the net modal gain (dot green line) for wavelengthindependent case.(c) Roundtrip gain (solid blue line) and the net modal gain (dot green line) for wavelength-dependent case. In this case, the currents applied on the front sampled grating, the rear sampled grating and the phase control section are 7.05 mA, 0 mA and 0 mA, respectively. The current set on the active section is near the threshold current. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

ð11Þ

where Lactive is the length of the active region and gnet is the net modal gain. Fig. 2a gives the spectrum of r1 and r2. The dependence of gain spectrum on wavelength is represented by a parabola model as

gðx; Na Þ ¼ g N ðNa  N0 Þ  g x ðx  xp ðNa ÞÞ2

ð12Þ

dx xp ðNa Þ ¼ xp ðN0 Þ þ p ðNa  N0 Þ; dN

ð13Þ

where gN is the differential gain coefficient, N0 is the transparent carrier density, gx is the gain curvature, and xp(Na) is the angular optical frequency of the gain peak for the carrier density Na. The ‘‘blue shift” of the gain spectrum with increasing carrier density is assumed to be linear with Na in (13). Fig. 2b gives a result of roundtrip gain without considering the dependence of gain on wavelength. The structure parameters are used here mainly from [17] and listed in Table 1. From Fig. 2b,

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Table 1 Parameters used in modeling Parameters

Symbo l

Active

Active section length Front SGDBR length Rear SGDBR length Phase control section length Section width Section thickness Coupling coefficient Bragg wavelength with Igtf = Igtr = 0 Internal optical loss Effective refractive index Group refractive index Nonradiative linear recombination Radiative bimolecular recombination Nonradiative Auger recombination Spontaneous emission coefficient Index derivative wrt carrier density Absorption derivative wrt carrier density Transparent carrier density Differential gain coefficient Gain peak for Na = N0 Shift of gain peak with carrier density Gain curvature

la lgtf lgtr lpc w d

450 lm

1.8 lm 0.15 lm

j ai

Passive

58  10 lm 64  12 lm 150 lm 1.8 lm 0.4 lm 3,5000/m 1550 nm

neff ng A

4000/m 3.72 3.72 1  108/s

1500/m 3.72 3.72 1  108/s

B

1  1016 m3/s

1  1016 m3/s

C

7.5  1041 m6/s

4  1041 m6/s

nsp

2.2

2.2

dn/dN

2.34  1026 m3

da/dN

2.56  1021 m2

N0 gN kp(N0) dxp/dN gx

1.5  1024/m3 3.6  1020 m2 1550 nm 2.12  1011 m3/ s 9  1024 s2/m

we can see that a supermode around 1575 nm would be the dominant (main) mode because it has the highest gain. Considering the dependence of gain on wavelength with (12) and (13). Fig. 2c displays a change of the roundtrip gain, where the roundtrip gain is plotted in blue solid line and the net modal gain is plotted in green dot line. Form Fig. 2c, we can see that the supermode around 1515 nm lasers instead of the previous one around 1575 nm as the net modal gain drops steeply past 1575 nm. This simulated result agrees well with the experimental result reported in [17]. The reason was believed that the compressively strained quantum well active region does not produce sufficient gain past 1575 nm. From the analysis above, it is clear that the shape of gain curve will play an important role in the design of the SG-DBR or any other widely tunable lasers. Thus the dependence of gain on wavelength should be considered during modeling.

4. Simulation results and discussion With the modeling described above, the static tuning characteristics were simulated and demonstrated with similar structure parameters as in [17]. In order to show the effect of the gain curve on the tuning range, we present simulated results of a design with wider tuning range in Fig. 3, including lasing wavelength, threshold current, output power, and SMSR. The curves on left are the three dimensional mesh of the tuning characteristics versus both the front SG-DBR and the rear SG-DBR currents, with 100 mA to the active section and no phase-control current. The contours of the corresponding tuning curves are shown on the right column. The fan shaped wavelength tuning curve with two sets of steps can be seen in Fig. 3a and b. Each of the steps represents a supermode when the front SG-DBR reflection peak coincides with the rear SG-DBR. Wavelength variations in each sloping plateau are visible. This is caused by longitudinal mode jumps [18,19]. The

longitudinal mode changes can be seen clearly in Fig. 3b with each one having two boundaries across the radiating direction of each step of the fan. The sets of the steps are caused when the lasing wavelength jumps from one side of the reflectivity spectrum to the other as shown in Fig. 2 and are referred to as cycling jumps. As explained in Fig. 2, the dependence of gain on wavelength causes the cycling jump range to be less than the prediction calculated by the product of the two reflectivity spectra. The simulated tuning range is about 71.7 nm (1499.9–1571.6 nm), similar with the measured result of 72 nm, but smaller than the design value of 90 nm [17]. If the gain spectrum can be flattened by some way, then the supermode around 1575 nm should be lasing, and then a wider tuning range can be achieved. The output power and the threshold current are shown in Fig. 3c–f. As explained in [18], the saddle points of the power contours are visible in Fig. 3f. These saddle points are corresponding to the situation when the lasing wavelength coincides with reflection peaks for both the front and rear SG-DBR. This means the saddle points will have the least threshold currents as shown in Fig. 3d and maximum SMSR (about 46 dB) as shown in Fig. 3g and h. The SMSR curves can bring helpful information for the device producer in the test and control process, because the lasers are supposed to be lasing with the maximum SMSR. A bad SMSR in the mode boundary area (see Fig. 3b and h) may cause cross talk between channels, especially in DWDM systems. From Fig. 3d and f, the output power is around 7 mW with a threshold current around 20 mA. These results agree with the measured results of the device in [17]. Based on static simulation, dynamic analysis of side-mode suppression can be carried out. For this purpose, we concentrate on one wavelength tuning plot as shown in Fig. 4. The main-mode wavelength is represented with a red line and the side-mode wavelength is plotted with blue stars in Fig. 4a, where the current to the front SG-DBR varies from 7.8 mA to 13.8 mA with a fixed rear SG-DBR current. In area i, the mode competition is between two adjacent longitudinal modes (see (i) case in Fig. 4b). As the current of the front SG-DBR increases, the overlap of the roundtrip gain will move towards to the short wavelength according the free carrier plasma effect and the possible side mode will change from the adjacent longitudinal mode to the one in the adjacent roundtrip gain peak (see (ii) case in Fig. 4b) and be well suppressed. Then the maximum SMSR will be achieved in this situation (see Fig. 4a). As the current increases further into the area (iii), the mode competition is between the longitudinal modes in different roundtrip gain peaks (see (iii) case in Fig. 4b). The mode jumping edges are corresponding to the boundaries of different longitudinal modes with two modes competing strongly with each other as the situation shown in (i) and (iii) in Fig. 4b. We can see that the SMSR drops steeply at the edges from Fig. 4a. To investigate wavelength switching dynamics, we apply a switching current If to the front SG-DBR, where

8 If1 t < t10 > > >   > > tt > < I þ ðI  I Þ 1  e s010 t10  t < t 20 f1 f2 f1 If ¼ > >   > tt > >  20 > : If2  ðIf2  If1 Þ 1  e s0 t  t20 ;

ð14Þ

where If1 and If2 are the low and high levels of the current pulse, respectively, and s0 is the time constant of the switching current [20]. During the switching, the currents into the gain section and phase control section are kept constant at 100 mA and 0 mA, respectively. By fitting the static tuning curve of Fig. 4a, seven longitudinal modes are considered in the switching event since they are potential lasing modes. It should be noticed that mode SD1 is the stron-

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Fig. 3. Static tuning curves of a SG-DBR laser. The three-dimensional meshes on the left are obtained by varying both the front and rear SGDBR current respectively. The curves on right are the contours of the corresponding 3D curves on the left. (a, b) Lasing wavelength. (c, d) Threshold current. (e, f) Output power, (g, h) SMSR.

gest side mode when mode D1 is lasing as the dominant mode. It is necessary to include effects of mode SD1 in the dynamic simulation, even if there is no chance for this side mode to be boosted

as the dominant mode for this specific case. Fig. 5 shows the mode competition during the switching with a current pulse on the front SG-DBR section of If1 = 7.8 mA and If2 = 13.8 mA.

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Fig. 4. (a) Static tuning curves of the switching range. The red step like line represents the main mode and the blue stars represent the corresponding side mode under the same currents. (b) A brief illustration of the mode competition of the three areas in (a). (i) Adjacent longitudinal modes competition. (ii) Side mode change from adjacent longitudinal mode to the one in another roundtrip gain peak. (iii) Longitudinal modes in different roundtrip gain peaks competition.

Fig. 5. Transient characteristics of wavelength switching. (a) Output mode power, where the dot line represents the current applied on the front SGDBR section. (b) Dynamic SMSR.

From Fig. 5a, we can find that A1 is the initial mode and D1 is the destination mode corresponding to the pulse current. During the switching transients, the modes lase one by one as the current increases from the low level to the high level and vice versa as shown in Fig. 5a. The forward switching time is about 5 ns while the backward switching time is about 14 ns. These results agree well with measurements reported in [19]. The backward switching takes a longer period since the backward dynamics of carrier density enhances the lasing of transient modes for a longer period, especially of mode B1. Fig. 5b displays evolution of SMSR versus time during the switching, which is referred to as Dynamic SMSR (DSMSR) here. Degradation of SMSR during switching transients can be observed from this figure. These results confirm possible degradation of WDM optical network performance due to wavelength switching applications. It has been proposed and demonstrated that an SOA integrated at the output of the devices can be used to blank the signal during the switching events to prevent performance degrada-

tion. However, it is not easy to manage well when a large number of tunable lasers are employed in a WDM network [21,22]. Simulation results here could be helpful for designers to optimize blanking times in timing control design. It should be noted that the switching time, and thus the blanking time, can be reduced by changing the drive current applied to the tunable laser [9,20]. Fig. 6 shows the transient characteristics of wavelength switching with different switching currents. A significant decrease of the switching time occurs as the difference between the low and high level of the switching current increases. This is in good agreement with experiment results [19]. It should also be noted that the required blanking time will also be dependent on the wavelengths that are being switched between, so it should be possible to optimize the blanking time if the actual wavelength transition is known. For wavelength switching dynamics, other important issues that need to be studied are thermal effects and nonlinear gain. Thermal effects can cause wavelength drift [18] which will have

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confirmed theoretically, which implicates that optimization of devices control is necessary for wavelength switching applications. Acknowledgments This work was supported by National Natural Science Foundation of China under Grant No. 60677024, the National High Technology Research Development Program of China under Grant No. 2006AA03Z0427, and the Science Foundation Ireland Investigator Programme. References [1] [2] [3] [4] [5] Fig. 6. Transient characteristics of wavelength switching with different switching current for If1 = 7.8 mA. (a) If2 = 12.5 mA, (b) If2 = 13.7 mA.

[6] [7]

a detrimental effect on system performance for some applications, such as a burst switching and wavelength routing. Nonlinear gain will possibly lead to hysteresis in wavelength versus temperature characteristics [23]. It is expected to extend this analysis to deal with these issues in future.

[8] [9] [10] [11]

5. Conclusion Based on the Transfer Matrix Method and multimode rate equations, a simple modeling method has been proposed and demonstrated for widely tunable SG-DBR lasers. Results of side-mode suppression ratio as well as lasing wavelength, output power, and threshold current over a wide range tuning were presented. The effect of dependence of gain spectrum on wavelength for widely tunable lasers is considered in the simulation for the first time. It has been clarified that the shape of the gain curve will play an important role in the design of such devices. Wavelength switching dynamics of the devices were also investigated with the simulations. Degradation of SMSR under switching has been

[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

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