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Suppression of thermal wavelength drift in widely tunable DS-DBR laser for fast channel-to-channel switching

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Abstract

We present a simple and effective method for suppressing thermally induced wavelength drift in a widely tunable digital supermode distributed Bragg reflector (DS-DBR) laser monolithically integrated with a semiconductor optical amplifier (SOA). For fast thermal compensation, pre-compensatory currents are injected into the gain medium section of the DS-DBR laser and the SOA. This method can be easily applied to existing commercial tunable lasers, since it is implemented without any modification to manufacturing process. Experimental results exhibit that wavelength stability is noticeably improved to ± 0.01 nm. We also experimentally demonstrate a fast channel-to-channel switching in a wavelength-routed optical switching system employing a 90 × 90 arrayed waveguide grating router (AWGR). The measured switching time is less than 0.81 µs.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Current data center networks (DCNs) based on multi-hop electrical switches are facing many challenges including high power consumption, high latencies, and throughput limitations. Optical switch-based DCNs have recently emerged as a promising solution to overcome such problems [1–8]. In particular, a wavelength-routed architecture exploiting several fast tunable lasers/tunable wavelength converters together with a cyclic arrayed waveguide grating router (AWGR) has gained popularity [4–8]. In the architecture, non-blocking switching is readily enabled by a simple wavelength control of the tunable lasers. Besides, AWGR has lower splitting loss (e.g., < 5 dB regardless of the number of channels) as compared to an optical power splitter (e.g., 19.5 dB for 90 × 90 splitting ratio) and does not require external power supplies, leading to a power-efficient implementation. In the switching scheme, switching time is one of the major parameters which is determined mainly by the wavelength tuning speed of the tunable lasers. Although multi-section distributed Bragg reflector (DBR) lasers have an intrinsic transient speed of a few nanoseconds [9], several hundred milliseconds are required to suppress the wavelength drift caused by temperature distribution change [10].

A lot of methods have already been proposed for suppressing the thermally induced wavelength drift. A fast wavelength locker greatly improves wavelength stability within a switching time of a few microseconds with the cost of optical/electrical components and optical alignment, but there is a fundamental limitation in improving the switching time due to the time delay in feedback loop circuits [11]. As an alternative, pre-compensation method has been introduced which injects a compensatory current into a thermal drift compensation mesa that is monolithically integrated to the laser mesa in parallel [10,12]. Even though the thermal drift compensator is effective for both fast and wide-range tuning, it requires device modification inside the packaging. Another group applied a film resistor outside the laser as a thermal controller [13]. However, due to the large heat resistance and capacitance, its response time was not shorter than tens of milliseconds. There have been few methods which are applicable to legacy tunable devices.

In this paper, we propose a simple and effective method of suppressing thermally induced wavelength drift without adding any special structures within the tunable device package. Instead, we control the pre-compensatory currents injected into the gain medium sections. As the tunable device, we chose a commercially available digital supermode DBR (DS-DBR) laser that is monolithically integrated with a semiconductor optical amplifier (SOA). Since the DS-DBR laser does not rely on Vernier tuning mechanism, it is more amenable to predictive tuning techniques than other alternatives. For the investigation of thermal drift suppression, we measured dynamic wavelength changes of the DS-DBR laser over time. We also characterized the output power fluctuations, an undesired effect, due to the compensatory current injection to the active sections of the laser and the SOA. Lastly, we experimentally demonstrated fast channel-to-channel switching with a 90 × 90 AWGR.

2. Device structure and principle of thermal wavelength drift suppression

Figure 1 shows a schematic diagram of a tunable transmitter optical sub-assembly (TOSA) and an electronic circuit board. We used Oclaro’s 36-pin butterfly-packaged tunable TOSA which incorporates a full C-band DS-DBR laser monolithically integrated with a SOA and a 10-Gb/s InP-based Mach-Zehnder intensity modulator (MZM) [14]. The DS-DBR laser has four separate sections: a laser gain section, a multi-contact chirped front grating (FG) section, a rear grating (RG) section, and a phase section [15]. More details of the laser and its basic operation are described in [16].

 figure: Fig. 1

Fig. 1 A schematic diagram of a tunable TOSA (orange-colored box) and an electronic circuit board.

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For fast wavelength switching, we have developed an electronic circuit board that controls the tunable TOSA. It can lase 90 International Telecommunication Union (ITU) channels with 50-GHz grids and we numbered them from #1 to #90. A channel number was sent to a field programmable gate array (FPGA) in the form of 8-line parallel bus data to set the lasing wavelength of the DS-DBR laser. A lookup table at the FPGA then determined corresponding current values supplied to the DS-DBR laser and the SOA. Currents to passive tuning sections (the FG, the RG, and the phase sections) were supplied by 16-bit digital-to-analog converters (DACs). Meanwhile, since active sections (the laser gain section and the SOA) are less sensitive to current change than the passive tuning sections, 14-bit DACs were used for supplying currents to them. The FG section currents should be injected to adjacent FG contact pair for a single wavelength operation. The number of required DACs for driving eight FG sections can thus be reduced to two by using two additional electrical 1 × 4 switches. Current drivers provide each amplified analog current to the RG section, the laser gain section, and the SOA, simultaneously. Two separate thermoelectric cooler (TEC) drivers control each integrated TEC (not shown) to maintain the temperature of the internal components and thereby providing a long-term wavelength stability.

Figure 2(a) shows the measured optical spectra of the tunable TOSA output from channel #1 to #90. Once the sub-band is selected by injecting drive currents into adjacent two of the eight FG sections (coarse tuning), the lasing wavelength is fine-tuned by adjusting the RG section current and the phase section current. The more injection current to the RG section, the shorter wavelength is emitted from the DS-DBR laser in each sub-band. The RG section current range of up to 54.5 mA (full scale) was required to completely cover the sub-band bandwidth. The measured spectra show side mode suppression ratio (SMSR) larger than 38-dB. If the current driver for the RG section is ideal (i.e., a perfect step wave with zero rising time), the wavelength will be blue-shifted by “carrier effect” in a few nanoseconds as shown in Fig. 2(b) [10]. Then heat inside the laser chip generated by the current injection reduces the refractive index of the laser resulting in red-shift [17], which grows for the next several hundred milliseconds or even seconds [13]. This thermal wavelength drift becomes worse as the switching scale of RG section current increases.

 figure: Fig. 2

Fig. 2 Measured optical spectra (solid lines) and side-mode suppression ratio (open square) with the largest and smallest channel number in each sub-band (a), a schematic explaining thermal wavelength drift (b), and conceptual drive currents for suppressing the thermal wavelength drift (c).

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For suppression of the thermal wavelength drift, we modified the driving condition of a start channel by injecting compensatory currents into the laser gain section and SOA (denoted as ∆IGain and ∆ISOA, respectively) as depicted in Fig. 2(c). Those drive currents of the start channel (I’Gain and I’SOA) and the destination channel (IGain and ISOA) were set to minimize the total current change to reduce the temperature change resulting from the current switching in the RG section (IRG). The laser gain section current and the SOA current were simultaneously controlled with the RG section current, using each current driver in parallel. In the case of other laser sections such as the FG sections, the RG section, and the phase section, a sophisticated control would be required for tracking the temperature change over time, since those have a large refractive index change with respect to the injection current [18]. On the contrary, the laser gain section indeed possesses relatively weak carrier effects and consumes a large amount of currents (i.e., large thermal heating source). Thus, the laser gain section can be used for reducing the laser temperature change by injecting the compensatory current without complex dynamic control. Even the SOA is thermally coupled with the DS-DBR laser, since it is monolithically integrated to the laser cavity. Manipulating the current to the SOA enables to keep the overall chip temperature constant independent of the carrier effects. For this reason, we chose the laser gain section and/or SOA for suppressing the thermal wavelength drift. It may be noted that the FG section and the phase section do not play an important role in our proposed method, so we let those sections just follow the basic DS-DBR laser operating conditions.

3. Experimental setup and results

3.1 Measuring thermal wavelength drift in DS-DBR laser

Figure 3(a) illustrates the experimental setup for measuring dynamic wavelength deviations of the DS-DBR laser with the integrated SOA. The optical output port of the tunable TOSA was connected to the 90 × 90 AWGR which has a channel spacing and a 1-dB (3-dB) bandwidth of 50 GHz and 0.1 nm (0.17 nm), respectively. The AWGR was utilized as an optical band pass filter for converting wavelength deviations to optical power fluctuations in the setup [19]. After the AWGR, the optical signal was passing through a variable optical attenuator (VOA) and delivered to a dc-coupled photodetector (PD) which has a bandwidth of 125 MHz. Electrical output voltage fluctuations from the PD were measured by a real-time oscilloscope (RTO) with a trigger signal from the FPGA of the electronic circuit board. When the channel number was given to the FPGA, control signals for the tunable TOSA and the trigger signal were generated simultaneously.

 figure: Fig. 3

Fig. 3 Experimental setup used to measure dynamic wavelength deviations (a) and normalized optical spectra of the 50-GHz spaced AWGR and tunable TOSA (b).

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As shown in Fig. 3(b), the wavelength of the destination channel (or target wavelength denoted as λtarget) in 2nd sub-band among the arbitrary sub-bands, 1555.832 nm, was set to be slightly longer than the center wavelength of the AWGR, 1555.728 nm, to observe the thermal wavelength drift. The start channel and destination channel were chosen to make full scale current change in the RG section or the worst case in terms of the heat generation. Both the laser gain section current and the SOA current of the start channel (I’Gain and I’SOA) were changed by injecting variable compensatory currents (the wavelength of the start channel was at ~1563.3 nm), while those of the destination channel were fixed at IGain = 100 mA and ISOA = 180 mA.

Figure 4 shows wavelength drift at various conditions. The wavelength was deduced from the measured output voltage at the PD and the insertion loss information of the AWGR channel shown in Fig. 3(b). When the laser gain section and SOA currents of the start channel and the destination channel were kept being same (i.e., I’Gain = IGain = 100 mA and I’SOA = ISOA = 180 mA), the wavelength was blue-shifted by ~0.1 nm (or ~12.4 GHz in frequency) within ~2 µs. It should be noted that the carrier effect is observed in a few µs time scale reflecting the rising time of the current driver for the RG section, compared to ns time scale in conceptual schematic of Fig. 2(b). Immediately after the current switching, the refractive index change in the laser cavity becomes larger with respect to the given RG section current change before temperature redistribution [17]. That is the reason why such a large blue-shift overshooting is observed. After the peak of the blue-shift, the wavelength started to move toward λtarget as the laser temperature increased. Within time order of seconds, the wavelength experienced red-shift by ~0.05 nm and then converged to λtarget with the help of the TEC. The peak-to-peak wavelength drift was ~0.15 nm (~18.6 GHz).

 figure: Fig. 4

Fig. 4 Calculated wavelengths from measured output voltages at the PD according to the laser gain section current and the SOA current of the start channel. The red-dotted line represents the target wavelength of 1555.832 nm.

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To suppress the thermal wavelength drift, we first increased the laser gain section current of the start channel to I’Gain = 125 mA without any change of the SOA current (compensatory current, ∆IGain = 25 mA and ∆ISOA = 0 mA). The result shows that the peak wavelength deviation of the blue-shift was considerably suppressed to less than 0.02 nm. However, a residual red-shift was still observed within a few seconds. This implies that the temperature of the laser was not perfectly compensated. At the beginning of the current switching in the RG section and the laser gain section (before the thermal distribution change from those sections), the suppression of the wavelength drift is attributed by not only the temperature increase of the start channel (thermal compensation), but also the carrier effects induced by the compensatory current injection [17]. Fortunately, at the laser gain section, a sign of the wavelength change with respect to the current change is negative, resulting in the suppression of the wavelength drift. This is also found in the experimental results from [19]. Thus, the mismatching in the laser temperature between the start channel and the destination channel is inevitable as the wavelength drift is suppressed by the carrier effects.

For the residual wavelength drift suppression, the SOA current of the start channel was increased to I’SOA = 215 mA (∆IGain = 25 mA and ∆ISOA = 35 mA). From the experimental results in [20], we can say that the thermal transient in the DS-DBR laser caused by the current injection to the SOA occurs after a few µs time delay. Thus, it is expected that the SOA is not efficient for suppressing the wavelength drift at the beginning of the dynamic switching in a few µs time scale. After that time scale, however, the effect of the pre-compensatory current injection into the SOA becomes evident, when the green- and orange-colored curves shown in Fig. 4 are compared. The red-shifted wavelength after ~2 × 10−2 sec was noticeably suppressed. As a result, wavelength stability in overall time span was improved to ± 0.01 nm ( ± 1.24 GHz). This satisfies the allowable frequency deviation of ± 2.5 GHz standardized in Optical Internetworking Forum-integrable tunable laser assembly-multisource agreement (OIF-ITLA-MSA) [21].

3.2 Characterizing output power saturation of tunable TOSA

Injecting a compensatory current to the gain medium sections may cause optical output power deviation of the tunable TOSA among the 90 channels. We measured the output power of the tunable TOSA as a function of the SOA current at various laser gain section currents as shown in Fig. 5. When the SOA current is small (< 100 mA), the output power linearly increases. However, it is clearly seen that the output power becomes saturated and even decreases when the SOA current exceeds 100 mA. This is explained by the self-heating effect of SOA as referred to [20].

 figure: Fig. 5

Fig. 5 Measured output power of the tunable TOSA as a function of the laser gain current and SOA current.

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The output power can be also saturated by injecting a high current into the laser gain section. Since the DS-DBR laser was monolithically integrated to the SOA, it is not possible to directly measure the light output power from DS-DBR laser (i.e., light input power to SOA). Thus, it was hard to distinguish the cause whether a gain saturation effect of the SOA due to a high optical input power [22] or a self-heating effect. Since the SOA was designed to have a low optical gain for high input power operation [16], optical output power was less than 6 µW, when laser gain section current was 0 mA.

Fortunately, the output power saturation by injecting the both laser gain section current and SOA current allows the proposed method working. An optical power difference was measured to be ~0.39 dB between the start channel condition of I’Gain = 125 mA and I’SOA = 215 mA (△) and the destination channel condition of IGain = 100 mA and ISOA = 180 mA (), respectively, as shown in Fig. 5. As mentioned above, the small optical power difference is attributed by the SOA features (i.e., the gain saturation effect and the self-heating effect) independent of the laser. Thus, we can expect that other kinds of SOA-integrated tunable laser including a sampled grating DBR laser will give similar performance in terms of the optical power difference after adopting the proposed thermal compensation method.

It may be noted here that when we manipulate the SOA current, there is a trade-off between optical gain and spectral linewidth. As the compensatory current is injected into the SOA, the linewidth of the DS-DBR laser may become widened due to undesired optical feedback from the SOA into the laser. Nevertheless, we can expect that the linewidth would not exceed 5 MHz by considering the maximum SOA current of 250 mA, as referred to [16]. This level of the linewidth seems to be enough for the DCN application based on optical switching with intensity modulation and direct detection.

3.3 Power dissipation of the tunable TOSA

To investigate power dissipation of the tunable TOSA, we measured the applied voltages under given currents for the laser gain section and the SOA. With the laser gain section current of IGain = 100 mA and the SOA current of ISOA = 180 mA, power dissipation of the laser gain section and SOA was 133.8 mW and 288.9 mW, respectively. With the additional compensatory current injection to the laser gain section and the SOA (∆IGain = 25 mA and ∆ISOA = 35 mA), the power dissipation increased to 181.4 mW (35.6% increment ratio) and 368.7 mW (27.6% increment ratio), respectively. If resistances of the laser gain section and SOA were constant, increment ratio of power dissipation would be 56.3% and 42.7%, respectively. However, less power dissipation was obtained through the applied voltage measurement compared to the calculated results. This implies that resistances of the laser gain section and the SOA become smaller as applied current increases.

By measuring resistance of a laser carrier thermistor packaged in the tunable TOSA, we could estimate temperature increase in the laser gain section and SOA. The relationship between resistance of the thermistor and temperature is given by [23],

1T=1βlnRR0+1T0
where, T is temperature of tunable TOSA chip (in Kelvin), R is resistance of the thermistor, T0 is 298.15K (25°C), R0 is 10 kΩ, and β-constant is 3950 for our tunable TOSA. The measured resistance of the thermistor with and without injecting compensatory currents into the laser gain section and SOA was 4.7623 kΩ and 4.0082 kΩ, respectively. Based on Eq. (1), the estimated temperature corresponding to each resistance was 315.84K and 320.25K, respectively. Thus, the maximum temperature increase due to the compensatory current injection was 4.41°C.

4. Fast channel-to-channel switching in 90 × 90 AWGR

Figure 6(a) shows the calibrated drive currents of the laser gain section, the SOA, and the RG section of the tunable TOSA for the 90 ITU channels (λ1 = 1564.271 nm, λ90 = 1528.773 nm). Following the basic operation principle of the DS-DBR laser [16], The RG section current was driven in nonlinear steps ranging from 2 to 60 mA. Given the number of steps for the RG section, the laser gain section current and the SOA current were also driven ranging from 125 to 100 mA and 215 to 180 mA, respectively. These optimum current range of the laser gain section and SOA was obtained by measuring the thermal wavelength drift introduced in Section 3.1. We have updated the lookup table of the FPGA to the current setting shown in Fig. 6(a) to obtain data shown in Figs. 6(b), 6(c), and 6(d).

 figure: Fig. 6

Fig. 6 The drive currents of the laser gain section, the SOA, and the RG section for thermal drift compensation (a), measured optical output power of tunable TOSA w/o and w/ injecting the compensatory currents (b), a demonstration of channel-to-channel switching as a function of time (c), and channel-to-channel switching time from channel #90 to each channel (d).

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We measured the output power of the tunable TOSA with injecting the compensatory currents into the laser gain section and the SOA. For comparison, without injecting the compensatory current (i.e., without the thermal drift compensation), the laser gain section current and the SOA current were fixed at 100 mA and 180 mA, respectively. As shown in Fig. 6(b), the output powers of both cases have similar channel number dependent patterns. The maximum power difference due to the compensatory current injection was observed at channels #6 and #89, 2.65 dB and 2.45 dB, respectively. The power difference change of 0.2 dB can be understood by the saturation features of the SOA as mentioned in Section 3.2. It should be noted that the SOA used to act as an optical power trimmer for constant output power among various channels. However, the SOA in our scheme was used for the thermal drift compensation at the expense of the output power deviation.

To measure an optical signal at the PD for both the start channel and the destination channel, a 2 × 1, 50:50 optical coupler (not shown) was inserted between the 90 × 90 AWGR and the VOA of the experimental setup shown in Fig. 3(a). Figure 6(c) shows the result when #90 and #38 output ports of the AWGR were connected to each input port of the 2 × 1 optical coupler (i.e., optical coupler was used as an optical power combiner). Note that the time from the onset of the trigger signal to the turning-off of the start channel takes ~0.24 µs including the electronic commend time of ~0.12 µs (denoted as tc) and light propagation time of ~0.12 µs from the tunable TOSA to the PD (denoted as tp). The channel-to-channel switching time is defined to be the time between the turning-off of the start channel optical signal and turning-on of the destination channel optical signal (50% of the rising time). At the switching time, we can say that the wavelength deviation was 0.085 nm from the target wavelength, since the AWGR has 3-dB optical bandwidth of 0.17 nm. The channel-to-channel switching was ~0.09 µs in the case.

Figure 6(d) shows measured channel-to-channel switching time from channel #90 to each channel. If we compare Figs. 6(a), 6(b), and 6(d), there is a strong correlation among the drive currents, output powers, and measured switching time. The start channel has one of the lowest RG section current and thus the measurement included the worst switching cases. Full scale change of the RG section current occurred at #3, #20, #37, #55, #72, and #89 destination channels as shown in Fig. 6(a). Though we did not measure all the possible combinations of 8,010 cases, it can be said that the channel-to-channel switching time was < 0.81 µs. In the case of the destination channel which has a RG section current value similar to that of the start channel #90, we could achieve very short switching times (#4, #21, #38, #56, and #73 destination channels) as shown in Fig. 6(d). The maximum difference between the shortest (#4) and the longest (#85) switching time was ~0.77 µs.

To clarify the reason of the switching time difference according to destination channel, we measured the driving voltages of the FG, the phase, and the RG sections as a function of time. Figure 7(a) shows that the FG and phase driving signals from ~0 V to ~0.3 V (corresponding to full scale of 5 mA) responded much faster than the RG driving signal from ~0.1 V to ~2 V (corresponding to full scale of 54.5 mA). Thus, when the difference of the RG section current between the start channel and the destination channel is very small with large FG section current change (in the cases of #4, #21, #38, #56, and #73 destination channels), the performance of the FG and phase current drivers rather than the RG current driver exert a strong influence on the channel-to-channel switching time.

 figure: Fig. 7

Fig. 7 Measured drive voltage of the FG, phase, and RG sections vs. time (a) and 50% rising time of the RG drive signal vs. the target value of the RG current (b).

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Meanwhile, as the RG switching current increases, the channel-to-channel switching is more affected by the RG current driver. Figure 7(b) shows the 50% rising time of the RG driving signal as a function of the target value of the RG current. The initial current of the RG section was 2.28 mA which corresponds to the channel #90. With increasing the target RG current up to 14 mA, the rising time of the RG driving signal increases. As the RG current increases more than 14 mA, the rising time decreases slightly. Because of this characteristic of the RG current driver, the worst channel-to-channel switching time of Fig. 6(d) occurred at middle destination channels in each sub-band (#65 and #90). However, other worst cases (#20, #37, and #55) were not observed around middle destination channels. In addition, we could see the fluctuations in the channel-to-channel switching time. The reason of those results can be understood by an effect of the instantaneous mode hopping in our tunable laser. As the RG current increases, the possibility of the mode hopping also increases and it delays the switching time.

The rising time of current driver for the RG section seems to have dominant contribution to the channel-to-channel switching time. Thus, if we adopted much faster current driver, the switching time would be more reduced. Here, we emphasize that the switching time only relies on the performance of electronic current drivers, due to the suppression of thermal wavelength drift.

5. Summary

This paper presents how to suppress thermally induced wavelength drift in a widely tunable DS-DBR laser by injecting pre-compensatory currents into the laser gain medium section and the integrated SOA. We have achieved the wavelength stability of ± 0.01 nm (or ± 1.24 GHz in frequency), satisfying the allowable maximum value of ± 2.5 GHz standardized in OIF-ITLA-MSA.

To accommodate the proposed method, the lookup table of the electronic current driver board has been updated including the compensatory current settings. Then, fast channel-to-channel switching with the use of a 90 × 90, 50-GHz spaced AWGR has been experimentally demonstrated. Even the worst case is exhibiting the switching time < 0.81 µs. It may be noted that the switching time in our scheme only relies on the rising time of current drivers, since we did not employ a wavelength locker which has a fundamental finite time delay in the feedback loop circuit. Thus, we believe that the proposed method enables to reach to an intrinsic transient time of the nanosecond-class tunable laser with improvements in the electronic current driver board.

It is noted that we have discussed whether the proposed thermal drift compensation method can be applied to burst mode lasers. For the burst mode operation, the gain section current of the laser is switched-on and -off by tens of mA [19]. This current change causes the laser chip temperature change like the temperature re-distribution owing to the RG switching current in the tunable DS-DBR laser. If the lasers for the burst mode operation were monolithically integrated with a SOA, the temperature change induced by the gain section current switching would be compensated by injecting pre-compensatory current to the SOA due to its large thermal capacity.

Funding

This work was supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIT) (2016-0-00573, Development of Data Center Optical Networking Core Technologies for Photonic Frame based Packet Switching)

Acknowledgments

We gratefully acknowledge NEON Photonics Co., Ltd. for supporting their 90 × 90, 50-GHz spaced arrayed-waveguide grating router (AWGR) in this work

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Figures (7)

Fig. 1
Fig. 1 A schematic diagram of a tunable TOSA (orange-colored box) and an electronic circuit board.
Fig. 2
Fig. 2 Measured optical spectra (solid lines) and side-mode suppression ratio (open square) with the largest and smallest channel number in each sub-band (a), a schematic explaining thermal wavelength drift (b), and conceptual drive currents for suppressing the thermal wavelength drift (c).
Fig. 3
Fig. 3 Experimental setup used to measure dynamic wavelength deviations (a) and normalized optical spectra of the 50-GHz spaced AWGR and tunable TOSA (b).
Fig. 4
Fig. 4 Calculated wavelengths from measured output voltages at the PD according to the laser gain section current and the SOA current of the start channel. The red-dotted line represents the target wavelength of 1555.832 nm.
Fig. 5
Fig. 5 Measured output power of the tunable TOSA as a function of the laser gain current and SOA current.
Fig. 6
Fig. 6 The drive currents of the laser gain section, the SOA, and the RG section for thermal drift compensation (a), measured optical output power of tunable TOSA w/o and w/ injecting the compensatory currents (b), a demonstration of channel-to-channel switching as a function of time (c), and channel-to-channel switching time from channel #90 to each channel (d).
Fig. 7
Fig. 7 Measured drive voltage of the FG, phase, and RG sections vs. time (a) and 50% rising time of the RG drive signal vs. the target value of the RG current (b).

Equations (1)

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1 T = 1 β ln R R 0 + 1 T 0
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