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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 7219–7227
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Photonic generation of ultra-wideband signals by direct current modulation on SOA section of an SOA-integrated SGDBR laser

Hui Lv, Yonglin Yu, Tan Shu, Dexiu Huang, Shan Jiang, and Liam P. Barry  »View Author Affiliations


Optics Express, Vol. 18, Issue 7, pp. 7219-7227 (2010)
http://dx.doi.org/10.1364/OE.18.007219


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Abstract

Photonic ultra-wideband (UWB) pulses are generated by direct current modulation of a semiconductor optical amplifier (SOA) section of an SOA-integrated sampled grating distributed Bragg reflector (SGDBR) laser. Modulation responses of the SOA section of the laser are first simulated with a microwave equivalent circuit model. Simulated results show a resonance behavior indicating the possibility to generate UWB signals with complex shapes in the time domain. The UWB pulse generation is then experimentally demonstrated for different selected wavelength channels with an SOA-integrated SGDBR laser.

© 2010 OSA

1. Introduction

Ultra-wideband (UWB), which is regulated by the Federal Communications Commission (FCC), has recently been developed for short range wireless communication within the frequency range from 3.1 to 10.6 GHz [1

1. Fed. Commun. Commission, Revision of Part 15 of the Commission’s Rules Regarding Ultra-Wideband Transmission Systems, Apr. 2002. Tech. Rep., ET-Docket 98–153, FCC02–48.

]. Compared to traditional wireless communication technologies, UWB technology has many advantages such as low power consumption, high bit rate, immunity to multipath fading and so on [2

2. D. Porcino, P. Research, and W. Hirt, “Ultra-wideband radio technology: Potential and challenges ahead,” IEEE Commun. Mag. 41(7), 66–74 (2003). [CrossRef]

,3

3. M. Ghavami, L. B. Michael, and R. Kohno, Ultra wide-band signals and systems in communication engineering, (Wiley, West Sussex, England, 2004).

]. Based on the FCC definition, a UWB signal should have a spectral bandwidth that is greater than 500 MHz or a fractional bandwidth that is greater than 20% [1

1. Fed. Commun. Commission, Revision of Part 15 of the Commission’s Rules Regarding Ultra-Wideband Transmission Systems, Apr. 2002. Tech. Rep., ET-Docket 98–153, FCC02–48.

].

In order to overcome the limitations of propagation distance of UWB signals and cost of radio-frequency (RF) electrical circuits or devices, radio-over-fiber (ROF) systems have been adopted to use the advantages provided by optical fiber, where the UWB signals can be directly generated in the optical domain and distributed over the optical fiber without the need for an extra electrical-to-optical conversion. There are three main methods for the optical generation of UWB pulses [4

4. J. Yao, F. Zeng, and Q. Wang, “Photonic generation of ultra-wideband signals,” J. Lightwave Technol. 25(11), 3219–3235 (2007).

]. One is to generate the first- or second-order derivative of a Gaussian pulse by using a photonic microwave delay-line filter, with two or three taps for monocycle or doublet, both with one negative tap. The negative coefficient can be generated based on cross-gain modulation (XGM) in a semiconductor optical amplifier (SOA) [5

5. Q. Wang, F. Zeng, S. Blais, and J. Yao, “Optical ultrawideband monocycle pulse generation based on cross-gain modulation in a semiconductor optical amplifier,” Opt. Lett. 31(21), 3083–3085 (2006). [CrossRef] [PubMed]

] or cross-polarization modulation (XPolM) in a polarization modulator (PolM) [6

6. J. Yao and Q. Wang, “Photonic microwave bandpass filter with negative coefficients using a polarization modulator,” IEEE Photon. Technol. Lett. 19(9), 644–646 (2007). [CrossRef]

]. The second method is based on optical spectral shaping and dispersion-induced frequency-to-time mapping using all-fiber components. The frequency-to-time mapping can be realized using a dispersive device, such as a dispersive fiber [7

7. C. Wang, F. Zeng, and J. P. Yao, “All-fiber ultra wideband pulse generation based on spectral shaping and dispersion-induced frequency-to-time conversion,” IEEE Photon. Technol. Lett. 19(3), 137–139 (2007). [CrossRef]

]. The third method is based on phase-modulation-to-intensity-modulation (PM-IM), where the PM–IM conversion can be implemented in the optical domain by using either a dispersive device [8

8. F. Zeng and J. Yao, “Investigation of phase modulator based all-optical bandpass filter,” J. Lightwave Technol. 23(4), 1721–1728 (2005). [CrossRef]

] or an optical frequency discriminator [9

9. F. Zeng and J. Yao, “Ultrawideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-Bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. 18(19), 2062–2064 (2006). [CrossRef]

]. Recently the generation of UWB signals with complex shape has been reported [10

10. X. Yu, T. Braidwood Gibbon, M. Pawlik, S. Blaaberg, and I. Tafur Monroy, “A photonic ultra-wideband pulse generator based on relaxation oscillations of a semiconductor laser,” Opt. Express 17(12), 9680–9687 (2009). [CrossRef] [PubMed]

], which is based on relaxation oscillations of a semiconductor laser.

As proposed in [11

11. A. Kaszubowska-Anandarajah, E. Connolly, L. P. Barry, and P. Perry, “Demonstration of wavelength packet switched radio-over-fiber system,” IEEE Photon. Technol. Lett. 19(4), 200–202 (2007). [CrossRef]

], a widely tunable laser can be employed as an optical transmitter at a central station in a ROF system to achieve addressing and routing of traffic by switching between the wavelengths assigned to different base stations. Here, we extend this concept to combine the wavelength flexibility of tunable lasers with photonic UWB generation. For this purpose, an SOA-integrated sampled grating distributed Bragg reflector (SGDBR) laser is used, where the SGDBR laser is for wavelength tuning while the integrated SOA section is for generation of UWB signals. Compared with the method in [10

10. X. Yu, T. Braidwood Gibbon, M. Pawlik, S. Blaaberg, and I. Tafur Monroy, “A photonic ultra-wideband pulse generator based on relaxation oscillations of a semiconductor laser,” Opt. Express 17(12), 9680–9687 (2009). [CrossRef] [PubMed]

], we take the advantage of the monolithically integrated widely tunable laser module to introduce the wavelength tunability to the photonic UWB generation. This feature will make the ROF systems more flexible.

Gain dynamics [12

12. H. Chen, M. Chen, C. Qiu, and S. Xie, “A novel composite method for ultra-wideband doublet pulses generation,” IEEE Photon. Technol. Lett. 19(24), 2021–2023 (2007). [CrossRef]

], XGM [5

5. Q. Wang, F. Zeng, S. Blais, and J. Yao, “Optical ultrawideband monocycle pulse generation based on cross-gain modulation in a semiconductor optical amplifier,” Opt. Lett. 31(21), 3083–3085 (2006). [CrossRef] [PubMed]

,13

13. W. Zhang, J. Sun, J. Wang, C. Cheng, and X. Zhang, “Ultra-wideband pulse train generation based on turbo-switch structures,” IEEE Photon. Technol. Lett. 21(5), 271–273 (2009). [CrossRef]

] and nonlinear polarization rotation [14

14. S. Fu, W.-D. Zhong, Y. J. Wen, and P. Shum, “Photonic monocycle pulse frequency up-conversion for ultrawideband-over-fiber applications,” IEEE Photon. Technol. Lett. 20(12), 1006–1008 (2008). [CrossRef]

] in SOAs have been widely demonstrated to generate UWB pulses. In this paper, however, resonance behavior of SOAs is exploited. Generation of UWB signals by direct current modulation of the SOA section integrated in the front of the SGDBR laser is demonstrated. With a microwave equivalent circuit model, modulation response in the time domain for the SOA section of the laser is first studied to theoretically produce the UWB pulse shapes. Then the UWB generation is demonstrated experimentally. For different selected wavelength channels the generated UWB pulses agree well with the Federal Communications Commission (FCC) mask in the frequency domain.

2. Small-signal equivalent circuit model of SOA section

The direct current modulation of an SOA monolithically integrated with an SGDBR laser has been well studied by Coldren’s group from UCSB [15

15. S.-L. Lee, M. E. Heimbuch, D. A. Cohen, L. A. Coldren, and S. P. DenBaars, “Integration of semiconductor laser amplifiers with sampled grating tunable lasers for WDM applications,” IEEE J. Sel. Top. Quantum Electron. 3(2), 615–627 (1997). [CrossRef]

]. Here, to predict the transient response of the SOA section of the SOA-integrated SGDBR laser, a small-signal equivalent circuit model of SOA, which can be derived from [16

16. R. S. Tucker and I. P. Kaminow, “High-frequency characteristics of directly modulated InGaAsP ridge waveguide and buried heterostructure lasers,” J. Lightwave Technol. 2(4), 385–393 (1984). [CrossRef]

,17

17. A. D. Barman, I. Sengupta, and P. K. Basu, “A simple SPICE model for traveling wave semiconductor laser amplifier,” Microw. Opt. Technol. Lett. 49(7), 1558–1561 (2007). [CrossRef]

], is introduced for theoretical analysis. As shown in Fig. 1
Fig. 1 Small-signal equivalent circuit model of the SOA section
, there are three parts in the total small-signal equivalent circuit model: source, parasitics and the intrinsic SOA. The small-signal current is(t) is set by the user or control system and Rin is the source resistance, which is usually regarded as 50 Ω. The parasitic effect of this model can be described with five parasitic elements, in which the three elements CP, LP and RP represent the package parasitics, and the two other elements Cs and Rs characterize the chip parasitics. C and R are derived from the linearization of the rate equation for SOA carrier density. The small-signal voltage v(t) can be regarded as the small-signal optical gain of SOA corresponding to is(t).

All the parameters in the SOA model shown in Fig. 1 can be extracted by fitting the circuit model with measured microwave reflection coefficient S11 and transmission coefficient S21 of the SOA section. The fitting, performed with Advanced Design System (Agilent commercial software) for linear and non-linear simulations, utilizes a solving method based on a random optimizer algorithm at first, and then by a gradient one [18

18. F. Delpiano, R. Paoletti, P. Audagnotto, and M. Puleo, “High frequency modeling and characterization of high performanceDFB laser modules,” IEEE Trans. Comp., Packag,” Manufact. Technol. 17, 412–417 (1994).

]. The measurement setup is illustrated in Fig. 2
Fig. 2 Microwave measurement setup for the SOA section of the SOA-integrated SGDBR laser.
. Gain section and tuning sections are driven by low noise and high stability current drivers to keep the SGDBR laser working at a certain wavelength. The SOA section is biased through a wide bandwidth Bias-Tee, while a thermoelectric cooler (TEC) controller is introduced to obtain a precise setting and stabilization of the lasing wavelength. The output modulated optical signal of the SGDBR laser is routed to the wide bandwidth optical receiver unit into the Network Analyzer (NA), which can provide both the S11 reflection response (when configured for electrical measurement) and the S21 transmission response (when configured for electro-optical measurement). Figure 3
Fig. 3 Measured and fitted S11 of the SOA section of the SOA-integrated SGDBR laser (SOA section biased at 90 mA, gain, phase, front and rear mirror section are driven at 110, 0, 29.5 and 25.5 mA respectively to set the output wavelength of the laser at 1538.85 nm).
and Fig. 4
Fig. 4 Measured and fitted S21 of the SOA section of the SOA-integrated SGDBR laser for three different operating wavelengths of the laser.
give the measured and fitted results of S11 and S21, respectively. The optimized results of all the elements for the SOA circuit model are shown in Table 1

Table 1. Extracted values of extrinsic and intrinsic circuit parameters of the SOA section of the SOA-integrated SGDBR laser

table-icon
View This Table
.

3. Simulation for generation of UWB signals by direct current modulation of the SOA section

From the measured S21 in Fig. 4, we can find there are main resonance peaks of the SOA section around 3.2 GHz. Additionally, minor resonance peaks around 6.5 GHz can be observed. Resonance behavior of SOAs was first predicated in [19

19. J. Mork, A. Mecozzi, and G. Eisenstein, “The modulation response of a semiconductor laser amplifier,” IEEE J. Sel. Top. Quantum Electron. 5(3), 851–860 (1999). [CrossRef]

], which is similar to the well-known relaxation oscillation found in semiconductor lasers, but of a different physical origin. When the SOA section is set around the resonance point, the relaxation oscillation of SOA gain will appear, which could be helpful for producing UWB pulses with complex shapes (close to the shapes of high-order Gaussian pulses) at the output of the SOA-integrated SGDBR laser.

4. Experimental results and discussion

5. Conclusion

Tunable UWB pulse generation was demonstrated by direct current modulation of the SOA section of an SOA-integrated SGDBR laser. A microwave equivalent circuit model was used to study modulation response of the SOA section. Numerical simulation was performed to show the generation of UWB signals which have complex shapes in the time domain. The pattern of 10Gbit/s 32-bit sequence “0111 1111 1111 1111 1111 1111 1111 1111” was then applied on the SOA section of the SOA-integrated SGDBR laser. The generated UWB pulses agreed well with the simulation results in the time domain and the corresponding spectral envelopes in frequency domain were compliant with the FCC requirement. Experimental results demonstrated that tunable UWB pulse generation can be achieved by control of the integrated tunable laser. This could be attractive for applications of tunable lasers in microwave photonics.

Acknowledgments

This work has been supported in part by the National High Technology Developing Program of China under Grant No. 2009AA03Z418, in part by the National Natural Science Foundation of China under Grant No. 60677024, and in part by Ministry of Education 111 Project of China under Grant No.B07038. The authors would like to thank technical supports from Wuhan Office, Anritsu Company with Pulse Pattern Generator (MP1800A) and Network Analyzer (37369D).

References and links

1.

Fed. Commun. Commission, Revision of Part 15 of the Commission’s Rules Regarding Ultra-Wideband Transmission Systems, Apr. 2002. Tech. Rep., ET-Docket 98–153, FCC02–48.

2.

D. Porcino, P. Research, and W. Hirt, “Ultra-wideband radio technology: Potential and challenges ahead,” IEEE Commun. Mag. 41(7), 66–74 (2003). [CrossRef]

3.

M. Ghavami, L. B. Michael, and R. Kohno, Ultra wide-band signals and systems in communication engineering, (Wiley, West Sussex, England, 2004).

4.

J. Yao, F. Zeng, and Q. Wang, “Photonic generation of ultra-wideband signals,” J. Lightwave Technol. 25(11), 3219–3235 (2007).

5.

Q. Wang, F. Zeng, S. Blais, and J. Yao, “Optical ultrawideband monocycle pulse generation based on cross-gain modulation in a semiconductor optical amplifier,” Opt. Lett. 31(21), 3083–3085 (2006). [CrossRef] [PubMed]

6.

J. Yao and Q. Wang, “Photonic microwave bandpass filter with negative coefficients using a polarization modulator,” IEEE Photon. Technol. Lett. 19(9), 644–646 (2007). [CrossRef]

7.

C. Wang, F. Zeng, and J. P. Yao, “All-fiber ultra wideband pulse generation based on spectral shaping and dispersion-induced frequency-to-time conversion,” IEEE Photon. Technol. Lett. 19(3), 137–139 (2007). [CrossRef]

8.

F. Zeng and J. Yao, “Investigation of phase modulator based all-optical bandpass filter,” J. Lightwave Technol. 23(4), 1721–1728 (2005). [CrossRef]

9.

F. Zeng and J. Yao, “Ultrawideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-Bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. 18(19), 2062–2064 (2006). [CrossRef]

10.

X. Yu, T. Braidwood Gibbon, M. Pawlik, S. Blaaberg, and I. Tafur Monroy, “A photonic ultra-wideband pulse generator based on relaxation oscillations of a semiconductor laser,” Opt. Express 17(12), 9680–9687 (2009). [CrossRef] [PubMed]

11.

A. Kaszubowska-Anandarajah, E. Connolly, L. P. Barry, and P. Perry, “Demonstration of wavelength packet switched radio-over-fiber system,” IEEE Photon. Technol. Lett. 19(4), 200–202 (2007). [CrossRef]

12.

H. Chen, M. Chen, C. Qiu, and S. Xie, “A novel composite method for ultra-wideband doublet pulses generation,” IEEE Photon. Technol. Lett. 19(24), 2021–2023 (2007). [CrossRef]

13.

W. Zhang, J. Sun, J. Wang, C. Cheng, and X. Zhang, “Ultra-wideband pulse train generation based on turbo-switch structures,” IEEE Photon. Technol. Lett. 21(5), 271–273 (2009). [CrossRef]

14.

S. Fu, W.-D. Zhong, Y. J. Wen, and P. Shum, “Photonic monocycle pulse frequency up-conversion for ultrawideband-over-fiber applications,” IEEE Photon. Technol. Lett. 20(12), 1006–1008 (2008). [CrossRef]

15.

S.-L. Lee, M. E. Heimbuch, D. A. Cohen, L. A. Coldren, and S. P. DenBaars, “Integration of semiconductor laser amplifiers with sampled grating tunable lasers for WDM applications,” IEEE J. Sel. Top. Quantum Electron. 3(2), 615–627 (1997). [CrossRef]

16.

R. S. Tucker and I. P. Kaminow, “High-frequency characteristics of directly modulated InGaAsP ridge waveguide and buried heterostructure lasers,” J. Lightwave Technol. 2(4), 385–393 (1984). [CrossRef]

17.

A. D. Barman, I. Sengupta, and P. K. Basu, “A simple SPICE model for traveling wave semiconductor laser amplifier,” Microw. Opt. Technol. Lett. 49(7), 1558–1561 (2007). [CrossRef]

18.

F. Delpiano, R. Paoletti, P. Audagnotto, and M. Puleo, “High frequency modeling and characterization of high performanceDFB laser modules,” IEEE Trans. Comp., Packag,” Manufact. Technol. 17, 412–417 (1994).

19.

J. Mork, A. Mecozzi, and G. Eisenstein, “The modulation response of a semiconductor laser amplifier,” IEEE J. Sel. Top. Quantum Electron. 5(3), 851–860 (1999). [CrossRef]

20.

R. Zhang, L. Dong, D. Wang, J. Zhang, L. Chen, S. Jiang, and Y. Yu, “Sampled grating DBR lasers with 35nm quasi-continuous tuning range,” Chin. J. Semicond. 29, 2301–2303 (2008).

21.

H. Lv, T. Shu, Y. Yu, D. Huang, L. Dong, and R. Zhang, “Fast power control and wavelength switching in a tunable SOA-integrated SGDBR laser,” IEEE OptoElectronics and Communications Conference (OECC 2009), Pap. ThPD4.

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(250.5980) Optoelectronics : Semiconductor optical amplifiers
(320.5550) Ultrafast optics : Pulses
(060.5625) Fiber optics and optical communications : Radio frequency photonics
(250.5960) Optoelectronics : Semiconductor lasers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 16, 2009
Revised Manuscript: February 27, 2010
Manuscript Accepted: March 4, 2010
Published: March 24, 2010

Citation
Hui Lv, Yonglin Yu, Tan Shu, Dexiu Huang, Shan Jiang, and Liam P. Barry, "Photonic generation of ultra-wideband signals by direct current modulation on SOA section of an SOA-integrated SGDBR laser," Opt. Express 18, 7219-7227 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7219


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References

  1. Fed. Commun. Commission, Revision of Part 15 of the Commission’s Rules Regarding Ultra-Wideband Transmission Systems, Apr. 2002. Tech. Rep., ET-Docket 98–153, FCC02–48.
  2. D. Porcino, P. Research, and W. Hirt, “Ultra-wideband radio technology: Potential and challenges ahead,” IEEE Commun. Mag. 41(7), 66–74 (2003). [CrossRef]
  3. M. Ghavami, L. B. Michael, and R. Kohno, Ultra wide-band signals and systems in communication engineering, (Wiley, West Sussex, England, 2004).
  4. J. Yao, F. Zeng, and Q. Wang, “Photonic generation of ultra-wideband signals,” J. Lightwave Technol. 25(11), 3219–3235 (2007).
  5. Q. Wang, F. Zeng, S. Blais, and J. Yao, “Optical ultrawideband monocycle pulse generation based on cross-gain modulation in a semiconductor optical amplifier,” Opt. Lett. 31(21), 3083–3085 (2006). [CrossRef] [PubMed]
  6. J. Yao and Q. Wang, “Photonic microwave bandpass filter with negative coefficients using a polarization modulator,” IEEE Photon. Technol. Lett. 19(9), 644–646 (2007). [CrossRef]
  7. C. Wang, F. Zeng, and J. P. Yao, “All-fiber ultra wideband pulse generation based on spectral shaping and dispersion-induced frequency-to-time conversion,” IEEE Photon. Technol. Lett. 19(3), 137–139 (2007). [CrossRef]
  8. F. Zeng and J. Yao, “Investigation of phase modulator based all-optical bandpass filter,” J. Lightwave Technol. 23(4), 1721–1728 (2005). [CrossRef]
  9. F. Zeng and J. Yao, “Ultrawideband impulse radio signal generation using a high-speed electrooptic phase modulator and a fiber-Bragg-grating-based frequency discriminator,” IEEE Photon. Technol. Lett. 18(19), 2062–2064 (2006). [CrossRef]
  10. X. Yu, T. Braidwood Gibbon, M. Pawlik, S. Blaaberg, and I. Tafur Monroy, “A photonic ultra-wideband pulse generator based on relaxation oscillations of a semiconductor laser,” Opt. Express 17(12), 9680–9687 (2009). [CrossRef] [PubMed]
  11. A. Kaszubowska-Anandarajah, E. Connolly, L. P. Barry, and P. Perry, “Demonstration of wavelength packet switched radio-over-fiber system,” IEEE Photon. Technol. Lett. 19(4), 200–202 (2007). [CrossRef]
  12. H. Chen, M. Chen, C. Qiu, and S. Xie, “A novel composite method for ultra-wideband doublet pulses generation,” IEEE Photon. Technol. Lett. 19(24), 2021–2023 (2007). [CrossRef]
  13. W. Zhang, J. Sun, J. Wang, C. Cheng, and X. Zhang, “Ultra-wideband pulse train generation based on turbo-switch structures,” IEEE Photon. Technol. Lett. 21(5), 271–273 (2009). [CrossRef]
  14. S. Fu, W.-D. Zhong, Y. J. Wen, and P. Shum, “Photonic monocycle pulse frequency up-conversion for ultrawideband-over-fiber applications,” IEEE Photon. Technol. Lett. 20(12), 1006–1008 (2008). [CrossRef]
  15. S.-L. Lee, M. E. Heimbuch, D. A. Cohen, L. A. Coldren, and S. P. DenBaars, “Integration of semiconductor laser amplifiers with sampled grating tunable lasers for WDM applications,” IEEE J. Sel. Top. Quantum Electron. 3(2), 615–627 (1997). [CrossRef]
  16. R. S. Tucker and I. P. Kaminow, “High-frequency characteristics of directly modulated InGaAsP ridge waveguide and buried heterostructure lasers,” J. Lightwave Technol. 2(4), 385–393 (1984). [CrossRef]
  17. A. D. Barman, I. Sengupta, and P. K. Basu, “A simple SPICE model for traveling wave semiconductor laser amplifier,” Microw. Opt. Technol. Lett. 49(7), 1558–1561 (2007). [CrossRef]
  18. F. Delpiano, R. Paoletti, P. Audagnotto, and M. Puleo, ““High frequency modeling and characterization of high performanceDFB laser modules,” IEEE Trans. Comp., Packag,” Manufact. Technol. 17, 412–417 (1994).
  19. J. Mork, A. Mecozzi, and G. Eisenstein, “The modulation response of a semiconductor laser amplifier,” IEEE J. Sel. Top. Quantum Electron. 5(3), 851–860 (1999). [CrossRef]
  20. R. Zhang, L. Dong, D. Wang, J. Zhang, L. Chen, S. Jiang, and Y. Yu, “Sampled grating DBR lasers with 35nm quasi-continuous tuning range,” Chin. J. Semicond. 29, 2301–2303 (2008).
  21. H. Lv, T. Shu, Y. Yu, D. Huang, L. Dong, and R. Zhang, “Fast power control and wavelength switching in a tunable SOA-integrated SGDBR laser,” IEEE OptoElectronics and Communications Conference (OECC 2009), Pap. ThPD4.

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