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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26936–26941
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A laterally-coupled distributed feedback laser with equivalent quarter-wave phase shift

Jingsi Li and Julian Cheng  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26936-26941 (2013)
http://dx.doi.org/10.1364/OE.21.026936


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Abstract

We report the first laterally-coupled distributed feedback (LC-DFB) laser with a quarter-wave equivalent phase shift (EPS) realized by interference lithography (IL) and conventional photolithography. A specially designed sampled grating is fabricated on both sidewalls of a ridge waveguide to provide a quarter-wave EPS at the center of the cavity. The resulting laser exhibits stable single-mode lasing operation over a wide range of injection currents, with a side mode suppression ratio (SMSR) of 41.1 dB. This provides a practical, low-cost method to fabricate quarter-wave phase shifted DFB lasers with high performance without any epitaxial regrowth or the use of electron-beam lithography, thereby simplifying the fabrication of DFB lasers with stable and precise wavelengths, as single devices or as arrays in photonic integrated circuits.

© 2013 Optical Society of America

1. Introduction

Distributed feedback (DFB) semiconductor lasers are of great interest and have been extensively utilized for their high-bit-rate transmission performance in long-haul optical fiber communication systems [1

1. W. Li, X. Zhang, and J. Yao, “Experimental demonstration of a multi-wavelength distributed feedback semiconductor laser array with an equivalent chirped grating profile based on the equivalent chirp technology,” Opt. Express 21(17), 19966–19971 (2013). [CrossRef] [PubMed]

3

3. J. Li, H. Wang, X. Chen, Z. Yin, Y. Shi, Y. Lu, Y. Dai, and H. Zhu, “Experimental demonstration of distributed feedback semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 17(7), 5240–5245 (2009). [CrossRef] [PubMed]

]. However, there are still some unsolved problems and improvements needed in their properties.

A DFB laser with uniform index-coupled gratings, which is normally realized using interference lithography (IL), intrinsically has two degenerate lasing modes [4

4. L. A. Coldren, S. W. Corzine, and M. L. Masanovic, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (John Wiley, 2012), Chap. 3.

]. At the Bragg wavelength, the optical mode is anti-resonant. There are two resonant modes that are symmetrically positioned on both sides of the Bragg wavelength. But due to the arbitrary phase at the cleaved facets, the effect of facet coating, non-uniform gain distribution, etc., the degeneracy may sometimes be destroyed, and the laser is able to lase in a single longitudinal mode. However, this uncertainty can result in problems such as low yield, an uncontrolled lasing wavelength, multi-mode lasing, mode-hopping, etc. One solution to the degenerate modes problem is to insert a quarter-wave phase shift [5

5. K. Sekartedjo, N. Eda, K. Furuya, Y. Suematsu, F. Koyama, and T. Tanbun-Ek, “1.5 µm phase-shifted DFB lasers for single-mode operation,” Electron. Lett. 20(2), 80–81 (1984). [CrossRef]

] into the gratings at the center of the laser cavity by increasing the grating pitch by a half period. The resulting optical mode has a strong resonance that is pinned at the resonant wavelength, which is strongly selective and therefore stable. Although there are some approaches that can potentially realize this phase shift [6

6. W. K. Chan, J. Chung, and R. J. Contolini, “Phase-shifted quarter micron holographic gratings by selective image reversal of photoresist,” Appl. Opt. 27(8), 1377–1380 (1988). [CrossRef] [PubMed]

], a precise and controllable quarter-wave phase-shift is still not achievable by any means other than electron-beam lithography (EBL). Compared to the cost-ineffective and low-throughput EBL, the widely used optical IL approach is scalable to larger wafer areas, but it is only capable of providing uniform gratings. To resolve this problem, a specially designed sampled Bragg grating (SBG) method has been proposed [3

3. J. Li, H. Wang, X. Chen, Z. Yin, Y. Shi, Y. Lu, Y. Dai, and H. Zhu, “Experimental demonstration of distributed feedback semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 17(7), 5240–5245 (2009). [CrossRef] [PubMed]

,7

7. Y. Dai and X. Chen, “DFB semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 15(5), 2348–2353 (2007). [CrossRef] [PubMed]

], by which an equivalent phase shift (EPS) can be realized in uniform IL-produced gratings.

Additionally, DFB lasers are usually fabricated using either a ridge-waveguide (RWG) structure [1

1. W. Li, X. Zhang, and J. Yao, “Experimental demonstration of a multi-wavelength distributed feedback semiconductor laser array with an equivalent chirped grating profile based on the equivalent chirp technology,” Opt. Express 21(17), 19966–19971 (2013). [CrossRef] [PubMed]

3

3. J. Li, H. Wang, X. Chen, Z. Yin, Y. Shi, Y. Lu, Y. Dai, and H. Zhu, “Experimental demonstration of distributed feedback semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 17(7), 5240–5245 (2009). [CrossRef] [PubMed]

], or a buried heterostructure (BH) [8

8. M. Mohrle, A. Sigmund, R. Steingruber, W. Furst, and A. Suna, “All-active tapered 1.55-µm InGaAsP BH-DFB laser with continuously chirped grating,” IEEE Photon. Technol. Lett. 15(3), 365–367 (2003). [CrossRef]

], both of which require at least two to three epitaxial growths. The regrowth process is expensive and complicated, placing critical demands on wafer cleanliness and surface morphology. To avoid epitaxial regrowth and the potential problems that it may bring, a laterally-coupled DFB (LC-DFB) laser has been proposed [9

9. L. M. Miller, J. T. Verdeyen, J. J. Coleman, R. P. Bryan, J. J. Alwan, K. J. Beernink, J. S. Hughes, and T. M. Cockerill, “A distributed feedback ridge waveguide quantum well heterostructure laser,” IEEE Photon. Technol. Lett. 3(1), 6–8 (1991). [CrossRef]

]. However, due to the non-planar topography on which the gratings are fabricated, the LC-DFB lasers are usually realized by using EBL. Recently, a LC-DFB laser with first-order gratings achieved by IL has been reported [10

10. J. Li and J. Cheng, “Laterally-coupled distributed feedback laser with first-order gratings by interference lithography,” Electron. Lett. 49(12), 764–766 (2013). [CrossRef]

], in which the gratings are first patterned on a planar surface and then transferred onto the sidewalls during the ridge etching process. Good single-mode lasing performance and strong mode selection were achieved, with a SMSR of 37 dB.

In this paper we report the first laterally-coupled DFB laser with an equivalent quarter-wave phase shift achieved by means of interference lithography. The laser contains a specially designed sampled grating fabricated on each sidewall of a ridge-waveguide structure, which effect an equivalent quarter-wave phase-shift at the center of the laser cavity, pinning the lasing mode at a new, strongly resonant wavelength. This is achieved without requiring EBL or regrowth, using a scalable, wafer-scale process. LC-DFB lasers with good lasing performance and excellent wavelength stability are obtained. It is also demonstrated that the lasing wavelength can be tuned over a wide range by simply adjusting the design parameters of the sampled gratings.

2. Principle

The EPS method was proposed and demonstrated previously in Bragg gratings [11

11. Y. Dai, X. Chen, L. Xia, Y. Zhang, and S. Xie, “Sampled Bragg grating with desired response in one channel by use of a reconstruction algorithm and equivalent chirp,” Opt. Lett. 29(12), 1333–1335 (2004). [CrossRef] [PubMed]

], fiber lasers [12

12. J. Li, Y. Cheng, Z. Yin, L. Jia, X. Chen, S. Liu, S. Li, and Y. Lu, “A multiexposure technology for sampled Bragg gratings and its applications in dual-wavelength lasing generation and OCDMA en/decoding,” IEEE Photon. Technol. Lett. 21(21), 1639–1641 (2009). [CrossRef]

], silicon waveguide [13

13. J. Sun, C. W. Holzwarth, and H. I. Smith, “Phase-shift Bragg grating in silicon using equivalent phase-shift method,” IEEE Photon. Technol. Lett. 24(1), 25–27 (2012). [CrossRef]

], conventional RWG lasers [3

3. J. Li, H. Wang, X. Chen, Z. Yin, Y. Shi, Y. Lu, Y. Dai, and H. Zhu, “Experimental demonstration of distributed feedback semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 17(7), 5240–5245 (2009). [CrossRef] [PubMed]

]. The basic principle can be described by the following two mechanisms.

Firstly, by sampling the gratings with a period of length P, an additional wave-vector is provided to enable phase-matching to a new resonance wavelength, λp, which is shifted away from the Bragg wavelength. The phase-matching condition for λp can be expressed as:
2πΛ±2πP=22πλP/nP.
(1)
where Λ is the grating pitch and np is the effective refractive index at λp. The “+” / “–” sign selects the Bragg wavelength that lies on the longer/shorter wavelength side of λp, respectively.

Secondly, a quarter-wave EPS, θp ( = π), can be obtained at the new resonance wavelength by increasing the sampling period P at the center of the laser cavity by an amount ΔP = P/2:

θP=2πΔPP=π.
(2)

The base grating is a uniform grating, which can be patterned by IL. Typically, P is of the order of micrometers, which can be defined using conventional photolithography. By applying the EPS to the LC-DFB lasers, the laser devices can be fabricated using an e-beam-free and regrowth-free method, which offers a batch processing capability that meets mass-production requirements.

3. Design and fabrication

Based on the principle described above, the sampled grating structure of the LC-DFB laser with EPS can be designed. The grating pitch, Λ, is set to be 254.8 nm. The interference lithography tool is set up in a Lloyd’s mirror configuration, using a 325 nm He-Cd UV laser. The sampling pitch, P, is designed to be 6.5 µm, and an EPS region of 3.25 µm is inserted at the center of the cavity (by extending one period to 9.75 µm), leading to a phase-matched resonant wavelength at λp = 1,571 nm. The Bragg wavelength will be at ~1,630 nm, which is sufficiently far away from the gain peak to eliminate the possibility of lasing at the Bragg wavelength. Here the “+” sign in Eq. (1) has been chosen mainly for a larger grating pitch, which is relatively easier to fabricate. The fabrication of the lateral gratings for the proposed laser has an etching aspect ratio of 1:16. If the “–” sign in Eq. (1) is chosen, the grating pitch will be smaller (236.3 nm), and in order to etch to the same depth, an even higher etching aspect ratio is needed. In this report, the EPS section with an additional length of 3.25 µm at the center of the cavity is designed to contain gratings, although the presence or absence of gratings in the EPS region will not affect the equivalent phase shift.

The wafer, which contains an AlGaInAs/InP epistructure designed for ridge-waveguide (RWG) lasers, was grown by Metal-Organic Vapor Phase Epitaxy (MOVPE) in a single growth run on a (100) n-InP substrate. The gain peak occurs at 1,560 nm. The epilayer structure contains an n-InP buffer layer, an n-InP cladding layer, an active region, a p-InP cladding layer and a contact layer. The active region consists of a Graded-Index (GRIN) separate confinement heterostructure (SCH), in which five AlGaInAs QWs are bounded between p-doped and n-doped GRIN layers, each of which contains an InAlAs carrier confinement layer.

In the fabrication process, a SiO2 mask layer is first deposited on the surface of the epiwafer by plasma-enhanced chemical vapor deposition (PECVD). Then a 20 nm thick Cr mask layer is evaporated onto the SiO2 surface. The sampling pattern containing the specially designed EPS region is first transferred from the photomask to the Cr layer by conventional photolithography followed by a Cl2/O2 Inductively-Coupled Plasma (ICP) etch. Regions in the SiO2 layer covered by Cr define the non-grating regions, while the exposed SiO2 will define the patterned grating regions. Optical interference lithography is used to pattern the gratings on top of the entire planar SiO2/Cr surface. Since the Cr layer is much thinner than the photoresist layer (160 nm), the surface flatness variation (20 nm) has a negligible effect on the IL grating patterning. The grating quality in the photoresist is equally good with or without the Cr sampling layer. The IL gratings are then transferred to the SiO2 mask by reactive-ion etching (RIE). The SiO2 that is covered by Cr is totally protected, giving rise to the non-grating regions. Another photolithography step is then performed to pattern the 2.2 µm wide ridge waveguides. Cl2/O2 ICP and RIE etching processes are used to remove the Cr and the SiO2 masks from regions where the ridge waveguide trenches will be etched. Before etching the ridge trenches, an oxygen RIE process [10

10. J. Li and J. Cheng, “Laterally-coupled distributed feedback laser with first-order gratings by interference lithography,” Electron. Lett. 49(12), 764–766 (2013). [CrossRef]

] is used to remove a 200 nm wide region of photoresist from each edge of the ridge photoresist mask, thereby exposing a 200 nm wide region of sampled SiO2 gratings along each sidewall of the ridge. The remaining photoresist now acts as a mask for etching the ridge in regions without gratings (Wr = 1.8 µm), while the narrow but exposed 200 nm wide sampled SiO2 gratings provide a mask for etching the deep lateral sampled grating (Wg = 200 nm) along both sidewalls as the trenches are etched. Cl2/CH4/H2 ICP etching is used for anisotropic etching of the III-V semiconductor materials. The grating aspect ratio is controlled to 0.5 for a maximized coupling efficiency.

The ridge and the gratings are both etched to a depth D = 2 µm, which is ~150 nm above the quantum well active region. Then the photoresist and Cr masks are removed, using O2 RIE for the photoresist, and a Buffered Oxide Etch (BOE) wet etch for the SiO2, leaving the etched ridge and sampled gratings along both sidewalls of the ridge.
Fig. 1 SEM image of the LC-DFB laser with the EPS region at the center of the laser cavity after etching the ridge trench.
Figure 1 shows a scanning electron microscope (SEM) image of the ridge at the center of the laser cavity, where the quarter-wave EPS exists. It can be seen that the non-grating ridge sidewalls are very smooth, without any vestiges of gratings. It is due to the ultra-high etching selection ratio of SiO2 to Cr. The sampling pattern is still visible on the bottom of the etched ridge trench. The pattern was partially transferred into the epiwafer contact layer during etching and removal of the SiO2 sampling mask, and propagates to the bottom of the ridge trench during ICP etching of the trench regions.

Following definition of the ridge waveguides and the sampled gratings, another SiO2 layer is deposited by PECVD for electrical isolation, followed by opening of the contact window on top of each ridge. Ti-Pt-Au is used as the p-contact metal, and Ti-Au is used as the n-contact metal, deposited on the top and back side of the device, respectively. The contacts are annealed by a rapid thermal annealing (RTA) process at 450 °C. After the wafer is cleaved into 900 µm long laser bars, a single-layer anti-reflection optical coating is deposited onto laser’s output facet to suppress lasing in the Fabry-Perot (FP) modes.

Fig. 2 SEM image showing the side view (a) and top view (b) of a LC-DFB laser with an EPS region after metallization.
The SEM images in Figs. 2(a) and 2(b) show the side-view and top-view of the LC-DFB laser with the EPS section after metallization.

4. Performance

Continuous-wave (CW) lasing is achieved over a wide range of temperatures and injection currents. At room temperature (~25 °C), the threshold current is 27 mA, corresponding to a threshold current density of 1.5 kA/cm2. The output power is 14 mW at a 100 mA injection current, and is 23.5 mW at a 200 mA injection current.

Fig. 3 Lasing spectrum of the LC-DFB laser with a quarter-wave EPS region under an injection current of 100 mA. A SMSR of 41.1 dB is obtained.
Figure 3 shows the lasing spectrum at 100 mA bias current under room temperature, CW operation. Single longitudinal mode lasing is obtained at 1,571.2 nm, with a side mode suppression ratio (SMSR) of 41.1 dB. The suppressed Bragg wavelength at ~1,630 nm can be seen clearly in an extended spectrum.

For lasers with an EPS, the possibility of lasing at the Bragg wavelength needs to be examined. If the Bragg wavelength is too close to the gain peak, as the injection current increases, and the gain spectrum shifts towards longer wavelengths, lasing at the Bragg wavelength becomes competitive [3

3. J. Li, H. Wang, X. Chen, Z. Yin, Y. Shi, Y. Lu, Y. Dai, and H. Zhu, “Experimental demonstration of distributed feedback semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 17(7), 5240–5245 (2009). [CrossRef] [PubMed]

]. As for the device design reported here, the Bragg wavelength does not lase at any temperature and injection current. The device exhibits a SMSR above 35 dB at up to 240 mA injection current.

The lasing mode shifts towards longer wavelengths with increasing bias current at the rate of ~10 pm/mA, under temperature control by a Thermoelectric Cooler (TEC). As the injection current is increased, even with TEC, the junction temperature still rises, causing the refractive index to increase [15

15. J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter 49(11), 7408–7417 (1994). [CrossRef] [PubMed]

]. However, for phase-shifted lasers the optical field intensity peaks at the phase shift region, where the higher carrier density under high injection current causes the effective refractive index to decrease [16

16. J. E. A. Whiteaway, G. H. B. Thompson, A. J. Collar, and C. J. Armistead, “The design and assessment of λ/4 phase shifted DFB laser structures,” IEEE J. Quantum Electron. 25(6), 1261–1279 (1989). [CrossRef]

], which partially reduces the temperature-induced red-shift, although the overall shift is still towards a longer wavelength.

The light-current-voltage (LIV) characteristics of the LC-DFB laser under different ambient temperatures has been measured and are shown in Fig. 4.
Fig. 4 LIV characteristics of the LC-DFB laser with EPS at different ambient temperatures.

6. Conclusion

In this paper we report the first LC-DFB lasers with a quarter-wave equivalent phase shift. The lasers operate in a single longitudinal mode over a very wide range of injection currents. A SMSR of 41.1 dB is achieved under a 100 mA DC bias. At room temperature (~25 °C), and under 100/200 mA bias current, a 14.0/23.5 mW optical output power is obtained. This method provides a scalable and low-cost approach to fabricating quarter-wave phase-shifted DFB lasers using e-beam-free and regrowth-free processes, which may be useful for the fabrication of DFB lasers with stable and precise wavelengths, as single devices or as arrays in photonic integrated circuits both in academic research and for industrial production.

References and links

1.

W. Li, X. Zhang, and J. Yao, “Experimental demonstration of a multi-wavelength distributed feedback semiconductor laser array with an equivalent chirped grating profile based on the equivalent chirp technology,” Opt. Express 21(17), 19966–19971 (2013). [CrossRef] [PubMed]

2.

L. Xie, J. W. Man, B. J. Wang, Y. Liu, X. Wang, H. Q. Yuan, L. J. Zhao, H. L. Zhu, N. H. Zhu, and W. Wang, “24-GHz directly modulated DFB laser modules for analog applications,” IEEE Photon. Technol. Lett. 24(5), 407–409 (2012). [CrossRef]

3.

J. Li, H. Wang, X. Chen, Z. Yin, Y. Shi, Y. Lu, Y. Dai, and H. Zhu, “Experimental demonstration of distributed feedback semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 17(7), 5240–5245 (2009). [CrossRef] [PubMed]

4.

L. A. Coldren, S. W. Corzine, and M. L. Masanovic, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (John Wiley, 2012), Chap. 3.

5.

K. Sekartedjo, N. Eda, K. Furuya, Y. Suematsu, F. Koyama, and T. Tanbun-Ek, “1.5 µm phase-shifted DFB lasers for single-mode operation,” Electron. Lett. 20(2), 80–81 (1984). [CrossRef]

6.

W. K. Chan, J. Chung, and R. J. Contolini, “Phase-shifted quarter micron holographic gratings by selective image reversal of photoresist,” Appl. Opt. 27(8), 1377–1380 (1988). [CrossRef] [PubMed]

7.

Y. Dai and X. Chen, “DFB semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express 15(5), 2348–2353 (2007). [CrossRef] [PubMed]

8.

M. Mohrle, A. Sigmund, R. Steingruber, W. Furst, and A. Suna, “All-active tapered 1.55-µm InGaAsP BH-DFB laser with continuously chirped grating,” IEEE Photon. Technol. Lett. 15(3), 365–367 (2003). [CrossRef]

9.

L. M. Miller, J. T. Verdeyen, J. J. Coleman, R. P. Bryan, J. J. Alwan, K. J. Beernink, J. S. Hughes, and T. M. Cockerill, “A distributed feedback ridge waveguide quantum well heterostructure laser,” IEEE Photon. Technol. Lett. 3(1), 6–8 (1991). [CrossRef]

10.

J. Li and J. Cheng, “Laterally-coupled distributed feedback laser with first-order gratings by interference lithography,” Electron. Lett. 49(12), 764–766 (2013). [CrossRef]

11.

Y. Dai, X. Chen, L. Xia, Y. Zhang, and S. Xie, “Sampled Bragg grating with desired response in one channel by use of a reconstruction algorithm and equivalent chirp,” Opt. Lett. 29(12), 1333–1335 (2004). [CrossRef] [PubMed]

12.

J. Li, Y. Cheng, Z. Yin, L. Jia, X. Chen, S. Liu, S. Li, and Y. Lu, “A multiexposure technology for sampled Bragg gratings and its applications in dual-wavelength lasing generation and OCDMA en/decoding,” IEEE Photon. Technol. Lett. 21(21), 1639–1641 (2009). [CrossRef]

13.

J. Sun, C. W. Holzwarth, and H. I. Smith, “Phase-shift Bragg grating in silicon using equivalent phase-shift method,” IEEE Photon. Technol. Lett. 24(1), 25–27 (2012). [CrossRef]

14.

A. Laakso, M. Dumitrescu, J. Viheriälä, J. Karinen, M. Suominen, and M. Pessa, “Optical modeling of laterally-corrugated ridge-waveguide gratings,” Opt. Quantum Electron. 40(11-12), 907–920 (2008). [CrossRef]

15.

J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter 49(11), 7408–7417 (1994). [CrossRef] [PubMed]

16.

J. E. A. Whiteaway, G. H. B. Thompson, A. J. Collar, and C. J. Armistead, “The design and assessment of λ/4 phase shifted DFB laser structures,” IEEE J. Quantum Electron. 25(6), 1261–1279 (1989). [CrossRef]

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(140.3490) Lasers and laser optics : Lasers, distributed-feedback
(140.5960) Lasers and laser optics : Semiconductor lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: September 24, 2013
Revised Manuscript: October 19, 2013
Manuscript Accepted: October 21, 2013
Published: October 30, 2013

Citation
Jingsi Li and Julian Cheng, "A laterally-coupled distributed feedback laser with equivalent quarter-wave phase shift," Opt. Express 21, 26936-26941 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26936


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References

  1. W. Li, X. Zhang, and J. Yao, “Experimental demonstration of a multi-wavelength distributed feedback semiconductor laser array with an equivalent chirped grating profile based on the equivalent chirp technology,” Opt. Express21(17), 19966–19971 (2013). [CrossRef] [PubMed]
  2. L. Xie, J. W. Man, B. J. Wang, Y. Liu, X. Wang, H. Q. Yuan, L. J. Zhao, H. L. Zhu, N. H. Zhu, and W. Wang, “24-GHz directly modulated DFB laser modules for analog applications,” IEEE Photon. Technol. Lett.24(5), 407–409 (2012). [CrossRef]
  3. J. Li, H. Wang, X. Chen, Z. Yin, Y. Shi, Y. Lu, Y. Dai, and H. Zhu, “Experimental demonstration of distributed feedback semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express17(7), 5240–5245 (2009). [CrossRef] [PubMed]
  4. L. A. Coldren, S. W. Corzine, and M. L. Masanovic, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (John Wiley, 2012), Chap. 3.
  5. K. Sekartedjo, N. Eda, K. Furuya, Y. Suematsu, F. Koyama, and T. Tanbun-Ek, “1.5 µm phase-shifted DFB lasers for single-mode operation,” Electron. Lett.20(2), 80–81 (1984). [CrossRef]
  6. W. K. Chan, J. Chung, and R. J. Contolini, “Phase-shifted quarter micron holographic gratings by selective image reversal of photoresist,” Appl. Opt.27(8), 1377–1380 (1988). [CrossRef] [PubMed]
  7. Y. Dai and X. Chen, “DFB semiconductor lasers based on reconstruction-equivalent-chirp technology,” Opt. Express15(5), 2348–2353 (2007). [CrossRef] [PubMed]
  8. M. Mohrle, A. Sigmund, R. Steingruber, W. Furst, and A. Suna, “All-active tapered 1.55-µm InGaAsP BH-DFB laser with continuously chirped grating,” IEEE Photon. Technol. Lett.15(3), 365–367 (2003). [CrossRef]
  9. L. M. Miller, J. T. Verdeyen, J. J. Coleman, R. P. Bryan, J. J. Alwan, K. J. Beernink, J. S. Hughes, and T. M. Cockerill, “A distributed feedback ridge waveguide quantum well heterostructure laser,” IEEE Photon. Technol. Lett.3(1), 6–8 (1991). [CrossRef]
  10. J. Li and J. Cheng, “Laterally-coupled distributed feedback laser with first-order gratings by interference lithography,” Electron. Lett.49(12), 764–766 (2013). [CrossRef]
  11. Y. Dai, X. Chen, L. Xia, Y. Zhang, and S. Xie, “Sampled Bragg grating with desired response in one channel by use of a reconstruction algorithm and equivalent chirp,” Opt. Lett.29(12), 1333–1335 (2004). [CrossRef] [PubMed]
  12. J. Li, Y. Cheng, Z. Yin, L. Jia, X. Chen, S. Liu, S. Li, and Y. Lu, “A multiexposure technology for sampled Bragg gratings and its applications in dual-wavelength lasing generation and OCDMA en/decoding,” IEEE Photon. Technol. Lett.21(21), 1639–1641 (2009). [CrossRef]
  13. J. Sun, C. W. Holzwarth, and H. I. Smith, “Phase-shift Bragg grating in silicon using equivalent phase-shift method,” IEEE Photon. Technol. Lett.24(1), 25–27 (2012). [CrossRef]
  14. A. Laakso, M. Dumitrescu, J. Viheriälä, J. Karinen, M. Suominen, and M. Pessa, “Optical modeling of laterally-corrugated ridge-waveguide gratings,” Opt. Quantum Electron.40(11-12), 907–920 (2008). [CrossRef]
  15. J. A. McCaulley, V. M. Donnelly, M. Vernon, and I. Taha, “Temperature dependence of the near-infrared refractive index of silicon, gallium arsenide, and indium phosphide,” Phys. Rev. B Condens. Matter49(11), 7408–7417 (1994). [CrossRef] [PubMed]
  16. J. E. A. Whiteaway, G. H. B. Thompson, A. J. Collar, and C. J. Armistead, “The design and assessment of λ/4 phase shifted DFB laser structures,” IEEE J. Quantum Electron.25(6), 1261–1279 (1989). [CrossRef]

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