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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 9 — May. 5, 2014
  • pp: 10202–10209
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Low threshold and high speed short cavity distributed feedback hybrid silicon lasers

Chong Zhang, Sudharsanan Srinivasan, Yongbo Tang, Martijn J. R. Heck, Michael L. Davenport, and John E. Bowers  »View Author Affiliations


Optics Express, Vol. 22, Issue 9, pp. 10202-10209 (2014)
http://dx.doi.org/10.1364/OE.22.010202


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Abstract

In this paper we investigate reducing threshold and improving the efficiency and speed of distributed feedback hybrid silicon lasers. A low threshold current of 8.8 mA was achieved for a 200 μm cavity at 20 °C. A 3 dB bandwidth of 9.5 GHz as well as 12.5 Gb/s direct modulation of DFB laser diode was achieved on the hybrid silicon platform for the first time.

© 2014 Optical Society of America

1. Introduction

The hybrid silicon platform is of interest for high efficiency lasers on silicon on insulator (SOI) substrates [1

1. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14(20), 9203–9210 (2006). [CrossRef] [PubMed]

, 2

2. M. J. R. Heck, J. F. Bauters, M. L. Davenport, J. K. Doylend, S. Jain, G. Kurczveil, S. Srinivasan, Y. Tang, and J. E. Bowers, “Hybrid silicon photonic integrated circuit technology,” IEEE J. Quantum Electron. 19(4), 6100117 (2013). [CrossRef]

]. Using a low-temperature bonding process, the laser diode structure is integrated with low-loss passive components on silicon. The laser is the key component as the light source for semiconductor photonic integrated chips. An integrated laser source with single wavelength emission as well as low power consumption is highly desirable in a cost-efficient wavelength division multiplexing (WDM) system [2

2. M. J. R. Heck, J. F. Bauters, M. L. Davenport, J. K. Doylend, S. Jain, G. Kurczveil, S. Srinivasan, Y. Tang, and J. E. Bowers, “Hybrid silicon photonic integrated circuit technology,” IEEE J. Quantum Electron. 19(4), 6100117 (2013). [CrossRef]

]. Therefore, high wall-plug efficiency is a very important aspect for the laser source, as well as the ability of operation over a large temperature range in the data center ambience.

Since Fang et al. demonstrated the first hybrid silicon laser in 2006 [1

1. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14(20), 9203–9210 (2006). [CrossRef] [PubMed]

], there have been continuous efforts on developing laser diodes on the hybrid silicon platform [2

2. M. J. R. Heck, J. F. Bauters, M. L. Davenport, J. K. Doylend, S. Jain, G. Kurczveil, S. Srinivasan, Y. Tang, and J. E. Bowers, “Hybrid silicon photonic integrated circuit technology,” IEEE J. Quantum Electron. 19(4), 6100117 (2013). [CrossRef]

]. Fang et al. demonstrated single wavelength emission hybrid distributed feedback (DFB) lasers with a 25 mA threshold current and 5.4 mW maximum output power at 10 °C [3

3. A. W. Fang, E. Lively, Y.-H. Kuo, D. Liang, and J. E. Bowers, “Distributed feedback silicon evanescent laser,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP15.

]. Liang et al. reported hybrid micro-ring laser with a threshold current as low as 5.4 mA and sub-mW output [4

4. D. Liang, M. Fiorentino, T. Okumura, H.-H. Chang, D. T. Spencer, Y.-H. Kuo, A. W. Fang, D. Dai, R. G. Beausoleil, and J. E. Bowers, “Electrically-pumped compact hybrid silicon microring lasers for optical interconnects,” Opt. Express 17(22), 20355–20364 (2009). [CrossRef] [PubMed]

]. Keyvaninia et al reported integrated DFB lasers on silicon with the wall plug efficiency higher than 9% [5

5. S. Keyvaninia, S. Verstuyft, L. Van Landschoot, F. Lelarge, G.-H. Duan, S. Messaoudene, J. M. Fedeli, T. De Vries, B. Smalbrugge, E. J. Geluk, J. Bolk, M. Smit, G. Morthier, D. Van Thourhout, and G. Roelkens, “Heterogeneously integrated III-V/silicon distributed feedback lasers,” Opt. Lett. 38(24), 5434–5437 (2013). [CrossRef] [PubMed]

]. Integrated multi-channel transmitters with DFB laser diodes and high speed modulators on the hybrid silicon platform were achieved with the quantum well intermixing method [6

6. S. R. Jain, Y. Tang, H.-W. Chen, M. N. Sysak, and J. E. Bowers, “Integrated hybrid silicon transmitters,” J. Lightwave Technol. 30(5), 671–678 (2012). [CrossRef]

]. In order to satisfy the requirements of low-power-consuming transmitters, there is need for further improvement on the hybrid laser diodes with both lower threshold current and higher slope efficiency.

A DFB laser diode is a good candidate for the laser source used in WDM optical networks. A single-frequency emission from a DFB is ensured by well-designed Bragg gratings within the gain region, which are etched corrugations on the silicon or III/V side in the hybrid silicon platform. In order to reduce the power consumption, a short cavity DFB (SC-DFB) is preferred to minimize the threshold current, and enhance the wall-plug efficiency for the power budget of the whole chip, which is usually milliwatt-level for on-chip interconnection. Another advantage of shortening the cavity length is that it improves the high speed performance for direct modulation [7

7. K. Nakahara, T. Tsuchiya, T. Kitatani, K. Shinoda, T. Taniguchi, T. Kikawa, M. Aoki, and M. Mukaikubo, “40-Gb/s direct modulation with high extinction ratio operation of 1.3-μm InGaAlAs multiquantum well ridge waveguide distributed feedback lasers,” IEEE Photon. Technol. Lett. 19(19), 1436–1438 (2007). [CrossRef]

]. Compared to an electro-absorption modulator integrated with a DFB, the directly modulated SC-DFB has the advantage of lower power consumption and higher flexibility of multi-channel integration [8

8. W. Kobayashi, T. Ito, T. Yamanaka, T. Fujisawa, Y. Shibata, T. Kurosaki, M. Kohtoku, T. Tadokoro, and H. Sanjoh, “50-Gb/s direct modulation of 1.3-μm InGaAlAs-based DFB laser with ridge waveguide structure,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1500908 (2013). [CrossRef]

].

In this paper we demonstrate the low threshold and high speed operation of hybrid silicon SC-DFB lasers. In Section 2 we illustrate the device structure of hybrid silicon DFB lasers and the fabrication procedure. In Section 3 we focus on the design of short DFB cavities. Cavity designs with varying phase-shifted sections and their effect on device performance are discussed. In Sections 4 and 5 we present the experimental results of SC-DFBs with low-threshold current as well as high-speed performance.

2. Device structure and fabrication

The structure of the hybrid silicon SC-DFB laser is shown schematically in Fig. 1(a).
Fig. 1 Illustration of (a) a hybrid DFB laser; (b) a microscope image of the laser chip after fabrication; (c) a schematic lateral view with a grating on the waveguide; (d) SEM image of a first order grating with a λ/4 phase shift.
The devices were fabricated with a III-V epitaxial wafer and an SOI wafer with a 500 nm device layer and a 1 μm buried oxide (BOX) layer. The III-V layer stack has seven strained InAlGaAs quantum wells (QWs) with graded index separate confinement hetero-structure (GRIN-SCH) layers, as shown in Table 1.

Table 1. Epitaxial III-V Layer Structure

table-icon
View This Table
The insert in Fig. 1(a) is in cross-section view of the calculated fundamental transverse electric (TE) mode. The confinement factor in the QW region is about 5.6%. 50% of the optical mode is confined in the silicon slab waveguide, and consequently gratings on silicon provide strong coupling constants.

The 1.5 μm wide silicon waveguide was etched 280 nm deep from a 500 nm thick device layer on the SOI substrate. The first-order grating sections on the silicon waveguide were defined with a JEOL JBX-6300FS E-beam lithography (EBL) system. Cleaved III-V pieces were bonded to a pre-patterned SOI substrate with a low temperature hydrophilic bonding process [9

9. D. Liang, A. W. Fang, H. Park, T. E. Reynolds, K. Warner, D. C. Oakley, and J. E. Bowers, “Low-temperature, strong SiO2-SiO2 covalent wafer bonding for III–V compound semiconductors-to-silicon photonic integrated circuits,” J. Electron. Mater. 37(10), 1552–1559 (2008). [CrossRef]

]. A reactive ion etch (RIE) tool was adopted to etch the III-V mesa down into the QW layer and then a selective wet etch was used to etch to the n-type contact layer. Pd/Ti/Pd/Au and Pd/Ge/Pd/Au metal stacks were deposited as contact metals for p- and n- type contacts, respectively. With the transmission line measurement (TLM) method the specific resistance of the n-contact was measured to be about 5 × 10−5 Ω⋅cm2 and that of the p-contact was about 6 × 10−6 Ω⋅cm2. As shown in Fig. 1(a), the different color in the center of the 24 μm mesa indicates the 4 μm current channel which was defined by proton implantation. 20 μm III-V tapers on the front and rear end of cavity work as the mode converter between the hybrid section and a 2 μm wide passive waveguide. This wide waveguide is then tapered back to 800 nm to make sure a single mode transmission. This approach minimizes coupling losses between hybrid section and passive waveguide [10

10. G. Kurczveil, P. Pintus, M. J. R. Heck, J. D. Peters, and J. E. Bowers, “Characterization of insertion loss and back reflection in passive hybrid silicon tapers,” IEEE Photon. J. 5(2), 6600410 (2013). [CrossRef]

].

The samples were diced into columns with DFB laser arrays, after processing. The diced silicon waveguide facets were mechanically polished and then coated with bi-layer anti-reflective (AR) films to reduce the facet reflection around the lasing wavelength. Figure 1(b) shows the top-view microscopic image of the finished devices, and Fig. 1(d) shows the scanning electron microscopic (SEM) image of the dry-etched grating on silicon. The duty cycle (DC) of the grating is defined by the ratio of the etched groove width relative to the pitch of grating. The first order grating we used has a DC of about 60%, as shown in Fig. 1(d).

3. Short DFB cavity design

The grating pitch Λ and coupling constant κ of first-order Bragg gratings can be estimated with the coupled mode theory [11

11. L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley-Interscience, 2012).

],

Λ=λ2n¯eff
κ=2Δn¯effλsin(DC*π)

In the equations, λ is the center wavelength defined by the grating pitches. n¯eff and Δn¯effare the average effective refractive index of the cavity and the perturbation by the grating corrugation, respectively. The first-order surface gratings were etched 90 nm deep on the silicon slab waveguide and a strong grating κ was achieved to be about 1000 cm−1 at 1550 nm, which provides flexibility in the short cavity design. The mirror loss of the DFB cavity can be tuned over a large range by choosing the length of the phase shift section in a fixed length cavity. Meanwhile it varies κLg value that represents the reflection strength of the DFB cavity.

Two designs with different types of the phase-shifted section were adopted for 100 μm and 200 μm DFB cavities. The upper image in Fig. 1(c) shows the quarter-wavelength phase-shifted DFB cavity design, which is widely used in DFB cavity designs since it is able to avoid the detuning away from the resonant wavelength of the grating and the degeneration of fundamental mode [12

12. K. Utaka, S. Akiba, K. Sakai, and Y. Matsushima, “λ/4 shifted InGaAsP/InP DFB lasers,” IEEE J. Quantum Electron. 22(7), 1042–1051 (1986). [CrossRef]

, 13

13. S. Srinivasan, A. W. Fang, D. Liang, J. D. Peters, B. Kaye, and J. E. Bowers, “Design of phase-shifted hybrid silicon distributed feedback lasers,” Opt. Express 19(10), 9255–9261 (2011). [CrossRef] [PubMed]

]. The lower image in Fig. 1(c) shows another strategy with a longer phase-shifted section. By changing the grating length from 5 μm to 40 μm, κLg values of the DFB cavity were tuned from 0.5 to 4, and then leave a relative long blank phase-shifted section. In comparison, a quarter-wavelength phase-shifted section design has a stronger grating with κLg of about 10 for 100 μm cavity and 20 for 200 μm.

4. Performance analysis of SC-DBR

The wide stop band width of the hybrid SC-DFBs is corresponding to the strong coupling coefficient of the gratings. With the fundamental matrix method as shown in Fig. 2(a), the stop band of 200 μm and 100 μm hybrid DFB with quarter wavelength phase- shifted section is about 22.9 nm and 25.2 nm, respectively. The measured stop band from the amplified spontaneous emission spectrum of these two lasers are 25.6 nm and 27.6 nm. But this measured stop band was also affected by the materials gain bandwidth.

The performance of SC-DFB with long phase-shifted section, on the other hand, depends on the cavity mirror loss that is decided by κLg value. Since it is a distributed-Bragg-reflection (DBR) like cavity, the cavity mirror reflection can be estimated by:Rtanh(kLg/2)2. Figures 4(a) and 4(b) show experimental data of threshold current and wall plug efficiency at 1 mW output for the 100 μm and 200 μm DFB lasers with a cavity varying κLg.
Fig. 4 (a) The threshold current and (b) wall plug efficiency with 1mW output for the 100 μm and 200 μm DFB lasers with long phase-shifted section. The dash curves are simulated results. The optical spectrum of (c) 100 μm cavity with κLg = 4 and (d) 200 μm cavity with κLg = 4 at 30 mA injection current.
They were compared with calculated curves assuming the internal loss of the cavity is 25 cm−1, materials gain is 966 cm−1 and injection efficiency is 60%. Both the calculation and measured data show a trend that the threshold current decreases with increasing κLg for both cavity lengths, and the optimum wall plug efficiency is around κLg = 1.5 with a compromise between slope efficiency and threshold current. The calculations show a lower threshold and higher wall plug efficiency is predicted for shorter cavity length but the experimental data behaves otherwise. Thermal degenerations is thought to be the main reason for this deviation other than device process variations.

Figures 4(c) and 4(d) show the optical spectrum of SC-DFB lasers with κLg = 4 and a drive current of 30 mA. The corresponding phase-shifted section length is 60 μm for 100 μm cavity and 160 μm for 200 μm cavity. The mode spacing is narrower, and multiple longitudinal mode peaks are observable, but a SMSR larger than 40 dB is still achieved.

In the hybrid silicon platform, one large barrier to improve the energy efficiency is the thermal performance of active devices due to the low thermal conductivity of BOX layer. Laser diodes with shorter cavities have worse thermal impedance, which needs to be compensated by lower working power consumption. The laser threshold degenerates exponentially with rising stage temperature [11

11. L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley-Interscience, 2012).

]. By measuring the threshold of short cavity DFB lasers with pulse injection, the temperature factor T0 of 200 μm and 100 μm quarter wavelength phase-shifted DFB lasers were 41.5 K and 30 K, respectively.

5. Direct modulation of the SC-DBR

The high speed characterization of SC-DBR laser was also studied. The small-signal measurement was performed at 20 °C with a light-wave component analyzer (LCA, Agilent N4373C) with a GSG probe. The electro-optical (EO) response of the 200 μm hybrid DFB with quarter wavelength phase-shift is shown in Fig. 6(a).
Fig. 6 (a) Small signal response of 200 μm hybrid DFB laser with quarter wavelength phase shifted section at different driving currents; the dependence of relaxation oscillation frequency on the driving current of (b) 200 μm and (c) 100 μm hybrid DFB laser.
The maximum 3 dB bandwidth of the device is about 9.5 GHz with 56mA driving current. Figure 6(b) shows the linear relation between the relaxation oscillation frequencies (fr) with the square root of bias current above the threshold. The slope of fr curve is about 1.185 GHz/mA1/2. The 100 μm hybrid DFB has a higher slope of 1.452 GHz/mA1/2 as shown in Fig. 6(c).

To evaluate the high bit rate performance of the hybrid SC-DBR, a large signal transmission measurement was carried out at 20 °C with 231-1 non-return-to-zero (NRZ) pseudorandom bit sequence (PRBS) pattern. The 200 μm DFB was driven above the threshold and the bias was tuned to reach the optimized eye diagram when the driving current was 62 mA. The driving electrical signal with a 1.5 V swing on the voltage is shown in Fig. 7(a) with a 6 dB attenuator.
Fig. 7 Eye diagram of (a) diving voltage signal and the digital modulation of 200 μm DFB with the bit rate of (b) 5 Gbps (c) 10 Gbps and (d) 12.5 Gbps.
Figures 7(b)7(d) indicate open eye diagrams up to 12.5 Gbps.

6. Summary

We demonstrated short cavity hybrid silicon DFB lasers with low thresholds and showed that quarter wavelength phase-shifted sections show better performance than long phase shift, both on mode stability and side mode suppression ratio. The large direct modulation bandwidth of the hybrid SC-DFB shows its potential for low cost and low power laser source.

Acknowledgments

References and links

1.

A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14(20), 9203–9210 (2006). [CrossRef] [PubMed]

2.

M. J. R. Heck, J. F. Bauters, M. L. Davenport, J. K. Doylend, S. Jain, G. Kurczveil, S. Srinivasan, Y. Tang, and J. E. Bowers, “Hybrid silicon photonic integrated circuit technology,” IEEE J. Quantum Electron. 19(4), 6100117 (2013). [CrossRef]

3.

A. W. Fang, E. Lively, Y.-H. Kuo, D. Liang, and J. E. Bowers, “Distributed feedback silicon evanescent laser,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP15.

4.

D. Liang, M. Fiorentino, T. Okumura, H.-H. Chang, D. T. Spencer, Y.-H. Kuo, A. W. Fang, D. Dai, R. G. Beausoleil, and J. E. Bowers, “Electrically-pumped compact hybrid silicon microring lasers for optical interconnects,” Opt. Express 17(22), 20355–20364 (2009). [CrossRef] [PubMed]

5.

S. Keyvaninia, S. Verstuyft, L. Van Landschoot, F. Lelarge, G.-H. Duan, S. Messaoudene, J. M. Fedeli, T. De Vries, B. Smalbrugge, E. J. Geluk, J. Bolk, M. Smit, G. Morthier, D. Van Thourhout, and G. Roelkens, “Heterogeneously integrated III-V/silicon distributed feedback lasers,” Opt. Lett. 38(24), 5434–5437 (2013). [CrossRef] [PubMed]

6.

S. R. Jain, Y. Tang, H.-W. Chen, M. N. Sysak, and J. E. Bowers, “Integrated hybrid silicon transmitters,” J. Lightwave Technol. 30(5), 671–678 (2012). [CrossRef]

7.

K. Nakahara, T. Tsuchiya, T. Kitatani, K. Shinoda, T. Taniguchi, T. Kikawa, M. Aoki, and M. Mukaikubo, “40-Gb/s direct modulation with high extinction ratio operation of 1.3-μm InGaAlAs multiquantum well ridge waveguide distributed feedback lasers,” IEEE Photon. Technol. Lett. 19(19), 1436–1438 (2007). [CrossRef]

8.

W. Kobayashi, T. Ito, T. Yamanaka, T. Fujisawa, Y. Shibata, T. Kurosaki, M. Kohtoku, T. Tadokoro, and H. Sanjoh, “50-Gb/s direct modulation of 1.3-μm InGaAlAs-based DFB laser with ridge waveguide structure,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1500908 (2013). [CrossRef]

9.

D. Liang, A. W. Fang, H. Park, T. E. Reynolds, K. Warner, D. C. Oakley, and J. E. Bowers, “Low-temperature, strong SiO2-SiO2 covalent wafer bonding for III–V compound semiconductors-to-silicon photonic integrated circuits,” J. Electron. Mater. 37(10), 1552–1559 (2008). [CrossRef]

10.

G. Kurczveil, P. Pintus, M. J. R. Heck, J. D. Peters, and J. E. Bowers, “Characterization of insertion loss and back reflection in passive hybrid silicon tapers,” IEEE Photon. J. 5(2), 6600410 (2013). [CrossRef]

11.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley-Interscience, 2012).

12.

K. Utaka, S. Akiba, K. Sakai, and Y. Matsushima, “λ/4 shifted InGaAsP/InP DFB lasers,” IEEE J. Quantum Electron. 22(7), 1042–1051 (1986). [CrossRef]

13.

S. Srinivasan, A. W. Fang, D. Liang, J. D. Peters, B. Kaye, and J. E. Bowers, “Design of phase-shifted hybrid silicon distributed feedback lasers,” Opt. Express 19(10), 9255–9261 (2011). [CrossRef] [PubMed]

14.

M. Yamada and K. Sakuda, “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26(16), 3474–3478 (1987). [CrossRef] [PubMed]

OCIS Codes
(140.3490) Lasers and laser optics : Lasers, distributed-feedback
(350.4010) Other areas of optics : Microwaves
(250.5960) Optoelectronics : Semiconductor lasers
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: February 14, 2014
Revised Manuscript: April 14, 2014
Manuscript Accepted: April 14, 2014
Published: April 21, 2014

Citation
Chong Zhang, Sudharsanan Srinivasan, Yongbo Tang, Martijn J. R. Heck, Michael L. Davenport, and John E. Bowers, "Low threshold and high speed short cavity distributed feedback hybrid silicon lasers," Opt. Express 22, 10202-10209 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-10202


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References

  1. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14(20), 9203–9210 (2006). [CrossRef] [PubMed]
  2. M. J. R. Heck, J. F. Bauters, M. L. Davenport, J. K. Doylend, S. Jain, G. Kurczveil, S. Srinivasan, Y. Tang, J. E. Bowers, “Hybrid silicon photonic integrated circuit technology,” IEEE J. Quantum Electron. 19(4), 6100117 (2013). [CrossRef]
  3. A. W. Fang, E. Lively, Y.-H. Kuo, D. Liang, and J. E. Bowers, “Distributed feedback silicon evanescent laser,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP15.
  4. D. Liang, M. Fiorentino, T. Okumura, H.-H. Chang, D. T. Spencer, Y.-H. Kuo, A. W. Fang, D. Dai, R. G. Beausoleil, J. E. Bowers, “Electrically-pumped compact hybrid silicon microring lasers for optical interconnects,” Opt. Express 17(22), 20355–20364 (2009). [CrossRef] [PubMed]
  5. S. Keyvaninia, S. Verstuyft, L. Van Landschoot, F. Lelarge, G.-H. Duan, S. Messaoudene, J. M. Fedeli, T. De Vries, B. Smalbrugge, E. J. Geluk, J. Bolk, M. Smit, G. Morthier, D. Van Thourhout, G. Roelkens, “Heterogeneously integrated III-V/silicon distributed feedback lasers,” Opt. Lett. 38(24), 5434–5437 (2013). [CrossRef] [PubMed]
  6. S. R. Jain, Y. Tang, H.-W. Chen, M. N. Sysak, J. E. Bowers, “Integrated hybrid silicon transmitters,” J. Lightwave Technol. 30(5), 671–678 (2012). [CrossRef]
  7. K. Nakahara, T. Tsuchiya, T. Kitatani, K. Shinoda, T. Taniguchi, T. Kikawa, M. Aoki, M. Mukaikubo, “40-Gb/s direct modulation with high extinction ratio operation of 1.3-μm InGaAlAs multiquantum well ridge waveguide distributed feedback lasers,” IEEE Photon. Technol. Lett. 19(19), 1436–1438 (2007). [CrossRef]
  8. W. Kobayashi, T. Ito, T. Yamanaka, T. Fujisawa, Y. Shibata, T. Kurosaki, M. Kohtoku, T. Tadokoro, H. Sanjoh, “50-Gb/s direct modulation of 1.3-μm InGaAlAs-based DFB laser with ridge waveguide structure,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1500908 (2013). [CrossRef]
  9. D. Liang, A. W. Fang, H. Park, T. E. Reynolds, K. Warner, D. C. Oakley, J. E. Bowers, “Low-temperature, strong SiO2-SiO2 covalent wafer bonding for III–V compound semiconductors-to-silicon photonic integrated circuits,” J. Electron. Mater. 37(10), 1552–1559 (2008). [CrossRef]
  10. G. Kurczveil, P. Pintus, M. J. R. Heck, J. D. Peters, J. E. Bowers, “Characterization of insertion loss and back reflection in passive hybrid silicon tapers,” IEEE Photon. J. 5(2), 6600410 (2013). [CrossRef]
  11. L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley-Interscience, 2012).
  12. K. Utaka, S. Akiba, K. Sakai, Y. Matsushima, “λ/4 shifted InGaAsP/InP DFB lasers,” IEEE J. Quantum Electron. 22(7), 1042–1051 (1986). [CrossRef]
  13. S. Srinivasan, A. W. Fang, D. Liang, J. D. Peters, B. Kaye, J. E. Bowers, “Design of phase-shifted hybrid silicon distributed feedback lasers,” Opt. Express 19(10), 9255–9261 (2011). [CrossRef] [PubMed]
  14. M. Yamada, K. Sakuda, “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26(16), 3474–3478 (1987). [CrossRef] [PubMed]

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