## Design of phase-shifted hybrid silicon distributed feedback lasers |

Optics Express, Vol. 19, Issue 10, pp. 9255-9261 (2011)

http://dx.doi.org/10.1364/OE.19.009255

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### Abstract

We present data on the design and performance analysis of phase shifted distributed feedback (DFB) lasers on the hybrid silicon platform. The lasing wavelength for various input currents and temperatures, for devices with standard quarter-wavelength, 60 μm and 120 μm-long phase shift are compared for mode stability and output power. The pros and cons of including a large phase shift region in the grating design are analyzed.

© 2011 OSA

## 1. Introduction

1. D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE **97**(7), 1166–1185 (2009). [CrossRef]

2. D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics **4**(8), 511–517 (2010). [CrossRef]

## 2. Device design and fabrication

^{−1}; this is large compared to gratings on passive silicon rib waveguides of similar dimension since the index difference between air and silicon is quite large and the index perturbation is located nearer to the center of the optical mode [6]. The κL product, where L is the length of the grating, is varied by changing L. In this paper, we compare the performance of eight designs, primarily distinguished by the phase-shift length introduced at the center of the grating (see Fig. 3 ). Long grating lengths were used in the DFB lasers of an earlier generation to minimize the negative effects of device heating, which lead to poor power extraction and low differential quantum efficiency. The goal of this paper is to find the effects of changing the phase-shift length and grating length on output power and mode stability. Two on-chip hybrid silicon photodetectors are integrated to detect the output power from both sides. We assume a responsivity of 1 A/W to conservatively estimate the device output power.

## 3. Threshold current and maximum output power

*T*) was kept constant at 20 °C for all the measurements. Figure 4 shows a typical L-I-V curve for one of the DFB laser designs under cw operation. The total cavity length is 240 μm with 120 μm long phase-shift region, resulting in κL = 3. The series resistance for all devices lie between 20 Ω and 35 Ω.

*h*,

*v*,

*q*, 〈

*α*〉,

_{i}*α*, and

_{m}, η_{i}*Z*are Planck’s constant, photon frequency, elementary charge, average internal modal loss, mirror loss, injection efficiency, and thermal impedance respectively.

_{T}*T*

_{0}= 51 K,

*T*

_{1}= 100 K,

*Z*= 3.6975 (°K.cm)/W and

_{L}*Z*=

_{T}*Z*are obtained experimentally [7

_{L}/L_{tot}7. M. N. Sysak, H. Park, A. W. Fang, J. E. Bowers, R. Jones, O. Cohen, O. Raday, and M. J. Paniccia, “Experimental and theoretical thermal analysis of a hybrid silicon evanescent Laser,” Opt. Express **15**(23), 15041–15046 (2007). [CrossRef] [PubMed]

*L*is the length of the gain region which is the sum of grating length and phase-shift length in our case. The values of internal quantum efficiency (

_{tot}*ηi*) and internal loss (

*<αi>*) extracted from fitting the experimental data to theory are 0.39 and 11 cm

^{−1}respectively. We assume a logarithmic dependence of gain on carrier density and the material gain and transparency carrier density used in the relation are

*g*

_{0}= 966 cm

^{−1}and

*N*= 1.86 × 10

_{tr}^{18}cm

^{−3}. Both theoretical and experimental data show that the threshold decreases to a minimum value and then grows with reducing device length,

*L*, due to changes in mirror loss and average internal model loss. Similarly, the output power increases at the optimum value and then falls off. As the length of the phase shift region increases, the minimum threshold current in Fig. 5(a) moves to higher value and lower κL. The reason is twofold: First, threshold current density remains constant, so longer phase-shift lengths result in a longer cavity, and subsequently higher threshold current. Second, for a smaller κL, shorter device length leads to higher thermal impedance and hence a higher threshold current (Eq. (1)), as is confirmed by the experimental data.

_{tot}## 4. Spectral Analysis

*Γg*)

_{th}- α_{i}*L,*for the cavity modes in a quarter-wave shifted DFB laser. The cavity is resonant at the Bragg wavelength. The higher order modes are symmetric about the null of detuning parameter,

*δL*= (

*β*

_{0})

*L*where

*β*

_{0}are the average propagation constant and Bragg wavenumber respectively.

## 5. Thermal Impedance

7. M. N. Sysak, H. Park, A. W. Fang, J. E. Bowers, R. Jones, O. Cohen, O. Raday, and M. J. Paniccia, “Experimental and theoretical thermal analysis of a hybrid silicon evanescent Laser,” Opt. Express **15**(23), 15041–15046 (2007). [CrossRef] [PubMed]

*dλ/dP*) and change in stage temperature (

_{elec}*dλ/dT*), for the eight designs under cw operation are plotted in Figs. 9(a) and (b) respectively. The data points in Fig. 9(b) are concentrated around the value of 0.1nm/°C for all designs. Thus the value of

*dλ/dP*is a good tracking point for the thermal impedance of the device.

_{elec}## 6. Conclusions

## Acknowledgments

## References and links

1. | D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE |

2. | D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics |

3. | G. Morthier and P. Vankwikelberge, |

4. | A. W. Fang, E. Lively, Y. Kuo, D. Liang, and J. Bowers, “Distributed Feedback Silicon Evanescent Laser,” in |

5. | H. Ghafouri-Shiraz, |

6. | W. Alexander, Fang, “Silicon evanescent lasers,” Ph.D. dissertation (Dept. of Elect. and Comp. Eng., Univ. of California, Santa Barbara, CA, 2008), pp. 104–105. |

7. | M. N. Sysak, H. Park, A. W. Fang, J. E. Bowers, R. Jones, O. Cohen, O. Raday, and M. J. Paniccia, “Experimental and theoretical thermal analysis of a hybrid silicon evanescent Laser,” Opt. Express |

**OCIS Codes**

(050.5080) Diffraction and gratings : Phase shift

(140.3490) Lasers and laser optics : Lasers, distributed-feedback

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: January 3, 2011

Revised Manuscript: February 25, 2011

Manuscript Accepted: February 28, 2011

Published: April 27, 2011

**Citation**

Sudharsanan Srinivasan, Alexander W. Fang, Di Liang, Jon Peters, Bryan Kaye, and John E. Bowers, "Design of phase-shifted hybrid silicon distributed feedback lasers," Opt. Express **19**, 9255-9261 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9255

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### References

- D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97(7), 1166–1185 (2009). [CrossRef]
- D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010). [CrossRef]
- G. Morthier and P. Vankwikelberge, Handbook of Distributed Feedback Laser Diodes (Artech House, Inc., 1997), Chaps. 10 and 11.
- A. W. Fang, E. Lively, Y. Kuo, D. Liang, and J. Bowers, “Distributed Feedback Silicon Evanescent Laser,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP15.
- H. Ghafouri-Shiraz, Distributed Feedback Laser Diodes and Optical Tunable Filters (Wiley, 2003), Chaps. 3 and 5.
- W. Alexander, Fang, “Silicon evanescent lasers,” Ph.D. dissertation (Dept. of Elect. and Comp. Eng., Univ. of California, Santa Barbara, CA, 2008), pp. 104–105.
- M. N. Sysak, H. Park, A. W. Fang, J. E. Bowers, R. Jones, O. Cohen, O. Raday, and M. J. Paniccia, “Experimental and theoretical thermal analysis of a hybrid silicon evanescent Laser,” Opt. Express 15(23), 15041–15046 (2007). [CrossRef] [PubMed]

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