## A novel concavely apodized DFB semiconductor laser using common holographic exposure |

Optics Express, Vol. 21, Issue 13, pp. 16022-16028 (2013)

http://dx.doi.org/10.1364/OE.21.016022

Acrobat PDF (1090 KB)

### Abstract

A novel concavely apodized (CA) distributed feedback (DFB) semiconductor laser was theoretically analyzed and experimentally demonstrated. The CA grating profile is equivalently realized by changing the duty cycle of the sampling structure along the cavity in the middle of which an equivalent phase shift is also inserted. Because the basic grating (seed grating) is uniform, only a common holographic exposure and a µm-level photolithography are required. Therefore, the fabrication cost is highly reduced compared with the true CA grating whose index modulation continuously changes along the cavity. The experimental results show that the laser has good single longitudinal mode operation.

© 2013 OSA

## 1. Introduction

1. K. Utaka, S. Akiba, K. Sakai, and Y. Matsushima, “Longitudinal-mode behaviour of λ/4-shifted InGaAsP/InP DFB lasers,” Electron. Lett. **21**(9), 367–369 (1985). [CrossRef]

2. M. Usami, S. Akiba, and K. Utaka, “Asymmetric λ/4-shifted InGaAsP/InP DFB lasers,” IEEE J. Quantum Electron. **23**(6), 815–821 (1987). [CrossRef]

3. 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]

5. J. Chen, R. J. Ram, and R. G. Helkey, “Linearity and third-order intermodulation distortion in DFB semiconductor lasers,” IEEE J. Quantum Electron. **35**(8), 1231–1237 (1999). [CrossRef]

6. M. Okai, N. Chinone, H. Taira, and T. Harada, “Corrugation-pitch-modulated phase-shifted DFB laser,” IEEE Photon. Technol. Lett. **1**(8), 200–201 (1989). [CrossRef]

7. G. P. Agrawal, J. E. Geusic, and P. J. Anthony, “Distributed feedback lasers with multiple phase-shift regions,” Appl. Phys. Lett. **53**(3), 178–179 (1988). [CrossRef]

8. G. G. Morthier, K. David, P. Vankwikelberge, and R. G. E. Baets, “A new DFB-laser diode with reduced spatial hole burning,” IEEE Photon. Technol. Lett. **2**(6), 388–390 (1990). [CrossRef]

9. G. G. Morthier and R. G. E. Baets, “Design of index-coupled DFB lasers with reduced longitudinal spatial hole burning,” J. Lightwave Technol. **9**(10), 1305–1313 (1991). [CrossRef]

10. D. W. Wiesmann, C. David, R. Germann, D. Emi, and G.-L. Bona, “Apodized surface-corrugated gratings with varying duty cycle,” IEEE Photon. Technol. Lett. **12**(6), 639–641 (2000). [CrossRef]

11. F. Girardin, G.-H. Duan, and T. Anna, “Modeling and measurement of spatial-hole-burning applied to amplitude modulated coupling distributed feedback lasers,” IEEE J. Quantum Electron. **31**(5), 834–841 (1995). [CrossRef]

12. 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]

14. Y. Shi, X. Chen, Y. Zhou, S. Li, L. Li, and Y. Feng, “Experimental demonstration of the three phase shifted DFB semiconductor laser based on Reconstruction-Equivalent-Chirp technique,” Opt. Express **20**(16), 17374–17379 (2012). [CrossRef] [PubMed]

15. Y. Shi, R. Gu, and X. Chen, “A concave tapered DFB semiconductor laser based on reconstruction-equivalent-chirp technology”, Photonics Global Conference (PGC), 9882 (2010). [CrossRef]

## 2. Principle

### 2.1 Realization of Apodization

*P*is the sampling period,

*Δn*is the index modulation of the basic grating (seed grating),

_{s}*Λ*is the seed grating period,

_{0}*F*is the m

_{m}^{th}order Fourier coefficient of the sampling structure.

*± 1st*order coefficient

*F*is usually used as the working sub-grating. The

_{± 1}*F*can be expressed as [15

_{± 1}15. Y. Shi, R. Gu, and X. Chen, “A concave tapered DFB semiconductor laser based on reconstruction-equivalent-chirp technology”, Photonics Global Conference (PGC), 9882 (2010). [CrossRef]

16. Y. Shi, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. **283**(9), 1840–1844 (2010). [CrossRef]

*γ*is the duty cycle of sampling structure. It is defined as the ratio between the length with grating in one sampling period and the sampling period

*P.*Fig. 2 shows the curve of the Eq. (2).

*F*is symmetric about the duty cycle of 0.5. So if the duty cycle varies along the cavity from 0 to 0.5 or 0.5 to 1.0, the apodization can be realized equivalently.

_{± 1}*R*is defined here as

_{apodization}*R*=

_{apodization}*L*/

_{apodization}*L*.

*L*is the grating length with varied duty cycle and

_{apodization}*L*is the whole grating length. The Transfer matrix method (TMM) is used to calculate the light intensity distribution along the grating.

*R*increases. It is easy to understand that the apodization decreases the reflectivity of the light at the front of the grating and help light to transmit deeper. Therefore, if the concavely symmetric apodized grating is used as shown in Fig. 4, the effective cavity length increases accordingly. If a DFB laser uses this kind of grating structure as resonant cavity, light will distribute in larger region along cavity. Then, light intensity will be flattened and SHB can be suppressed.

_{apodization}### 2.2 *Realization of phase shift*

12. 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]

13. Y. Shi, X. Chen, Y. Zhou, S. Li, L. Lu, R. Liu, and Y. Feng, “Experimental demonstration of eight-wavelength distributed feedback semiconductor laser array using equivalent phase shift,” Opt. Lett. **37**(16), 3315–3317 (2012). [CrossRef] [PubMed]

^{th}orderFourier component

*ΔS*of the sampling structure with the duty cycle of

_{m}*γ*can be expressed as,

*S(z)*denotes the sampling structure. For simplicity, the −1st order sub-grating is used, then the phase characteristic of 1-exp(j2mπ

*γ*) in Eq. (3) can be explained in Fig. 5.

*γ*changes. Particularly, when

*γ*is equal to 0.5, Eq. (3) turns out to be –j/π and has the largest amplitude. It is consistent with the normally equivalent π phase shift. But if the equivalent apodization is applied, the duty cycle is continuously changed along the cavity. Because the phase of the grating changes with the duty cycle, it is hard to determine the phase of the whole equivalent apodized sampled grating. In order to insert a phase shift, the reflective phase is then analyzed by simulation. Assuming the grating is a mirror, we found that the reflective phase in the stop-band is from 0.0 radian to about 4.0 radian when the

*R*is 0.5 as shown in Fig. 6(a). So if the symmetric structure is used as in Fig. 4, the resonant modes at 0.0 radian and π radian can be built. But because the reflectivity is much larger around the point of 0.0 radian than that of the π radian, a prominent resonant mode at 0.0 radian can be obtained. To further verify this point, we also simulated the transmission characteristic of the structure in Fig. 4. As shown in Fig. 6(b), a transmission peak corresponding to the reflective phase of around 0.0 radian in Fig. 6(a) is formed. Fortunately, we also found that the equivalent shift can always be obtained under different

_{apodization}*R*. Therefore, a phase shift can also be equivalently inserted in such a symmetric structure.

_{apodization}## 3. Simulation analysis

*R*. The light intensity is flattened when

_{apodization}*R*increases. The lasing spectra are also calculated. It shows that the side mode intensity for

_{apodization}*R*equal to 0.5 is smaller than that of

_{apodization}*R*equal to 0.0 when bias current is around 70mA as shown in Fig. 7(b). This is because the SHB of

_{apodization}*R*equal to 0.5 is much less than that of

_{apodization}*R*equal to 0.0, as shown in Fig. 7(a).

_{apodization}## 4. Fabrication and experimental results

## 5. Conclusion

## Acknowledgment

## References and links

1. | K. Utaka, S. Akiba, K. Sakai, and Y. Matsushima, “Longitudinal-mode behaviour of λ/4-shifted InGaAsP/InP DFB lasers,” Electron. Lett. |

2. | M. Usami, S. Akiba, and K. Utaka, “Asymmetric λ/4-shifted InGaAsP/InP DFB lasers,” IEEE J. Quantum Electron. |

3. | 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. |

4. | A. J. Lowery and H. Olesen, “Dynamics of mode-instabilities in quarter-wave-shifted DFB semiconductor lasers,” Electron. Lett. |

5. | J. Chen, R. J. Ram, and R. G. Helkey, “Linearity and third-order intermodulation distortion in DFB semiconductor lasers,” IEEE J. Quantum Electron. |

6. | M. Okai, N. Chinone, H. Taira, and T. Harada, “Corrugation-pitch-modulated phase-shifted DFB laser,” IEEE Photon. Technol. Lett. |

7. | G. P. Agrawal, J. E. Geusic, and P. J. Anthony, “Distributed feedback lasers with multiple phase-shift regions,” Appl. Phys. Lett. |

8. | G. G. Morthier, K. David, P. Vankwikelberge, and R. G. E. Baets, “A new DFB-laser diode with reduced spatial hole burning,” IEEE Photon. Technol. Lett. |

9. | G. G. Morthier and R. G. E. Baets, “Design of index-coupled DFB lasers with reduced longitudinal spatial hole burning,” J. Lightwave Technol. |

10. | D. W. Wiesmann, C. David, R. Germann, D. Emi, and G.-L. Bona, “Apodized surface-corrugated gratings with varying duty cycle,” IEEE Photon. Technol. Lett. |

11. | F. Girardin, G.-H. Duan, and T. Anna, “Modeling and measurement of spatial-hole-burning applied to amplitude modulated coupling distributed feedback lasers,” IEEE J. Quantum Electron. |

12. | 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 |

13. | Y. Shi, X. Chen, Y. Zhou, S. Li, L. Lu, R. Liu, and Y. Feng, “Experimental demonstration of eight-wavelength distributed feedback semiconductor laser array using equivalent phase shift,” Opt. Lett. |

14. | Y. Shi, X. Chen, Y. Zhou, S. Li, L. Li, and Y. Feng, “Experimental demonstration of the three phase shifted DFB semiconductor laser based on Reconstruction-Equivalent-Chirp technique,” Opt. Express |

15. | Y. Shi, R. Gu, and X. Chen, “A concave tapered DFB semiconductor laser based on reconstruction-equivalent-chirp technology”, Photonics Global Conference (PGC), 9882 (2010). [CrossRef] |

16. | Y. Shi, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun. |

**OCIS Codes**

(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: April 9, 2013

Revised Manuscript: June 10, 2013

Manuscript Accepted: June 18, 2013

Published: June 27, 2013

**Citation**

Yuechun Shi, Simin Li, Renjia Guo, Rui Liu, Yating Zhou, and Xiangfei Chen, "A novel concavely apodized DFB semiconductor laser using common holographic exposure," Opt. Express **21**, 16022-16028 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-16022

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### References

- K. Utaka, S. Akiba, K. Sakai, and Y. Matsushima, “Longitudinal-mode behaviour of λ/4-shifted InGaAsP/InP DFB lasers,” Electron. Lett.21(9), 367–369 (1985). [CrossRef]
- M. Usami, S. Akiba, and K. Utaka, “Asymmetric λ/4-shifted InGaAsP/InP DFB lasers,” IEEE J. Quantum Electron.23(6), 815–821 (1987). [CrossRef]
- 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]
- A. J. Lowery and H. Olesen, “Dynamics of mode-instabilities in quarter-wave-shifted DFB semiconductor lasers,” Electron. Lett.30(12), 965–967 (1994). [CrossRef]
- J. Chen, R. J. Ram, and R. G. Helkey, “Linearity and third-order intermodulation distortion in DFB semiconductor lasers,” IEEE J. Quantum Electron.35(8), 1231–1237 (1999). [CrossRef]
- M. Okai, N. Chinone, H. Taira, and T. Harada, “Corrugation-pitch-modulated phase-shifted DFB laser,” IEEE Photon. Technol. Lett.1(8), 200–201 (1989). [CrossRef]
- G. P. Agrawal, J. E. Geusic, and P. J. Anthony, “Distributed feedback lasers with multiple phase-shift regions,” Appl. Phys. Lett.53(3), 178–179 (1988). [CrossRef]
- G. G. Morthier, K. David, P. Vankwikelberge, and R. G. E. Baets, “A new DFB-laser diode with reduced spatial hole burning,” IEEE Photon. Technol. Lett.2(6), 388–390 (1990). [CrossRef]
- G. G. Morthier and R. G. E. Baets, “Design of index-coupled DFB lasers with reduced longitudinal spatial hole burning,” J. Lightwave Technol.9(10), 1305–1313 (1991). [CrossRef]
- D. W. Wiesmann, C. David, R. Germann, D. Emi, and G.-L. Bona, “Apodized surface-corrugated gratings with varying duty cycle,” IEEE Photon. Technol. Lett.12(6), 639–641 (2000). [CrossRef]
- F. Girardin, G.-H. Duan, and T. Anna, “Modeling and measurement of spatial-hole-burning applied to amplitude modulated coupling distributed feedback lasers,” IEEE J. Quantum Electron.31(5), 834–841 (1995). [CrossRef]
- 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]
- Y. Shi, X. Chen, Y. Zhou, S. Li, L. Lu, R. Liu, and Y. Feng, “Experimental demonstration of eight-wavelength distributed feedback semiconductor laser array using equivalent phase shift,” Opt. Lett.37(16), 3315–3317 (2012). [CrossRef] [PubMed]
- Y. Shi, X. Chen, Y. Zhou, S. Li, L. Li, and Y. Feng, “Experimental demonstration of the three phase shifted DFB semiconductor laser based on Reconstruction-Equivalent-Chirp technique,” Opt. Express20(16), 17374–17379 (2012). [CrossRef] [PubMed]
- Y. Shi, R. Gu, and X. Chen, “A concave tapered DFB semiconductor laser based on reconstruction-equivalent-chirp technology”, Photonics Global Conference (PGC), 9882 (2010). [CrossRef]
- Y. Shi, J. Li, L. Jia, S. Liu, and X. Chen, “An apodized DFB semiconductor laser realized by varying duty cycle of sampling Bragg grating and reconstruction-equivalent-chirp technology,” Opt. Commun.283(9), 1840–1844 (2010). [CrossRef]

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