## Self-mixing speckle interference in DFB lasers

Optics Express, Vol. 14, Issue 8, pp. 3312-3317 (2006)

http://dx.doi.org/10.1364/OE.14.003312

Acrobat PDF (113 KB)

### Abstract

Theoretical analysis and experimental results of self-mixing speckle interference in a distributed feedback (DFB) laser are presented in this paper. Self-mixing speckle interference occurs when external optical feedback comes from a moving rough surface. Dynamic output variations in the DFB laser as well as their probability density functions (PDFs) are analyzed on the basis of speckle theory and self-mixing interference in the DFB laser. Numeric simulations and experiments are in agreement with each other. The both results show that self-mixing speckle interference in DFB laser can be used to measure velocity of target.

© 2006 Optical Society of America

## 1. Introduction

1. T. Shibata and S. Shinohara et al. “Laser speckle velocimeter using self-mixing laser diode,” IEEE Trans. Instrum. Meas. **45**, 499–503 (1996). [CrossRef]

8. T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, and M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode”, IEEE Trans. Instrum. Meas. **48**, 1062–1067 (1999). [CrossRef]

11. H. Huan, M. Wang, and D. Guo et al. “Self-mixing interference effect of DFB semiconductor lasers,” Appl. Phys. B **79**, 1554–1559 (2004). [CrossRef]

## 2. Theoretic analysis

*M*and

_{1}*M*, posited at

_{2}*Z*=-

*L/2*and

*Z*=

*L/2*, are left facet and right facet of the DFB cavity respectively. The length of the DFB cavity is

*L*. S, an external reflector with rough surface, as well as

*M*, form an external cavity.

_{2}*L*is the length of external cavity. We suppose that

_{E}*ρ*=

_{r}*ρ*̂

_{r}

*e*

^{+ψr},

*ρ*=

_{l}*ρ*̂

_{l}

*e*

^{+ψl}are the reflection coefficient

*M*and

_{1}*M*respectively, and

_{2}*ψ*(

_{r}*ψ*) is the phase term depending on the position of the right (left) facet.

_{l}*M*projects onto S. The backscattered radiations from different elements of the rough surface reenter the cavity, generating random interference, which is known as speckle. Based on the theory of Fraunhofer diffraction [13], the speckles optical field at

_{2}*M*can be calculated in the following.

_{2}*E*is the original optical field at

_{r}*M*,

_{2}*t*is the coupling coefficient of the laser coupled from laser cavity to external cavity,

*τ*is the single trip time of the light in the external cavity,

*λ*is the optical wavelength,

*(X, Y)*,

*(x, y)*are the coordinates along the speckles field and the scattering area on the rough surface respectively,

*A(x, y)*is the aperture function of scattering area,

*h(x, y)*is the altitude function of a random surface. We can assume that the random rough surface profile function

*h(x, y)*obeys the statistics [14

14. E. I. Thorsos, “The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acous. Soc. Am. **83**, 78–92 (1988). [CrossRef]

15. A. K. Fung and M. F. Chen, “Numerical simulation of scattering from simple and composite random surfaces,” J. Opt. Soc. Am. A **2**, 2274–2284 (1985). [CrossRef]

- <
*h(x,y)*>=0, *w*=[<*h(x,y)h(x,y)*>]^{1/2}, where*w*is root-mean-square (RMS) height,- The autocorrelation function 〈
*h*(*x*,*y*)*h*(*x*+*l*,*y*+*l*)〉 =*w*^{2}exp(-*l*^{2}/*T*^{2}), here*T*is the correlation length along the surface,*l*is the distance between two successive points on the surface.

*M*is a superposed field, which can be written as

_{2}*t*’ is the coupling coefficient of the laser coupled from external cavity to laser cavity,

*ξ*is the feedback ratio of external optical field coupled into laser cavity,

*U(X, Y)*is the complex amplitude of the speckles coupled into the laser cavity.

*ϕ*, we can get the equivalent reflection coefficient of the laser facet

*ρ*is the change of

_{r}*ρ*due to the feedback light from S.

_{r}11. H. Huan, M. Wang, and D. Guo et al. “Self-mixing interference effect of DFB semiconductor lasers,” Appl. Phys. B **79**, 1554–1559 (2004). [CrossRef]

*α*denotes threshold loss,

*δ*is the departure of the oscillation frequency from the Bragg frequency,

*κ*is the couple coefficient, and

*γ*is the complex propagation constant.

*ρ*, we can define the deviations of

_{r}*α*and

*δ*in the same way as reference [16

16. F. Favre, “Theoretical analysis of external optical feedback on DFB semiconductor lasers,” IEEE J. Quantum Electron. **23**, 81–88 (1987). [CrossRef]

*c*is the velocity of light,

*η*is the equivalent refractive index of the DFB cavity.

## 3. Simulations and experiments

*w*is 1.5um, the correlation length

*l*is 3um, the wavelength of laser λ is 1550 nm, the length of DFB cavity

*L*is 0.04cm, the external cavity

*L*1cm,

_{E}*κ*is 2,

*ρ*is 0, and

_{l}*ρ*is 0.53.

_{r}## 4. Conclusion

## Acknowledgments

## References and Links

1. | T. Shibata and S. Shinohara et al. “Laser speckle velocimeter using self-mixing laser diode,” IEEE Trans. Instrum. Meas. |

2. | P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers,” IEEE Photonics Technol. Lett. |

3. | G. Giuliani, S. Bozzi-Pietra, and S. Donati, “Self-mixing laser diode vibrometer” Meas. Sci. Tech. |

4. | M. Norgia and S. Donati, “A displacement-measuring instrument utilizing self-mixing interferometry”, IEEE Trans. Instrum. Meas. |

5. | L. Scalise, Y. G. Yu, and G. Giuliani, et al. “Self-mixing laser diode velocimetry: Application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. |

6. | J. W. Choi, M. J. Yu, and M. Kopica, “Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser,” Proc. Soc. Photo-Opt. Instrum. |

7. | M. Laroche, L. Kervevan, H. Gilles, S. Girard, and J.K. Sahu, “Doppler velocimetry using self-mixing effect in a short Er-Yb-doped phosphate glass fiber laser,” Appl. Phys. B |

8. | T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, and M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode”, IEEE Trans. Instrum. Meas. |

9. | Sahin Kaya zdemir, S. Ito, S. Shinohara, H. Yoshida, and M. Sumi, “Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode,” Appl. Opt. |

10. | M. Norgi, S. Donati, and D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. |

11. | H. Huan, M. Wang, and D. Guo et al. “Self-mixing interference effect of DFB semiconductor lasers,” Appl. Phys. B |

12. | J. Zhou and M. Wang, “Effects of self-mixing interference on gain-coupled distributed-feedback lasers,” Opt. Express |

13. | Max Born and Emil Worlf, Principles of Optics, Pergamon press, (1975). |

14. | E. I. Thorsos, “The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acous. Soc. Am. |

15. | A. K. Fung and M. F. Chen, “Numerical simulation of scattering from simple and composite random surfaces,” J. Opt. Soc. Am. A |

16. | F. Favre, “Theoretical analysis of external optical feedback on DFB semiconductor lasers,” IEEE J. Quantum Electron. |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

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

(260.3160) Physical optics : Interference

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: January 3, 2006

Revised Manuscript: April 6, 2006

Manuscript Accepted: April 6, 2006

Published: April 17, 2006

**Citation**

Daofu Han, Ming Wang, and Junping Zhou, "Self-mixing speckle interference in DFB lasers," Opt. Express **14**, 3312-3317 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3312

Sort: Year | Journal | Reset

### References

- T. Shibata, S. Shinohara et al. "Laser speckle velocimeter using self-mixing laser diode," IEEE Trans. Instrum. Meas. 45,499-503 (1996). [CrossRef]
- P. A. Porta, D. P. Curtin and J. G. McInerney, "Laser Doppler velocimetry by optical self-mixing in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 14, 1717-1721 (2002). [CrossRef]
- G. Giuliani, S. Bozzi-Pietra, S. Donati, "Self-mixing laser diode vibrometer" Meas. Sci. Tech. 14, 24-32 (2003). [CrossRef]
- M. Norgia, S. Donati, "A displacement-measuring instrument utilizing self-mixing interferometry", IEEE Trans. Instrum. Meas. 52, 1765-1770 (2003). [CrossRef]
- L. Scalise, Y. G. Yu, G. Giuliani, et al. "Self-mixing laser diode velocimetry: Application to vibration and velocity measurement," IEEE Trans. Instrum. Meas. 53, 223-232 (2004). [CrossRef]
- J. W. Choi, M. J. Yu, M. Kopica, "Photoacoustic laser Doppler velocimetry using the self-mixing effect of CO2 laser," Proc. Soc. Photo-Opt.Instrum. 5240, 230-234 (2004).
- M. Laroche, L. Kervevan, H. Gilles, S. Girard, J.K. Sahu, "Doppler velocimetry using self-mixing effect in a short Er-Yb-doped phosphate glass fiber laser," Appl. Phys. B 80, 603-607 (2005). [CrossRef]
- T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, "Automatic measurement of velocity and length of moving plate using self-mixing laser diode", IEEE Trans. Instrum. Meas. 48, 1062-1067 (1999). [CrossRef]
- Sahin Kaya zdemir, S. Ito, S. Shinohara, H. Yoshida, M . Sumi, "Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode," Appl. Opt. 38, 6859-6865(1999). [CrossRef]
- M. Norgi, S. Donati, D. D’Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001). [CrossRef]
- H. Huan, M. Wang, D. Guo et al. "Self-mixing interference effect of DFB semiconductor lasers," Appl. Phys. B 79,1554-1559 (2004). [CrossRef]
- J. Zhou, M. Wang, "Effects of self-mixing interference on gain-coupled distributed-feedback lasers," Opt. Express 13,1848-1854 (2005). [CrossRef] [PubMed]
- Max Born and Emil Worlf, Principles of Optics, Pergamon press, (1975).
- E. I. Thorsos, "The validity of the kirchoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acous. Soc. Am. 83, 78-92 (1988). [CrossRef]
- A. K. Fung, M. F. Chen, "Numerical simulation of scattering from simple and composite random surfaces," J. Opt. Soc. Am. A 2, 2274-2284 (1985). [CrossRef]
- F. Favre, "Theoretical analysis of external optical feedback on DFB semiconductor lasers," IEEE J. Quantum Electron. 23, 81-88 (1987). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.