## Self-mixing interference effects of orthogonally polarized dual frequency laser

Optics Express, Vol. 12, Issue 25, pp. 6100-6105 (2004)

http://dx.doi.org/10.1364/OPEX.12.006100

Acrobat PDF (4187 KB)

### Abstract

The self-mixing interference in birefringent dual frequency laser is systematically studied for the first time. The output intensities of two orthogonal modes are both modulated by external cavity length, and their phase relationship is experimentally and theoretically demonstrated. When frequency difference is greater than line width of homogeneous broadening gain curve, the phase relationship is determined by phase difference of two modes. If the frequency difference is smaller than the line width, modes competion will play an important role. Our results can advance the research of self-mixing interferometer of orthogonally polarized dual frequency laser.

© 2004 Optical Society of America

## 1. Introduction

1. T. Mukai and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. **55**, 1711–1714 (1985). [CrossRef] [PubMed]

3. H. Osmundsen and N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. QE. **19**, 465–469 (1983). [CrossRef]

4. N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Intrum. Meas. **46**, 847–850 (1997). [CrossRef]

5. P. A. Roos, M. Stephens, and C. Wiemen, “Laser Vibrometer based on optical feedback induced frequency modulation of a single mode laser diode,” Appl. Opt. **35**, 6754–6761 (1996). [CrossRef] [PubMed]

7. W. M. Wang, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference inside a single mode diode laser for optical sensing applications,” IEEE J. Lightwave Tech. **12**, 1577–1587 (1994). [CrossRef]

8. W. M. Wang, W. J. O. Boyle, and K. T. V. Grattan, “Self-mixing interference in a diode laser: Experimental observations and Theoretical Analysis,” Appl. Opt. **32**, 1551–1558 (1993). [CrossRef] [PubMed]

8. W. M. Wang, W. J. O. Boyle, and K. T. V. Grattan, “Self-mixing interference in a diode laser: Experimental observations and Theoretical Analysis,” Appl. Opt. **32**, 1551–1558 (1993). [CrossRef] [PubMed]

9. P. J. D. Groot, G. M. Gallatin, and S. H. Macomber, “Ranging and velocimetry signal generation in a backscatter-modulated laser diode,” Appl. Opt. **27**, 4475–4479 (1988). [CrossRef] [PubMed]

10. S. Gao, D. Lin, C. Yin, and J. Guo, “A 5MHz beat frequency He-Ne laser equipped with bireflectance cavity mirror,” Opt. Laser Tech. **33**, 335–339 (2001). [CrossRef]

11. S. Yang and S. Zhang, “The frequency split phenomenon in a HeNe laser with a rotation quartz crystal plate in its cavity,” Opt. Commun. **68**, 55–57 (1988). [CrossRef]

13. S. Zhang, K. Li, M. Wu, and G. Jin, “The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,” Opt. Commun. **90**, 279–282 (1992). [CrossRef]

14. Y. Xiao, S. Zhang, and Y. Li, “Tuning characteristics of frequency difference tuning of Zeeman-birefringence He-Ne dual frequency laser,” Chin. Phys. Lett. **20**, 230–233 (2003). [CrossRef]

*λ*/2 change of the external cavity length makes the two intensities both undulate one period. The phase relationship of the two intensity modulation curves is determined by frequency difference between the two orthogonally polarized lights, initial length of external cavity and modes competion. When the frequency difference is smaller than the line width of homogeneous broadening gain curve, the phase relationship mainly depends on modes competion. However, if the frequency difference is greater than the line width, the phase relationship is determined by the frequency difference and initial length of external cavity. According to these results, the self-mixing interference effects of orthogonally polarized dual frequency laser are promising for application in precision measurement.

## 2. Experimental setup

^{20}:Ne

^{22}=1:1.

_{1}and M

_{2}are laser mirrors with the amplitude reflectivity of r

_{1}=0.999 and r

_{2}=0.994, respectively, and the distance

*L*between them is 135mm. QC and the half-intracavity laser form an orthogonally polarized dual frequency laser. Due to the birefringent effect of QC, a single mode of the laser can be split into two orthogonally polarized modes, which are called o-light and e-light. When the angle between the crystalline axis of QC and the laser axis is changed, the frequency difference between the two orthogonally polarized modes can be adjusted. M

_{E}is external reflective mirror with the amplitude reflectivity of r

_{3}=0.2, used to reflect beams back into laser. M

_{E}and M

_{2}together form the feedback external cavity, whose length is

*l*. The photodetectors, D

_{1}and D

_{2}can be used to detect the output intensities of two orthogonally polarized lights, respectively. The laser modes are observed by SI. SP is used to measure the frequency difference of the two orthogonal modes.

## 3. Theoretical analyses

_{3}is much smaller than the reflection coefficient r

_{2}, the multiple reflection effect within the external cavity can be neglected. In the presence of optical feedback, the light beams can be divided into two parts. The first one travels within the internal cavity, while the second one travels in the external cavity and then couples into the internal cavity. These two parts of electric fields superpose in the internal cavity and construct the self-mixing interference. The oscillating condition of a dual frequency laser with optical feedback can be given by [15

15. G. A. Acket, D. Lenstra, A. D. Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. QE. **20**, 1163–1169 (1984). [CrossRef]

17. A. Olsson and C.L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. QE. **17**, 1320–1323 (1981). [CrossRef]

_{2}and external mirror M

_{E}respectively,

*g*

_{o}and

*g*

_{e}are the laser linear gains,

*α*

_{o}and

*α*

_{e}are the internal losses,

*ω*

_{o}and

*ω*

_{e}are the optical angular frequencies of o-light and e-light,

*τ*

_{c}=

*2L/c*is the laser beam round-trip time in internal cavity, and

*c*is light velocity in vacuum. Since r

_{3}is very small and the external mirror is perfectly aligned, we can get

*r*

_{2}[1+

*ζ*exp(

*iω*

_{o}

*τ*)] and

*r*

_{2}[1+

*ζ*exp(

*iω*

_{e}

*τ*)], where

*τ*=

*2l/c*represents the laser beam round-trip time in external cavity, and

*ζ*=(1-

*r*

_{3}/

*r*

_{2}is optical feedback factor. The threshold gains change

*Δg*

_{o}=

*g*

_{o}

*-g*

_{o0}and Δge=ge-ge0 due to the optical feedback, where go0 and ge0 are the threshold gains of laser without optical feedback, can be obtained from Eq. (1). To make the result independent of internal cavity length

*L*, we define normalized threshold gains change

*ΔG*

_{o}=

*Δg*

_{o}

*L*and

*ΔG*

_{e}

*=Δg*

_{e}

*L*. Because

*ζ*≪1, Δ

*G*

_{o}=-ln(|

*r*

_{2})≈

*η*

_{o}cos(

*ω*

_{o}

*τ*) and Δ

*G*

_{e}≈

*η*

_{e}cos(

*ω*

_{e}

*τ*) where

*η*

_{o}and

*η*

_{e}are intensity optical feedback factors, which can be obtained from Eq. (1). Because variations of laser intensities are proportional to

*ΔG*

_{o}and

*ΔG*

_{e}, the output intensities of two orthogonally polarized lights with optical feedback can be written as:

*I*

_{o0}and

*I*

_{e0}are intensities of two orthogonally polarized lights without optical feedback,

*ε*

_{o}and

*ε*

_{e}are constants. Equation (2) shows that intensities of two orthogonally polarized lights are both modulated when the feedback loop is on, and are similar to sine waves. For convenience, we rewrite the Eq. (2) as:

*ν*

_{o}and

*ν*

_{e}are the optical frequencies of o-light and e-light. From Eq. (3), we can find that both of the two intensities vary one period when the length of external cavity changes λ/2. However, there is a phase difference

*δ*between

*I*

_{o}and

*I*

_{e},

*ν*is frequency difference between the two orthogonal polarized lights, and Λ=1100

*MHz*is longitudinal mode spacing of laser. From Eq. (4), when laser is fixed,

*δ*is determined by and is proportional to the length of external cavity and frequency difference. However, if Δ

*ν*is smaller than the line width of homogeneous broadening gain curve (about 100–300MHz), the hole-burnings of the two orthogonal modes will cross. Consequently, the modes competion must be considered. The phase relationship between

*I*

_{o}and

*I*

_{e}does not only depend on Eq. (4), and a phenomenon that increase of one mode intensity will be accompanied decrease of the other mode will be observed. If Δ

*ν*is greater than the line width, the modes competion can be neglected, and the phase relationship between

*I*

_{o}and

*I*

_{e}is determined only by Eq. (4).

_{2}) is nearly 1 and |

*r*

_{3}|≪|

*r*

_{2}| in our experiments, the frequency shifts caused by optical feedback are very small [8

8. W. M. Wang, W. J. O. Boyle, and K. T. V. Grattan, “Self-mixing interference in a diode laser: Experimental observations and Theoretical Analysis,” Appl. Opt. **32**, 1551–1558 (1993). [CrossRef] [PubMed]

18. P.J. Brannon, “Laser feedback: its effect on laser frequency,” Appl. Opt. **15**, 1119–1120 (1976). [CrossRef] [PubMed]

## 4. Experimental results and discussion

*l*=

*L/2*, the intensity modulation curves of two orthogonally polarized lights with different frequency differences are shown in Fig. 2.

*π*, 0.14

*π*, 0.254

*π*, 0.5

*π*, 0.664

*π*and

*π*respectively. But, Fig.2 (a) and (b) disagree with the results of Eq. (3), and the phase differences between

*I*

_{o}and

*I*

_{e}shown in Figs. 2(a) and 2(b) are far greater than the values calculated from Eq. (4). In Fig. 2(a) and 2(b), since the frequency difference of two orthogonal modes is smaller than the line width of homogeneous broadening gain curve, the hole-burnings of the two orthogonal modes cross. Due to the existence of competion between two modes, increase of one mode intensity will lead to decrease of the other mode. In this case, the phase relationship of

*I*

_{o}and

*I*

_{e}mainly depends on modes competion. Once the frequency difference of two orthogonal modes is greater than the line width of homogeneous broadening gain curve, the phase relationship of

*I*

_{o}and

*I*

_{e}will be determined by phase difference given by Eq. (4), as shown by Figs. 2(c)–(f), which agree with the calculated results by Eq. (3).

*l*=

*L*, the intensity modulation curves of the two orthogonal polarized lights with different frequency differences are shown by Fig. 3.

*I*

_{o}and

*I*

_{e}will be mainly determined by modes competion. Otherwise, the phase relationship is determined by phase difference given by Eq. (4).

*π*, 0.545

*π*, 1.02

*π*, 2

*π*, 2.66

*π*and 4

*π*respectively. The figure also show, when the frequency difference of two orthogonal modes is smaller than the line width of homogeneous broadening gain curve, the phase relationship of

*I*

_{o}and

*I*

_{e}is mainly determined by modes competion. Otherwise, the phase relationship is determined by phase difference given by Eq. (4).

*ν*is small, the phase relationship of

*I*

_{o}and

*I*

_{e}disagree with the calculated results from Eq. (3), due to the existence of modes competion. In this case, considering Fig. 2(a) and 2(b)–Fig. 4(a) and 4(b), we can find, for a certain Δ

*ν*, the phase difference between two modes can finely change the phase relationship of

*I*

_{o}and

*I*

_{e}. However, it is difficult to accurately calculate the influence of modes competion on the phase relationship of

*I*

_{o}and

*I*

_{e}. More experiments, which are not presented here, have proven that the line width of homogeneous broadening gain curve of He-Ne laser used by our experiments is about 200MHz. As long as Δ

*ν*is greater than 200MHz, the phase relationship between

*I*

_{o}and

*I*

_{e}agrees well with the calculated result by Eq. (3), so the modes competion can be neglected. For example, when Δ

*ν*=550

*MHz*, from Eq. (4), the initial external cavity lengths of 67.5mm, 135mm, and 270mm are corresponding to the phase differences of 0.5

*π, π*, and 2

*π*respectively. Comparing the theoretical results with experimental results shown by Fig. 2(d)–Fig. 4(d), we can find that they are in good agreement. Therefore, the phase relationship between

*I*

_{o}and

*I*

_{e}can be controlled easily. Meanwhile, by spectrometer, we also find that the frequency difference is almost unchanged in the presence of optical feedback.

## 5. Conclusions

## Acknowledgments

## References and links

1. | T. Mukai and K. Otsuka, “New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,” Phys. Rev. Lett. |

2. | M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Megret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. |

3. | H. Osmundsen and N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. QE. |

4. | N. Servagent, T. Bosch, and M. Lescure, “A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,” IEEE Trans. Intrum. Meas. |

5. | P. A. Roos, M. Stephens, and C. Wiemen, “Laser Vibrometer based on optical feedback induced frequency modulation of a single mode laser diode,” Appl. Opt. |

6. | S. S. Hara, A. Yoshida, and M. Sumi, “Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,” Appl. Opt. |

7. | W. M. Wang, K. T. V. Grattan, and A. W. Palmer, “Self-mixing interference inside a single mode diode laser for optical sensing applications,” IEEE J. Lightwave Tech. |

8. | W. M. Wang, W. J. O. Boyle, and K. T. V. Grattan, “Self-mixing interference in a diode laser: Experimental observations and Theoretical Analysis,” Appl. Opt. |

9. | P. J. D. Groot, G. M. Gallatin, and S. H. Macomber, “Ranging and velocimetry signal generation in a backscatter-modulated laser diode,” Appl. Opt. |

10. | S. Gao, D. Lin, C. Yin, and J. Guo, “A 5MHz beat frequency He-Ne laser equipped with bireflectance cavity mirror,” Opt. Laser Tech. |

11. | S. Yang and S. Zhang, “The frequency split phenomenon in a HeNe laser with a rotation quartz crystal plate in its cavity,” Opt. Commun. |

12. | S. Zhang, K. Li, and G. Jin, “Birefringent tuning double frequency He-Ne laser,” Appl. Opt. |

13. | S. Zhang, K. Li, M. Wu, and G. Jin, “The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,” Opt. Commun. |

14. | Y. Xiao, S. Zhang, and Y. Li, “Tuning characteristics of frequency difference tuning of Zeeman-birefringence He-Ne dual frequency laser,” Chin. Phys. Lett. |

15. | G. A. Acket, D. Lenstra, A. D. Boef, and B. H. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. QE. |

16. | R.W. Tkach and A.R. Chraplyvy, “Regimes of feedback effects in 1.5-µm distributed feedback lasers,” J. Lightwave Technol. |

17. | A. Olsson and C.L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. QE. |

18. | P.J. Brannon, “Laser feedback: its effect on laser frequency,” Appl. Opt. |

**OCIS Codes**

(140.1340) Lasers and laser optics : Atomic gas lasers

(260.1440) Physical optics : Birefringence

(260.3160) Physical optics : Interference

**ToC Category:**

Research Papers

**History**

Original Manuscript: October 25, 2004

Revised Manuscript: November 9, 2004

Published: December 13, 2004

**Citation**

Ligang Fei and Shulian Zhang, "Self-mixing interference effects of orthogonally polarized dual frequency laser," Opt. Express **12**, 6100-6105 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-25-6100

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### References

- T. Mukai, and K. Otsuka, ???New route to optical chaos: Successive-subharmonic-oscillation cascade in a semiconductor laser coupled to an external cavity,??? Phys. Rev. Lett. 55, 1711-1714 (1985). [CrossRef] [PubMed]
- M.Sciamanna, K.Panajotov, H.Thienpont, I.Veretennicoff, P.Megret and M.Blondel, ???Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,??? Opt. Lett. 28, 1543-1545 (2003). [CrossRef] [PubMed]
- H. Osmundsen and N. Gade, ???Influence of optical feedback on laser frequency spectrum and threshold conditions,??? IEEE J. QE. 19, 465-469 (1983). [CrossRef]
- N. Servagent, T. Bosch and M. Lescure, ???A laser displacement sensor using the self-mixing effect for modal analysis and defect detection,??? IEEE Trans. Intrum. Meas. 46, 847-850 (1997). [CrossRef]
- P. A. Roos, M. Stephens and C. Wiemen, ???Laser Vibrometer based on optical feedback induced frequency modulation of a single mode laser diode,??? Appl. Opt. 35, 6754-6761 (1996). [CrossRef] [PubMed]
- S. S. Hara, A. Yoshida and M. Sumi, ???Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,??? Appl. Opt. 25, 1471-179 (1986).
- W. M. Wang, K. T. V. Grattan and A. W. Palmer, ???Self-mixing interference inside a single mode diode laser for optical sensing applications,??? IEEE J. Lightwave Tech. 12, 1577-1587 (1994). [CrossRef]
- W. M. Wang, W. J. O. Boyle and K. T. V. Grattan, ???Self-mixing interference in a diode laser: Experimental observations and Theoretical Analysis,??? Appl. Opt. 32, 1551-1558 (1993). [CrossRef] [PubMed]
- P. J. D. Groot, G. M. Gallatin and S. H. Macomber, ???Ranging and velocimetry signal generation in a backscatter-modulated laser diode,??? Appl. Opt. 27, 4475-4479 (1988). [CrossRef] [PubMed]
- S. Gao, D. Lin, C. Yin and J. Guo, ???A 5MHz beat frequency He???Ne laser equipped with bireflectance cavity mirror,??? Opt. Laser Tech. 33, 335-339 (2001). [CrossRef]
- S. Yang and S. Zhang, ???The frequency split phenomenon in a HeNe laser with a rotation quartz crystal plate in its cavity,??? Opt. Commun. 68, 55-57 (1988). [CrossRef]
- S. Zhang, K. Li and G. Jin, ???Birefringent tuning double frequency He-Ne laser,??? Appl. Opt. 29, 1265-1267 (1990). [CrossRef] [PubMed]
- S. Zhang, K. Li, M. Wu and G. Jin, ???The pattern of mode competion between two frequencies produced by mode split technology with tuning of the cavity length,??? Opt. Commun. 90, 279-282 (1992). [CrossRef]
- Y. Xiao, S. Zhang and Y. Li, ???Tuning characteristics of frequency difference tuning of Zeemanbirefringence He-Ne dual frequency laser,??? Chin. Phys. Lett. 20, 230-233 (2003). [CrossRef]
- G. A. Acket, D. Lenstra, A. D. Boef and B. H. Verbeek, ???The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,??? IEEE J. QE. 20, 1163-1169 (1984). [CrossRef]
- R.W. Tkach and A.R. Chraplyvy, ???Regimes of feedback effects in 1.5-µm distributed feedback lasers,??? J. Lightwave Technol. 4, 1655-1661 (1986). [CrossRef]
- A.Olsson and C.L.Tang, ???Coherent optical interference effects in external-cavity semiconductor lasers,??? IEEE J. QE. 17, 1320-1323 (1981). [CrossRef]
- P.J.Brannon, ???Laser feedback: its effect on laser frequency,??? Appl. Opt. 15, 1119-1120 (1976). [CrossRef] [PubMed]

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