## Polarization control in a He-Ne laser using birefringence feedback

Optics Express, Vol. 13, Issue 8, pp. 3117-3122 (2005)

http://dx.doi.org/10.1364/OPEX.13.003117

Acrobat PDF (138 KB)

### Abstract

The polarization dynamics of laser subjected to weak optical feedback from birefringence external cavity are studied theoretically and experimentally. It is found that polarization flipping with hysteresis is induced by birefringence feedback, and the intensities of two eigenstates are both modulated by external cavity length. The variations of hysteresis loop and duty ratios of two eigenstates in one period of intensity modulation with phase differences of birefringence element in external cavity are observed. When the phase difference is *π*/2, the two eigenstates will equally alternatively oscillate, and the width of hysteresis loop is the smallest.

© 2005 Optical Society of America

## 1. Introduction

1. J. Kannelaud and W. Culshaw, “Coherence effects in gaseous laser with axial magnetic field. II. Experimental,” Phys. Rev. **141**, 237–245 (1966). [CrossRef]

2. A. L. Floch, G. Ropars, J. M. Lenornamd, and R. L. Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. **52**, 918–921 (1984). [CrossRef]

3. G. Ropars, A. L. Floch, and R. L. Naour, “Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,” Phys. Rev. A **46**, 623–640 (1992). [CrossRef] [PubMed]

4. G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical,” Phys. Rev. Lett. **55**, 703–706 (1985). [CrossRef] [PubMed]

5. W. Xiong, P. Glanzning, P. Paddon, A. D. May, M. Bourouis, S. Laniepce, and G. Stephan, “Stability of polarized modes in a quasi-isotropic laser,” J. Opt. Soc. Am. B **8**, 1236–1243 (1991). [CrossRef]

6. K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. **84**, 2763–2765 (2004). [CrossRef]

9. J. Houlihan, L. Lewis, and G. Huyet, “Feedback induced polarization switching in vertical cavity surface emitting lasers,” Opt. Comm. **232**, 391–397 (2004). [CrossRef]

## 2. Experimental setup

^{20}:Ne

^{22}=1:1.

_{1}and M

_{2}are laser mirrors with reflectivities of R

_{1}=99.8% and R

_{2}=98.8%, respectively, and the distance

*L*between them is 150mm. M

_{E}is external mirror with reflectivity of R

_{3}=10%, used to reflect laser beams back into the laser. M

_{E}, together with M

_{2}and G can form a birefringence external cavity. The length of external cavity

*l*is 100mm. D

_{1}is used to detect the laser intensity. D

_{2}is used to detect the variations of laser polarization state. Due to the stress birefringence effect, when a force is applied on G, the two optical axes of G are parallel to the two principal stress directions, and the force-induced birefringence phase difference is proportional to the magnitude of force. According to the coordinates system shown in Fig. 1, the two optical axes of G are along y-axis and x-axis, respectively.

## 3. Experimental results

*δ*can be given by

*δ*=8

*λF*/

*πDf*

_{0}, where

*D*is the diameter of

*G*,

*f*is the fringe value of the optical materials, and

_{0}*F*is the force applied on G. Therefore, the different phase differences between the two principal optical axes of G can be obtained by changing the magnitudes of force. When the length of external cavity is scanned by PZT, the intensity modulation curves can be obtained, and different phase differences of G correspond to different intensity modulation curves as shown in Fig. 2.

_{E}moves toward the laser and the length of external cavity is decreased. The dash lines represent the intensity modulation curves that PZT voltage is decreased, i.e., M

_{E}moves away from the laser, and the length of external cavity is increased.

_{y}) to x-polarization (P

_{x}) is at point D. If PZT voltage is decreased, the position of polarization flipping from P

_{x}to P

_{y}is at point C. From Figs. 2(a)–2(d), we can find, if the phase difference of G is changed, the position of polarization flipping is also different. This indicates that the duty ratios of the two eigenstates in a period of intensity modulation curve vary with the phase difference. The relationship between the duty ratios of the two eigenstates and the phase difference are shown in Fig. 3(a). Meanwhile, for a certain phase difference of G, when the moving direction of feedback mirror (M

_{E}) is different, the polarization flipping points C and D are not superposition. This indicates the hysteresis effect of polarization flipping. When the phase difference is changed, the width of hysteresis loop is also changed. Using this result, we can control the polarization switching outside the laser. As known, the length variation of external cavity is proportional to the voltage applied on PZT, so the voltage increments on PZT can be used to represent the width of hysteresis loop shown by the space between point C and D. The relationship curve of the hysteresis loop width and the phase difference is shown in Fig. 3(b). When

*δ*=π/2, the width of hysteresis loop is the smallest.

*δ*=π/2, the curve of intensity modulation is similar to the full wave rectification of sine wave, as shown in Fig. 2(d). Observing the output intensity through a polarizer, we can find that the duty ratios are nearly equal and the profile of intensity curve is similar to a square wave due to the existence of the laser initial intensity. Because

*λ*/2 change of the external cavity length corresponds to one period of intensity modulation, in this case, each polarization switching will correspond to

*λ*/4 change of the external cavity length.

## 4. Theoretical analyses

2. A. L. Floch, G. Ropars, J. M. Lenornamd, and R. L. Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. **52**, 918–921 (1984). [CrossRef]

3. G. Ropars, A. L. Floch, and R. L. Naour, “Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,” Phys. Rev. A **46**, 623–640 (1992). [CrossRef] [PubMed]

_{y}to P

_{x}will occur

*α*is laser net gain,

*β*and

*θ*are self and cross saturation coefficient,

*ρ*is self pushing coefficient, ΔΦ

*is the phase anisotropy in internal cavity,*

_{xy}*t*and

_{x}*t*represent the transmission coefficients of P

_{y}_{x}and P

_{y}respectively. The first term of Eq. (1) represents the effect of the active medium, the second term represents the effect of the phase anisotropy of intracavity and the third term represents the effect of the loss anisotropy.

*R*

_{3}≪

*R*

_{2}, according to the model [10

10. T. H. Peek, P. T. Bolwijn, and T. J. Alkemade, “Axial mode number of gas lasers from moving-mirror experiments,” Am. J. Phys. **35**, 820–831 (1967). [CrossRef]

*φf*=4

*πl*/

*λ*represents the phase of external cavity. Due to

*R*≠

_{y-y}*R*, the two eigenstates of one laser mode will subject to different losses. Substitute Eq. (2) into Eq. (1), we can get the condition of polarization flipping from P

_{y-x}_{y}to P

_{x}

*R*

_{3}/

*R*

_{2})

^{1/2}(1-

*R*

_{2}). Because the frequency shift caused by optical feedback and the intracavity anisotropy are very small [11

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

*φ*0) or x-axis (cos

_{>}*φ*<0). When polarization direction of laser is along y-axis, the intensity variation can be obtained by ΔI

_{f}_{y}=

*η*cos

*φ*[8

_{f}8. L. G. Fei, S. L. Zhang, and X. J. Wan, “Influence of optical feedback from birefringence external cavity on intensity tuning and polarization of laser,” Chin. Phys. Lett. **21**, 1944–1947 (2004). [CrossRef]

*η*represents optical feedback factor. Similarly, when the polarization direction of laser is parallel to x-axis, the equivalent mirror reflectivities along x-axis and y-axis are given by

*δ*is the phase difference between two principal optical axes of G. The P

_{x}to P

_{y}flip condition is similar to Eq. (1), and only the signs of the first and third terms are changed. The condition of polarization flipping from P

_{x}to P

_{y}can be written as

*φf*-2

*δ*)>0) or y-axis (cos(

*φ*-2

_{f}*δ*)<0). If polarization direction of laser is along x-axis, the intensity variation is ΔI

_{x}=

*η*cos(

*φ*-2

_{f}*δ*). When the length of external cavity is changed, the dependence of laser intensity and polarization flipping on

*δ*can be illustrated in Fig. 4. The horizontal dot lines in Fig. 4 represent the right-hand sides of Eqs. (3) and (5), which are nearly equal to zero.

_{y}, the intensity variation is ΔI

_{y}shown by solid lines in Fig. 4. In Figs. 4(a)–4(c), when starts from point A to the right and reaches point D, the condition of polarization flipping from P

_{y}to P

_{x}is satisfied from Eq. (3). The polarization direction of laser jumps from P

_{y}to P

_{x}, i.e., from point D to point E, and the intensity turns into ΔI

_{x}shown by dash lines. At point F, the polarization should jump from P

_{x}to P

_{y}from Eq. (5). However, due to

*R*>

_{x-x}*R*, P

_{y-y}_{y}will subject to more losses and be suppressed. The polarization still remains P

_{x}. Once reaches point H, due to

*R*>

_{y-y}*R*, from Eq. (5), the polarization will jump back to P

_{x-x}_{y}. The intensity becomes ΔI

_{y}again till point I, and then begins another period. The trace of intensity modulation within a period is

_{x}, the intensity variation is ΔI

_{x}shown by dash lines. In Figs. 4(a)–4(c), when reaches point C, from Eq. (5), the polarization will jump from P

_{x}to P

_{y}, i.e., from point C to point B. At point J, the polarization will jump back to P

_{x}. The intensity becomes ΔI

_{x}again till point K, and then begins another period. The trace of intensity modulation within a period is

_{y}=2(

*π*-

*δ*) and

*D*=2

_{x}*δ*. The normalized curves that the duty ratios vary with

*δ*are shown in Fig. 5(a).

*δ*. The relationship between the width of hysteresis loop and the phase difference of birefringence element can be given by

*W*=

_{H}*π*-2

*δ*. The curve that the width of hysteresis loop varies with

*δ*is shown in Fig. 5(b).

_{y}→P

_{x}and P

_{x}→P

_{y}. The width of hysteresis loop CD shown by lower traces in Figs. 4(a)–4(d) decreases with increasing the phase difference of birefringence element. If

*δ*=

*π*/2, the width of hysteresis loop is the smallest, and nearly equal to zero. Meanwhile, in a period of laser intensity modulation, the duty ratios of two eigenstates also vary with the value of phase difference. The greater phase difference the smaller difference of duty ratios. When

*δ*=

*π*/2, the duty ratios of two eigenstates are equal. The theoretical analyses are in good agreement with the experimental results.

## 5. Conclusions

*δ*=

*π*/2, the duty ratios are equal, and intensity curve is similar to the full wave rectification of sine wave. If we observe the laser intensity through a polarizer, the square wave can be output. In this case, the width of hysteresis loop is the smallest, and each polarization switching corresponds to

*λ*/4 change of the external cavity length. Our results are promising for applications in optical switching, optical bistability, and precision measurements of some physical quantities.

## Acknowledgments

## References and links

1. | J. Kannelaud and W. Culshaw, “Coherence effects in gaseous laser with axial magnetic field. II. Experimental,” Phys. Rev. |

2. | A. L. Floch, G. Ropars, J. M. Lenornamd, and R. L. Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. |

3. | G. Ropars, A. L. Floch, and R. L. Naour, “Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,” Phys. Rev. A |

4. | G. Stephan and D. Hugon, “Light polarization of a quasi-isotropic laser with optical,” Phys. Rev. Lett. |

5. | W. Xiong, P. Glanzning, P. Paddon, A. D. May, M. Bourouis, S. Laniepce, and G. Stephan, “Stability of polarized modes in a quasi-isotropic laser,” J. Opt. Soc. Am. B |

6. | K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. |

7. | 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. |

8. | L. G. Fei, S. L. Zhang, and X. J. Wan, “Influence of optical feedback from birefringence external cavity on intensity tuning and polarization of laser,” Chin. Phys. Lett. |

9. | J. Houlihan, L. Lewis, and G. Huyet, “Feedback induced polarization switching in vertical cavity surface emitting lasers,” Opt. Comm. |

10. | T. H. Peek, P. T. Bolwijn, and T. J. Alkemade, “Axial mode number of gas lasers from moving-mirror experiments,” Am. J. Phys. |

11. | 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: March 15, 2005

Revised Manuscript: April 5, 2005

Published: April 18, 2005

**Citation**

Ligang Fei, Shulian Zhang, Yan Li, and Jun Zhu, "Polarization control in a He-Ne laser using birefringence feedback," Opt. Express **13**, 3117-3122 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-8-3117

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### References

- J. Kannelaud and W. Culshaw, �??Coherence effects in gaseous laser with axial magnetic field. II. Experimental,�?? Phys. Rev. 141, 237-245 (1966). [CrossRef]
- A. L. Floch, G. Ropars, J. M. Lenornamd and R. L. Naour, �??Dynamics of laser eigenstates,�?? Phys. Rev. Lett. 52, 918-921 (1984). [CrossRef]
- G. Ropars, A. L. Floch and R. L. Naour, �??Polarization control mechanisms in vectorial bistable lasers for one-frequency systems,�?? Phys. Rev. A 46, 623-640 (1992). [CrossRef] [PubMed]
- G. Stephan and D. Hugon, �??Light polarization of a quasi-isotropic laser with optical,�?? Phys. Rev. Lett. 55, 703-706 (1985). [CrossRef] [PubMed]
- W. Xiong, P. Glanzning, P. Paddon, A. D. May, M. Bourouis, S. Laniepce and G. Stephan, �??Stability of polarized modes in a quasi-isotropic laser,�?? J. Opt. Soc. Am. B 8, 1236-1243 (1991). [CrossRef]
- K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann and R. Michalzik, �??Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,�?? Appl. Phys. Lett. 84, 2763-2765 (2004). [CrossRef]
- 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]
- L. G. Fei, S. L. Zhang and X. J. Wan, �??Influence of optical feedback from birefringence external cavity on intensity tuning and polarization of laser,�?? Chin. Phys. Lett. 21, 1944-1947 (2004). [CrossRef]
- J. Houlihan, L. Lewis and G. Huyet, �??Feedback induced polarization switching in vertical cavity surface emitting lasers,�?? Opt. Comm. 232, 391-397 (2004). [CrossRef]
- T. H. Peek, P. T. Bolwijn and T. J. Alkemade, �??Axial mode number of gas lasers from moving-mirror experiments,�?? Am. J. Phys. 35, 820-831 (1967). [CrossRef]
- J. Brannon, �??Laser feedback: its effect on laser frequency,�?? Appl. Opt. 15, 1119-1120 (1976). [CrossRef] [PubMed]

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