## Single mode fiber birefringence compensation in Sagnac and “plug & play” interferometric setups

Optics Express, Vol. 17, Issue 6, pp. 4485-4494 (2009)

http://dx.doi.org/10.1364/OE.17.004485

Acrobat PDF (485 KB)

### Abstract

Single mode fiber (SMF) birefringence effects have been a limiting factor for a variety of Sagnac applications over longer distance SMF links. In this report, we present a new concept of the SMF birefringence compensation in a Sagnac interferometric setup, based on a novel polarization control system. For the destructive interference, our control system guarantees a perfect compensation of both the SMF birefringence and imperfect propagation times matching of the setup’s components. For the stabilization of the constructive interference, we have applied a fiber stretcher and a simple proportional-integral-derivative (PID) controller. The enclosed experimental data of the setup’s visibility confirm validity of our polarization control system. We have also showed that the SMF birefringence model used in a “plug & play” interferometric setup [

© 2009 Optical Society of America

## 1. Introduction

## 2. Birefringence in Sagnac

*k*= 0.5, assumed to be the same for both parts (

*E*and

_{x}*E*) of the electric vector

_{y}**E**, i.e.

*k*=

_{x}*k*. The x-part of the electric vector will later be called the horizontal, while the y-part the vertical component. The analysis can easily be extended to Sagnac interferometers with attenuation losses [16

_{y}16. D. B. Mortimore, ”Fiber loop reflectors,” J. Lightwave Technol. **6**, 1217–1224 (1988). [CrossRef]

*k*=

_{x}*k*, can be found in [16

_{y}16. D. B. Mortimore, ”Fiber loop reflectors,” J. Lightwave Technol. **6**, 1217–1224 (1988). [CrossRef]

16. D. B. Mortimore, ”Fiber loop reflectors,” J. Lightwave Technol. **6**, 1217–1224 (1988). [CrossRef]

17. F. P. Kapron, N. F. Borrelli, and D. B. Keck, “Birefringence in. dielectric optical waveguides,” IEEE J. uantum Electron. **QE-8**, 222–230 (1972) [CrossRef]

16. D. B. Mortimore, ”Fiber loop reflectors,” J. Lightwave Technol. **6**, 1217–1224 (1988). [CrossRef]

*P*

^{*},

*Q*

^{*}are complex conjugates of

*P*and

*Q*, respectively.

16. D. B. Mortimore, ”Fiber loop reflectors,” J. Lightwave Technol. **6**, 1217–1224 (1988). [CrossRef]

**E**and counterclockwise one

^{clk}_{2}**E**are easily found using the electric field amplitude transmission equation for a symmetrical (

^{cnt}_{3}*k*=

_{x}*k*= 0.5) coupler

_{y}**E**is given by

^{in}_{1}**E**and

^{clk}_{3}**E**are given by

^{cnt}_{2}**E**and

^{out}_{1}**E**are found by again applying the electric field amplitude transmission equation for a symmetrical (

^{out}_{4}*k*=

_{x}*k*= 0.5) coupler

_{y}*k*=

_{x}*k*= 0.5), the Eq. (13) corresponds to the constructive interference, while the Eq. (14) corresponds to the destructive one. It can be easily shown (by substituting, first Eq. (4) and Eq. (5) into Eq. (6) and Eq. (7), and finally Eq. (6 ) and Eq. (7) into Eq. (11) and Eq. (12)) that both constructive and destructive interference strongly depends on the asymmetry between the clockwise and counterclockwise birefringence (described by Eqs. (4) – (7)) unless the inclination rotation Φ is assumed to be equal to -Ω (the axis rotation corresponding to a circular retardation). However, such an assumption does not correspond to the general SMF birefringence.

_{y}## 3. Birefringence compensation in the “plug and play” interferometric setup

11. N. Gisin, G. Ribordy, W. Tittel, and H Zbinden, “Quantum cryptography,” Rev. Mod. Phys. **74**, 145–195 (2002). [CrossRef]

12. D. S. Bethune and W. P. Risk, “Autocompensating quantum cryptography,” New J. Phys. **4**, 42.1–42.15 (2002). [CrossRef]

13. A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, “Plug and play systems for quantum cryptography,” Appl. Phys. Lett. **70**, 793–795 (1997). [CrossRef]

_{2}if the phase difference

*φ*= 0 ± 2

*nπ*, where n is an integer number; or in DET

_{1}if

*φ*=

*π*± 2

*nπ*; or in both detectors for other

*φ*values. Thus, the “plug & play” system is auto-compensated for propagation time difference between the long arm and short arm pulses since they travel the same path length. For a high interference visibility, the long arm pulse should arrive to the PBS horizontally and the short arm vertically polarized. Thus, the SMF link’s birefringence should be analyzed in order to find how it influences the polarization change of the pulses. Furthermore, the pulses should arrive to the coupler CPL at the same amplitude.

19. M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. **72**, 341–344 (1989). [CrossRef]

19. M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. **72**, 341–344 (1989). [CrossRef]

12. D. S. Bethune and W. P. Risk, “Autocompensating quantum cryptography,” New J. Phys. **4**, 42.1–42.15 (2002). [CrossRef]

19. M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. **72**, 341–344 (1989). [CrossRef]

## 4. Analysis of single mode fiber birefringence compensation in Sagnac

_{3}) with the coupling ratio

*k*= 0.5, equally dividing the light into clockwise and counterclockwise parts that later enter two interferometers INT

_{1}and INT

_{2}, respectively.

_{2}contains a polarizing beam splitter (PBS

_{2}) and a 50/50 coupler (CPL

_{2}). The INT

_{1}has additionally a fiber stretcher (STR), controlled by a digital acquisition card (DAQ), and a delay line (DL), whose length is matched to stretcher’s fiber length. The interferometers are used for removing the SMF birefringence effects on the clockwise and counterclockwise pulses by converting their polarization (into the horizontal one) after they have propagated over the Sagnac loop. The conversion is necessary since the birefringent SMF, as already mentioned, differently changes polarization of the clockwise and counterclockwise pulses, which would decrease interference’s visibility in the coupler CPL

_{3}, being a part of the INT

_{3}. The stretcher’s main function is to minimize the amount of energy loss in the couplers’ CPL

_{1}and CPL

_{2}arms not connected into the coupler CPL

_{3}. This energy is monitored by an additional detector (DET

_{3}) connected to the coupler CPL

_{1}. The detector’s output is read, once per reading period TR, by the DAQ card. After the reading process, a simple proportional-integral-derivative (PID) controller adjusts stretcher’s length, thus the phase of the signal in stretcher’s arm. This arrangement maximizes the amount of energy flowing into the coupler CPL3 and minimizes the interference losses in the couplers CPL

_{1}and CPL

_{2}.

_{1}, INT

_{2}, and INT

_{3}are polarization maintaining and aligned to the horizontal (slow) axis. Also outputs of the polarizing beam splitters PBS

_{1}and PBS

_{2}are aligned to the horizontal axis as well as the interconnecting fiber cords. The signal transmitted from the polarizing beam splitter’s output R into the input 1 shifts its polarization (from the horizontal to the vertical), while there is no such shift for the signal transmitted from the output T into the input 1. The clockwise and counterclockwise pulses leaving the interferometers Int.1 and Int.2 (see Fig. 3) are generally elliptically polarized (due to the propagation timing skews

*δ*

_{1}and

*δ*

_{2}, discussed below), which is shown in the following Jones vector

*δ*

_{1}and

*δ*

_{2}) between the arms in the interferometers Int.1 and Int.2, respectively.

**E**and counterclockwise one

^{clk}_{a}**E**are found by applying the equation for the transmission of the electric field amplitude in a symmetrical (k=0.5) coupler

^{cnt}_{d}**E**, the clockwise electric field amplitude at the CIR output

^{clk}_{cir}_{1}is given by

**E**is given by

^{clk}_{b}_{2}is given by

_{1}(Eq. (24)) depends on the order in which the inputs of the couplers CPL

_{1}and CPL

_{2}have been connected into the coupler CPL

_{3}. The operator

*i*shows that the clockwise signal transmitted from the port R of the PBS

_{2}into the port d of the coupler CPL

_{3}is phase shifted by

*π*/2 relative to the signal on the port T. The opposite applies for the interferometer INT

_{1}(Eq. (24)).

**E**is given by

^{clk}_{d}*J*

^{cnt}_{int1}and

*J*

^{cnt}_{int2}are the transpose matrices of the matrices

*J*

^{clk}_{int1}(Eq. (24)) and

*J*

^{clk}_{int2}(Eq. (27)), respectively [16

16. D. B. Mortimore, ”Fiber loop reflectors,” J. Lightwave Technol. **6**, 1217–1224 (1988). [CrossRef]

**E**and

^{clk}_{d}**E**) have interfered in the CPL

^{cnt}_{a}_{3}, we are getting the following vectors at the detectors DET

_{1}and DET

_{2}

**E**and

_{DET1}**E**

_{DET}_{2}**E**and

_{DET1}**E**. Both have horizontal components only, which has been anticipated taking into account the polarization conversion in the interferometers INT

_{DET2}_{1}and INT

_{2}, see Fig. 3. What really astonish is the fact that the horizontal component

*E*

_{D1x}of the vector

**E**has vanished, providing a perfect destructive interference, independent of the birefringence and the propagation time skews

_{DET1}*δ*

_{1}and

*δ*

_{2}! This counterintuitive finding is our main result reported here. It opens the door to many Sagnac applications over longer distance SMF links, including high accuracy measurements, quantum key distribution, and quantum secret sharing [10

10. J. Bogdanski, J. Ahrens, and M. Bourennane, “Sagnac secret sharing over telecom fiber networks,” Opt. Express **17**, 1055–1063 (2009). [CrossRef] [PubMed]

*E*

_{D1y}of the vector

**E**has vanished). Instead, the horizontal component

_{DET2}*E*

_{D2x}of the vector

**E**depends on both the birefringence and the propagation time skews

_{DET2}*δ*

_{1}and

*δ*

_{2}. However, the visibility of the interference remains perfect (i.e. the visibility V= 1) since the destructive interference, as already mentioned, does neither depend on the SMF birefringence nor on the propagation time skews in the interferometers INT

_{1}and INT

_{2}. In order to control the stability of the constructive interference we have, as already mentioned, applied a fiber stretcher, see Fig. 3.

## 5. Experimental data

10. J. Bogdanski, J. Ahrens, and M. Bourennane, “Sagnac secret sharing over telecom fiber networks,” Opt. Express **17**, 1055–1063 (2009). [CrossRef] [PubMed]

_{1}and DET

_{2}) reading per second due to the fact that the DAQ card’s reading period of the photo detector DET

_{3}, being a part of our PID regulator, was set to 1 sec. Finally, it should be emphasized that the measurements were carried out in a noisy environment due to the temporary construction works, close to our lab.

## 6. Conclusions

1. E. Udd, “Sensing and instrumentation applications of the Sagnac fiber optic interferometer,” in *Interferometric Fiber Sensing*Proc. SPIE **2341**, 52–59 (1994). [CrossRef]

10. J. Bogdanski, J. Ahrens, and M. Bourennane, “Sagnac secret sharing over telecom fiber networks,” Opt. Express **17**, 1055–1063 (2009). [CrossRef] [PubMed]

16. D. B. Mortimore, ”Fiber loop reflectors,” J. Lightwave Technol. **6**, 1217–1224 (1988). [CrossRef]

17. F. P. Kapron, N. F. Borrelli, and D. B. Keck, “Birefringence in. dielectric optical waveguides,” IEEE J. uantum Electron. **QE-8**, 222–230 (1972) [CrossRef]

16. D. B. Mortimore, ”Fiber loop reflectors,” J. Lightwave Technol. **6**, 1217–1224 (1988). [CrossRef]

## Acknowledgments

## References and links

1. | E. Udd, “Sensing and instrumentation applications of the Sagnac fiber optic interferometer,” in |

2. | J. Zheng, “Differential singlemode fibre frequency-modulated continuous-wave Sagnac gyroscope,” Electron. Lett. |

3. | B. Culshaw, “The optical fibre Sagnac interferometer: an overview of its principles and applications,” Meas. Sci. Technol. |

4. | L. R. Jaroszewicz, “Fiber-optic Sagnac Interferometer as real sensor of the physical quantities,” in |

5. | L. R. Jaroszewicz and Z. Krajewski, “Application of fiber-optic Sagnac interferometer for detection of rotational seismic events,” Molecular and Quantum Acoustics |

6. | T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, “Circular type quantum key distribution,” IEEE Photon. Technol. Lett. |

7. | C. Zhou, G. Wu, L. Ding, and H. Zeng, “Single-photon routing by time-division phase modulation in a Sagnac interferometer,” Appl. Phys. Lett. |

8. | B. Qi, L. L. Huang, H. K. Lo, and L. Qian, “Quantum key distribution based on a Sagnac loop interferometer and polarization-insensitive phase modulators,” in |

9. | W. A. de Brito and R. V. Ramos, “Quantum information technology with Sagnac interferometer: interaction-free measurement, quantum key distribution and quantum secret sharing,” J. Mod. Opt. |

10. | J. Bogdanski, J. Ahrens, and M. Bourennane, “Sagnac secret sharing over telecom fiber networks,” Opt. Express |

11. | N. Gisin, G. Ribordy, W. Tittel, and H Zbinden, “Quantum cryptography,” Rev. Mod. Phys. |

12. | D. S. Bethune and W. P. Risk, “Autocompensating quantum cryptography,” New J. Phys. |

13. | A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, “Plug and play systems for quantum cryptography,” Appl. Phys. Lett. |

14. | A. Kuzin, H. Cerecedo Nún̈ez, and N. Korneev, “Alignment of a birefringent fiber Sagnac interferometer by fiber twist,” Opt. Commun. |

15. | B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, “Fiber optical loop mirror with a symmetrical coupler and a quarter-wave retarder plate in the loop,” Opt. Commun. |

16. | D. B. Mortimore, ”Fiber loop reflectors,” J. Lightwave Technol. |

17. | F. P. Kapron, N. F. Borrelli, and D. B. Keck, “Birefringence in. dielectric optical waveguides,” IEEE J. uantum Electron. |

18. | C. Tsao, |

19. | M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. |

**OCIS Codes**

(040.5570) Detectors : Quantum detectors

(060.4080) Fiber optics and optical communications : Modulation

(040.1345) Detectors : Avalanche photodiodes (APDs)

(270.5565) Quantum optics : Quantum communications

(270.5568) Quantum optics : Quantum cryptography

(060.3510) Fiber optics and optical communications : Lasers, fiber

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 8, 2009

Revised Manuscript: February 11, 2009

Manuscript Accepted: February 23, 2009

Published: March 5, 2009

**Citation**

Jan Bogdanski, Johan Ahrens, and Mohamed Bourennane, "Single mode fiber birefringence compensation in Sagnac and "plug & play" interferometric setups," Opt. Express **17**, 4485-4494 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-6-4485

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### References

- E. Udd, "Sensing and instrumentation applications of the Sagnac fiber optic interferometer," in Interferometric Fiber Sensing, Proc. SPIE 2341, 52-59 (1994). [CrossRef]
- J. Zheng, "Differential singlemode fibre frequency-modulated continuous-wave Sagnac gyroscope," Electron. Lett. 41, 727-728 (2005). [CrossRef]
- B. Culshaw, "The optical fibre Sagnac interferometer: an overview of its principles and applications," Meas. Sci. Technol. 17, 1-16 (2006). [CrossRef]
- L. R. Jaroszewicz, "Fiber-optic Sagnac Interferometer as real sensor of the physical quantities," in Proceedings of the Symposium on Photonics Technologies (Wroclaw, Poland, 2006), pp. 99-101.
- L. R. Jaroszewicz and Z. Krajewski, "Application of fiber-optic Sagnac interferometer for detection of rotational seismic events," Molecular Quantum Acoustics 22, 133-134 (2001).
- T. Nishioka, H. Ishizuka, T. Hasegawa, and J. Abe, "Circular type quantum key distribution," IEEE Photon. Technol. Lett. 14, 576-578 (2002). [CrossRef]
- C. Zhou, G. Wu, L. Ding, and H. Zeng, "Single-photon routing by time-division phase modulation in a Sagnac interferometer," Appl. Phys. Lett. 83, 15-17 (2003). [CrossRef]
- B. Qi, L. L. Huang, H. K. Lo, and L. Qian, "Quantum key distribution based on a Sagnac loop interferometer and polarization-insensitive phase modulators," in IEEE International Symposium on Information Theory (Institute of Electrical and Electronics Engineers, 2006), pp. 2090-2093. [CrossRef]
- W. A. de Brito and R. V. Ramos, "Quantum information technology with Sagnac interferometer: interaction-free measurement, quantum key distribution and quantum secret sharing," J. Mod. Opt. 55, 1231-1241 (2008). [CrossRef]
- J. Bogdanski, J. Ahrens, and M. Bourennane, "Sagnac secret sharing over telecom fiber networks," Opt. Express 17, 1055-1063 (2009). [CrossRef] [PubMed]
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002). [CrossRef]
- D. S. Bethune and W. P. Risk, "Autocompensating quantum cryptography," New J. Phys. 4, 42.1-42.15 (2002). [CrossRef]
- A. Muller, T. Herzog, B. Huttner, W. Tittel, H. Zbinden, and N. Gisin, "Plug and play systems for quantum cryptography," Appl. Phys. Lett. 70, 793-795 (1997). [CrossRef]
- A. Kuzin, H. Cerecedo Nunez, and N. Korneev, "Alignment of a birefringent fiber Sagnac interferometer by fiber twist," Opt. Commun. 160, 37-41 (1999). [CrossRef]
- B. Ibarra-Escamilla, E. A. Kuzin, O. Pottiez, J. W. Haus, F. Gutierrez-Zainos, R. Grajales-Coutin, and P. Zaca-Moran, "Fiber optical loop mirror with a symmetrical coupler and a quarter-wave retarder plate in the loop," Opt. Commun. 242, 191-197 (2004). [CrossRef]
- D. B. Mortimore, "Fiber loop reflectors," J. Lightwave Technol. 6, 1217-1224 (1988). [CrossRef]
- F. P. Kapron, N. F. Borrelli, and D. B. Keck, "Birefringence in. dielectric optical waveguides," IEEE J. Quantum Electron. QE-8, 222-230 (1972) [CrossRef]
- C. Tsao, Optical fibre waveguide analysis (Oxford Science Publ. 1992).
- M. Martinelli, "A universal compensator for polarization changes induced by birefringence on a retracing beam," Opt. Commun. 72, 341-344 (1989). [CrossRef]

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