## Optimization of all-optical EDFA-based Sagnac-interferometer switch

Optics Express, Vol. 15, Issue 21, pp. 14234-14243 (2007)

http://dx.doi.org/10.1364/OE.15.014234

Acrobat PDF (1168 KB)

### Abstract

We perform optimization of all-optical EDFA-based Sagnac – interferometer switch through an analytical model and numerical simulations by solving nonlinear Schrödinger equations. The effects of the performance of EDFA on the bit rate and the switching power are investigated for all-optical switch based on self-phase or cross-phase modulation. The simulated results show that ultra-low switching power (<1mW) all-optical switch for 40 Gb/s data can be realized by properly selecting the length of highly nonlinear photonic crystal fiber and adjusting the performance of EDFA.

© 2007 Optical Society of America

## 1. Introduction

2. T. Y. Yeow, K. L. E. Law, and A. Goldenberg, “MEMS optical switches,” IEEE Commun. Mag. **39**, 158–163 (2001). [CrossRef]

3. M. H. Lee, Y. H. Min, J. J. Ju, J. Y. Do, and S. K. Park, “Polymeric electrooptical 2×2 switch consisting of bifurcation optical active waveguides and a Mach-Zehnder interferometer,”IEEE Journal of Selected Topics in Quantum Electronics. **7**, 812–818(2001). [CrossRef]

5. R. Kasahara, M. Yanagisawa, T. Goh, A. Sugita, A. Himeno, M. Yasu, and S. Matsui, “New structure of silica-based planar lightwave circuits for low power thermooptic switch and its application to 8×8 optical matrix switch,” IEEE/OSA J. Lightw. Technol. **20**, 993–1000 (2002). [CrossRef]

7. K. J. Blow, N. J. Doran, and B. K. Nayar, “Experimental demonstration of optical soliton switching in an all-fiber nonlinear Sagnac interferometer,” Opt. Lett. **14**, 754–756 (1989). [CrossRef] [PubMed]

8. Chunfei Li and B. Alireza, “Finesse-enhanced ring resonator coupled Mach-Zehnder interferometer all-optical switches,” Chin. Phys. Lett. **21**, 90–93(2004). [CrossRef]

9. G. Berrettini, G. Meloni, A. Bogoni, and L. Potì, “All-optical 2×2 switch based on Kerr effect in highly nonlinear fiber for ultrafast applications,” IEEE Photonics Technology Letters. **18**, 2439–2441 (2006). [CrossRef]

7. K. J. Blow, N. J. Doran, and B. K. Nayar, “Experimental demonstration of optical soliton switching in an all-fiber nonlinear Sagnac interferometer,” Opt. Lett. **14**, 754–756 (1989). [CrossRef] [PubMed]

10. D. J. Richardson, R. I. Laming, and D. N. Payne, “Very low threshold Sagnac switch incorporating an erbium dopedfibre amplifier,” Electron. Lett. **26**, 1779–1781 (1990). [CrossRef]

## 2. Modeling of all-optical EDFA-based Sagnac-interferometer switches

*π*/2 -phase difference, and propagate oppositely in the same loop with the same phase shift. After they pass through the coupler again to produce another

*π*/2 -phase deference, and then they interfere with each other at the two output ports. In the reflected port, two beams have same phase (

*π*/2), while at the transmitted port, they have reversed phase (0 and

*π*), therefore, all the signal power will be output from the reflected point [6].

*π*-phase difference; the two signals have same phase at reflected point and have reversed phase at reflected point. Therefore, the device can accomplish a complete optical switching: the high-power signal will be transmitted, while the signal at low-power level will be reflected.

_{0}= 30 dB at 1550 nm, the saturated output power P

_{S}= 35 or 100 mW, the effective length of erbium-doped fiber (EDF) L

_{E}= 2.3 m, the group velocity dispersion parameter of EDF β

_{2}= -20 ps

^{2}/km at 1550 nm, the nonlinear parameter of EDF γ

_{E}= 3.78 /(W∙km) at 1550 nm), one meter long single mode fiber (SMF) to connect the EDFA with highly nonlinear photonic crystal fiber together (the group velocity dispersion parameter of SMF β

_{2}= -20 ps

^{2}/km at 1550 nm, the nonlinear parameter of SMF γ

_{S}= 3.78 /(W∙km) at 1550 nm, and L

_{S}= 1 m), and a certain length of high nonlinear photonic crystal fibers (HNPCF) (the effective length of HNPCF L

_{P}= 1~1000 m range, the group velocity dispersion parameter of HNPCF β

_{2}= 0.1 ps

^{2}/km at 1550 nm, the nonlinear parameter of HNPCF γ

_{P}= 45.38 /(W∙km) at 1550 nm). The envelope of input signals (40 or 10 Gb/s non-return-to-zero bit streams) is assumed to be

*t*

^{2}/(2

*T*

_{0}

^{2})⌋, where

*P*is the peak power of input pulse,

_{in}*T*

_{0}= 5 ps the half-width at 1 /

*e*-intensity point.

*A*

_{3}(

*z*,

*t*) or

*A*

_{4}[

*z*,

*t*) be the envelope of clockwise or anti-clockwise propagating pulse, z the propagating distance of pulse along the fiber loop. So the envelope of the pulse output from the port 3 after amplified by EDFA is

_{2}the GVD parameter of HNPCF,

*T*=

*t*-

*z*/

*ν*(

_{g}*ν*the group velocity of the signal), and γ the nonlinear parameter of HNPCF. By neglecting the effect of the GVD on the pulse propagation due to small GVD value of HNPCF, the envelope of the pulse

_{g}*A*

_{3}after propagating from the port 3 to the port 4 is

*A*

_{4}after propagating from the port 4 to the port 3 is

*ϕ*

_{0}=

*βL*is the linear phase shift, and

*β*the mode-propagation constant.

*T*= |

_{SPM}*A*|

_{t}^{2}/|

*A*

_{0}|

^{2}of the nonlinear Sagnac loop mirror

*P*is the peak power for switching.

_{SPM}*P*is the averaged power of input signals for EDFA. By substituting

_{i}*P*into Eq. (7), we obtained the required gain for switching

_{SPM}*T*= |

_{XPM}*A*|

_{t}^{2}/|

*A*

_{0}|

^{2}of the nonlinear Sagnac loop mirror

*t*

^{2}/(2

*T*

_{0}

^{2}

_{0})) is the envelope of the pump pulse) and the switching pump power of all-optical Sagnac-interferometer switch based on XPM

*P*into Eq. (11), we obtained the required gain for switching

_{xpm}## 3. Simulated results and discussion

_{s}= 35 mW) with different small signal gain values (G

_{0}=20, 30, 40, and 50 dB, respectively) and 40 Gb/s data. It is seen that, with increasing the small signal gain value G

_{0}of EDFA, the switching power decreases and the required gain for switching increases when the effective fiber length is fixed. The switching power decreases and the required gain for switching increase with increasing the effective fiber length of HNPCF when the small signal gain value of EDFA is fixed. As aforementioned, the EDFA requires that the ratio

_{s}= 35 mW) with different small signal gain values (G

_{0}=20, 30, 40, and 50 dB, respectively) and 40 Gb/s data. As we can see from Fig. 2(b), the effective fiber length of HNPCF must be larger than 800 m to satisfy Eq. (10) for EDFA (P

_{s}= 35 mW) with different small signal gain values (G

_{0}=20, 30, 40, and 50 dB, respectively) and 40 Gb/s data. It means that the required effective fiber length of HNPCF should be larger than 800m to get switching. Let us move from Fig. 2(b) to Fig. 2(a), the data of Fig. 2(a) does not show that the fiber loop composed of less than 800 m long HNPCF could not give switching, which indicates that Eqs. (8), (9) do not consider the gain saturation effects of EDFA inside the fiber loop. These results show that we must consider the gain saturation effects of EDFA by using Eq. (10) to get switching. Otherwise, we can not get switching if we just use Eqs. (8), (9) to optimize the device. This is the first time to optimize all-optical EDFA-based Sagnac-interferometer switch by considering Eq. (10), to our best knowledge.

_{s}= 35 mW) with different small signal gain value (G

_{0}=20, 30, 40, and 50 dB, respectively) and 10 Gb/s data. Fig. 2(d) presents the corresponding critical ratio as a function of the effective fiber length for EDFA (P

_{s}= 35 mW) with different small signal gain value (G

_{0}=20, 30, 40, and 50 dB, respectively) and 40 Gb/s data. In comparison with Fig. 2(a) and Fig. 2(b) for 40 Gb/s data, the switching power become smaller and the required gain for switching larger for 10 Gb/s data, and the required effective fiber length of HNPCF to satisfy Eq. (10) is reduced from 800 m to 200 m. This is because that the averaged power for 10 Gb/s data is substantially smaller than that for 40 Gb/s when the input peak power is same for both cases, which make the suffered gain G for 10 Gb/s larger than that for 40 Gb/s data due to weak gain saturation effects of EDFA, and furthermore the output power after amplified by the EDFA for 10 Gb/s data higher than the case for 40 Gb/s data. Therefore, the switching power becomes smaller with decreasing the bit rate from 40 Gb/s to 10 Gb/s. As a result, the required effective fiber length of HNPCF to satisfy Eq. (10) is reduced from 800 m to 200 m, as shown in Fig. 2(d).

_{s}= 100 mW as a function of the effective fiber length of HNPCF for 40 Gb/s and 10 Gb/s data, respectively. Fig. 3(b) and Fig. 3(d) show the corresponding critical ratio as a function of the effective fiber length for 40 Gb/s and 10 Gb/s data, respectively. In comparison with Fig.2, the switching power become smaller and the required gain for switching larger, and the required effective fiber length of HNPCF to satisfy Eq. (10) is reduced substantially for both cases due to weak gain saturation effects with enhancing P

_{s}from 35 mW to 100 mW.

_{0}= 30 dB is 0.7 mW for 40 Gb/s data.

_{0}= 30 dB and P

_{s}= 100 mW, a 300 m long HNPCF for 40 Gb/s data. It is seen that the switching power is about 1.16 mW, which agree well with the analytical value show in Fig. 3(a). In addition, the gain saturation effects occur with increasing the input signal power after switching. Fig. 5(b) presents the pulse evolution of the input signal propagating clockwisely inside the fiber loop when the device is switched on, which shows that no substantially pulse widening occurs due to small GVD value (0.1 ps

_{2}/km at 1550 nm) [6]. Fig. 5(c) shows the corresponding phase difference evolution of the input pulse inside the fiber loop, which give a phase difference of ~ π when two counter-propagating pulse meet before the 3 dB fiber coupler. Fig. 5(d) gives the corresponding spectral evolution of the input signal inside the fiber loop, which describes a general feature of SPM for phase shifting from 0 to

*π*[6].

_{0}= 30 dB and P

_{s}= 100 mW, a 150 m long HNPCF for 40 Gb/s data. It is seen that the switching pump power is about 1.21 mW, which agree well with the analytical value show in Fig. 4(a). Fig. 6(b) shows the pulse evolution of the input signal propagating clockwisely inside the fiber loop when the device is switched on, which shows that no substantially pulse widening occurs due to small GVD value (0.1 ps

^{2}/km at 1550 nm). Fig. 6(c) shows the corresponding phase difference evolution of the input pulse inside the fiber loop, which give a phase difference of ~

*π*when two counter-propagating pulse meet before the 3 dB fiber coupler. Fig. 6(d) gives the corresponding spectral evolution of the input signal inside the fiber loop, which gives a general feature of XPM for phase shifting from 0 to

*π*.

## 4. Conclusion

## Acknowledgments

## References and links

1. | G. P. Agrawal, “Applications of nonlinear fiber optics,” (Academic Press, New York,2001), 319–360. |

2. | T. Y. Yeow, K. L. E. Law, and A. Goldenberg, “MEMS optical switches,” IEEE Commun. Mag. |

3. | M. H. Lee, Y. H. Min, J. J. Ju, J. Y. Do, and S. K. Park, “Polymeric electrooptical 2×2 switch consisting of bifurcation optical active waveguides and a Mach-Zehnder interferometer,”IEEE Journal of Selected Topics in Quantum Electronics. |

4. | H. S. Pask, “All-fiber wavelength-tunable acousto-optic switch,” Pro. OFC 2001. |

5. | R. Kasahara, M. Yanagisawa, T. Goh, A. Sugita, A. Himeno, M. Yasu, and S. Matsui, “New structure of silica-based planar lightwave circuits for low power thermooptic switch and its application to 8×8 optical matrix switch,” IEEE/OSA J. Lightw. Technol. |

6. | G. P. Agrawal, “Nonlinear fiber optics,” (Academic Press, New York,2001), 97–437. |

7. | K. J. Blow, N. J. Doran, and B. K. Nayar, “Experimental demonstration of optical soliton switching in an all-fiber nonlinear Sagnac interferometer,” Opt. Lett. |

8. | Chunfei Li and B. Alireza, “Finesse-enhanced ring resonator coupled Mach-Zehnder interferometer all-optical switches,” Chin. Phys. Lett. |

9. | G. Berrettini, G. Meloni, A. Bogoni, and L. Potì, “All-optical 2×2 switch based on Kerr effect in highly nonlinear fiber for ultrafast applications,” IEEE Photonics Technology Letters. |

10. | D. J. Richardson, R. I. Laming, and D. N. Payne, “Very low threshold Sagnac switch incorporating an erbium dopedfibre amplifier,” Electron. Lett. |

11. | J. G. Liu, G. Y. Kai, and L. F. Xue
, et al., “An all-optical switch based on highly nonlinear photonic crystal fiber Sagnac loop mirror,” Acta. Phys. Sin. |

**OCIS Codes**

(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators

(190.0190) Nonlinear optics : Nonlinear optics

(190.3270) Nonlinear optics : Kerr effect

(230.1150) Optical devices : All-optical devices

(250.6715) Optoelectronics : Switching

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: August 20, 2007

Revised Manuscript: September 23, 2007

Manuscript Accepted: September 25, 2007

Published: October 12, 2007

**Citation**

Fei Wang and Chunfei Li, "Optimization of all-optical EDFA-based Sagnac-interferometer switch," Opt. Express **15**, 14234-14243 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-14234

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### References

- G. P. Agrawal, "Applications of nonlinear fiber optics," (Academic Press, New York, 2001), 319-360.
- T. Y. Yeow, K. L. E. Law, and A. Goldenberg, "MEMS optical switches," IEEE Commun. Mag. 39, 158-163 (2001). [CrossRef]
- M. H. Lee, Y. H. Min, J. J. Ju, J. Y. Do, S. K. Park, "Polymeric electrooptical 2×2 switch consisting of bifurcation optical active waveguides and a Mach-Zehnder interferometer," IEEE Journal of Selected Topics in Quantum Electronics. 7, 812-818(2001). [CrossRef]
- H. S. Pask, "All-fiber wavelength-tunable acousto-optic switch," Pro. OFC 2001. 3, WJ4_1- WJ4_3 (2001).
- R. Kasahara, M. Yanagisawa, T. Goh, A. Sugita, A. Himeno, M. Yasu, and S. Matsui, "New structure of silica-based planar lightwave circuits for low power thermooptic switch and its application to 8×8 optical matrix switch," IEEE/OSA J.Lightw. Technol. 20, 993-1000 (2002). [CrossRef]
- G. P. Agrawal, "Nonlinear fiber optics," (Academic Press, New York, 2001), 97-437.
- K. J. Blow, N. J. Doran, and B. K. Nayar, "Experimental demonstration of optical soliton switching in an all-fiber nonlinear Sagnac interferometer," Opt. Lett. 14, 754-756 (1989). [CrossRef] [PubMed]
- Chunfei Li and B. Alireza, "Finesse-enhanced ring resonator coupled Mach-Zehnder interferometer all-optical switches," Chin. Phys. Lett. 21, 90-93 (2004). [CrossRef]
- G. Berrettini, G. Meloni, A. Bogoni, L. Potì, "All-optical 2×2 switch based on Kerr effect in highly nonlinear fiber for ultrafast applications," IEEE Photonics Technology Letters. 18, 2439-2441 (2006). [CrossRef]
- D. J. Richardson, R. I. Laming, D. N. Payne, "Very low threshold Sagnac switch incorporating an erbium dopedfibre amplifier," Electron. Lett. 26, 1779-1781 (1990). [CrossRef]
- J. G. Liu, G. Y. Kai, L. F. Xue, et al., "An all-optical switch based on highly nonlinear photonic crystal fiber Sagnac loop mirror," Acta. Phys. Sin. 56, 941-945 (2007).

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