Effect of shift in refractive index of dispersive elements in waveband-shift-free optical-phase conjugator based on DFG


In this study, the effect of the shift in the refractive index between two dispersive elements on the output phase-conjugated (PC) wave power of waveband-shift-free optical-phase conjugators based on difference-frequency generation (DFG-OPCs) is analyzed. First, a numerical model of the DFG-OPC is built by considering the shift ∆n in the refractive index. The derived formula shows that the output PC wave power of DFG-OPCs depends on the shift in the refractive index. Subsequently, the dependence of the output PC wave power on the shift is confirmed analytically. Calculations indicate that the output PC wave power varies according to the shift. For a relatively fractional shift ∆n = 1.0e-6, the output PC power is degraded by 3 dB. Finally, acceptable values of the shift and temperature difference are calculated as functions of the length of the dispersive element. It is illustrated in this study that the acceptable value of shift in the refractive index increases as the length of the dispersive element is reduced and that the output PC wave power can be stabilized against changes in temperature.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5


  1. 1.

    Winzer, P.J., Neilson, D.T., Chraplyvy, A.R.: Fiber-optic transmission and networking: the previous 20 and the next 20 years [Invited]. Opt Express (2018). https://doi.org/10.1364/OE.26.024190

    Article  Google Scholar 

  2. 2.

    Mitra, P.P., Stark, J.B.: Nonlinear limits to the information capacity of optical fibre communications. Nature (2001). https://doi.org/10.1038/35082518

    Article  Google Scholar 

  3. 3.

    Essiambre, R.-J., Foschini, G.J., Kramer, G., Winzer, P.J.: Capacity limits of information transport in fiber-optic networks. Phys. Rev. Lett. (2008). https://doi.org/10.1103/PhysRevLett.101.163901

    Article  Google Scholar 

  4. 4.

    Ip, E., Kahn, J.M.: Compensation of dispersion and nonlinear impairments using digital backpropagation. J. Lightwave Technol. (2008). https://doi.org/10.1109/JLT.2008.927791

    Article  Google Scholar 

  5. 5.

    Ip, E.: Nonlinear compensation using backpropagation for polarization-multiplexed transmission. J. Lightwave Technol. (2010). https://doi.org/10.1109/JLT.2010.2040135

    Article  Google Scholar 

  6. 6.

    Peddanarappagari, K.V., Brandt-Pearce, M.: Volterra series transfer function of single-mode fibers. J. Lightwave Technol. (1997). https://doi.org/10.1109/50.643545

    Article  Google Scholar 

  7. 7.

    Giacoumidis, E., Le, S.T., Ghanbarisabagh, M., McCarthy, M., Aldaya, I., Mhatli, S., Jarajreh, M.A., Haigh, P.A., Doran, N.J., Ellis, A.D., Eggleton, B.J.: Fiber nonlinearity-induced penalty reduction in CO-OFDM by ANN-based nonlinear equalization. Opt. Lett. (2015). https://doi.org/10.1364/OL.40.005113

    Article  Google Scholar 

  8. 8.

    Hager, C., Pfister, H.D.: Nonlinear interference mitigation via deep neural networks. OFC (2018). https://doi.org/10.1364/OFC.2018.W3A.4

    Article  Google Scholar 

  9. 9.

    Vasilyev, M.: Distributed phase-sensitive amplification. Opt. Express (2005). https://doi.org/10.1364/OPEX.13.007563

    Article  Google Scholar 

  10. 10.

    Tang, R., Lasri, J., Devgan, P.S., Grigoryan, V., Kumar, P., Vasilyev, M.: Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input. Opt. Express (2005). https://doi.org/10.1364/OPEX.13.010483

    Article  Google Scholar 

  11. 11.

    Tang, R., Devgan, P.S., Grigoryan, V.S., Kumar, P., Vasilyev, M.: In-line phase-sensitive amplification of multi-channel CW signals based on frequency nondegenerate four-wave-mixing in fiber. Opt. Express (2008). https://doi.org/10.1364/OE.16.009046

    Article  Google Scholar 

  12. 12.

    Olsson, S.L.I., Corcoran, B., Lundström, C., Tipsuwannakul, E., Sygletos, S., Ellis, A.D., Tong, Z., Karlsson, M., Andrekson, P.A.: Injection locking-based pump recovery for phase-sensitive amplified links. Opt. Express (2013). https://doi.org/10.1364/OE.21.014512

    Article  Google Scholar 

  13. 13.

    Kazama, T., Umeki, T., Abe, M., Enbutsu, K., Miyamoto, Y., Takenouchi, H.: Low-parametric-crosstalk phase-sensitive amplifier for guard-band-less DWDM signal using PPLN waveguides. J. Lightwave Technol. (2017). https://doi.org/10.1109/JLT.2016.2603186

    Article  Google Scholar 

  14. 14.

    Tian, Y., Huang, Y.-K., Zhang, S., Prucnal, P.R., Wang, T.: Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy. Opt. Express (2013). https://doi.org/10.1364/OE.21.005099

    Article  Google Scholar 

  15. 15.

    Yariv, A., Fekete, D., Pepper, D.M.: Compensation for channel dispersion by nonlinear optical phase conjugation. Opt. Lett. (1979). https://doi.org/10.1364/OL.4.000052

    Article  Google Scholar 

  16. 16.

    Schmidt-Langhorst, C., Sackey, I., Elschner, R., Kato, T., Tanimura, T., Watanabe, S., Hoshida, T., Schubert, C.: Fiber nonlinearity mitigation in 800-km Transmission of a 16-Tb/s superchannel using waveband-shift-free optical phase conjugation. ECOC (2017). https://doi.org/10.1109/ECOC.2017.8346052

    Article  Google Scholar 

  17. 17.

    Sackey, I., Schmidt-Langhorst, C., Elschner, R., Kato, T., Tanimura, T., Watanabe, S., Hoshida, T.: Waveband-shift-free optical phase conjugator for spectrally efficient fiber nonlinearity mitigation. J. Lightwave Technol. (2018). https://doi.org/10.1109/JLT.2018.2790799

    Article  Google Scholar 

  18. 18.

    Yoshima, S., Sun, Y., Liu, Z., Bottrill, K.R.H., Parmigiani, F., Richardson, D.J., Petropoulos, P.: Mitigation of nonlinear effects on WDM QAM signals enabled by optical phase conjugation with efficient bandwidth utilization. J. Lightwave Technol. (2017). https://doi.org/10.1109/JLT.2016.2623740

    Article  Google Scholar 

  19. 19.

    Saavedra, G., Sun, Y., Bottrill, K.R.H., Galdino, L., Parmigiani, F., Liu, Z., Richardson, D.J., Petropoulos, P., Killey, R.I., Bayvel, P.: Optical phase conjugation in installed optical networks. OFC (2018). https://doi.org/10.1364/OFC.2018.W3E.2

    Article  Google Scholar 

  20. 20.

    Ellis, A.D., Tan, M., Asif Iqbal, M., Al-Khateeb, M.A.Z., Gordienko, V., Mondaca, G.S., Fabbri, S., Stephens, M.F.C., McCarthy, M.E., Perentos, A., Phillips, I.D., Lavery, D., Liga, G., Maher, R., Harper, P., Doran, N., Turitsyn, S.K., Sygletos, S., Bayvec, P.: 4 Tb/s transmission reach enhancement using 10 × 400 Gb/s super-channels and polarization insensitive dual band optical phase conjugation. J. Lightwave Technol. (2016). https://doi.org/10.1109/JLT.2016.2521430

    Article  Google Scholar 

  21. 21.

    Umeki, T., Kazama, T., Sano, A., Shibahara, K., Suzuki, K., Abe, M., Takenouchi, H., Miyamoto, Y.: Simultaneous nonlinearity mitigation in 92 × 180-Gbit/s PDM-16QAM transmission over 3840 km using PPLN-based guard-band-less optical phase conjugation. Opt. Express (2016). https://doi.org/10.1364/OE.24.016945

    Article  Google Scholar 

  22. 22.

    Kobayashi, T., Umeki, T., Kasahara, R., Yamazaki, H., Nagatani, M., Wakita, H., Takenouchi, H., Miyamoto, Y.: 96-Gbaud PDM-8QAM single channel transmission over 9,600 km by nonlinear tolerance enhancement using PPLN-based optical phase conjugation. OFC (2018). https://doi.org/10.1364/OFC.2018.Th3E.4

    Article  Google Scholar 

  23. 23.

    Okamura, Y., Takada, A.: Waveband-shift-free optical phase conjugator based on difference-frequency generation. Opt. Express (2020). https://doi.org/10.1364/OE.387590

    Article  Google Scholar 

  24. 24.

    Mori, K., Morioka, T., Saruwatari, M.: Wavelength-shift-free spectral inversion with an optical parametric loop mirror. Opt. Lett. (1996). https://doi.org/10.1364/OL.21.000110

    Article  Google Scholar 

  25. 25.

    Mori, K., Takara, H., Saruwatari, M.: Wavelength-shift-free FWM based dispersion compensation in non-DSF transmission utilizing optical parametric loop mirror. CLEO (1997). https://doi.org/10.1109/CLEO.1997.603397

    Article  Google Scholar 

  26. 26.

    Okamura Y, Takada A (2019) Influence of phase constant difference between dispersive elements in difference-frequency generation based optical-phase-conjugation circuit. 24th Microoptics Conference (MOC2019) https://doi.org/10.23919/MOC46630.2019.8982755

  27. 27.

    Yariv, A., Yeh, P.: Photonics: Optical Electronics in Modern Communications, 6th edn. Oxford, Oxford (2007)

    Google Scholar 

  28. 28.

    Smith, D.S., Riccius, H.D., Edwin, R.P.: Refractive indices of lithium niobate. Opt. Commun. (1976). https://doi.org/10.1016/0030-4018(76)90273-X

    Article  Google Scholar 

  29. 29.

    Wang W, Yu Y, Geng Y, Li X (2015) Measurements of thermo-optic coefficient of standard single mode fiber in large temperature range. 2015 Int Confer Optical Instrum Technol https://doi.org/10.1117/12.2193091

  30. 30.

    Lu, L., Wang, W., Wu, L., Jiang, X., Xiang, Y., Li, J., Fan, D., Zhang, H.: All-optical switching of two continuous waves in few layer bismuthene based on spatial cross-phase modulation. ACS Photonics (2017). https://doi.org/10.1021/acsphotonics.7b00849

    Article  Google Scholar 

  31. 31.

    Jiang, X., Zhang, L., Liu, S., Zhang, Y., He, Z., Li, W., Zhang, F., Shi, Y., Lü, W., Li, Y., Wen, Q., Li, J., Feng, J., Ruan, S., Zeng, Y., Zhu, X., Lu, Y., Zhang, H.: Ultrathin Metal-Organic Framework: An Emerging Broadband Nonlinear Optical Material for Ultrafast Photonics. Adv. Opt. Mater. (2018). https://doi.org/10.1002/adom.201800561

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Yasuhiro Okamura.

Ethics declarations

Conflicts of interest/Competing interests (include appropriate disclosures)

Not applicable.

Code availability (software application or custom code)

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Okamura, Y., Takada, A. Effect of shift in refractive index of dispersive elements in waveband-shift-free optical-phase conjugator based on DFG. Opt Rev 28, 174–180 (2021). https://doi.org/10.1007/s10043-021-00647-7

Download citation


  • Optical nonlinear compensation
  • Optical phase conjugation
  • Waveband-shift-free
  • Difference-frequency generation
  • Refractive index shift
  • Dispersive elements