Optical Review

, Volume 26, Issue 6, pp 644–651 | Cite as

Interference phenomenon on the complex degree of coherence

  • Nori Shibata
  • Kimitaka WatanabeEmail author
  • Masaharu Ohashi
  • Ryo Maruyama
  • Nobuo Kuwaki
  • Kazuhiko Aikawa
Regular Paper


A two-beam interferometer (TBI) with a two-mode fiber (TMF) as a dispersive medium in one arm and air in the other provides evidence of interference related to the complex degree of coherence \(\gamma \). A TMF with a low differential group delay (DGD) is used to measure the interference effect, since the overlapping of each individual mode at the output of a TMF is easily and artificially created in the vicinity of the zero DGD wavelength. When \(\gamma _{01}\) and \(\gamma _{11}\), respectively, are the complex degrees of coherence for the interferences between the \(\hbox {LP}_{01}\) and \(\hbox {LP}_{11}\) modes propagating through a TMF and a wave traversing air-path, the interference effect can be verified using the relationship \(|\gamma |^2=|\gamma _{01}+\gamma _{11}|^2\). The experiments are carried out using a low coherence source and three kinds of TMFs with zero DGD wavelengths around 1550 nm. It is clearly observed that \(|\gamma |^2\)-response waveforms have oscillatory structures due to the interference between \(\gamma _{01}\) and \(\gamma _{11}\). A \(|\gamma |^2\)-response measurement employing the TBI reveals that the theoretically obtained \(|\gamma |^2\)-curves well reflect \(|\gamma |^2\)-curve obtained experimentally for a temporally overlapped wave composed of the two modes. To the best of our knowledge, this is the first experimental demonstration of the interference between complex degrees of coherence.


Fiber optics Interference Coherence 



  1. 1.
    Klein, A.G., Opat, G.I., Hamilton, W.A.: Longitudinal coherence in neutron interferometry. Phys. Rev. Lett. 50(8), 563–565 (1983)ADSCrossRefGoogle Scholar
  2. 2.
    Kaiser, H., Werner, S.A., George, E.A.: Direct measurement of the longitudinal coherence length of a thermal neutron beam. Phys. Rev. Lett. 50(8), 560–563 (1983)ADSCrossRefGoogle Scholar
  3. 3.
    Comsa, G.: Comment on Direct measurement of the longitudinal coherence length of a thermal neutron beam. Phys. Rev. Lett. 51(12), 1105 (1983)ADSCrossRefGoogle Scholar
  4. 4.
    Shibata, N., Tateda, M., Seikai, S., Uchida, N.: Spatial technique for measuring modal delay differences in a dual-mode optical fiber. Appl. Opt. 19(9), 1489–1492 (1980)ADSCrossRefGoogle Scholar
  5. 5.
    Tateda, M., Shibata, N., Seikai, S.: Interferometric method for chromatic dispersion measurement in a single-mode optical fiber. IEEE J. Quantum Electron. QE–17(3), 404–407 (1981)ADSCrossRefGoogle Scholar
  6. 6.
    Shibata, N., Watanabe, K., Ohashi, M., Aikawa, K.: Square of the degree of coherence and dispersion-induced pulse broadening in a fiber-optic transmission. IEICE Commun. Express 5(12), 454–460 (2016)CrossRefGoogle Scholar
  7. 7.
    Shibata, N., Watanabe, K., Ohashi, M., Aikawa, K.: Pulse distortion and the square of the degree of coherence in the presence of second- and third-order dispersions. Opt. Express 25(26), 32640–32649 (2017)ADSCrossRefGoogle Scholar
  8. 8.
    Agrawal, G.P.: Nonlinear Fiber Optics, 4th edn. Elsevier/Academic (2007)Google Scholar
  9. 9.
    Grüner-Nielsen, L., Sun, Y., Nicholson, J.W., Jespersen, K., Lingle, R., Pálsdóttir, B.: Few mode transmission fiber with low DGD, low mode coupling, and low loss. J. Lightw. Technol. 30(23), 3693–3698 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    Maruyama, R., Ohashi, M., Watanabe, K., Shibata, N., Kuwaki, N., Matsuo, S.: Study of fabrication reproducibility of two-mode optical fibers for mode-division multiplexing with MIMO processing. Opt. Express 26(9), 11100–11109 (2018)ADSCrossRefGoogle Scholar
  11. 11.
    Ryf, R., Randel, S., Gnauck, A,H., Bolle, C., Sierra, A., Mumtaz, A., Esmaeelpour, M., Burrows, E.C., Essiambre, R.-J., Winzer, P.J., Peckham, D.W., McCurdy, A.H., Lingle Jr., R.: Mode-division multiplexing over 96 km of few-mode fiber using coherent 6\(\times \)6 MIMO processing. J. Lightw. Technol. 30(4), 521–531 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    Koebele, C., Salsi, M., Sperti, D., Tran, P., Brindel, P., Mardoyan, H., Bigo, S., Boutin, A., Verluise, F., Sillard, P., Astruc, M., Provost, L., Ceron, F., Charlet, G.: Two mode transmission at 2\(\times \)100 Gb/s, over 40 km-long prototype few-mode fiber using LCOS-based programmable mode multiplexer and demultiplexer. Opt. Express 19(17), 16593–16600 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    Born, M., Wolf, E.: Chapter10 in Principles of Optics, vol. 4. Oxford, Pergamon (1970)Google Scholar
  14. 14.
    Hamilton, W.A., Klein, A.G., Opat, G.I.: Longitudinal coherence and interferometry in dispersive media. Phys. Rev. A 28(28), 3149–3152 (1983)ADSCrossRefGoogle Scholar
  15. 15.
    Shibata, N., Nakazono, A., Inoue, Y.: Interference between two orthogonally polarized modes traversing a highly birefringent air-silica microstructure fiber. J. Lightw. Technol. 23(3), 1244–1252 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    Shibata, N., Tsubokawa, M., Nakashima, T., Seikai, S.: Temporal coherence properties of a dispersively propagating beam in a fiber-optic interferometer. J. Opt. Soc. Am. A 4(3), 494–497 (1987)ADSCrossRefGoogle Scholar
  17. 17.
    Diddams, S., Diels, J.-C.: Dispersion measurements with white-light interferometry. J. Opt. Soc. Am. B 13(6), 1120–1129 (1996)ADSCrossRefGoogle Scholar
  18. 18.
    Oughstun, K.E.: Electromagnetic and Optical Pulse Propagation 2, Temporal Pulse Dynamics in Dispersive. Attenuative Media, Springer (2009)Google Scholar
  19. 19.
    Shibata, N., Watanabe, K., Ohashi, M.: Chromatic dispersion diagnosis for the two-modes of few-mode photonic crystal fiber. IEEE Photon. Technol. Lett. 28(4), 437–440 (2016)ADSCrossRefGoogle Scholar

Copyright information

© The Optical Society of Japan 2019

Authors and Affiliations

  1. 1.Nihon UniversityKoriyamaJapan
  2. 2.Osaka Prefecture UniversitySakaiJapan
  3. 3.Fujikura LtdSakuraJapan
  4. 4.Fujikura High Opt Co., LtdTokyoJapan

Personalised recommendations