Skip to main content
SpringerLink
Log in

Dynamics of optoelectronic oscillators with band-pass filter and laser nonlinearities: theory and experiment

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

In this paper, we present a study of a simplified optoelectronic oscillator (OEO) that features both the laser and the filter nonlinearities. We show that this optoelectronic oscillator depicts the phenomena of quasi-sinusoidal oscillations when the feedback gain is small, relaxation and chaos oscillations when the feedback gain increases. It is analytically confirmed that the frequencies of the limit-cycle oscillations increase with the cubic-nonlinear term and the feedback gain but decrease with the time-delay of the system. The experimental measurements are qualitatively in agreement with the theoretical and numerical analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Ai, J., Wang, L., Wang, J.: Secure communications of CAP-4 and OOK signals over MMF based on electro-optics chaos. Opt. Lett. 42(18), 3662–3665 (2017)

    ADS  Google Scholar 

  • Argyris, A., Syvridis, D., Larger, L., Annovazzi-Lodi, V., Colet, P., Fischer, I., Garcia-Ojalvo, J., Mirasso, C.R., Pesquera, L., Shore, K.A.: Chaos-based communication at high bit rates using commercial fibre-optic links. Nature 438, 343–346 (2015)

    Google Scholar 

  • Barron-Zambrano, J.H., Torres-Huitzil, C.: FPGA implementation of a configurable neuromorphic CPG-based locomotion controller. Neural. Netw. 45, 50–61 (2013)

    Google Scholar 

  • Brian, S., Romanelli, M., Bouhier, S., Frein, L., Alouini, M., Vallet, M.: Low phase noise direct-modulation optoelectronic oscillator. IEEE J. Lightw. Technol. (2021). https://doi.org/10.1109/JLT.2021.3111703

    Article  Google Scholar 

  • Broms, M., Kaper, T.J., Rotstein, H.G.: Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis. Chaos 18(1), 015101 (2008)

    ADS  Google Scholar 

  • Bruner, D., Soriano, M.C., Mirasso, C.R., Fischer, I.: Parallel photonic information processing at gigabyete per second data rates using transient states. Nat. Commun. 4, 1364 (2013)

    ADS  Google Scholar 

  • Callan, K.E., Illing, L., Gao, Z., Gauthier, D.J., Scholl, E.: Broadband chaos generated by an optoelectronic oscillator. Phys. Rev. Lett. 104, 113901 (2010)

    ADS  Google Scholar 

  • Chang, C.Y., Choi, D., Michael, A.L., Wishon, J., Merghem, K., Ramdane, A., Lelarge, F., Martinez, A., Citrin, D.S.: Tunable X-band optoelectronic oscillators on external-cavity semiconductor laser. IEEE J. Quantum Electron. 53(3), 16 (2017)

    Google Scholar 

  • Chang, C.Y., Choi, D., Michael, A.L., Wishon, J., Merghem, K., Ramdane, A., Lelarge, F., Martinez, A., Citrin, D.S.: A multi- GHz chaotic optoelectronic oscillator based on laser terminal voltage. Appl. Phys. Lett.108(19) Art. (191109) 27628–27638 (2016)

  • Chembo, Y.K., Brunner, D., Jacquot, M., Larger, L.: Optoelectronic oscillators with time-delayed feedback. Rev. Mod. Phys. 91(3), 035006 (2019)

    MathSciNet  ADS  Google Scholar 

  • Chembo, Y.K., Larger, L., Bendoula, R., Colet, P.: Effects of gain and bandwidth on the multimode behavior of optoelectronic microwave oscillators. Opt. Express 16(12), 9067–9072 (2008)

    ADS  Google Scholar 

  • Chembo, Y.K., Colet, P., Gastaud, N.: Chaotic breathers in delayed electro-optical systems. Phys. Rev. Lett. 95, 203903 (2005)

  • Chembo, Y.K.: Laser-based optoelectronic generation of narrowband microwave chaos for radar and radio-communication scrambling. Opt. Lett. 42(17), 3431–3434 (2017)

  • Chen, G., Lu, D., Guo, L., Zhao, W., Huang, Y., Zhao, L.: Frequency-tunable OEO using a DFB laser at period-one oscillations with optoelectronic feedback. IEEE Photon. Tech. Lett. 30(18), 1593–1596 (2018)

    ADS  Google Scholar 

  • Chengui, G.R.G., Talla, A.F., Talla Mbé, J.H., Coillet, A., Saled, K., Larger, L., Woafo, P., Chembo, Y.K.: Theoretical and experimental study of slow-scale hopf limit-cycles in laser-based wideband optoelectronic oscillators. J. Opt. Soc. Am. B 31(10), 2310–2316 (2014)

    ADS  Google Scholar 

  • Dai, H., Chembo, Y.K.: Classification of IQ-modulated signals based on reservoir computing with narrowband optoelectronic oscillators. IEEE J. Quantum Electron. 57(3), 1–8 (2021)

    Google Scholar 

  • Desroches, M., Guckenheinmer, J., Krauskopf, B., Kuehn, C., Osinga, H.M., Wechselberger, M.: Mixed-mode oscillations with multiple times scales. SIAM Rev. 54(2), 211–288 (2012)

    MathSciNet  MATH  Google Scholar 

  • Duhram, J., Moehlis, J.: Feedback control of canards. Chaos 18, 015101 (2008)

    MathSciNet  ADS  Google Scholar 

  • Duport, F., Smerieri, A., Akrout, A., Haelterman, M., Massar, S.: Fully analogue photonic reservoir computer. Sci. Rep. 6(1), 1–8 (2016)

  • Goune Chengui, G.R., Woafo, P., Chembo, Y.K.: The simplest laser-based optoelectronic oscillator: an experimental and theoretical study. J. Lightw. Technol. 0733–8724 (2015)

  • Goune Chengui, G.R., Talla Mbé, J.H., Talla, A.F., Woafo, P., Chembo, Y.K.: Dynamics of optoelectronic oscillators with electronic and laser nonlinearities. IEEE J. Quantum Electron. 54(1), 1–7 (2018)

  • Ha, M., Chembo, Y.K.: Nonlinear dynamics of continuously tunable optoelectronic oscillators based on stimulated Brillouin amplification. Opt. Express 29(10), 14630–14648 (2021)

    ADS  Google Scholar 

  • Hao, T., Liu, Y., Tang, J., Cen, Q., Li, W., Zhu, N., Dai, Y., Capmany, J., Yao, J., Li, M.: Recent advances in optoelectronic oscillators. Adv. Photon. 2(4), 044001 (2020)

  • Huack, T., Scheinder, F.W.: Mixed-mode and quasiperiodic oscillations in the peroxidase reaction. J. Chem. Phys. 97, 391 (1993)

    Google Scholar 

  • Huang, L., Deng, L., Fu, S., Tang, M., Cheng, M., Zhang, M., Liu, D.: Stable and compact dual-loop optoelectronic oscillator using self-polarization-stabilization technique and multicore fiber. J. Lightw. Technol. 36(22), 5196–5202 (2018)

    ADS  Google Scholar 

  • Jia, S., Yu, J., Wang, J., Wu, Q., Huang, G., Yang, E.: A novel optoelectronic oscillator based on wave-length multiplexing. J. Opt. Soc. Am. B. 13(8), 1725–1735 (1996)

    Google Scholar 

  • Jiang, X., Cheng, M., Luo, F., Deng, L., Fu, S., Ke, C., Zhang, M., Tang, M., Shum, P., Liu, D.: Electro-optic chaotic system based o the reverse-time chaos theory and a nonlinear hybrid feedback loop. Opt. Express 24, 28804–28814 (2016)

    ADS  Google Scholar 

  • Kamaha, J.S.D., Talla Mbé, J.H., Woafo, P.: Routes to chaos and characterization of limit-cycle oscillations in wideband time-delayed optoelectronic oscillators with nonlinear filters. J. Opt. Soc. Am. B., 37(11), A75–A81 (2020)

  • Kim, J.M., Cho, D.: Optoelectronic oscillator stabilized to an intraloop Fabry–Perot cavity by a dual servo system. Opt. Express 18(14), 14905–14912 (2010)

    ADS  Google Scholar 

  • Kouayep, R.B., Talla, A.F., Talla Mbé, J.H., Woafo, P.: Bursting oscillations in Colpitts oscillator and application in otoelectronics for the generation of complex optical signals. Opt. Quantum Electron. 52, 1–13 (2020)

    Google Scholar 

  • Larger, L., Baylon-Fuentes, A., Martinenghi, R., Udaltsov, V.S., Chembo, Y.K., Jacquot, M.: High-speed photonic reservoir computing using a time-delay-base architecture: million words per second classification. Phys. Rev. X 7, 011015 (2017)

    Google Scholar 

  • Lelievre, O., Crozatier, V., Berger, P., Baili, G., Liopis, O., Dolfi, D., Nouchi, P., Goldfard, F., Bretenaker, F., Morvan, L., Pillet, G.: A model designing ultralow noise single-and dual-loop 10-GHz optoelectronique oscillators. J. Lightw. Technol. 35(20), 4366–4374 (2017)

    ADS  Google Scholar 

  • Li, W., Yao, J.: An optically tunable optoelectronic oscillator. J. Lightw. Technol. 28(18), 2640–2645 (2010)

    ADS  Google Scholar 

  • Ly, A., Auroux, V., Khayatzadeh, R., Gutierrez, N., Fernandez, A., Llopis, O.: Highly spectrally pure 90 GHz signal synthesis using a coupled optoelectronic oscillator. IEEE Photon. Technol. Lett. 30(14), 1313–1316 (2018)

    ADS  Google Scholar 

  • Maleki, L.: The optoelectronic oscillator. Nat. Photon 5(12), 728–730 (2011)

    ADS  Google Scholar 

  • Martinez-Llinas, J., Colet, P., Erneux, T.: Tuning the period of square-wave oscillations for delay-coupled optoelectronic systems. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 89, 042908 (2014)

    Google Scholar 

  • Munnelly, P., Lingnau, B., Karow, M.M., Heindel, T., Kamp, M., Hofling, S., Ludge, K., Schneider, C., Reitzenstein, S.: On-chip optoelectronic feedback in a micropillar laser-detector assembly. Optica 4(3), 303–306 (2017)

    ADS  Google Scholar 

  • Murphy, T.E., Cohen, A.B., Ravoori, B., Schmitt, K.R., Setty, A.V., Sorrentino, F., Williams, C.R., Ott, E., Roy, R.: Complex dynamics and synchronization of delayed-feedback nonlinear oscillators. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 368, 343–366 (2010)

    MATH  ADS  Google Scholar 

  • Neyer, A., Vogues, E.: Dynamics of electroopic bistable devices with delayed feedback. IEEE J. Quantum Electron. 104(12), 2009–2015 (1982)

    ADS  Google Scholar 

  • Nguewou-Hyousse, H., Chembo, Y.K.: Nonlinear dynamics of miniature optoelectronic oscillators based on whispering-gallery mode electrooptical modulators. Opt. Express 28(21), 30656–30674 (2020)

    ADS  Google Scholar 

  • Nguewou-Hyousse, H., Chembo, Y.K.: Stochastic analysis of miniature optoelectronic oscillators based on whispering-gallery mode electrooptical modulators. IEEE Photon. J. 13(3), 3000110 (2021)

    Google Scholar 

  • Nguimdo, R.M., Chembo, Y.K., Colet, P., Larger, L.: On the phase noise performance of nonlinear double-loop optoelectronic microwave oscillators. IEEE J. Quantum Electron. 48(11), 1415–1423 (2012)

    ADS  Google Scholar 

  • Nguimdo, R.M., Chembo, Y.K., Colet, P., Larger, L.: On the phase noise performance of nonlinear double-loop optoelectronic microwave oscillators. IEEE J. Quantum Electron. 48(11), 1415–21423 (2012)

    ADS  Google Scholar 

  • Nguimdo, R.M., Lavrov, R., Colet, P., Jacquot, M., Chembo, Y.K., Larger, L.: Effects of fiber dispertion on broadband chaos communication implemented by electro optic nonlinear delay phase dynamics. J. Lightw. Technol. 28(18), 2688–2689 (2010)

    ADS  Google Scholar 

  • Okasuga, O., Adles, E.J., Levy, E.C., Zhou, W., Carter, G.M., Menyuk, C.R., Hrowitz, M.: Spurious mode reduction in dual injection-locked opotoelectronic oscillators. Opt. Exp. 19(7), 5839–5854 (2011)

    Google Scholar 

  • Ozdur, I., Akbulut, M., Hoghooghi, N., Mandridis, D., Piracha, M.U., Delfyett, P.J.: Optoelectronic loop design with 1000 finesse Fabry–Perot etalon. IEEE Photon. Technol. Lett. 27(2), 213–216 (2014)

    Google Scholar 

  • Paquot, Y., Dupont, F., Smerieri, A., Dambre, J., Schrauwen, B., Haelterman, M., Massar, S.: Optoelectronic reservoir computing. Sci. Rep. 2, 287 (2012)

    ADS  Google Scholar 

  • Petrov, V., Scott, S.K., Showalter, K.: Mixed-mode oscillations in chemical systems. J. Chem. Phys. 97(9), 6191–6198 (1992)

    ADS  Google Scholar 

  • Qin, B.W., Chung, K.W., Algaba, A.: High-order study of the canard explosion in an aircraft ground dynamics model. Nonlinear Dyn. 100, 1079–1090 (2020)

    MATH  Google Scholar 

  • Qin, B.W., Kwok-Wai, C., Algaba, A., Rodríguez-Luis, A.J.: High-order analysis of canard explosion in Brusselator equations. Int. J. Bifurcation Chaos 30(05), 2050078 (2020)

    MathSciNet  MATH  ADS  Google Scholar 

  • Qin, B.W., Kwok-Wai, C., Algaba, A., Rodríguez-Luis, A.J.: Asymptotic expansions for a degenerate canard explosion. Physica D Nonlinear Phenomena 418, 132841 (2021)

    MathSciNet  MATH  Google Scholar 

  • Romeira, B., Javaloyes, J., Figueiredo, J.M.L., Ironside, C.N., Cantu, H.I., Kelly, A.E.: Delayed feedback dynamics of Liénard-type resonant tunneling-photo-detector optoelectronic oscillators. IEEE J. Quantum Electron. 49(1), 31–42 (2013)

    ADS  Google Scholar 

  • Saleh, K., Lin, G. Chembo, Y.K.: Effect of laser coupling and active stabilization on the phase noise performance of optoelectronic microwave oscillator based on whispering-gallery mode-oscillator resonators. IEEE photon. J. 7(1), Art.(5500111) (2015)

  • Sekikawa, M., Inaba, N., Yoshinaga, T., Hikihara, T.: Period-doubling cascades of canards from the extended Bonhoeffer–Van der Pol oscillator. Phys. Lett. A 374, 3745 (2010)

    MATH  ADS  Google Scholar 

  • Shchepakina, E., Korotkova, O.: Canard explosion in chemical and optical systems. Discrete Continuous Dyn. Syst. 18, 495–5512 (2013)

    MathSciNet  MATH  Google Scholar 

  • Shi, M., Yi, L., Wei, W., Hu, W.: Generation and phase noise analysis of a wide optoelectronic oscillator with ultra-high resolution based on stimulated Brillouin scattering. Opt. Express 5(13), 16113–16124 (2018)

    ADS  Google Scholar 

  • Soriano, M.C., Ortin, S., Larger, L., Mirasso, C.R., Fischer, I., Pesquera, L.: Optoelectronic reservoir computing: tackling noise-induced performance degradation. Opt. Express 21(1), 12–20 (2013)

    ADS  Google Scholar 

  • Talla Mbé, J.H., Atchoffo, N.W., Tchitnga, R., Woafo, P.: Dynamics of time-delayed optoelectronic oscillators with nonlinear amplifiers and its potential application to random numbers generation. IEEE J. Quantum Electron. 57(5), 5000507 (2021)

    Google Scholar 

  • Talla Mbé, J.H., Woafo, P., Fotsin, H.B.: Experimental direct modulation of a laser diode with a van der pol circuit and applications. Opt. Eng. 58(6), 066114 (2019)

    ADS  Google Scholar 

  • Talla, A.F., Marteninghi, R., Woafo, P., Chembo, Y.K.: Breather and pulse-package dynamics in multi-nonlinear electro-optical systems with delay feedback. IEEE Photon. J. 8(4), 1–8 (2016)

  • Talla, A.F., Martinenghi, R., Talla. Mbé, J.H., Saleh, K., Lin, G., Chengui, G.R.G., Coillet, A., Woafo, P. Chembo, Y.K.: Analysis of phase locking in narrow-band optoelectronic oscillators with intermediate frequency. J. Quantum Electron. 51(6), 1–8 (2015)

  • Talla Mbé, J.H., Talla, A. F., Chengui, G.R.G., Coillet, A., Larger, L., Woafo, P., Chembo, Y.K.: Mixed-mode oscillations in slow–fast delayed optoelectronic systems. Phys. Rev. E 91(012902) Art (2015)

  • Talla Mbé, J.H., Woafo, P., Chembo, Y.K.: A normal form method for the determination of oscillations characteristics near the primary Hopf bifurcation in bandpass optoelectronic oscillators: Theory and experiment. Chaos, 29(033104) Art (2019)

  • Talla Mbé, J.H., Woafo, P.: Modulation of distributed feedback (DBF) laser diode with an autonomous Chua’s circuit: Theory and experiment. Opt. Laser Technol. 100, 145–152 (2018)

  • Talla Mbé, J.H., Kamaha, J.S.D., Woafo, P., Chembo, Y.K. (2019) Dynamics of wideband time-delayed optoelectronic oscillators with nonlinear filters. IEEE J. Quantum Electron. 55(4), 5000106 (2019)

    Google Scholar 

  • Tang, S., Liu, J.M.: Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback. IEEE J. Quantum Electron. 37(3), 329–336 (2001)

    ADS  Google Scholar 

  • Tang, S., Liu, J.M.: Chaos synchronization in semiconductor lasers with optoelectronic feedback. IEEE J. Quantum Electron. 39(6), 708–715 (2003)

    ADS  Google Scholar 

  • Uchida, A.: Optical communication with chaotic lasers: applications of nonlinear dynamics and synchronization. Wiley, New York (2012)

    MATH  Google Scholar 

  • Vo, T., Bertram, R., Tabak, J., Wechselberger, M.: Mixed mode oscillations as a mechanism for pseudo-plateau bursting. J. Comput. Neurosci. 28, 443 (2010)

    MathSciNet  MATH  Google Scholar 

  • Wang, S., Fang, N., Wang, L.: Signal recovery based on optoelectronic reservoir computing for high speed optical fiber communication system. Opt. Commun. 495(15), 127082 (2021)

    Google Scholar 

  • Weicker, L., Erneux, T.: Slow–fast dynamics of time-delayed electro-optic oscillator. Philos. Trans. Roy. Soc. A Math. Phys 371(1999), 20120459 (2013)

    MathSciNet  MATH  ADS  Google Scholar 

  • Weicker, L., Erneux, T., Jacquot, M., Chembo, Y., Larger, L.: Crenelated fast oscillatory outputs of tow-delay electro-optic oscillator. Phys. Rev. E Stat Phys. Plasmas Fluids Relat. Top 85, 026206 (2012)

    ADS  Google Scholar 

  • Williams, C.R.S., Murphy, T.E., Roy, R., Sorrentino, F., Dahms, T., Scholl, E.: Experimental observations of group synchrony in a system of chaotic optoelectronic oscillators. Phys. Rev. Lett. 110, 064104 (2013)

    ADS  Google Scholar 

  • Wu, B., et al.: Magnetic field sensor based on dual- frequency optoelectronic oscillators using cascaded magnetostrictive alloy-fiber Bragg grating-Fabry Perot and fiber Bragg grating-Fabry Perot filters. Opt. Express 26(21), 27628–27638 (2018)

    ADS  Google Scholar 

  • Yang, J., Jin-Long, Y., Yao-Tian, W., Li-Tai, Z., En-Ze, Y.: An optical domain combined dual-loop optoelectronic oscillator. IEEE Photon. Technol. Lett. 19(11), 807–809 (2007)

    ADS  Google Scholar 

  • Yao, J.: Optoelectronic oscillator for high speed and high resolution optical sensing. J. lightw. Technol. 35(16), 3489–3497 (2017)

    ADS  Google Scholar 

  • Yao, X.S., Maleki: High frequency optical subcarrier generator. Electron. Lett. 19(11), 1525–1526 (1994)

    ADS  Google Scholar 

  • Yao, X.S., Maleki: Optoelectronic microwave oscillator. J. Opt. Soc. Am. B. 13(8), 1725–1735 (1996)

    ADS  Google Scholar 

  • Zhang, Y., Hou, D., Zhao, J.: Long-term frequency stabilization of an optoelectronic oscillator using phase-locked loop. J. Lightw. Technol. 32(13), 2408–2414 (2014)

    Google Scholar 

  • Zhou, P., Pan, S., Zhu, D., Guo, R., Zhang, F., Zhao, Y.: A compact optoelectronic oscillator based on an electroabsorption modulated laser. IEEE Photon. Technol. Lett. 26(1), 86–88 (2014)

    ADS  Google Scholar 

  • Zou, X., Xinkai, L., Li, W., Li, P.: Optoelectronic oscillators (OEOs) to sensing, measurement, and detection. IEEE J. Quantum Electron. 52(1), 0601116 (2016)

    Google Scholar 

  • Zou, F., Zou, L., Yang, B., Ma, Q., Zou, X., Zou, J., Chen, S., Milosevic, D., Cao, Z., Liu, H.: Optoelectronic oscillator for 5G wireless networks and beyond. J. Phys. D Appl. Phys. (2021). https://doi.org/10.1088/1361-6463/ac13f2

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge Della Tamin (South Africa) for providing some experimental equipments.

Author information

Authors and Affiliations

  1. Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes, Department of Physics, University of Yaoundé I, P. O. Box 812, Yaoundé, Cameroon

    Juliette S. D. Kamaha & Paul Woafo

  2. Research Unit of Condensed Matter, Electronics and Signal Processing, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Jimmi Hervé Talla Mbé & Hilaire Bertrand Fotsin

  3. Research Unit of Industrial Systems Engineering and Environment (RU-ISEE), Fotso-Victor University Institute of Technology, University of Dschang, Bandjoun, Cameroon

    Samuel Noubissie

Authors
  1. Juliette S. D. Kamaha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jimmi Hervé Talla Mbé
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Samuel Noubissie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hilaire Bertrand Fotsin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Paul Woafo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jimmi Hervé Talla Mbé.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kamaha, J.S.D., Talla Mbé, J.H., Noubissie, S. et al. Dynamics of optoelectronic oscillators with band-pass filter and laser nonlinearities: theory and experiment. Opt Quant Electron 54, 178 (2022). https://doi.org/10.1007/s11082-022-03546-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-022-03546-6

Keywords

Search

Navigation