Frequency domain computation and stability analysis of oscillation modes of wideband optoelectronic oscillators

Document Type : Original Article


Faculty of Electrical and Computer Engineering, University of Kashan, Kashan, Iran


Optoelectronic oscillators (OEOs) use a long optical fiber delay line as a very high-Q resonator to produce very low phase noise RF/microwave oscillations. Computing all the oscillation modes and stability analysis of them in the frequency domain, in case of having wide band RF/microwave filters in their oscillation loops, is addressed in the current paper.  Such a large bandwidth can be used to produce harmonic components of the oscillation or to give the possibility of sweeping the oscillation frequency in a large bandwidth by using a phase shifter and a small fiber. It is shown that in the case of OEOs with wideband RF filters, considering only the fundamental harmonic, instead of adequate number of them, may result in noticeable error in steady state computations as well as erroneous judgment about the stability of the modes. A relaxation algorithm is introduced for computing the oscillation modes. Stability analysis is performed by implementing the Nyquist stability test on a spectral domain system of equations governing the perturbations. The validity of the analysis approaches of this paper are verified by comparing their results against the time-consuming time-domain integrations.


[1]      محمد عظیم کریمی، میثاق انصاریان و سوده عقلی مقدم، «نوسان‌ساز حلقوی جدید کنترل‌شده با ولتاژ با استفاده از اثر میلر»، مجله مهندسی برق دانشگاه تبریز، جلد 47، شماره یک، صفحات 221-228، 1396
[2]      رضا بستانی و جواد یاوند حسنی، «تحلیل اثر پارازیتی عناصر بر عملکرد نوسانگر تزویج ضرب‌دری در محدوده باند میلی‌متری»، مجله مهندسی برق دانشگاه تبریز، جلد 47، شماره 3، صفحات 867-875، 1396
[3]      D. A. Howe and A. Hati, “Low-noise X-band oscillator and amplifier technologies: Comparison and status,” in Proceedings of the 2005 IEEE International Frequency Control Symposium and Exposition, pp. 481-487, 2005.
[4]      U. L. Rhode, A. K. Poddar and G. Bock, The design of modern microwave oscillators for wireless applications, John Wiley & Sons, 2005.
[5]      X. S. Yao and L. Maleki, “Converting light into spectrally pure microwave oscillation,” Opt. Lett. vol. 21, no. 7, pp. 483-485, 1996.
[6]      X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B, vol. 13, no. 8, pp. 1725-1735, 1996.
[7]      S. Rosmisch, J. Kitching, E. Ferre-Pikal, L. Hollberg, and F. L. Walls, “Performance evaluation of an optoelectronic oscillator,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 47, no. 5, pp. 1159-1165, 2000.
[8]      D. Eliyahu and D. Maleki, “Tunable, ultra-low phase noise YIG based optoelectronic oscillator,” in IEEE MTT-S International Microwave Symposium Digest, pp. 2185-2187, 2003.
[9]      E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B, vol. 26, no. 1, pp. 148-159, 2009.
[10]      Y. K. Chembo, K. Volyanisky, L. Larger, E. Rubiola and P. Colet, “Determination of phase noise spectra in optoelectronic microwave oscillator: A Langevin approach,” IEEE J. Quantum. Electron. vol. 45, no. 2, pp. 178-186, 2009.
[11]      S. Jahanbakht, S. E. Hosseini and A. Banai, “Prediction of the noise spectrum in optoelectronic oscillators: an analytical conversion matrix approach,” J. Opt. Soc. Am. B, vol. 31, no. 8,  pp. 1915-1925, 2014.
[12]      S. Jahanbakht, “Noise spectrum characterization of optoelectronic oscillators in the presence of laser frequency noise,” Applied optics (OSA), vol. 55, no. 8, pp. 1854-1862, 2016.
[13]      S. Jahanbakht and S. E. Hosseini, “Frequency domain noise analysis of optoelectronic oscillators considering the nonlinearity of the RF amplifier,” J. Opt. Soc. Am. B, vol. 33, no. 4, pp. 548-557, 2016.
[14]      Y. K. Chembo, L. Larger, H. Tavernier, R. Bendoula, E. Rubiola and P. Colet, “Dynamic instabilities of microwaves generated with optoelectronic oscillators,” Optics letters, vol. 32, no. 17, pp. 2571-2573, 2007.
[15]      Y. K. Chembo, L. Larger and P. Colet, “Nonlinear dynamics and spectral stability of optoelectronic microwave oscillators,” IEEE J. Quantum. Electron. vol. 44, no. 9, pp. 858-866, 2008.
[16]      S.Jahanbakht, "Frequency domain computation of steady state modes of optoelectronic oscillators with stability analysis," Applied Optics (Optical Society of America), vol. 56, no. 4, pp. 975-984, 2017.
[17]      S.Jahanbakht, "Frequency domain approach to the steady state and stability analysis of dual injection-locked optoelectronic oscillators," Applied Optics (Optical Society of America), vol. 56, no. 20, pp. 5705-5715, 2017.
[18]      S. E. Hosseini and A. Banai, “Theoretical investigation of the capture effect in intensity-modulation direct-detection microwave photonic links,” Applied optics (OSA), vol. 52, no. 28, pp. 7011-7021, 2013.
[19]      M. Peil, M. Jacquot, Y. K. Chembo, L. Larger and T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators”, Physical Review E, vol. 79, no.2, pp.026208, 2009
[20]      K. E. Callan, L. Illing, Z. Gao, D. J. Gauthier and E. Scholl, “Broadband chaos generated by an optoelectronic oscillator,” Physical review letters, vol. 104, no. 11, p. 113901, 2010. 
[21]      B. M. Romeira,  J. Javaloyes, J. M. L., Figueiredo, C. N. Ironside, H. I. Cantú and A. E. Kelly, “Delayed feedback dynamics of Lienard-type resonant tunneling-photo-detector optoelectronic oscillators,” IEEE Journal of Quantum Electronics, vol. 49, no. 1, pp. 31-42, 2013.
[22]      L. Weicker, T. Erneux, O. D'Huys, J. Danckaert, M. Jacquot, Y. C. Chembo and L. Larger, “Slow–fast dynamics of a time-delayed electro-optic oscillator,” Phil. Trans. R. Soc. A, 371, 2013.
[23]      R. Romeira, F. Kong, W. Li, J. M. L. Figueiredo, J. Javaloyes and J. Jianping “Broadband chaotic signals and breather oscillations in an optoelectronic oscillator incorporating a microwave photonic filter,” Journal of Lightwave Technology, vol. 32, no. 20, pp. 3933-3942, 2014.
[24]      O. Okusaga, W. Zhou, E. C. Levy, M. Horowitz, G. Carter and C. R. Menyuk, “Experimental and simulation study of dual injection-locked OEOs,” IEEE International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum, pp. 875-879, 2009.
[25]      E. C. Levy, O. Okusaga, M. Horowitz, C. R. Menyuk, W. Zhou, and G. M. Carter, “Comprehensive computational model of single and dual loop optoelectronic oscillators with experimental verification,” Optics express, vol. 18, pp. 21461-21476, 2010.
[26]      A. Suarez, R. Quere, Stability analysis of nonlinear microwave circuits, Artech House, 2002.
[27]      A. Suarez, Analysis and design of autonomous microwave circuits, John Wiley & Sons, 2009.
[28]      S. A. Maas, Nonlinear microwave and RF circuits, 2nd edition, Artech house, 2003.
[29]      S.E. Hosseini, A. Karimi and S. Jahanbakht, “Q factor of optical delay line based cavities and oscillators,” Optics communications, Published online, to be appear in vol. 407, pp. 349-354, January 2018.