OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 16 — Aug. 11, 2014
  • pp: 19204–19218

Time-domain simulations of nonlinear interaction in microring resonators using finite-difference and coupled mode techniques

Roman Shugayev and Peter Bermel  »View Author Affiliations

Optics Express, Vol. 22, Issue 16, pp. 19204-19218 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1888 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Nonlinear interactions within compact, on-chip microring resonant cavities is a topic of increasing interest in current silicon photonics research. Frequency combs, one of the emerging nonlinear applications in microring optics, offers great potential from both scientific and practical perspectives. However, the mechanisms of comb formation appear to differ from traditional frequency combs formed by pulsed femtosecond lasers, and thus require detailed elucidation through theory and simulation. Here we propose a technique to mimic the accuracy of finite-difference time domain (FDTD) full wave nonlinear optical simulations with only a small fraction of the computational resources. Our new hybrid approach combines a single linear FDTD simulation of the key interaction parameters, then directly inserts them into a coupled-mode theory simulation. Comparison of the hybrid approach and full FDTD shows a good match both in frequency domain and in time domain. Thus, it retains the advantage of FDTD in terms of direct connection with experimental designs, while finishing much faster and sidestepping stability issues associated with direct simulation of nonlinear phenomena. The hybrid technique produces several key results explored in this paper, including: demonstrating that comb formation can occur with both anomalous and normal dispersion; suggesting a new mechanism for incoherent (Type II) frequency comb formation; and illustrating a method for creating soliton-like pulses in on-chip microresonators.

© 2014 Optical Society of America

OCIS Codes
(130.4310) Integrated optics : Nonlinear
(140.4780) Lasers and laser optics : Optical resonators
(190.3270) Nonlinear optics : Kerr effect
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

ToC Category:
Nonlinear Optics

Original Manuscript: May 9, 2014
Revised Manuscript: June 26, 2014
Manuscript Accepted: July 14, 2014
Published: July 31, 2014

Roman Shugayev and Peter Bermel, "Time-domain simulations of nonlinear interaction in microring resonators using finite-difference and coupled mode techniques," Opt. Express 22, 19204-19218 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007). [CrossRef]
  2. J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Kluwer, 2005). [CrossRef]
  3. P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109, 263901 (2012). [CrossRef]
  4. I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a CaF2 resonator,” Opt. Lett. 34, 878–880 (2009). [CrossRef] [PubMed]
  5. W. C. Jiang, X. Lu, J. Zhang, O. Painter, and Q. Lin, “Ultra-bright photon-pair generation on a silicon chip,” in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FW6C.10. [CrossRef]
  6. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16, 2263–2265 (2004). [CrossRef]
  7. T. Barwicz, M. A. Popović, P. T. Rakich, M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-drop filters in SiN: fabrication and analysis,” Opt. Express 12, 1437–1442 (2004). [CrossRef] [PubMed]
  8. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photon. 4, 37–40 (2010). [CrossRef]
  9. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photon. 4, 41–45 (2010). [CrossRef]
  10. F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photon. 5, 770–776 (2011). [CrossRef]
  11. S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A 84, 053833 (2011). [CrossRef]
  12. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011). [CrossRef] [PubMed]
  13. A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011). [CrossRef] [PubMed]
  14. M. Popovic, Theory and design of High-Index-Contrast microphotonic circuits (MIT libraries thesis collection, Cambridge, MA, 2008).
  15. A. Rodriguez, M. Soljacic, J. Joannopoulos, and S. Johnson, “Chi(2) and Chi(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007). [CrossRef] [PubMed]
  16. T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon. 6, 480–487 (2012). [CrossRef]
  17. Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys Rev. A 82, 033801 (2010). [CrossRef]
  18. E. Granados, D. W. Coutts, and D. J. Spence, “Mode-locked deep ultraviolet Ce:LiCAF laser,” Opt. Lett. 34, 1660–1662 (2009). [CrossRef] [PubMed]
  19. L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987). [CrossRef] [PubMed]
  20. S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38, 37–39 (2013). [CrossRef] [PubMed]
  21. M. R. Lamont, Y. Okawachi, and A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs,” Opt. Lett. 38, 3478–3481 (2013). [CrossRef] [PubMed]
  22. M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992). [CrossRef]
  23. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).
  24. A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, “Chaotic dynamics of frequency combs generated with continuously pumped nonlinear microresonators,” Opt. Lett. 38, 525–527 (2013). [CrossRef] [PubMed]
  25. T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of Kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014). [CrossRef]
  26. M. Peccianti, A. Pasquazi, Y. Park, B.E. Little, S.T. Chu, D.J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nature Comm. 3, 765 (2012). [CrossRef]
  27. Y. Dumeige, C. Arnaud, and P. Feron, “Combining FDTD with coupled mode theories for bistability in micro-ring resonators,” Opt. Commun. 250, 376–383 (2005). [CrossRef]
  28. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010). [CrossRef]
  29. V. A. Mandelshtam, “FDM: the filter diagonalization method for data processing in NMR experiments,” Prog. Nucl. Mag. Res. Sp. 38, 159–196 (2001). [CrossRef]
  30. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997). [CrossRef]
  31. W. Yang, A. Josh, and X. Min, “Effects of side-coupling on the phase response of cascaded microring all-pass filters,” Opt. Commun. 232, 209–216 (2004). [CrossRef]
  32. Rosen Center for Advanced Computing: Carter User Information., http://www.rcac.purdue.edu/userinfo/resources/carter/ , last accessed on May 31, 2013.
  33. G. P. Agrawal, Fiber-Optic Communications Systems, 3rd ed. (John Wiley, 2002). [CrossRef]
  34. F. Leo, S. Coen, P. Kockaert, S. P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photon. 4, 471–476 (2010). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited