OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8641–8655

Analysis of light propagation in slotted resonator based systems via coupled-mode theory

Kirankumar R. Hiremath, Jens Niegemann, and Kurt Busch  »View Author Affiliations

Optics Express, Vol. 19, Issue 9, pp. 8641-8655 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1569 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Optical devices with a slot configuration offer the distinct feature of strong electric field confinement in a low refractive index region and are, therefore, of considerable interest in many applications. In this work we investigate light propagation in a waveguide-resonator system where the resonators consist of slotted ring cavities. Owing to the presence of curved material interfaces and the vastly different length scales associated with the sub-wavelength sized slots and the waveguide-resonator coupling regions on the one hand, and the spatial extent of the ring on the other hand, this prototypical system provides significant challenges to both direct numerical solvers and semi-analytical approaches. We address these difficulties by modeling the slot resonators via a frequency-domain spatial Coupled-Mode Theory (CMT) approach, and compare its results with a Discontinuous Galerkin Time-Domain (DGTD) solver that is equipped with curvilinear finite elements. In particular, the CMT model is built on the underlying physical properties of the slotted resonators, and turns out to be quite efficient for analyzing the device characteristics. We also discuss the advantages and limitations of the CMT approach by comparing the results with the numerically exact solutions obtained by the DGTD solver. Besides providing considerable physical insight, the CMT model thus forms a convenient basis for the efficient analysis of more complex systems with slotted resonators such as entire arrays of waveguide-coupled resonators and systems with strongly nonlinear optical properties.

© 2011 OSA

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(130.3120) Integrated optics : Integrated optics devices
(130.6010) Integrated optics : Sensors
(230.5750) Optical devices : Resonators

ToC Category:
Integrated Optics

Original Manuscript: January 13, 2011
Manuscript Accepted: March 11, 2011
Published: April 19, 2011

Kirankumar R. Hiremath, Jens Niegemann, and Kurt Busch, "Analysis of light propagation in slotted resonator based systems via coupled-mode theory," Opt. Express 19, 8641-8655 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method , 3rd ed. (Artech House Inc., 2005).
  2. J. Jin, The Finite Element Method in Electromagnetics , 2nd ed. (Wiley-Interscience Publication, 2002).
  3. G. W. Pan, Wavelets in Electromagnetics and Device Modeling , Microwave and Optical engineering, (Wiley Interscience, 2003). [CrossRef]
  4. J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications , Number 54 in Texts in Applied Mathematics, (Springer-Verlag, 2007).
  5. J. Niegemann, M. König, K. Stannigel, and K. Busch, “Higher-order time-domain methods for the analysis of nano-photonic systems,” Photon. Nanostr.: Fundam. Appl. 7(1), 2–11 (2009). [CrossRef]
  6. J. Niegemann, W. Pernice, and K. Busch, “Simulation of optical resonator using DGTD and FDTD,” IOP J. Opt. A: Pure Appl. Opt. 11, 114015:1–10 (2009). [CrossRef]
  7. K. Stannigel, M. König, J. Niegemann, and K. Busch, “Discontinuous Galerkin time-domain computations of metallic nanostructures,, Opt. Express 17(17), 14934–14947 (2009). [CrossRef] [PubMed]
  8. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997). [CrossRef]
  9. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12(3), 320–322 (2000). [CrossRef]
  10. H. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, “High-Q channel-dropping filters using ring resonators with integrated SOAs,” IEEE Photon. Technol. Lett. 14(10), 1442–1444 (2002). [CrossRef]
  11. A. Melloni, R. Costa, P. Monguzzi, and M. Martinelli, “Ring-resonator filters in silicon oxynitride technology for dense wavelength-division multiplexing systems,” Opt. Lett. 28(17), 1567–1569 (2003). [CrossRef] [PubMed]
  12. C. K. Madsen, G. Lenz, A. J. Bruce, M. A. Capuzzo, L. T. Gomez, T. N. Nielsen, and I. Brener, “Multistage dispersion compensator using ring resonators,” Opt. Lett. 24(22), 1555–1557 (1999). [CrossRef]
  13. A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-Q microcavities,” Opt. Lett. 31(12), 1896–1898 (2006). [CrossRef] [PubMed]
  14. S. Pereira, P. Chak, S. E. Sipe, L. Tkeshelashvili, and K. Busch, “All-optical diode in an asymmetrically apodized kerr nonlinear microresonator system,” Photon. Nanostr.: Fundam. Appl. 2, 181–190 (2004). [CrossRef]
  15. V. R. Almeida, Q. Xu, C. A. Barios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]
  16. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 2(3), 216–219 (2009). [CrossRef]
  17. T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86, 081101 (2005). [CrossRef]
  18. T. Baehr-Jones, M. Hochberg, G. Wang, R. Lawson, Y. Liao, P. Sullivan, L. Dalton, A. Jen, and A. Scherer, “Optical modulation and detection in slotted silicon waveguides,” Opt. Express 13(14), 5216–5226 (2005). [CrossRef] [PubMed]
  19. K. R. Hiremath, “Analytical modal analysis of bent slot waveguides,” J. Opt. Soc. Am. A 26(11), 2321–2326 (2009). [CrossRef]
  20. X. Ji, T. Lu, W. Cai, and P. Zhang, “Discontinuous Galerkin Time Domain (DGTD) methods for the study of 2-D waveguide-coupled microring resonators,” J. Lightwave Technol. 23(11), 3864–3874 (2005). [CrossRef]
  21. K. R. Hiremath, R. Stoffer, and M. Hammer, “Modeling of circular integrated optical microresonators by 2-D frequency domain coupled mode theory,” Opt. Commun. 257, 277–297 (2006). [CrossRef]
  22. K. R. Hiremath, Coupled mode theory based modeling and analysis of circular optical microresonators , PhD thesis, University of Twente, The Netherlands (2005).
  23. M. Hammer, K. R. Hiremath, and R. Stoffer, “Analytical approaches to the description of optical microresonator devices,” in F. Michelotti, A. Driessen, and M. Bertolotti, editors, Microresonators as building blocks for VLSI photonics , volume 709 of AIP conference proceedings, pages 48–71. American Institute of Physics, Melville, New York (2004).
  24. K. R. Hiremath, M. Hammer, S. Stoffer, L. Prkna, and J. Čtyroký, “Analytic approach to dielectric optical bent slab waveguides,” Opt. Quantum Electron. 37(1–3), 37–61 (2005). [CrossRef]
  25. T. Tamir, editor, Integrated Optics (Second Corrected and Updated Edition) , Topics in Applied Physics, vol. 7, (Springer-Verlag, 1982).
  26. A. Ghatak and K. Thyagarajan, Optical Electronics (Cambridge University Press, 1993).
  27. 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,” Comput. Phys. Commun. 181(3), 687–702 (2010). [CrossRef]
  28. R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Čtyroký, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory,” Opt. Commun. 256, 46–67 (2005). [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