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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 27, Iss. 11 — Nov. 1, 2010
  • pp: 2237–2246

HCMT models of optical microring-resonator circuits

Manfred Hammer  »View Author Affiliations

JOSA B, Vol. 27, Issue 11, pp. 2237-2246 (2010)

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Circuits of dielectric integrated optical microring resonators are addressed through a two-dimensional hybrid analytical/numerical coupled mode theory (HCMT) model. Analytical modes of all straight and curved cores form templates for the optical fields of the entire circuits. Our variational technique then generates solutions for the amplitude functions in their natural Cartesian and polar coordinates, discretized by one-dimensional finite elements. Bidirectional wave propagation through all channels and pronounced reflections can be taken into account. The series of examples includes rings coupled in parallel, rows of cavities (coupled resonator optical waveguides) of varying lengths, a triangular photonic molecule, and a resonator with a slit ring to illustrate the role of intra-cavity reflections.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Integrated Optics

Original Manuscript: June 24, 2010
Manuscript Accepted: July 18, 2010
Published: October 12, 2010

Manfred Hammer, "HCMT models of optical microring-resonator circuits," J. Opt. Soc. Am. B 27, 2237-2246 (2010)

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  1. M.Bertolotti, A.Driessen, and F.Michelotti, eds., Microresonators as Building Blocks for VLSI Photonics, Vol. 709 of AIP Conference Proceedings (American Institute of Physics, 2004).
  2. I.Chremmos, N.Uzunoglu, and O.Schwelb, eds., Photonic Microresonator Research and Applications, Springer Series in Optical Sciences, Vol. 156 (Springer, 2010). [CrossRef]
  3. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett. 7, 288–290 (1982). [CrossRef] [PubMed]
  4. K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).
  5. A. Yariv, “Universal relations for coupling of optical power between miroresonators and dielectric waveguide,” Electron. Lett. 36, 321–322 (2000). [CrossRef]
  6. M. Hammer, K. R. Hiremath, and R. Stoffer, “Analytical approaches to the description of optical microresonator devices,” in Microresonators as Building Blocks for VLSI Photonics, Vol. 709 of AIP Conference Proceedings, M.Bertolotti, A.Driessen, and F.Michelotti, eds. (American Institute of Physics, 2004), pp. 48–71.
  7. D. J. W. Klunder, E. Krioukov, F. S. Tan, T. van der Veen, H. F. Bulthuis, G. Sengo, C. Otto, H. J. W. M. Hoekstra, and A. Driessen, “Vertically and laterally waveguide-coupled cylindrical microresonators in Si3N4 on SiO2 technology,” Appl. Phys. B 73, 603–608 (2001). [CrossRef]
  8. D. J. W. Klunder, M. L. M. Balistreri, F. C. Blom, H. J. W. M. Hoekstra, A. Driessen, L. Kuipers, and N. F. van Hulst, “Detailed analysis of the intracavity phenomena inside a cylindrical microresonator,” J. Lightwave Technol. 20, 519–529 (2002). [CrossRef]
  9. D. J. W. Klunder, F. S. Tan, T. van der Veen, H. F. Bulthuis, G. Sengo, B. Docter, H. J. W. M. Hoekstra, and A. Driessen, “Experimental and numerical study of SiON microresonators with air and polymer cladding,” J. Lightwave Technol. 21, 1099–1110 (2003). [CrossRef]
  10. C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).
  11. D.G.Hall and B.J.Thompson, eds., Selected Papers on Coupled-Mode Theory in Guided-Wave Optics, Vol. MS 84 of SPIE Milestone Series (SPIE Optical Engineering, 1993).
  12. D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc.-J: Optoelectron. 140, 177–188 (1993). [CrossRef]
  13. M. K. Chin and S. T. Ho, “Design and modeling of waveguide-coupled single-mode microring resonators,” J. Lightwave Technol. 16, 1433–1446 (1998). [CrossRef]
  14. 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]
  15. R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, and J. Čtyroký, “Cylindrical integrated optical microresonators: Modeling by 3-D vectorial frequency domain coupled mode theory,” Opt. Commun. 256, 46–67 (2005). [CrossRef]
  16. M. Hammer, “Hybrid analytical/numerical coupled-mode modeling of guided wave devices,” J. Lightwave Technol. 25, 2287–2298 (2007). [CrossRef]
  17. M. Hammer, “Chains of coupled square dielectric optical microcavities,” Opt. Quantum Electron. 40, 821–835 (2009). [CrossRef]
  18. K. R. Hiremath, M. Hammer, R. Stoffer, L. Prkna, and J. Čtyroký, “Analytical approach to dielectric optical bent slab waveguides,” Opt. Quantum Electron. 37, 37–61 (2005). [CrossRef]
  19. K. R. Hiremath, “Coupled mode theory based modeling and analysis of circular optical microresonators,” Ph.D. dissertation (University of Twente, 2005).
  20. M. Hammer, “METRIC—Mode expansion tools for 2D rectangular integrated optical circuits,” http://www.math.utwente.nl/~hammerm/Metric/.
  21. K. R. Hiremath, “CIRCURS—Circular resonator simulator,” http://www.math.utwente.nl/aamp/FormMem/Hiremath/circurs/.
  22. The fields ψf, ψb, ψc that constitute template satisfy formally the same equations, but each with different permittivity functions that represent the upper core, the lower core, or the cavity only, always on a homogeneous background.
  23. One might observe that this interpolation process is quite analogous to the usual analytical evaluation of parametric CMT models , where one takes into account first or second order wavelength derivatives of effective mode indices and neglects the wavelength dependence of coupling coefficients.
  24. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, 1992).
  25. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999). [CrossRef]
  26. 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]
  27. F. Morichetti, A. Melloni, A. Breda, A. Canciamilla, C. Ferrari, and M. Martinelli, “A reconfigurable architecture for continuously variable optical slow-wave delay lines,” Opt. Express 15, 17273–17281 (2007). [CrossRef] [PubMed]
  28. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999). [CrossRef]
  29. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999). [CrossRef]
  30. M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999). [CrossRef]
  31. S. V. Boriskina, “Spectrally engineered photonic molecules as optical sensors with enhanced sensitivity: a proposal and numerical analysis,” J. Opt. Soc. Am. 23, 1565–1573 (2006). [CrossRef]
  32. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Threshold reduction in a cyclic photonic molecule laser composed of identical microdisks with whispering-gallery modes,” Opt. Lett. 31, 921–923 (2006). [CrossRef] [PubMed]
  33. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, “Cold-cavity thresholds of microdisks with uniform and nonuniform gain: Quasi-3-D modeling with accurate 2-D analysis,” IEEE J. Sel. Top. Quantum Electron. 11, 1135–1142 (2005). [CrossRef]
  34. J. Čtyroký, I. Richter, and M. Šiňor, “Dual resonance in a waveguide-coupled ring microresonator,” Opt. Quantum Electron. 38, 781–797 (2006). [CrossRef]
  35. This might well relate to actual physical effects, e.g., to a pronounced surface roughness .
  36. M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef] [PubMed]
  37. Y. M. Kang, A. Arbabi, and L. L. Goddard, “A microring resonator with an integrated Bragg grating: a compact replacement for a sampled grating distributed Bragg reflector,” Opt. Quantum Electron. 41, 689–697 (2010) (available online). [CrossRef]
  38. M. Hammer, “Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics,” Opt. Commun. 235, 285–303 (2004). [CrossRef]
  39. L. Prkna, J. Čtyroký, and M. Hubálek, “Ring microresonator as a photonic structure with complex eigenfrequency,” Opt. Quantum Electron. 36, 259–269 (2004). [CrossRef]

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