OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 4 — Apr. 1, 2013
  • pp: 1048–1057

Interaction of whispering gallery modes in integrated optical microring or microdisk circuits: hybrid coupled mode theory model

Ellen F. Franchimon, Kirankumar R. Hiremath, Remco Stoffer, and Manfred Hammer  »View Author Affiliations


JOSA B, Vol. 30, Issue 4, pp. 1048-1057 (2013)
http://dx.doi.org/10.1364/JOSAB.30.001048


View Full Text Article

Enhanced HTML    Acrobat PDF (1690 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Whispering gallery modes supported by open circular dielectric cavities are embedded into a nonparametric two-dimensional frequency domain hybrid coupled mode theory framework. Regular aggregates of these cavities, including straight access channels, are investigated. The model enables convenient studies of the guided wave scattering process, the response of the circuit to guided wave excitation. Transmission resonances can be characterized directly in terms of resonance frequency and linewidth by computing supermodes of the entire composite circuits, comprising both cavities and bus waveguides. Examples of single ring and disk filters, a coupled-resonator optical waveguide, and a three-cavity photonic molecule in a reflector configuration allow the approach to be assessed.

© 2013 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

History
Original Manuscript: December 7, 2012
Revised Manuscript: February 14, 2013
Manuscript Accepted: February 14, 2013
Published: March 29, 2013

Citation
Ellen F. Franchimon, Kirankumar R. Hiremath, Remco Stoffer, and Manfred Hammer, "Interaction of whispering gallery modes in integrated optical microring or microdisk circuits: hybrid coupled mode theory model," J. Opt. Soc. Am. B 30, 1048-1057 (2013)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-4-1048


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, “Microring resonator arrays for VLSI photonics,” IEEE Photon. Technol. Lett. 12, 323–325 (2000). [CrossRef]
  2. F. Michelotti, A. Driessen, and M. Bertolotti, eds., Microresonators as Building Blocks for VLSI Photonics, Vol. 709 of AIP Conference Proceedings (American Institute of Physics, 2004).
  3. I. Chremmos, N. Uzunoglu, and O. Schwelb, eds., Photonic Microresonator Research and Applications, Vol. 156 of Springer Series in Optical Sciences (Springer, 2010).
  4. M. Hammer, “HCMT models of optical microring-resonator circuits,” J. Opt. Soc. Am. B 27, 2237–2246 (2010). [CrossRef]
  5. A. Yariv, “Universal relations for coupling of optical power between miroresonators and dielectric waveguide,” Electron. Lett. 36, 321–322 (2000). [CrossRef]
  6. K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).
  7. 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]
  8. D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc. J 140, 177–188 (1993). [CrossRef]
  9. L. Prkna, J. Čtyroký, and M. Hubálek, “Ring microresonator as a photonic structure with complex eigenfrequency,” Opt. Quantum Electron. 36, 259–269 (2004). [CrossRef]
  10. E. Franchimon, “Modelling circular optical microresonators using whispering gallery modes,” M.Sc. thesis (University of Twente, 2010).
  11. M. Hammer, “Hybrid analytical/numerical coupled-mode modeling of guided wave devices,” J. Lightwave Technol. 25, 2287–2298 (2007). [CrossRef]
  12. P. T. Leung, S. Y. Liu, and K. Young, “Completeness and orthogonality of quasinormal modes in leaky optical cavities,” Phys. Rev. A 49, 3057–3067 (1994). [CrossRef]
  13. M. Bertolotti, “Linear one dimensional resonant cavities,” in Microresonators as Building Blocks for VLSI Photonics, F. Michelotti, A. Driessen, and M. Bertolotti, eds., Vol. 709 of AIP Conference Proceedings (American Institute of Physics, 2004), pp. 19–47.
  14. M. Maksimovic, M. Hammer, and E. van Groesen, “Field representation for optical defect microcavities in multilayer structures using quasi-normal modes,” Opt. Commun. 281, 1401–1411 (2008). [CrossRef]
  15. M. Maksimovic, M. Hammer, and E. van Groesen, “Coupled optical defect microcavities in 1d photonic crystals and quasi-normal modes,” Opt. Eng. 47, 114601 (2008). [CrossRef]
  16. M. Maksimovic, “Optical resonances in multilayer structures,” Ph.D. thesis (University of Twente, 2008).
  17. M. A. Popović, C. Manolatou, and M. R. Watts, “Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters,” Opt. Express 14, 1208–1222 (2006). [CrossRef]
  18. Q. Li, T. Wang, Y. Su, M. Yan, and M. Qiu, “Coupled mode theory analysis of mode splitting in coupled cavity system,” Opt. Express 18, 8367–8382 (2010). [CrossRef]
  19. O. Schwelb, “On the nature of resonance splitting in coupled multiring optical resonators,” Opt. Commun. 281, 1065–1071 (2008). [CrossRef]
  20. Q. Li, M. Soltani, A. H. Atabaki, S. Yegnanarayanan, and A. Adibi, “Quantitative modeling of coupling-induced resonance frequency shift in microring resonators,” Opt. Express 17, 23474–23486 (2009). [CrossRef]
  21. L. Y. M. Tobing, L. Tjahjana, S. Darmawan, and D. H. Zhang, “Numerical and experimental studies of coupling-induced phase shift in resonator and interferometric integrated optics devices,” Opt. Express 20, 5789–5801 (2012). [CrossRef]
  22. D. E. Amos, “A portable package for Bessel functions of a complex argument and nonnegative order,” http://www.netlib.org/amos .
  23. K. R. Hiremath, “CIRCURS—Circular resonator simulator,” http://www.zib.de/hiremath/circurs/ .
  24. C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).
  25. M. Hammer, “METRIC—Mode expansion tools for 2D rectangular integrated optical circuits,” http://www.math.utwente.nl/~hammerm/Metric .
  26. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).
  27. B. Kettner, “Detection of spurious modes in resonance mode computations—Pole condition method,” PhD Dissertation (Freie Universität zu Berlin, 2012).
  28. L. Zschiedrich, “Transparent boundary conditions for Maxwells equations: numerical concepts beyond the PML method,” PhD Dissertation (Freie Universität zu Berlin, 2009).
  29. M. Lohmeyer, N. Bahlmann, and P. Hertel, “Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory,” Opt. Commun. 163, 86–94 (1999). [CrossRef]
  30. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002). [CrossRef]
  31. PhoeniX BV, P. O. Box 545, 7500 AM Enschede, The Netherlands, http://www.phoenixbv.com/http://www.phoenixbv.com/ .
  32. JCMwave GmbH, Haarer Str. 14a, 85640 Putzbrunn/Munich, Germany, http://www.jcmwave.com .
  33. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, 1992).
  34. 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]
  35. J. Čtyroký, I. Richter, and M. Šiňor, “Dual resonance in a waveguide-coupled ring microresonator,” Opt. Quantum Electron. 38, 781–797 (2006). [CrossRef]
  36. 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]
  37. A. Canciamilla, M. Torregiani, C. Ferrari, F. Morichetti, R. M. De La Rue, A. Samarelli, M. Sorel, and A. Melloni, “Silicon coupled-ring resonator structures for slow light applications: potential, impairments and ultimate limits,” J. Opt. 12, 104008 (2010). [CrossRef]
  38. S. V. Pishko, P. D. Sewell, T. M. Benson, and S. V. Boriskina, “Efficient analysis and design of low-loss whispering-gallery-mode coupled resonator optical waveguide bends,” J. Lightwave Technol. 25, 2487–2494 (2007). [CrossRef]
  39. O. Schwelb and I. Chremmos, “Defect assisted coupled resonator optical waveguide: weak perturbations,” Opt. Commun. 283, 3686–3690 (2010). [CrossRef]
  40. 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]
  41. J. K. S. Poon, J. Scheuer, and A. Yariv, “Wavelength-selective reflector based on a circular array of coupled microring resonators,” IEEE Photon. Technol. Lett. 16, 1331–1333 (2004). [CrossRef]
  42. O. Schwelb and I. Chremmos, “Band-limited microresonator reflectors and mirror structures,” in Photonic Microresonator Research and Applications, I. Chremmos, N. Uzunoglu, and O. Schwelb, eds., Vol. 156 of Springer Series in Optical Sciences (Springer, 2010), pp. 139–163.
  43. S. V. Boriskina, “Theoretical prediction of a dramatic Q-factor enhancement and degeneracy removal of whispering gallery modes in symmetrical photonic molecules,” Opt. Lett. 31, 338–340 (2006). [CrossRef]
  44. S. I. Schmid, K. Xia, and J. Evers, “Pathway interference in a loop array of three coupled microresonators,” Phys. Rev. A 84, 013808 (2011). [CrossRef]
  45. C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Observation of optical coupling in microdisk resonators,” Phys. Rev. A 80, 043841 (2009). [CrossRef]
  46. C. Schmidt, M. Liebsch, A. Klein, N. Janunts, A. Chipouline, T. Käsebier, C. Etrich, F. Lederer, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Near-field mapping of optical eigenstates in coupled disk microresonators,” Phys. Rev. A 85, 033827 (2012). [CrossRef]
  47. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B 83, 235427 (2011). [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