HCMT models of optical microring-resonator circuits

Journal of the Optical Society of America B: Optical Physics

Volumn 27, Issue 11, 2010, Pages 2237-2246

  Hammer, Manfred ^a  

^a UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

RESONATORS; VARIATIONAL TECHNIQUES; WAVE PROPAGATION;

AMPLITUDE FUNCTIONS; CARTESIANS; COUPLED MODE THEORY; COUPLED-RESONATOR OPTICAL WAVEGUIDES; FINITE ELEMENT; INTRACAVITIES; MICRORINGS; OPTICAL FIELD; OPTICAL MICRORING RESONATOR; PHOTONIC MOLECULES; POLAR COORDINATE;

COUPLED CIRCUITS;

EID: 78149371957     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.27.002237     Document Type: Article

References (39)

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).
3. L. F. Stokes, M. Chodorow, and H. J. Shaw, "All-singlemode fiber resonator," Opt. Lett. 7, 288-290 (1982).
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).
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. 2 technology," Appl. Phys. B 73, 603-608 (2001).
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).
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).
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).
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).
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).
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).
16. M. Hammer, "Hybrid analytical/numerical coupled-mode modeling of guided wave devices," J. Lightwave Technol. 25, 2287-2298 (2007).
17. M. Hammer, "Chains of coupled square dielectric optical microcavities," Opt. Quantum Electron. 40, 821-835 (2009).
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).
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 f, b, c that constitute template (3) 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 [6], 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, "Coupledresonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
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).
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).
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).
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).
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).
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).
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). (Pubitemid 43837506)
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).
34. J. Čtyroký, I. Richter, and M. Šiňor, "Dual resonance in a waveguide-coupled ring microresonator," Opt. Quantum Electron. 38, 781-797 (2006).
35. This might well relate to actual physical effects, e.g., to a pronounced surface roughness [34,36].
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).
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).
38. M. Hammer, "Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics," Opt. Commun. 235, 285-303 (2004).
39. L. Prkna, J. Čtyroký, and M. Hubálek, "Ring microresonator as a photonic structure with complex eigenfrequency," Opt. Quantum Electron. 36, 259-269 (2004).