OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 9 — Sep. 1, 2014
  • pp: 2239–2245

Graded index optical microresonators: analytical and numerical analyses

Khalil Dadashi, Hamza Kurt, Kadir Üstün, and Ramazan Esen  »View Author Affiliations

JOSA B, Vol. 31, Issue 9, pp. 2239-2245 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (674 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



It is known that the spectra of optical modes supported by microresonators are shape and size dependent. We have introduced an additional parameter, i.e., spatially varying refractive index, to tailor the spectra of optical modes in a microdisk resonator while keeping size and shape intact. A new class of whispering gallery mode microresonators, referred to as graded index (GRIN) microresonators, is proposed. The GRIN profile belongs to a special inhomogeneous medium known as Maxwell’s fish eye. The modal analysis of the structure is investigated both analytically and numerically. Solution of the Helmholtz equation is attempted under the spatially varying refractive index scenario and numerical verification of the analytical findings is tested by the finite-difference time-domain method. It is found that the two approaches support each other. It is expected that the findings of the GRIN microresonator may open up new research and device opportunities in photonics.

© 2014 Optical Society of America

OCIS Codes
(110.2760) Imaging systems : Gradient-index lenses
(230.3990) Optical devices : Micro-optical devices
(140.3948) Lasers and laser optics : Microcavity devices
(230.4555) Optical devices : Coupled resonators

ToC Category:
Optical Devices

Original Manuscript: June 2, 2014
Revised Manuscript: July 16, 2014
Manuscript Accepted: August 3, 2014
Published: August 29, 2014

Khalil Dadashi, Hamza Kurt, Kadir Üstün, and Ramazan Esen, "Graded index optical microresonators: analytical and numerical analyses," J. Opt. Soc. Am. B 31, 2239-2245 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003). [CrossRef]
  2. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, and A. Imamogùlu, “A quantum dot single-photon turnstile device,” Science 290, 2282–2285 (2000). [CrossRef]
  3. T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488–490 (2007). [CrossRef]
  4. V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996). [CrossRef]
  5. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007). [CrossRef]
  6. E. F. Franchimon, K. R. Hiremath, R. Stoffer, and M. 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). [CrossRef]
  7. K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk tunable resonant filters and switches,” IEEE Photon. Technol. Lett. 14, 828–830 (2002). [CrossRef]
  8. C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).
  9. R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).
  10. U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009). [CrossRef]
  11. J. Liu, R. Mendis, and D. M. Mittleman, “A Maxwell’s fish eye lens for the terahertz region,” Appl. Phys. Lett. 103, 031104 (2013). [CrossRef]
  12. U. Leonhardt and T. G. Philbin, “Perfect imaging with positive refraction in three dimensions,” Phys. Rev. A 81, 011804 (2010). [CrossRef]
  13. C. T. Tai, “Maxwell fish-eye treated by Maxwell equations,” Nature 182, 1600–1601 (1958). [CrossRef]
  14. H. Rosu and M. Reyes, “Electromagnetic modes of Maxwell fisheye lens,” Nuovo Cimento D 16, 517–522 (1994). [CrossRef]
  15. S. Liu, L. Li, Z. Lin, H. Y. Chen, J. Zi, and C. T. Chan, “Graded index photonic hole: analytical and rigorous full wave solution,” Phys. Rev. B 82, 054204 (2010). [CrossRef]
  16. E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009). [CrossRef]
  17. C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7, 902–906 (2013). [CrossRef]
  18. Y. Wang, C. Sheng, H. Liu, Y. J. Zheng, C. Zhu, S. M. Wang, and S. N. Zhu, “Transformation bending device emulated by graded-index waveguide,” Opt. Express 20, 13006–13013 (2012). [CrossRef]
  19. D. Zhu, Y. Zhou, X. Yu, P. Shum, and F. Luan, “Radially graded index whispering gallery mode resonator for penetration enhancement,” Opt. Express 20, 26285–26291 (2012). [CrossRef]
  20. T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011). [CrossRef]
  21. H. Quan and Z. Guo, “Analyses of whispering-gallery modes in small resonators,” J. Micro/Nanolith. MEMS MOEMS 8, 033060 (2009). [CrossRef]
  22. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Elsevier, 2005).
  23. A. Taflove and S. C. Hagness, Computational Electrodynamics The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  24. 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, 687–702 (2010). [CrossRef]
  25. L. Prkna, J. Ctyroky, and M. Hubalek, “Ring microresonator as a photonic structure with complex eigenfrequency,” Opt. Quantum Electron. 36, 259–269 (2004). [CrossRef]
  26. A. D. Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express 19, 5156–5162 (2011). [CrossRef]
  27. L. H. Gabrielli and M. Lipson, “Integrated Luneburg lens via ultra-strong index gradient on silicon,” Opt. Express 19, 20122–20127 (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.

Supplementary Material

» Media 1: AVI (1277 KB)     

« Previous Article

OSA is a member of CrossRef.

CrossCheck Deposited