Vol. 25, No. 12 | 12 Jun 2017 | OPTICS EXPRESS 13125 Fano resonances from coupled whispering–gallery modes in photonic molecules THANH XUAN HOANG,1,* SARA NICOLE NAGELBERG,2 MATHIAS KOLLE,2 AND GEORGE BARBASTATHIS1,2 1Singapore–MIT Alliance for Research and Technology (SMART) Centre, Singapore 138602, Singapore 2Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA *[email protected] Abstract: We present a rigorous investigation of resonant coupling between microspheres based on multipole expansions. The microspheres have diameters in the range of several micrometers and can be used to realize various photonic molecule configurations. We reveal and quantify the interactions between the whispering gallery modes inside individual microspheres and the propagation modes of the entire photonic molecule structures. We show that Fano-like resonances in photonic molecules can be engineered by tuning the coupling between the resonant and radiative modes when the structures are illuminated with simple dipole radiation. © 2017 Optical Society of America OCIS codes: (230.4555) Coupled resonators; (260.5740) Resonance; (290.4020) Mie theory; (130.2790) Guided waves. References and links 1. U. Fano,“Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d’arco,” Nuovo Cimento 12, 154–161 (1935). 2. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961). 3. H. Beutler, “Über Absorptionsserien von Argon, Krypton und Xenon zu Termen zwischen den beiden Ionisierungs- 2P0 2P0 grenzen 3 2 und 1 2,” Z. Phys. A 93, 177–196 (1935). 4. C. P. Holfeld,/ F. Loser,/ M. Sudzius, K. Leo, D. M. Whittaker, and K. Kohler, “Fano Resonances in Semiconductor Superlattices,” Phys. Rev. Lett. 81, 874–877 (1998). 5. R. A. Vicencio, J. Brand, and S. Flach, “Fano Blockade by a Bose-Einstein Condensate in an Optical Lattice,” Phys. Rev. Lett. 98, 184102 (2007). 6. H. Feshbach, “Unified Theory of Nuclear Reactions,” Ann. Phys. (N. Y.) 5, 357–390, (1958). 7. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257 (2010). 8. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. R. Soc. London 18, 269–275 (1902). 9. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999). 10. M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke , P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81, 2582–2585 (1998). 11. S. V. Boriskina, “Photonic Molecules and Spectral Engineering,” in Springer Series in Optical Sciences 156 (Springer, 2010), Chapter 16, pp. 393–421. 12. Y. P. Rakovich and J. F. Donegan, “Photonic atoms and molecules,” Laser & Photon. Rev. 4, 179–191 (2010). 13. K. Totsuka, N. Kobayashi, and M. Tomita, “Slow Light in Coupled-Resonator-Induced Transparency,” Phys. Rev. Lett. 98, 213904 (2007). 14. Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94, 203905 (2005). 15. H. J. Kimble, “The quantum internet,” Nature 453, 1023 (2008). 16. V. N. Astratov, “Fundamentals and Applications of Microsphere Resonator Circuits,” in Springer Series in Optical Sciences 156 (Springer, 2010), Chapter 17, pp. 423–457. 17. J. M. Ward, N. Dhasmana, and S. N. Chormaic, “Hollow Core, Whispering Gallery Resonator Sensors,” Eur. Phys. J. Special Topics 223, 1917–1935 (2014). 18. M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photonics 7, 168–240 (2015). 19. M. Gerlach, Y. P. Rakovich, J. F. Donegan, “Nanojets and directional emission in symmetric photonic molecules,” Opt. Express 15, 17343–13350 (2007). #284536 https://doi.org/10.1364/OE.25.013125 Journal © 2017 Received 17 Jan 2017; revised 10 May 2017; accepted 10 May 2017; published 31 May 2017 Vol. 25, No. 12 | 12 Jun 2017 | OPTICS EXPRESS 13126 20. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004). 21. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials," Phys. Rev. Lett. 101, 047401 (2008). 22. J. Sancho-Parramon and S. Bosch, “Dark modes and Fano resonances in plasmonic clusters excited by cylindrical vector beams,” ACS Nano 6, 8415–8423 (2012). 23. J. M. Gérardy, M. Ausloos, “Absorption Spectrum of Clusters of Spheres from the General Solution of Maxwell’s Equations, II. Optical Properties of Aggregated Metal Spheres,” Phys. Rev. B 25, 4204–4229 (1982). 24. G. Gouesbet and G. Grehan, Generalized Lorenz-Mie Theories (Springer, 2011). 25. D. W. Mackowski and M. I. Mishchenko, “A multiple sphere T-matrix FORTRAN code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transfer, 112, 2182–2192 (2011). 26. L. Wei, Z. Xi, N. Bhattacharya, and H. P. Urbach, “Excitation of the radiationless anapole mode,” Optica 3, 799–802 (2016). 27. D. Smirnova and Y. S. Kivshar, “Multipolar nonlinear nanophotonics,” Optica 3, 1241–1255 (2016). 28. T. X. Hoang, X. Chen, and C. J. R. Sheppard, “Multipole theory for tight focusing of polarized light, including radially polarized and other special cases,” J. Opt. Soc. Am. A 29, 32–43 (2012). 29. S. Orlov, U. Peschel, T. Bauer, and P. Banzer, “Analytical expansion of highly focused vector beams into vector spherical harmonics and its application to Mie scattering,” Phys. Rev. A 85, 063825 (2012). 30. C. G. B. Garret, W. Kaiser, and W.L. Bond, “Stimulated Emission into Optical Whispering Modes of Spheres,” Phys. Rev. 124, 1807–1809 (1961). 31. T. X. Hoang, Y. Duan, X. Chen, and G. Barbastathis, “Focusing and imaging in microsphere-based microscopy,” Opt. Express 23, 12337–12353 (2015). 32. W. J. Wiscombe, “Improved Mie Scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). 33. U. Fano and J. W. Cooper, “Line Profiles in the Far-uv Absorption Spectra of the Rare Gases,” Phys. Rev. 137, A1364 (1965). 34. Z. Chen, A. Taflove, and V. Backman, “Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres,” Opt. Lett. 31, 389–391 (2006). 35. K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991). 36. H. Miyazaki and Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bisphere,” Phys. Rev. B 62, 7976–7997 (2000). 37. S. H. Autler and C. H. Townes, “Stark Effect in Rapidly Varying Fields,” Phys. Rev. 100, 703 (1955). 38. A. Imamogluˇ and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989). 39. S. V. Boriskina, “Coupling of whispering–gallery modes in size–mismatched microdisk photonic molecules,” Opt. Lett. 32, 1557–1559 (2007). 40. 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). 41. A. V. Kanaev, V. N. Astratov, and W. Cai, “Optical coupling at a distance between detuned spherical cavities,” Appl. Phys. Lett. 88, 111111 (2006). 42. B. M. Möller, U. Woggon, and M. V. Artemyev, “Bloch modes and disorder phenomena in coupled resonator chains,” Phys. Rev. B 75, 245327 (2007). 43. L. I. Deych, C. Schmidt, A. Chipouline, T. Pertsch, and A. Tünnermann, “Optical coupling of fundamental whispering-gallery modes in bispheres,” Phys. Rev. A 77, 051801(R) (2008). 44. A. M. Kapitonov and V. N. Astratov “Observation of nanojet-induced modes with small propagation losses in chains of coupled spherical cavities,” Opt. Lett. 32, 409–411 (2007). 45. S. Yang and V. N. Astratov, “Photonic nanojet-induced modes in chains of size-disordered microspheres with an attenuation of only 0.08 dB per sphere,” Appl. Phys. Lett. 92, 261111 (2008). 46. K. W. Allen, A. Darafsheh, F. Abolmaali, N. Mojaverian, N. I. Limberopoulos, A. Lupu, and V. N. Astratov, “Microsphere-chain waveguides: Focusing and transport properties,” Appl. Phys. Lett. 105, 021112 (2014). 47. J. D. Joannopoulos, S. G. Johnson, J.N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Edition (Princeton University, 2008). 48. V. N. Astratov, J. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett. 85, 5508–5510 (2004). 49. V. N. Astratov and S. P. Ashili, “Percolation of light through whispering gallery modes in 3D lattices of coupled microspheres,” Opt. Express 15, 17351–17361 (2007). 50. C. S. Deng, H. Xu, and L. Deych, “Effect of size disorder on the optical transport in chains of coupled microspherical resonators,” Opt. Express 19, 6923–6937 (2011). 51. A. V. Maslov and V. N. Astratov, “Microspherical photonics: Sorting resonant photonic atoms by using light,” Appl. Phys. Lett. 105, 121113 (2014). 52. S. Yang and V. N. Astratov, “Spectroscopy of coherently coupled whispering–gallery modes in size–matched bispheres assembled on a substrate,” Opt. Lett. 34, 2057–2059 (2009). 53. A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk. “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016). Vol. 25, No. 12 | 12 Jun 2017 | OPTICS EXPRESS 13127 54. P. Woüniak, P. Banzer, and G. Leuchs, “Selective switching of individual multipole resonances in single dielectric nanoparticles,” Laser Photon. Rev. 9, 231–240 (2015). 55. M. Neugebauer, P. Woüniak, A. Bag, G. Leuchs, and P. Banzer, “Polarization-controlled directional scattering for nanoscopic position sensing,” Nat. Commun. 7, 11286 (2016). 56. M. Karg, T. A .F. König, M. Retsch, C. Stelling, P. M. Reichstein, T.