Skip to main content

Fundamentals and Applications of Microsphere Resonator Circuits

  • Chapter
  • First Online:
Photonic Microresonator Research and Applications

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 156))

Abstract

Dielectric microspheres, with sizes on the order of several wavelengths, support high-quality whispering gallery (WG) modes and provide nonresonant focusing of light into tiny spots termed nanoscale photonic jets. In this chapter, we review properties of more complicated multiple-cavity systems that are formed by microspheres assembled in chip-scale structures. The resonant optical properties of such systems can be engineered on the basis of tight-binding WG modes in photonic atoms. In practical systems of coupled cavities, the optical transport properties are strongly influenced by disorder effects, leading to scattering, localization, and percolation of light. The desirable tight-binding properties require selecting more uniform spheres, which can be achieved by novel methods based on using size-selective radiative pressure. Due to controllable dispersions for photons, collective emission and absorption, and enhanced light–matter coupling, such structures can be used for developing coupled arrays of microlasers, ultracompact high-resolution spectrometers, and sensors. The nonresonant properties of such systems are connected through subwavelength focusing of light in chains and arrays of microspheres that can be used in a variety of biomedical applications including ultraprecise laser tissue surgery.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ashcroft, N.W., Mermin, N.D. Solid state Physics. Saunders (1976)

    Google Scholar 

  2. Kittel, C. Introduction to solid state Physics. John Wiley and Sons, New York, 7th ed. (1996)

    Google Scholar 

  3. De Sterke, C.M. Superstructure gratings in the tight-binding approximation. Phys. Rev. E 57, 3502–3509 (1998)

    Article  Google Scholar 

  4. Stefanou, N., Modinos, A. Impurity bands in photonic insulators. Phys. Rev. B 57, 12127–12133 (1998)

    Article  Google Scholar 

  5. Lidorikis, E., Sigalas, M.M., et al. Tight-binding parametrization for photonic band gap materials. Phys. Rev. Lett. 81, 1405-1408 (1998)

    Article  Google Scholar 

  6. Yariv, A., Xu, Y., et al. Coupled-resonator optical waveguide: A proposal and analysis. Opt. Lett. 24, 711–713 (1999)

    Article  Google Scholar 

  7. Bayindir, M., Temelkuran, B., et al. Tight-binding description of the coupled defect modes in three-dimensional photonic crystals. Phys. Rev. Lett. 84, 2140–2143 (2000)

    Article  Google Scholar 

  8. Little, B.E., Chu, S.T., et al. Microring resonator channel dropping filters. J. Lightw. Tehnnol. 15, 998–1005 (1997)

    Article  Google Scholar 

  9. Heebner, J.E., Boyd, R.W., et al. SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides. J. Opt. Soc. Am. B 19, 722–731 (2002)

    Article  Google Scholar 

  10. Sumetsky, M., Eggleton, B.J. Modeling and optimization of complex photonic resonant cavity circuits. Opt. Express 11, 381–391 (2003)

    Article  Google Scholar 

  11. Smith, D.D., Chang, H., et al. Whispering-gallery mode splitting in coupled microresonators. J. Opt. Soc. Am. B 20, 1967–1974 (2003)

    Article  Google Scholar 

  12. Heebner, J.E., Chak, P., et al. Distributed and localized feedback in microresonator sequences for linear and nonlinear optics. J. Opt. Soc. Am. B 21, 1818–1832 (2004)

    Article  Google Scholar 

  13. Matsko, A.B., Savchenkov, A.A., et al. Interference effects in lossy resonator chains. J. Modern Opt. 51, 2515–2522 (2004)

    Article  MATH  Google Scholar 

  14. Deng, S., Cai, W., et al. Numerical study of light propagation via whispering gallery modes in microcylinder coupled resonator optical waveguides. Opt. Express 12, 6468–6480 (2004)

    Article  Google Scholar 

  15. Khurgin, J.B. Expanding the bandwidth of slow-light photonic devices based on coupled resonators. Opt. Lett. 30, 513–515 (2005)

    Article  Google Scholar 

  16. Boriskina, S.V., Benson, T.M., et al. Optical modes in 2-D imperfect square and triangular microcavities. IEEE J. Quant. Electron. 41, 857–862 (2005)

    Article  Google Scholar 

  17. Zhuk, V., Regelman, D.V., et al. Near-field mapping of the electromagnetic field in con-fined photon geometries. Phys. Rev. B 66, 115302 (2002)

    Article  Google Scholar 

  18. Oliver, S., Smith, C., et al. Miniband transmission in a photonic crystal coupled-resonator optical waveguide. Opt. Lett. 26, 1019–1021 (2001)

    Article  Google Scholar 

  19. Bristow, A.D., Whittaker, D.M., et al. Defect states and commensurability in dual-period AlxGa1-xAs photonic crystal waveguides. Phys. Rev. B 68, 033303 (2003)

    Article  Google Scholar 

  20. Guven, K., Ozbay, E. Coupling and phase analysis of cavity structures in two-dimensional photonic crystals. Phys. Rev. B 71, 085108 (2005)

    Article  Google Scholar 

  21. Little, B.E., Chu, S.T., et al. Very high-order microring resonator filters for WDM applications. IEEE Photon. Technol. Lett. 16, 2263–2265 (2004)

    Article  Google Scholar 

  22. Poon, J.K.S., Zhu, L., et al. Transmission and group delay of microring coupled-resonator optical waveguides. Opt. Lett. 31, 456–458 (2006)

    Article  Google Scholar 

  23. Xia, F., Sekaric, L., et al. Ultra-compact optical buffers on a silicon chip. Nat. Photon. 1, 65–71 (2007)

    Article  Google Scholar 

  24. Möller, B.M., Woggon, U., et al. Bloch modes and disorder phenomena in coupled resonator chains. Phys. Rev. B 75, 245327 (2007)

    Article  Google Scholar 

  25. Mookherjea, S., Park, J.S., et al. Localization in silicon nano-photonic slow-light waveguides. Nat. Photon. 2, 90–93 (2008)

    Article  Google Scholar 

  26. Fussell, D.P., Hughes, S., et al. Influence of fabrication disorder on the optical properties of coupled cavity photonic crystal waveguides. Phys. Rev. B 78, 144201 (2008)

    Article  Google Scholar 

  27. Choi, S.J., Peng, Z., et al. Tunable microdisk resonators vertically coupled to bus waveguides using epitaxial regrowth and wafer bonding techniques. Appl. Phys. Lett. 84, 651–653 (2004)

    Article  Google Scholar 

  28. Maune, B., Lawson, R., et al. Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers. Appl. Phys. Lett. 83, 4689–4691 (2003)

    Article  Google Scholar 

  29. Armani, D., Min, B., et al. Electrical thermo-optic tuning of ultra-high-Q microtoroid resonators. Appl. Phys. Lett. 85, 5439–5441 (2004)

    Article  Google Scholar 

  30. For a review see articles in Chang, R.K., Campillo, A.J. Optical Processes in Micro-cavities. World Scientific, Singapore (1996)

    Google Scholar 

  31. Benner, R.E., Barber, P.W., et al. Observation of structure resonances in the fluorescence spectra from microspheres. Phys. Rev. Lett. 44, 475–478 (1980)

    Article  Google Scholar 

  32. Gorodetsky, M.L., Savchenkov, A.A., et al. Ultimate Q of optical micro-sphere resonators. Opt. Lett. 21, 453–455 (1996)

    Article  Google Scholar 

  33. Vahala, K.J. Optical microcavities. Nature 424, 839–846 (2003)

    Article  Google Scholar 

  34. For a recent review see: Matsko, A.B., Ilchenko, V.S. Optical resonators with whispering gallery modes – part I: Basics. IEEE J. Sel. Top. Quant. Electron. 12, 3–14 (2006)

    Google Scholar 

  35. For a recent review see: Ilchenko, V.S., Matsko, A.B. Optical resonators with whisper-ing-gallery modes – part II: Applications. IEEE J. Sel. Top. Quant. Electron. 12, 15–32 (2006)

    Google Scholar 

  36. http://www.thermofisher.com/global/en/home.asp. Assessed 22 August 2009.

  37. http://www.bangslabs.com/products/nist_traceable_particle_size_standards. Assessed 22 August 2009.

  38. http://www.polysciences.com/. Assessed 22 August 2009.

  39. http://www.microspheres-nanospheres.com/. Assessed 22 August 2009.

  40. Serpengüzel, A., Kurt, A., et al. Silicon microspheres for electronic and photonic integration. Photonics and Nanostructures – Fundamentals and Applications 6, 179–182 (2008)

    Article  Google Scholar 

  41. Fuller, K.A. Optical resonances and two-sphere systems. Appl. Optics 30, 4716 (1991)

    Article  Google Scholar 

  42. Mukaiyama, T., Takeda, K., et al. Tight-binding photonic molecule modes of resonant biospheres. Phys. Rev. Lett. 82, 4623–4626 (1999)

    Article  Google Scholar 

  43. Miyazaki, H., Jimba, Y. Ab initio tight-binding description of morphology-dependent resonance in a biosphere. Phys. Rev. B 62, 7976–7997 (2000)

    Article  Google Scholar 

  44. Hara Y., Mukaiyama, T., et al. Photonic molecule lasing. Opt. Lett. 28, 2437–2439 (2003)

    Article  Google Scholar 

  45. Möller, B.M., Woggon, U., et al. Photonic molecules doped with semiconductor nanocrystals. Phys. Rev. B 70, 115323 (2004)

    Article  Google Scholar 

  46. Rakovich, Y.P., Donegan, J.F., et al. Fine structure of coupled optical modes in photonic molecules. Phys. Rev. A 70, 051801 (2004)

    Article  Google Scholar 

  47. Kanaev, A.V., Astratov, V.N., et al. Optical coupling at a distance between detuned spherical cavities. Appl. Phys. Lett. 88, 111111 (2006)

    Article  Google Scholar 

  48. Ashili, S.P., Astratov, V.N., et al. The effects of inter-cavity separation on optical coupling in dielectric biospheres. Opt. Express 14, 9460–9466 (2006)

    Article  Google Scholar 

  49. Deych, L.I., Schmidt, C., et al. Optical coupling of fundamental whispering-gallery modes in bispheres. Phys. Rev. A 77, 051801(R) (2008)

    Article  Google Scholar 

  50. Barnes, M.D., Mahurin, S.M., et al. Three-dimensional photonic “molecules” from sequentially attached polymer-blend microparticles. Phys. Rev. Lett. 88, 015508 (2002)

    Article  Google Scholar 

  51. Furukawa, H., Tenjimbayashi, K. Light propagation in periodic microcavities. Appl. Phys. Lett. 80, 192–194 (2002)

    Article  Google Scholar 

  52. Astratov, V.N., Franchak, J.P., et al. Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder. Appl. Phys. Lett. 85, 5508–5510 (2004)

    Article  Google Scholar 

  53. Hara, Y., Mukaiyama, T., et al. Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres. Phys. Rev. Lett. 94, 203905 (2005)

    Article  Google Scholar 

  54. Möller, B.M., Woggon, U., et al. Coupled-resonator optical waveguides doped with nanocrystals. Opt. Lett. 30, 2116–2118 (2005)

    Article  Google Scholar 

  55. Chen, Z., Taflove, A., et al. Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres. Opt. Lett. 31, 389–391 (2006)

    Article  Google Scholar 

  56. Deych, L.I., Roslyak, O. Photonic band mixing in linear chains of optically coupled microspheres. Phys. Rev. E 73, 036606 (2006)

    Article  Google Scholar 

  57. Kapitonov, A.M., Astratov, V.N. Observation of nanojet-inducing modes with small propagation losses in chains of coupled spherical cavities. Opt. Lett. 32, 409–411 (2007)

    Article  Google Scholar 

  58. Yang, S., Astratov, V.N. Photonic nanojet-induced modes in chains of size-disordered microspheres with an attenuation of only 0.08dB per sphere. Appl. Phys. Lett. 92, 261111 (2008)

    Article  Google Scholar 

  59. Mitsui, T., Wakayama, Y., et al. Light propagation within colloidal crystal wire fabricated by a dewetting process. Nano Lett. 8, 853–858 (2008)

    Article  Google Scholar 

  60. Mitsui, T., Wakayama, Y., et al. Observation of light propagation across a 900 corner in chains of microspheres on a patterned substrate. Opt. Lett. 33, 1189–1191 (2008)

    Article  Google Scholar 

  61. Kondo, T., Hangyo, M., et al. Transmission characteristics of a two-dimensional photonic crystal array of dielectric spheres us-ing subterahertz time domain spectroscopy. Phys. Rev. B 66, 033111 (2002)

    Article  Google Scholar 

  62. Gerlach, M., Rakovich, Y.P., et al. Nanojets and directional emission in sym-metric photonic molecules. Opt. Express 15, 17343–17350 (2007)

    Article  Google Scholar 

  63. Guo, H., Chen, H., et al. Transmission modulation in the passband of polystyrene photonic crystals. Appl. Phys. Lett. 82, 373–375 (2003)

    Article  Google Scholar 

  64. Astratov, V.N., Ashili, S.P. Percolation of light through whispering gallery modes in 3D lattices of coupled microspheres. Opt. Express 15, 17351–17361 (2007)

    Article  Google Scholar 

  65. Yang, S., Astratov, V.N. Spectroscopy of coherently coupled whispering-gallery modes in size-matched bispheres assembled on a substrate. Opt. Lett. 34, 2057–2059 (2009)

    Article  Google Scholar 

  66. Yang, S., Astratov, V.N. Spectroscopy of photonic molecular states in supermonodispersive biospheres. Published in Laser Resonators and Beam Control XI. In: Ku-dryashov, A.V., Paxton, A.H., Ilchenko, V.S., Aschke, L. Proc. of SPIE, Vol. 7194, paper 719411-1, Photonics West 2009, San Jose, January 24–29, 9 pp.

    Google Scholar 

  67. Ng, J., Chan, C.T. Size-selective optical forces for microspheres using evanescent wave excitation of whispering gallery modes. Appl. Phys. Lett. 92, 251109 (2008)

    Article  Google Scholar 

  68. Xiao, J.J., Ng, J., et al. Whispering gallery mode enhanced optical force with resonant tunneling excitation in the Kretschmann geometry. Appl. Phys. Lett. 94, 011102 (2009)

    Article  Google Scholar 

  69. Vyawahare, S., Craig, K.M., et al. Patterning lines by capillary flows. Nano Lett. 6, 271–276 (2006)

    Article  Google Scholar 

  70. Suh, K.Y. Surface-tension-driven patterning: combining tailored physical self-organization with microfabrication methods. Small 2, 832–834 (2006)

    Article  Google Scholar 

  71. Yin, Y., Lu, Y., et al. Template-assisted self-assembly: a practical route to complex aggregates of monodispersed colloids with well-defined sizes, shapes, and structures. J. Am. Chem. Soc. 123, 8718–9729 (2001)

    Article  Google Scholar 

  72. Ozin, G.A., Yang, S.M. The race for the photonic chip: colloidal crystal assembly in silicon wafers. Adv. Funct. Mater. 11, 95–104 (2001)

    Article  Google Scholar 

  73. Gates, B., Qin, D., et al. Assembly of nanoparticles into opaline structures over large areas. Adv. Mater. 11, 466–469 (1999)

    Article  Google Scholar 

  74. Curtis, J.E., Koss, B.A., et al. Dynamic holographic optical tweezers. Opt. Comm. 207, 169–175 (2002)

    Article  Google Scholar 

  75. Sinclair, G., Jordan, P., et al. Assembly of 3-dimensional structures using programmable holographic optical tweezers. Opt. Express 12, 5475–5480 (2004)

    Article  Google Scholar 

  76. Roichman, Y., Grier, D.G. Holographic assembly of quasicrystalline photonic het-erostructures, Opt. Express 13, 5434–5439 (2005)

    Article  Google Scholar 

  77. White, G., Gibson, G., et al. An optical trapped microhand for manipulating micron-sized objects. Opt. Express 14, 12497–12502 (2006)

    Article  Google Scholar 

  78. Erenso, D., Shulman, A., et al. Formation of synthetic structures with micron size silica beads using optical tweezers. J. Mod. Opt. 207, 169–175 (2002)

    Google Scholar 

  79. Benito, D.C., Carberry, D.M., et al. Constructing 3D crystal templates for photonic band gap materials using holographic optical tweezers. Opt. Express 16, 13005–13015 (2008)

    Article  Google Scholar 

  80. Chiou, P.Y., Ohta, A.T., et al. Massively parallel manipulation of single cells and microparticles using optical images. Nature 436, 370–372 (2005)

    Article  Google Scholar 

  81. Garcia-Santamaria, F., Miyazaki, H.T., et al. Nanorobotic manipulation of microspheres for on-chip diamond architectures. Adv. Mater. 14, 1144–1147 (2002)

    Article  Google Scholar 

  82. Lorenz, C.D., Ziff, R.M. Precise determination of the bond percolation thresholds in finite-size scaling corrections for the sc, fcc, and bcc lattices. Phys. Rev. E 57, 230–236 (1998)

    Article  Google Scholar 

  83. For a review on complex networks see: Albert, R., Barabasi, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)

    Google Scholar 

  84. Burlak, G., Diaz-de-Anda, A., et al. Critical behavior of nanoemitter radiation in a percolation material. Phys. Lett. A 373, 1492–1499 (2009)

    Article  Google Scholar 

  85. Burlak, G., Vlasova, M., et al. Optical percolation in ceramics assisted by porous clusters. Opt. Comm. 282, 2850–2856 (2009)

    Article  Google Scholar 

  86. Chen, Z., Taflove, A., et al. Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique. Opt. Express 12, 1214–1220 (2004).

    Article  Google Scholar 

  87. Li, X., Chen, Z., et al. Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets. Opt. Express 13, 526–533 (2005)

    Article  Google Scholar 

  88. Lecler, S., Takakura, Y., et al. Properties of a three-dimensional photonic jet. Opt. Lett. 30, 2641–2643 (2005)

    Article  Google Scholar 

  89. Itagi, A.V., Challener, W.A. Optics of photonic nanojets. J. Opt. Soc. Am. A 22, 2847–2858 (2005)

    Article  Google Scholar 

  90. Heifetz, A., Huang, K., et al. Experimental confirmation of backscattering enhancement induced by a photonic jet. Appl. Phys. Lett. 89, 221118 (2006).

    Article  Google Scholar 

  91. Ferrand, P., Wenger, J., et al. Direct imaging of photonic nanojets. Opt. Express 16, 6930–6940 (2008)

    Article  Google Scholar 

  92. Kong, S.-C., Sahakian, A., et al. Photonic nanojet-enabled optical data storage, Opt. Express 16, 13713–13719 (2008)

    Article  Google Scholar 

  93. Schweiger, G., Nett, R., et al. Microresonator array for high-resolution spectroscopy. Opt. Lett. 32, 2644–2646 (2007)

    Article  Google Scholar 

  94. Francois, A., Himmelhaus, M. Optical biosensor based on whispering gallery mode excitations in clusters of microparticles. Appl. Phys. Lett. 92, 141107 (2008)

    Article  Google Scholar 

  95. Guzatov, D.V., Woggon, U. Coupled microsphere clusters for detecting molecule’s dipole moment orientation. Appl. Phys. Lett. 94, 241104 (2009)

    Article  Google Scholar 

  96. Vollmer, F., Braun, D., et al. Protein detection by optical shift of a resonant microcavity. Appl. Phys. Lett. 80, 4057–4059 (2002)

    Article  Google Scholar 

  97. Teraoka, I., Arnold, S. Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications. J. Opt. Soc. Am. B 23, 1381–1389 (2006)

    Article  Google Scholar 

  98. Armani, A.M., Kulkarni, R.P., et al. Label-free, single-molecule detection with optical microcavities. Science 317, 783–787 (2007)

    Article  Google Scholar 

  99. Hiremath, K.R., Astratov, V.N. Perturbations of whispering gallery modes by nanoparticles embedded in microcavities. Opt. Express 16, 5421–5426 (2008)

    Article  Google Scholar 

  100. Lutti, J., Langbein, W., et al. A monolithic optical sensor based on whispering-gallery modes in polystyrene microspheres. Appl. Phys. Lett. 93, 151103 (2008)

    Article  Google Scholar 

  101. Pang, S., Beckham, R.E., et al. Quantum dot-embedded microspheres for remote refractive index sensing. Appl. Phys. Lett. 92, 221108 (2008)

    Article  Google Scholar 

  102. Teraoka, I., Arnold, S. Resonance shifts of counterpropagating whispering-gallery modes: degenerate perturbation theory and application to resonator sensors with axial symmetry. J. Opt. Soc. of Am. B 26, 1321–1329 (2009)

    Article  Google Scholar 

  103. Astratov, V.N. Fundamentals and applications of microsphere resonator circuits. Proceedings of 11th International Conference on Transparent Optical Networks, Azores, June 28-July 2, 1–4 (2009)

    Google Scholar 

  104. Le Thomas, N., Woggon, U., et al. Effect of a dielectric substrate on whispering-gallery-mode sensors. J. Opt. Soc. Am. B 23, 2361–2365 (2006)

    Article  Google Scholar 

  105. Buck, J.R., Kimble, H.J. Optimal sizes of dielectric microspheres for cavity QED with strong coupling. Phys. Rev. A 67, 033806 (2003)

    Google Scholar 

  106. Chang, R.K., Campillo, A.J. Optical processes in microcavities. World Scientific, Singapore (1996)

    Google Scholar 

  107. van de Hulst, H.C. Light scattering by small particles. Wiley, New York (1981)

    Google Scholar 

  108. Lam, C.C., Leung, P.T., et al. Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering. J. Opt. Soc. Am. B 9, 1585–1592 (1992)

    Article  Google Scholar 

  109. Arnaud, C., Boustimi, M., et al. Wavelength shifts in erbium doped glass micro-spherical whispering gallery mode lasers. Proceedings of the International Workshop on Photonics and Applications, Hanoi, Vietnam, 209–220 (2004)

    Google Scholar 

  110. Braginsky, V.B., Gorodetsky, M.L., et al. Quality-factor and nonlinear properties of optical whispering gallery modes. Phys. Lett. A 137, 393–397 (1989)

    Article  Google Scholar 

  111. Ilchenko V.S., Volkov P.S., et al. Strain-tunable high-Q optical microsphere resonator. Opt. Comm. 145, 86–90 (1998)

    Article  Google Scholar 

  112. Gerlach, M., Rakovich, Y.P., et al. Radiation-pressure-induced mode splitting in a spherical microcavity with an elastic shell. Opt. Express 15, 3597–3606 (2007)

    Article  Google Scholar 

  113. Quake, S.R., Scherer, A. From micro- to nanofabrication with soft materials. Science 290, 1536–1540 (2000)

    Article  Google Scholar 

  114. Psaltis, D., Quake, S.R., et al. Developing optofluidic technology through the fusion of microfluidic and optics. Nature 442, 381–386 (2006)

    Article  Google Scholar 

  115. Astratov, V.N., Bogomolov, V.N., et al. Optical spectroscopy of opal matrices with CdS embedded in its pores: quantum confinement and photonic band gap effects. Nuovo Ci-mento D 17, 1349–1354 (1995)

    Article  Google Scholar 

  116. Astratov, V.N., Vlasov, Y.A., et al. Photonic band gaps in 3D ordered FCC silica matrices. Phys. Lett. A 222, 349–353 (1996)

    Article  Google Scholar 

  117. Vlasov, Y.A., Astratov, V.N., et al. Manifestation of intrinsic defects in the optical properties of self-organized opal photonic crystals. Phys. Rev. E 61, 5784–5793 (2000)

    Article  Google Scholar 

  118. Astratov, V.N., Adawi, A.M., et al. Interplay of order and disorder in the optical properties of opal photonic crystals. Phys. Rev. B 66, 165215 (2002)

    Article  Google Scholar 

  119. Denkov, N., Velev, O., et al. Two-dimensional crystallization. Nature (London) 361, 26 (1993)

    Article  Google Scholar 

  120. Bertone, J.F., Jiang, P., et al. Thickness dependence of the optical properties of ordered silica-air and air-polymer photonic crystals. Phys. Rev. Lett. 83, 300–303 (1999)

    Article  Google Scholar 

  121. van Blaaderen, A., Ruel, R., et al. Template-directed colloidal crystallization, Nature (London) 385, 321–324 (1997)

    Article  Google Scholar 

  122. Lin, K.-h., Crocker, J.C., et al. Entropically driven colloidal crystallization on patterned substrates. Phys. Rev. Lett. 85, 1770–1773 (2000)

    Article  Google Scholar 

  123. Yang, S.M., Miguez, H., et al. Opal circuits of light – planarized micophotonic crystal chips. Adv. Funct. Mater. 12, 425–431 (2002)

    Article  Google Scholar 

  124. Möller, B.M., Artemyev, M.V., et al. Bloch modes and group velocity delay in coupled resonator chains. Phys. Stat. Sol. (a) 204, 3636–3646 (2007)

    Article  Google Scholar 

  125. Ashkin, A., Dziedzic, J.M., et al. Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 11, 288–290 (1986)

    Article  Google Scholar 

  126. Grier, D.G. A revolution in optical manipulation. Nature 124, 810–816 (2003)

    Article  Google Scholar 

  127. Curtis, J.E., Koss, B.A., et al. Dynamic holographic optical tweezers. Opt. Commun. 207, 169–175 (2002)

    Google Scholar 

  128. Armitage, A., Skolnick, M.S., et al. Optically induced splitting of bright excitonic states in coupled quantum microcavities. Phys. Rev. B. 57, 14877–14881 (1998)

    Article  Google Scholar 

  129. Atlasov, K.A., Karlsson, K.F., et al. Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities. Opt. Express 16, 16255–16264 (2008)

    Article  Google Scholar 

  130. Ryu, J.-W., Lee, S.-Y., et al. Directional interacting whispering-gallery modes in coupled dielectric microdisks. Phys. Rev. A 74, 013804 (2006)

    Article  Google Scholar 

  131. Boriskina, S.V. Theoretical prediction of a dramatic Q-factor enhancement and de-generacy removal of whispering gallery modes in symmetrical photonic molecules. Opt. Lett. 31, 338–340 (2006)

    Article  Google Scholar 

  132. Chremmos, I., Uzunoglu, N. Modes of the infinite square lattice of coupled microring resonators. J. Opt. Soc. Am. A 25, 3043–3050 (2008)

    Article  Google Scholar 

  133. Schwefel, H.G.L., Poulton, C.G. An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane. Opt. Express 17, 13178–13186 (2009)

    Article  Google Scholar 

  134. Yang, S. Ph.D. thesis entitled “Spectroscopic study of optical confinement and transport effects in coupled microspheres and pillar cavities.” University of North Carolina at Charlotte (2009)

    Google Scholar 

  135. Spreeuw, R.J.C., Beijersbergen, M.W., et al. Optical ring cavities as tailored four-level systems: An application of the group U (2,2). Phys. Rev. A 45, 1213–1229 (1992)

    Article  Google Scholar 

  136. Kavokin, A.V., Baumberg, J.J., et al. Microcavities. Oxford University Press Inc., New York (2007)

    Book  Google Scholar 

  137. Weisbuch, C., Nishioka, M., et al. Observation of coupled exciton–photon mode splitting in a semiconductor quantum microcavity. Phys. Rev. Lett. 69, 3314–3317 (1992)

    Article  Google Scholar 

  138. Whittaker, D.M., Kinsler, P., et al. Motional narrowing in semiconductor microcavities. Phys. Rev. Lett. 77, 4792–4795 (1996)

    Article  Google Scholar 

  139. Sermage, B., Long, S., et al. Time-resolved spontaneous emission of excitons in a microcavity: Behavior of the individual exciton-photon mixed states. Phys. Rev. B 53, 16516–16523 (1996)

    Article  Google Scholar 

  140. Heiss, W.D. Repulsion of resonance states and exceptional points. Phys. Rev. E 61, 929–932 (2000)

    Article  Google Scholar 

  141. Wiersig, J. Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities. Phys. Rev. Lett. 97, 253901 (2006)

    Article  Google Scholar 

  142. Boriskina, S.V. Coupling of whispering-gallery modes in size mismatched microdisk photonic molecules. Opt. Lett. 32, 1557–1559 (2007)

    Article  Google Scholar 

  143. Ryu, J.-W., Lee, S.-Y., et al. Coupled nonidentical microdisks: Avoided crossing of energy levels and unidirectional far-field emission. Phys. Rev. A 79, 053858 (2009)

    Article  Google Scholar 

  144. Nakagawa, A., Ishii, S., et al. Photonic molecule laser composed of GaInAsP microdisks. Appl. Phys. Lett. 86, 041112 (2005)

    Article  Google Scholar 

  145. Benyoucef, M., Kiravittaya, S., et al. Strongly cou-pled semiconductor microcavities: A route to couple artificial atoms over micrometric distances. Phys. Rev. B 77, 035108 (2008)

    Article  Google Scholar 

  146. Fano, U. Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124, 1866–1878 (1961)

    Article  MATH  Google Scholar 

  147. Astratov, V.N., Whittaker, D.M., et al. Photonic Band Structure Effects in the Reflectivity of Periodically Patterned Waveguides. Phys. Rev. B 60, R16255–R16258 (1999)

    Article  Google Scholar 

  148. Fan, S. Sharp asymmetric line shapes in side-coupled waveguide-cavity systems. Appl. Phys. Lett. 80, 908–910 (2002)

    Article  Google Scholar 

  149. Hecht, E. Optics (4th ed.). Pearson Education, Inc., San Francisco, CA, USA (2002).

    Google Scholar 

  150. Mosbacher, M., Münzer, H.-J., et al. Optical field enhancement effects in laser-assisted particle removal. Appl. Phys. A: Mater. Sci. Process. 72, 41–44 (2001)

    Article  Google Scholar 

  151. Piglmayer, K., Denk, R., et al. Laser-induced surface patterning by means of microspheres. Appl. Phys. Lett. 80, 4693–4695 (2002)

    Article  Google Scholar 

  152. Luk’yanchuk, B.S., Arnold, N., et al. Three-dimensional effects in dry laser cleaning. Appl. Phys. A: Mater. Sci. Process. 77, 209–215 (2003)

    Google Scholar 

  153. Luk’yanchuk, B.S., Wang, Z.B., et al. Particle on surface: 3D-effects in dry laser cleaning. Appl. Phys. A: Mater. Sci. Process. 79, 747–751 (2004)

    Article  Google Scholar 

  154. Zhou, Y., Hong, M.H., et al. Direct femtosecond laser nanopatterning of glass substrate by particle-assisted near-field enhancement. Appl. Phys. Lett. 88, 023110 (2006)

    Article  Google Scholar 

  155. Ferrari, C., Morichetti, F., et al. Disorder in coupled-resonator optical wave-guides. J. Opt. Soc. Am. B 26, 858–866 (2009)

    Article  Google Scholar 

  156. Kippenberg, T.J., Vahala, K.J. Cavity opto-mechanics, Opt. Express 15, 17172–17205 (2007)

    Article  Google Scholar 

  157. Li, M., Pernice, W.H.P., et al. Harnessing optical forces in integrated photonic circuits. Nature 456, 480–484 (2008)

    Article  Google Scholar 

  158. Camacho, R.M., Chan, J., et al. Characterization of radiation pressure and thermal effects in a nanoscale optomechanical cavity. Opt. Express 17, 15726–15735 (2009)

    Article  Google Scholar 

  159. Mellor, C.D., Bain, C.D. Array formation in evanescent waves. ChemPhysChem 7, 329–332 (2006).

    Article  Google Scholar 

  160. Povinelli, M.L., Johnson, S.G., et al. High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery-mode resonators. Opt. Express 13, 8286–8295 (2005)

    Article  Google Scholar 

  161. Ishii, S., Baba, T. Bistable lasing in twin microdisk photonic molecules. Appl. Phys. Lett. 87, 181102 (2005)

    Article  Google Scholar 

  162. Altug, H., Vuckovic, J. Photonic crystal nanocavity array laser. Opt. Express. 13, 8819–8828 (2005)

    Article  Google Scholar 

  163. Gourley, P.L, Warren, M.E., et al. Coherent beams from high efficiency two-dimensional surface-emitting semiconductor laser arrays. Appl. Phys. Lett. 58, 890–892 (1991).

    Article  Google Scholar 

  164. Serkland, D.K., Choquette, K.D., et al. Two-element phased array of antiguided vertical-cavity lasers. Appl. Phys. Lett. 75, 3754–3756 (1999)

    Article  Google Scholar 

  165. Raftery, J.J., Jr., Lehman, A.C., et al. In-phase evanescent coupling of two-dimensional arrays of defect cavities in photonic crystal vertical cavity surface emitting lasers. Appl. Phys. Lett. 89, 081119 (2006)

    Article  Google Scholar 

  166. Schwelb, O. Band-Limited optical mirrors based on ring resonators: Analysis and design. J. Lightw. Technol. 23, 3931–3946 (2005)

    Article  Google Scholar 

  167. Chremmos, I., Schwelb, O. Optimization, bandwidth and the effect of loss on the characteristics of the coupled ring reflector. Opt. Comm. 282 3712–3719 (2009)

    Article  Google Scholar 

  168. Morichetti, F., Melloni, A., et al. Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line. Opt. Express 16, 8395–8405 (2008)

    Article  Google Scholar 

  169. Matsko, A.B., Savchenkov, A.A., et al. Collective emission and absorption in a linear resonator chain. Opt. Express 17,15210–15215 (2009)

    Article  Google Scholar 

  170. Smith, D.D., Chang, H., et al. Coupled-resonator-induced transparency. Phys. Rev. A 69, 063804 (2004)

    Article  Google Scholar 

  171. Matsko, A.B., Savchenkov, A.A., et al. Interference effects in lossy resonator chains. J. Mod. Opt. 51, 2515–2522 (2004)

    Article  MATH  Google Scholar 

  172. Naweed, A., Farca, G., et al. Induced transparency and absorption in coupled whispering-gallery microresonators. Phys. Rev. A 71, 043804 (2005)

    Article  Google Scholar 

  173. Xu, Q., Sandhu, S., et al. Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency. Phys. Rev. Lett. 96, 129901 (2006)

    Article  Google Scholar 

  174. Ivchenko, E.L., Nesvizhskii, A.I., et al. Bragg reflection of light from quantum-well structures. Phys. Solid State 36, 1156–1161 (1994).

    Google Scholar 

  175. Hubner, M., Prineas, J.P., et al. Optical lattices achieved by excitons in periodic quantum well structures. Phys. Rev. Lett. 83, 2841–2844 (1999)

    Article  Google Scholar 

  176. Xu, Z.C., Wang, Z.L., et al. Multimodal multiplex spectroscopy using photonic crystals. Opt. Express 11, 2126–2133 (2004)

    Article  Google Scholar 

  177. Yi, K.J., Wang, H., et al. Enhanced Raman scattering by self-assembled silica spherical microparticles. J. Appl. Phys. 101, 063528 (2007)

    Article  Google Scholar 

  178. Kasim, J., Ting, Y., et al. Near-field Raman imaging using optically trapped dielectric microsphere. Opt. Express 16, 7976–7984 (2008)

    Article  Google Scholar 

  179. McLeod, E., Arnold, C.B. Subwavelength direct-write nanopatterning using optically trapped microspheres. Nature Nanotech. 3, 413–417 (2008)

    Article  Google Scholar 

  180. Chremmos, I., Uzunoglu, N.K. Analysis of scattering by a linear chain of spherical inclusions in an optical fiber. J. Opt. Soc. Am. A 23, 3054–3062 (2006)

    Article  MathSciNet  Google Scholar 

  181. Cai, M., Painter, O., et al. Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system, Phys. Rev. Lett. 85, 74–76 (2000)

    Article  Google Scholar 

  182. Di Falco, A., Conti, C., et al. Impedance matching in photonic crystal micro-cavities for second-harmonic generation. Opt. Lett. 31, 250–253 (2006)

    Article  Google Scholar 

  183. Preble, S., Xu, Q., et al. Changing the colour of light in a silicon resonator, Nat. Photon. 1, 293–296 (2007)

    Article  Google Scholar 

Download references

Acknowledgments

The author would like to thank S.V. Boriskina, A.B. Matsko, M. Sumetsky, U. Woggon, A. Taflove, S. Arnold, A. Melloni, Y.A. Vlasov, M.S. Skolnick, J.J. Baumberg, and M.A. Fiddy for useful discussions. The author thanks M.D. Kerr and R. Hudgins for a critical reading of the manuscript and useful comments. This work was supported by the US Army Research Office (ARO) under grant No. W911NF-09-1-0450 (J.T. Prater), by the National Science Foundation (NSF) under grant ECCS-0824067, and, in part, by funds provided by The University of North Carolina at Charlotte.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vasily N. Astratov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag US

About this chapter

Cite this chapter

Astratov, V.N. (2010). Fundamentals and Applications of Microsphere Resonator Circuits. In: Chremmos, I., Schwelb, O., Uzunoglu, N. (eds) Photonic Microresonator Research and Applications. Springer Series in Optical Sciences, vol 156. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1744-7_17

Download citation

Publish with us

Policies and ethics