Abstract

We report on coupling of two whispering gallery mode resonators in the Terahertz frequency range. Due to the long wavelength in the millimeter to submillimeter range, the resonators can be macroscopic allowing for accurate size and shape control. This is necessary to couple specific modes of two or more resonators. Sets of polyethylene (PE) and quartz disk resonators are demonstrated, with medium (loaded) quality (Q)-factors of 40-800. Both exhibit coinciding resonance frequency spectra over more than ten times the free spectral range. Loading effects of single resonators are investigated which provide strong Q-factor degradation and red-shifts of the resonances in the 0.2% range. By coupling two resonators of the same size, we observe mode splitting, in very good agreement with our numerical calculations.

© 2008 Optical Society of America

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2008 (1)

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, "Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances," Phys. Rev. B 77, 035108 (2008).
[CrossRef]

2007 (3)

H. E. Tureci and H. G. L. Schwefel, "An efficient Fredholm method for the calculation of highly excited states of billiards," J. Phys. A 40, 13869-13882 (2007).
[CrossRef]

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

T. Carmon, S. Y. T. Wang, E. P. Ostby, and K. J. Vahala, "Wavelength-independent coupler from fiber to an on-chip cavity, demonstrated over an 850nm span," Opt. Express 15, 7677-7681 (2007).
[CrossRef] [PubMed]

2006 (4)

A. Matsko and V. Ilchenko, "Optical resonators with whispering-gallery modes-part I: basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. Ilchenko and A. Matsko, "Optical resonators with whispering-gallery modes-part II: applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

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] [PubMed]

S. P. Ashili, V. N. Astratov, and E. C. H. Sykes, "The effects of inter-cavity separation on optical coupling in dielectric bispheres," Opt. Express 14, 9460-9466 (2006).
[CrossRef] [PubMed]

2005 (5)

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71, 043804 (2005).
[CrossRef]

I. Chremmos and N. Uzunoglu, "Reflective properties of double-ring resonator system coupled to a waveguide," IEEE Photon. Technol. Lett. 17, 2110-2112 (2005).
[CrossRef]

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

M. L. Povinelli, S. G. Johnson, M. Lonear, M. Ibanescu, E. J. Smythe, F. Capasso, J. D. Joannopoulos, "High-Q enhancement of attractive and repulsive optical forces between coupled whispering gallery mode resonators," Opt. Express 13, 8286-8295 (2005)
[CrossRef] [PubMed]

H. E. Tureci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, "Modes of wave-chaotic dielectric resonators," Prog. Opt. 47, 75-137 (2005).
[CrossRef]

2004 (1)

2003 (2)

2002 (1)

2000 (1)

K. Pance, L. Viola, and S. Sridhar, "Tunneling proximity resonances: interplay between symmetry and dissipation," Phys. Lett. A 268, 399-405 (2000).
[CrossRef]

1999 (3)

1998 (1)

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

1997 (1)

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, "Whispering gallery modes in a dielectric resonator: Characterization at millimeter wavelength," IEEE Trans. Microwave Theory Tech. 45, 2025 (1997).
[CrossRef]

1994 (1)

K. Lo, R. McPhedran, I. Bassett, and G. Milton, "An electromagnetic theory of dielectric waveguides with multiple embedded cylinders," J. Lightwave Technol. 12, 396-410 (1994).
[CrossRef]

1991 (1)

1990 (1)

D. Cross and P. Guillon, "Whispering gallery dielectric resonator modes for W-band-devices," IEEE Trans. Microwave Theory Tech. 38, 1667-1673 (1990).
[CrossRef]

1987 (1)

X. H. Jiao, P. Guillon, L. A. Bermudez, and P. Auxemery, "Whispering-gallery modes of dielectric structures: Applications to millimeter-wave bandstop filters," IEEE Trans. Microwave Theory Tech. 35, 1169-1175 (1987).
[CrossRef]

1967 (1)

J. R. Wait, "Electromagnetic whispering gallery modes in a dielectric rod," Radio Sci. 2, 1005 (1967).

Annino, G.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, "Whispering gallery modes in a dielectric resonator: Characterization at millimeter wavelength," IEEE Trans. Microwave Theory Tech. 45, 2025 (1997).
[CrossRef]

Ashili, S. P.

Astratov, V. N.

Auxemery, P.

X. H. Jiao, P. Guillon, L. A. Bermudez, and P. Auxemery, "Whispering-gallery modes of dielectric structures: Applications to millimeter-wave bandstop filters," IEEE Trans. Microwave Theory Tech. 35, 1169-1175 (1987).
[CrossRef]

Bassett, I.

K. Lo, R. McPhedran, I. Bassett, and G. Milton, "An electromagnetic theory of dielectric waveguides with multiple embedded cylinders," J. Lightwave Technol. 12, 396-410 (1994).
[CrossRef]

Bayer, M.

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

Benech, P.

Benyoucef, M.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, "Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances," Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Bermudez, L. A.

X. H. Jiao, P. Guillon, L. A. Bermudez, and P. Auxemery, "Whispering-gallery modes of dielectric structures: Applications to millimeter-wave bandstop filters," IEEE Trans. Microwave Theory Tech. 35, 1169-1175 (1987).
[CrossRef]

Boriskina, S. V.

Botten, L. C.

Brown, E. R.

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

Capasso, F.

Carmon, T.

Cassettari, M.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, "Whispering gallery modes in a dielectric resonator: Characterization at millimeter wavelength," IEEE Trans. Microwave Theory Tech. 45, 2025 (1997).
[CrossRef]

Chang, H.

Chremmos, I.

I. Chremmos and N. Uzunoglu, "Reflective properties of double-ring resonator system coupled to a waveguide," IEEE Photon. Technol. Lett. 17, 2110-2112 (2005).
[CrossRef]

Cross, D.

D. Cross and P. Guillon, "Whispering gallery dielectric resonator modes for W-band-devices," IEEE Trans. Microwave Theory Tech. 38, 1667-1673 (1990).
[CrossRef]

D¨ohler, G. H.

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

de Sterke, C. M.

Desieres, Y.

Dohler, G. H.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Dremin, A. A.

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

Driscoll, D.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Eckardt, M.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Farca, G.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71, 043804 (2005).
[CrossRef]

Forchel, A.

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

Fuller, K. A.

Gorodetsky, M. L.

Gossard, A.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Gossard, A. C.

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

Guillon, P.

D. Cross and P. Guillon, "Whispering gallery dielectric resonator modes for W-band-devices," IEEE Trans. Microwave Theory Tech. 38, 1667-1673 (1990).
[CrossRef]

X. H. Jiao, P. Guillon, L. A. Bermudez, and P. Auxemery, "Whispering-gallery modes of dielectric structures: Applications to millimeter-wave bandstop filters," IEEE Trans. Microwave Theory Tech. 35, 1169-1175 (1987).
[CrossRef]

Gutbrod, T.

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

Hanson, M.

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Ibanescu, M.

Ilchenko, V.

A. Matsko and V. Ilchenko, "Optical resonators with whispering-gallery modes-part I: basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. Ilchenko and A. Matsko, "Optical resonators with whispering-gallery modes-part II: applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

Ilchenko, V. S.

Jacquod, P.

H. E. Tureci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, "Modes of wave-chaotic dielectric resonators," Prog. Opt. 47, 75-137 (2005).
[CrossRef]

Jiao, X. H.

X. H. Jiao, P. Guillon, L. A. Bermudez, and P. Auxemery, "Whispering-gallery modes of dielectric structures: Applications to millimeter-wave bandstop filters," IEEE Trans. Microwave Theory Tech. 35, 1169-1175 (1987).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Kiravittaya, S.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, "Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances," Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Klar, O.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Knipp, P. A.

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

Kuhlmey, B. T.

Kulakovskii, V. D.

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

Kuwata-Gonokami, M.

T. Mukaiyama, K. Takeda, H. Miyazaki, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Lee, R. K.

Lo, K.

K. Lo, R. McPhedran, I. Bassett, and G. Milton, "An electromagnetic theory of dielectric waveguides with multiple embedded cylinders," J. Lightwave Technol. 12, 396-410 (1994).
[CrossRef]

Loata, G.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Loffler, T.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Lonear, M.

Longo, I.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, "Whispering gallery modes in a dielectric resonator: Characterization at millimeter wavelength," IEEE Trans. Microwave Theory Tech. 45, 2025 (1997).
[CrossRef]

Malzer, S.

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Martinelli, M.

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, "Whispering gallery modes in a dielectric resonator: Characterization at millimeter wavelength," IEEE Trans. Microwave Theory Tech. 45, 2025 (1997).
[CrossRef]

Matsko, A.

A. Matsko and V. Ilchenko, "Optical resonators with whispering-gallery modes-part I: basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. Ilchenko and A. Matsko, "Optical resonators with whispering-gallery modes-part II: applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

Maystre, D.

McPhedran, R.

K. Lo, R. McPhedran, I. Bassett, and G. Milton, "An electromagnetic theory of dielectric waveguides with multiple embedded cylinders," J. Lightwave Technol. 12, 396-410 (1994).
[CrossRef]

McPhedran, R. C.

Mei, Y. F.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, "Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances," Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Milton, G.

K. Lo, R. McPhedran, I. Bassett, and G. Milton, "An electromagnetic theory of dielectric waveguides with multiple embedded cylinders," J. Lightwave Technol. 12, 396-410 (1994).
[CrossRef]

Miyazaki, H.

T. Mukaiyama, K. Takeda, H. Miyazaki, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Morand, A.

Mukaiyama, T.

T. Mukaiyama, K. Takeda, H. Miyazaki, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Naweed, A.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71, 043804 (2005).
[CrossRef]

Ostby, E. P.

Pance, K.

K. Pance, L. Viola, and S. Sridhar, "Tunneling proximity resonances: interplay between symmetry and dissipation," Phys. Lett. A 268, 399-405 (2000).
[CrossRef]

Phan-Huy, K.

Povinelli, M. L.

Preu, S.

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

Rastelli, A.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, "Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances," Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Reinecke, T. L.

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

Reithmaier, J. O.

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

Renner, F.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Renner, F. H.

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

Renversez, G.

Rosenberger, A. T.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71, 043804 (2005).
[CrossRef]

Roskos, H.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Scherer, A.

Schmidt, O. G.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, "Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances," Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Schwanhau??er, A.

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Schwefel, H. G. L.

H. E. Tureci and H. G. L. Schwefel, "An efficient Fredholm method for the calculation of highly excited states of billiards," J. Phys. A 40, 13869-13882 (2007).
[CrossRef]

H. E. Tureci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, "Modes of wave-chaotic dielectric resonators," Prog. Opt. 47, 75-137 (2005).
[CrossRef]

Shopova, S. I.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71, 043804 (2005).
[CrossRef]

Smith, D. D.

Smythe, E. J.

Sridhar, S.

K. Pance, L. Viola, and S. Sridhar, "Tunneling proximity resonances: interplay between symmetry and dissipation," Phys. Lett. A 268, 399-405 (2000).
[CrossRef]

Stone, A. D.

H. E. Tureci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, "Modes of wave-chaotic dielectric resonators," Prog. Opt. 47, 75-137 (2005).
[CrossRef]

Sykes, E. C. H.

Takeda, K.

T. Mukaiyama, K. Takeda, H. Miyazaki, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Tureci, H. E.

H. E. Tureci and H. G. L. Schwefel, "An efficient Fredholm method for the calculation of highly excited states of billiards," J. Phys. A 40, 13869-13882 (2007).
[CrossRef]

H. E. Tureci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, "Modes of wave-chaotic dielectric resonators," Prog. Opt. 47, 75-137 (2005).
[CrossRef]

Uzunoglu, N.

I. Chremmos and N. Uzunoglu, "Reflective properties of double-ring resonator system coupled to a waveguide," IEEE Photon. Technol. Lett. 17, 2110-2112 (2005).
[CrossRef]

Vahala, K. J.

Viola, L.

K. Pance, L. Viola, and S. Sridhar, "Tunneling proximity resonances: interplay between symmetry and dissipation," Phys. Lett. A 268, 399-405 (2000).
[CrossRef]

Wait, J. R.

J. R. Wait, "Electromagnetic whispering gallery modes in a dielectric rod," Radio Sci. 2, 1005 (1967).

Wang, L. J.

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

Wang, S. Y. T.

White, T. P.

Wilkinson, T. L. J.

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

Xu, Y.

Yariv, A.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. Preu, F. H. Renner, S. Malzer, G. H. D¨ohler, L. J. Wang, M. Hanson, A. C. Gossard, T. L. J. Wilkinson, and E. R. Brown, "Efficient Terahertz emission from ballistic transport enhanced n-i-p-n-i-p superlattice photomixers," Appl. Phys. Lett. 90, 212115 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

A. Matsko and V. Ilchenko, "Optical resonators with whispering-gallery modes-part I: basics," IEEE J. Sel. Top. Quantum Electron. 12, 3-14 (2006).
[CrossRef]

V. Ilchenko and A. Matsko, "Optical resonators with whispering-gallery modes-part II: applications," IEEE J. Sel. Top. Quantum Electron. 12, 15-32 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

I. Chremmos and N. Uzunoglu, "Reflective properties of double-ring resonator system coupled to a waveguide," IEEE Photon. Technol. Lett. 17, 2110-2112 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (3)

D. Cross and P. Guillon, "Whispering gallery dielectric resonator modes for W-band-devices," IEEE Trans. Microwave Theory Tech. 38, 1667-1673 (1990).
[CrossRef]

G. Annino, M. Cassettari, I. Longo, and M. Martinelli, "Whispering gallery modes in a dielectric resonator: Characterization at millimeter wavelength," IEEE Trans. Microwave Theory Tech. 45, 2025 (1997).
[CrossRef]

X. H. Jiao, P. Guillon, L. A. Bermudez, and P. Auxemery, "Whispering-gallery modes of dielectric structures: Applications to millimeter-wave bandstop filters," IEEE Trans. Microwave Theory Tech. 35, 1169-1175 (1987).
[CrossRef]

J. Lightwave Technol. (2)

A. Morand, K. Phan-Huy, Y. Desieres, and P. Benech, "Analytical study of the microdisk�??s resonant modes coupling with a waveguide based on perturbation theory," J. Lightwave Technol. 22, 827-832 (2004).
[CrossRef]

K. Lo, R. McPhedran, I. Bassett, and G. Milton, "An electromagnetic theory of dielectric waveguides with multiple embedded cylinders," J. Lightwave Technol. 12, 396-410 (1994).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. A (1)

H. E. Tureci and H. G. L. Schwefel, "An efficient Fredholm method for the calculation of highly excited states of billiards," J. Phys. A 40, 13869-13882 (2007).
[CrossRef]

Nature (1)

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Lett. A (1)

K. Pance, L. Viola, and S. Sridhar, "Tunneling proximity resonances: interplay between symmetry and dissipation," Phys. Lett. A 268, 399-405 (2000).
[CrossRef]

Phys. Rev. A (1)

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, "Induced transparency and absorption in coupled whispering-gallery microresonators," Phys. Rev. A 71, 043804 (2005).
[CrossRef]

Phys. Rev. B (1)

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, "Strongly coupled semiconductor microcavities: A route to couple artificial atoms over micrometric distances," Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

T. Mukaiyama, K. Takeda, H. Miyazaki, and M. Kuwata-Gonokami, "Tight-binding photonic molecule modes of resonant bispheres," Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

M. Bayer, T. Gutbrod, J. O. 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 (1998).
[CrossRef]

Prog. Opt. (1)

H. E. Tureci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, "Modes of wave-chaotic dielectric resonators," Prog. Opt. 47, 75-137 (2005).
[CrossRef]

Radio Sci. (1)

J. R. Wait, "Electromagnetic whispering gallery modes in a dielectric rod," Radio Sci. 2, 1005 (1967).

Semicond. Sci. Technol. (1)

G. H. Dohler, F. Renner, O. Klar, M. Eckardt, A. Schwanhau�?er, S. Malzer, D. Driscoll, M. Hanson, A. Gossard, G. Loata, T. Loffler, and H. Roskos, "THz-photomixer based on quasi-ballisitc transport," Semicond. Sci. Technol. 20, 178 (2005).
[CrossRef]

Other (6)

MicroTech, Terahertz resources. http://www.mtinstruments.com/thzresources/.

H. G. L. Schwefel, C. G. Poulton, and L. J. Wang, "Numerically efficient multipole method for photonic molecules," in preparation (2008).

A. B. Movchan, N. Movchan, and C. G. Poulton, Asymptotics of dilute and densely packed composites (Imperial College Press, London, 2002).
[CrossRef]

R. K. Chang and A. K. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
[CrossRef]

L. I. Deych, C. Schmidt, T. Pertsch, and A. Tunnermann, "Coupling of the fundamental whispering gallery mode in bi-spheres," IEEE ICTON 2007 (79-82).

L. Rayleigh, The problem of the whispering gallery (Cambridge University, Cambridge, UK, 1912), pp. 617-620.

Supplementary Material (1)

» Media 1: MOV (1973 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(Color online) (a) Setup for scanning the WGM resonances by measuring the transmittance, T=IT /I 0. (b) Normalized frequency shift of a PE disk’s resonances caused by approaching the waveguide for 0.218 THz (λ=1.37 mm, TM16,1), 0.252 THz (λ=1.19 mm, TM19,1), 0.263 THz (λ=1.13 mm, TM20,1), and 0.283 THz (λ=1.05 mm, TM22,1). The normalization is done with respect to the weakly loaded case. The inset shows the Q-factor degradation due to loading. Due to deviations from the ideal shape of the disks, the minimum distance was estimated to be 80µm.

Fig. 2.
Fig. 2.

(Color online) (a) Loaded PE disk resonance spectra (modes TM13,1 to TM25,1) and resonance spectra for the two disks in touch (lowest graph). A theoretical calculation, including cavity loading and absorptive losses, is also included (uppermost graph). For clarity, the graphs are offset. (b) Magnified resonance peak at 0.252 THz. The calculated field distribution for the bonding (c) and antibonding (d) mode at 0.252 THz. (e) Photograph of one disk. [Media 1]

Fig. 3.
Fig. 3.

(Color online) Quartz disk resonance spectra and resonance spectra for two resonators in touch (lowest graph). A theoretical calculation, including cavity loading and absorption, is also included (uppermost graph). For clarity, the graphs are offset. A zoom at the peak at 0.226 THz and a picture of the resonator are inset.

Fig. 4.
Fig. 4.

(Color online) (a) Frequency difference of the split mode peaks of the PE disks at 0.218 THz (TM16,1) (red) and 0.252 THz (TM19,1) (black) with theoretical expectations (solid lines) for the PE disks. (b) Splitting vs. frequency for disks (nearly) in contact for PE (black) and quartz disks (green).

Metrics