Abstract

In the Terahertz (THz) domain, we investigate both numerically and experimentally the directional emission of whispering gallery mode resonators that are perturbed by a small scatterer in the vicinity of the resonators rim. We determine quality factor degradation, the modal structure and the emission direction for various geometries. We find that scatterers do allow for directional emission without destroying the resonator’s quality factor. This finding allows for new geometries and outcoupling scenarios for active whispering gallery mode structures such as quantum cascade lasers and passive resonators such as evanescent sensors. The experimental results agree well with finite difference time domain simulations.

© 2013 OSA

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2012

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett.108, 243902 (2012).
[CrossRef] [PubMed]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Y.-C. Liu, Y.-F. Xiao, X.-F. Jiang, B.-B. Li, Y. Li, and Q. Gong, “Cavity-QED treatment of scattering-induced free-space excitation and collection in high-Q whispering-gallery microcavities,” Phys. Rev. A85, 013843 (2012).
[CrossRef]

D. C. Aveline, L. Baumgartel, B. Ahn, and N. Yu, “Focused ion beam engineered whispering gallery mode resonators with open cavity structure,” Opt. Express20, 18091–18096 (2012).
[CrossRef] [PubMed]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. OBrien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

S. Preu, S. Kim, R. Verma, P. G. Burke, M. S. Sherwin, and A. C. Gossard, “An improved model for non-resonant terahertz detection in field-effect transistors,” J. Appl. Phys.111, 024502 (2012).
[CrossRef]

S. Preu, H. Lu, M. S. Sherwin, and A. C. Gossard, “Detection of nanosecond-scale, high power THz pulses with a field effect transistor,” Rev. Sci. Instrum.83(2012).
[CrossRef] [PubMed]

2011

C.-L. Zou, H. G. L. Schwefel, F.-W. Sun, Z.-F. Han, and G.-C. Guo, “Quick root searching method for resonances of dielectric optical microcavities with the boundary element method,” Opt. Express19, 15669–15678 (2011).
[CrossRef] [PubMed]

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys.109, 061301 (2011).
[CrossRef]

S. I. Schmid, K. Xia, and J. Evers, “Pathway interference in a loop array of three coupled microresonators,” Phys. Rev. A84, 013808 (2011).
[CrossRef]

R. F. M. Hales, M. Sieber, and H. Waalkens, “Trace formula for a dielectric microdisk with a point scatterer,” J. Phys. A44, 155305 (2011).
[CrossRef]

2010

H.-P. Loock, J. A. Barnes, G. Gagliardi, R. Li, R. D. Oleschuk, and H. Wächter, “Absorption detection using optical waveguide cavities,” Can. J. Chemistry88, 401–410 (2010).
[CrossRef]

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. (2010).

J. T. Rubin and L. Deych, “Ab initio theory of defect scattering in spherical whispering-gallery-mode resonators,” Phys. Rev. A81, 053827 (2010).
[CrossRef]

2009

H. G. L. Schwefel and C. G. Poulton, “An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane,” Opt. Express17, 13178–13186 (2009).
[CrossRef] [PubMed]

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics3, 46–49 (2009).
[CrossRef]

M. Hentschel, T.-Y. Kwon, M. A. Belkin, R. Audet, and F. Capasso, “Angular emission characteristics of quantum cascade spiral microlasers,” Opt. Express17, 10335–10343 (2009).
[CrossRef] [PubMed]

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, “Unidirectional emission from circular dielectric microresonators with a point scatterer,” Phys. Rev. A80, 063813 (2009).
[CrossRef]

2008

E. N. Shaforost, N. Klein, S. A. Vitusevich, A. Offenhusser, and A. A. Barannik, “Nanoliter liquid characterization by open whispering-gallery mode dielectric resonators at millimeter wave frequencies,” J. Appl. Phys.104, 074111 (2008).
[CrossRef]

S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the terahertz frequency range,” Opt. Express16, 7336–7343 (2008).
[CrossRef] [PubMed]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods5, 591–596 (2008).
[CrossRef] [PubMed]

2007

H. E. Türeci and H. G. L. Schwefel, “An efficient Fredholm method for the calculation of highly excited states of billiards,” J. Phys. A40, 13869–13882 (2007).
[CrossRef]

S. Preu, F. H. Renner, S. Malzer, G. H. Döhler, 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]

A. A. Danylov, J. Waldman, T. M. Goyette, A. J. Gatesman, R. H. Giles, K. J. Linden, W. R. Neal, W. E. Nixon, M. C. Wanke, and J. L. Reno, “Transformation of the multimode terahertz quantum cascade laser beam into a gaussian, using a hollow dielectric waveguide,” Appl. Opt.46, 5051–5055 (2007).
[CrossRef] [PubMed]

2006

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A73, 031802 (2006).
[CrossRef]

2004

S.-K. Kim, S.-H. Kim, G.-H. Kim, H.-G. Park, D.-J. Shin, and Y.-H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett.84, 861–863 (2004).
[CrossRef]

H. G. L. Schwefel, N. B. Rex, H. E. Türeci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B21, 923–934 (2004).
[CrossRef]

2003

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A5, 53–60 (2003).
[CrossRef]

1999

S. A. Backes, J. R. A. Cleaver, A. P. Heberle, J. J. Baumberg, and K. Köhler, “Threshold reduction in pierced microdisk lasers,” Appl. Phys. Lett.74, 176–178 (1999).
[CrossRef]

1998

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

1997

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol.15, 2154–2165 (1997).
[CrossRef]

1994

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. of Comput. Phys.114, 185–200 (1994).
[CrossRef]

Ahn, B.

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods5, 591–596 (2008).
[CrossRef] [PubMed]

Audet, R.

Aveline, D. C.

Backes, S. A.

S. A. Backes, J. R. A. Cleaver, A. P. Heberle, J. J. Baumberg, and K. Köhler, “Threshold reduction in pierced microdisk lasers,” Appl. Phys. Lett.74, 176–178 (1999).
[CrossRef]

Barannik, A. A.

E. N. Shaforost, N. Klein, S. A. Vitusevich, A. Offenhusser, and A. A. Barannik, “Nanoliter liquid characterization by open whispering-gallery mode dielectric resonators at millimeter wave frequencies,” J. Appl. Phys.104, 074111 (2008).
[CrossRef]

Barnes, J. A.

H.-P. Loock, J. A. Barnes, G. Gagliardi, R. Li, R. D. Oleschuk, and H. Wächter, “Absorption detection using optical waveguide cavities,” Can. J. Chemistry88, 401–410 (2010).
[CrossRef]

Baumberg, J. J.

S. A. Backes, J. R. A. Cleaver, A. P. Heberle, J. J. Baumberg, and K. Köhler, “Threshold reduction in pierced microdisk lasers,” Appl. Phys. Lett.74, 176–178 (1999).
[CrossRef]

Baumgartel, L.

Beere, H. E.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics3, 46–49 (2009).
[CrossRef]

Belkin, M. A.

Beltram, F.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics3, 46–49 (2009).
[CrossRef]

Ben-Messaoud, T.

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. of Comput. Phys.114, 185–200 (1994).
[CrossRef]

Brown, E. R.

S. Preu, F. H. Renner, S. Malzer, G. H. Döhler, 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]

Burke, P. G.

S. Preu, S. Kim, R. Verma, P. G. Burke, M. S. Sherwin, and A. C. Gossard, “An improved model for non-resonant terahertz detection in field-effect transistors,” J. Appl. Phys.111, 024502 (2012).
[CrossRef]

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. OBrien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

Cao, H.

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett.108, 243902 (2012).
[CrossRef] [PubMed]

Capasso, F.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. (2010).

M. Hentschel, T.-Y. Kwon, M. A. Belkin, R. Audet, and F. Capasso, “Angular emission characteristics of quantum cascade spiral microlasers,” Opt. Express17, 10335–10343 (2009).
[CrossRef] [PubMed]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Chang, R. K.

Cho, A. Y.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Cleaver, J. R. A.

S. A. Backes, J. R. A. Cleaver, A. P. Heberle, J. J. Baumberg, and K. Köhler, “Threshold reduction in pierced microdisk lasers,” Appl. Phys. Lett.74, 176–178 (1999).
[CrossRef]

Danylov, A. A.

Dettmann, C. P.

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, “Unidirectional emission from circular dielectric microresonators with a point scatterer,” Phys. Rev. A80, 063813 (2009).
[CrossRef]

Deych, L.

J. T. Rubin and L. Deych, “Ab initio theory of defect scattering in spherical whispering-gallery-mode resonators,” Phys. Rev. A81, 053827 (2010).
[CrossRef]

Diehl, L.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. (2010).

Döhler, G. H.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys.109, 061301 (2011).
[CrossRef]

S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the terahertz frequency range,” Opt. Express16, 7336–7343 (2008).
[CrossRef] [PubMed]

S. Preu, F. H. Renner, S. Malzer, G. H. Döhler, 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]

Dong, C.-H.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Edamura, T.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. (2010).

Evers, J.

S. I. Schmid, K. Xia, and J. Evers, “Pathway interference in a loop array of three coupled microresonators,” Phys. Rev. A84, 013808 (2011).
[CrossRef]

Faist, J.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics3, 46–49 (2009).
[CrossRef]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Gagliardi, G.

H.-P. Loock, J. A. Barnes, G. Gagliardi, R. Li, R. D. Oleschuk, and H. Wächter, “Absorption detection using optical waveguide cavities,” Can. J. Chemistry88, 401–410 (2010).
[CrossRef]

Gatesman, A. J.

Ge, L.

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett.108, 243902 (2012).
[CrossRef] [PubMed]

Giles, R. H.

Gmachl, C.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Gong, Q.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Y.-C. Liu, Y.-F. Xiao, X.-F. Jiang, B.-B. Li, Y. Li, and Q. Gong, “Cavity-QED treatment of scattering-induced free-space excitation and collection in high-Q whispering-gallery microcavities,” Phys. Rev. A85, 013843 (2012).
[CrossRef]

Gossard, A. C.

S. Preu, S. Kim, R. Verma, P. G. Burke, M. S. Sherwin, and A. C. Gossard, “An improved model for non-resonant terahertz detection in field-effect transistors,” J. Appl. Phys.111, 024502 (2012).
[CrossRef]

S. Preu, H. Lu, M. S. Sherwin, and A. C. Gossard, “Detection of nanosecond-scale, high power THz pulses with a field effect transistor,” Rev. Sci. Instrum.83(2012).
[CrossRef] [PubMed]

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys.109, 061301 (2011).
[CrossRef]

S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the terahertz frequency range,” Opt. Express16, 7336–7343 (2008).
[CrossRef] [PubMed]

S. Preu, F. H. Renner, S. Malzer, G. H. Döhler, 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]

Goyette, T. M.

Guo, G.-C.

Hagness, S. C.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol.15, 2154–2165 (1997).
[CrossRef]

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method,3rd ed. (Artech HouseBoston, 2005).

Hales, R. F. M.

R. F. M. Hales, M. Sieber, and H. Waalkens, “Trace formula for a dielectric microdisk with a point scatterer,” J. Phys. A44, 155305 (2011).
[CrossRef]

Han, Z.-F.

Hanson, M.

S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the terahertz frequency range,” Opt. Express16, 7336–7343 (2008).
[CrossRef] [PubMed]

S. Preu, F. H. Renner, S. Malzer, G. H. Döhler, 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]

He, L.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Heberle, A. P.

S. A. Backes, J. R. A. Cleaver, A. P. Heberle, J. J. Baumberg, and K. Köhler, “Threshold reduction in pierced microdisk lasers,” Appl. Phys. Lett.74, 176–178 (1999).
[CrossRef]

Hentschel, M.

M. Hentschel, T.-Y. Kwon, M. A. Belkin, R. Audet, and F. Capasso, “Angular emission characteristics of quantum cascade spiral microlasers,” Opt. Express17, 10335–10343 (2009).
[CrossRef] [PubMed]

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A73, 031802 (2006).
[CrossRef]

Ho, S. T.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol.15, 2154–2165 (1997).
[CrossRef]

Jacquod, P.

H. E. Türeci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” in “Progress in Optics” 47E. Wolf, ed. (Elsevier Science Bv, Amsterdam), pp. 75–137 (2005).
[CrossRef]

Jiang, X.-F.

Y.-C. Liu, Y.-F. Xiao, X.-F. Jiang, B.-B. Li, Y. Li, and Q. Gong, “Cavity-QED treatment of scattering-induced free-space excitation and collection in high-Q whispering-gallery microcavities,” Phys. Rev. A85, 013843 (2012).
[CrossRef]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. OBrien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

Kan, H.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. (2010).

Kim, G.-H.

S.-K. Kim, S.-H. Kim, G.-H. Kim, H.-G. Park, D.-J. Shin, and Y.-H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett.84, 861–863 (2004).
[CrossRef]

Kim, S.

S. Preu, S. Kim, R. Verma, P. G. Burke, M. S. Sherwin, and A. C. Gossard, “An improved model for non-resonant terahertz detection in field-effect transistors,” J. Appl. Phys.111, 024502 (2012).
[CrossRef]

Kim, S.-H.

S.-K. Kim, S.-H. Kim, G.-H. Kim, H.-G. Park, D.-J. Shin, and Y.-H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett.84, 861–863 (2004).
[CrossRef]

Kim, S.-K.

S.-K. Kim, S.-H. Kim, G.-H. Kim, H.-G. Park, D.-J. Shin, and Y.-H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett.84, 861–863 (2004).
[CrossRef]

Klein, N.

E. N. Shaforost, N. Klein, S. A. Vitusevich, A. Offenhusser, and A. A. Barannik, “Nanoliter liquid characterization by open whispering-gallery mode dielectric resonators at millimeter wave frequencies,” J. Appl. Phys.104, 074111 (2008).
[CrossRef]

Köhler, K.

S. A. Backes, J. R. A. Cleaver, A. P. Heberle, J. J. Baumberg, and K. Köhler, “Threshold reduction in pierced microdisk lasers,” Appl. Phys. Lett.74, 176–178 (1999).
[CrossRef]

Kwon, T.-Y.

Lee, Y.-H.

S.-K. Kim, S.-H. Kim, G.-H. Kim, H.-G. Park, D.-J. Shin, and Y.-H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett.84, 861–863 (2004).
[CrossRef]

Li, B.-B.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Y.-C. Liu, Y.-F. Xiao, X.-F. Jiang, B.-B. Li, Y. Li, and Q. Gong, “Cavity-QED treatment of scattering-induced free-space excitation and collection in high-Q whispering-gallery microcavities,” Phys. Rev. A85, 013843 (2012).
[CrossRef]

Li, R.

H.-P. Loock, J. A. Barnes, G. Gagliardi, R. Li, R. D. Oleschuk, and H. Wächter, “Absorption detection using optical waveguide cavities,” Can. J. Chemistry88, 401–410 (2010).
[CrossRef]

Li, Y.

Y.-C. Liu, Y.-F. Xiao, X.-F. Jiang, B.-B. Li, Y. Li, and Q. Gong, “Cavity-QED treatment of scattering-induced free-space excitation and collection in high-Q whispering-gallery microcavities,” Phys. Rev. A85, 013843 (2012).
[CrossRef]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Linden, K. J.

Liu, Y.-C.

Y.-C. Liu, Y.-F. Xiao, X.-F. Jiang, B.-B. Li, Y. Li, and Q. Gong, “Cavity-QED treatment of scattering-induced free-space excitation and collection in high-Q whispering-gallery microcavities,” Phys. Rev. A85, 013843 (2012).
[CrossRef]

Loock, H.-P.

H.-P. Loock, J. A. Barnes, G. Gagliardi, R. Li, R. D. Oleschuk, and H. Wächter, “Absorption detection using optical waveguide cavities,” Can. J. Chemistry88, 401–410 (2010).
[CrossRef]

Lu, H.

S. Preu, H. Lu, M. S. Sherwin, and A. C. Gossard, “Detection of nanosecond-scale, high power THz pulses with a field effect transistor,” Rev. Sci. Instrum.83(2012).
[CrossRef] [PubMed]

Mahler, L.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics3, 46–49 (2009).
[CrossRef]

Malzer, S.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys.109, 061301 (2011).
[CrossRef]

S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the terahertz frequency range,” Opt. Express16, 7336–7343 (2008).
[CrossRef] [PubMed]

S. Preu, F. H. Renner, S. Malzer, G. H. Döhler, 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]

Morozov, G. V.

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, “Unidirectional emission from circular dielectric microresonators with a point scatterer,” Phys. Rev. A80, 063813 (2009).
[CrossRef]

Narimanov, E. E.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Neal, W. R.

Nixon, W. E.

Nöckel, J. U.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

OBrien, J. L.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. OBrien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

Offenhusser, A.

E. N. Shaforost, N. Klein, S. A. Vitusevich, A. Offenhusser, and A. A. Barannik, “Nanoliter liquid characterization by open whispering-gallery mode dielectric resonators at millimeter wave frequencies,” J. Appl. Phys.104, 074111 (2008).
[CrossRef]

Oleschuk, R. D.

H.-P. Loock, J. A. Barnes, G. Gagliardi, R. Li, R. D. Oleschuk, and H. Wächter, “Absorption detection using optical waveguide cavities,” Can. J. Chemistry88, 401–410 (2010).
[CrossRef]

Park, H.-G.

S.-K. Kim, S.-H. Kim, G.-H. Kim, H.-G. Park, D.-J. Shin, and Y.-H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett.84, 861–863 (2004).
[CrossRef]

Pflügl, C.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. (2010).

Poulton, C. G.

Preu, S.

S. Preu, H. Lu, M. S. Sherwin, and A. C. Gossard, “Detection of nanosecond-scale, high power THz pulses with a field effect transistor,” Rev. Sci. Instrum.83(2012).
[CrossRef] [PubMed]

S. Preu, S. Kim, R. Verma, P. G. Burke, M. S. Sherwin, and A. C. Gossard, “An improved model for non-resonant terahertz detection in field-effect transistors,” J. Appl. Phys.111, 024502 (2012).
[CrossRef]

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys.109, 061301 (2011).
[CrossRef]

S. Preu, H. G. L. Schwefel, S. Malzer, G. H. Döhler, L. J. Wang, M. Hanson, J. D. Zimmerman, and A. C. Gossard, “Coupled whispering gallery mode resonators in the terahertz frequency range,” Opt. Express16, 7336–7343 (2008).
[CrossRef] [PubMed]

S. Preu, F. H. Renner, S. Malzer, G. H. Döhler, 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]

Rafizadeh, D.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol.15, 2154–2165 (1997).
[CrossRef]

Redding, B.

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett.108, 243902 (2012).
[CrossRef] [PubMed]

Renner, F. H.

S. Preu, F. H. Renner, S. Malzer, G. H. Döhler, 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]

Reno, J. L.

Rex, N. B.

Ritchie, D. A.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics3, 46–49 (2009).
[CrossRef]

Rubin, J. T.

J. T. Rubin and L. Deych, “Ab initio theory of defect scattering in spherical whispering-gallery-mode resonators,” Phys. Rev. A81, 053827 (2010).
[CrossRef]

Schmid, S. I.

S. I. Schmid, K. Xia, and J. Evers, “Pathway interference in a loop array of three coupled microresonators,” Phys. Rev. A84, 013808 (2011).
[CrossRef]

Schwefel, H. G. L.

Shaforost, E. N.

E. N. Shaforost, N. Klein, S. A. Vitusevich, A. Offenhusser, and A. A. Barannik, “Nanoliter liquid characterization by open whispering-gallery mode dielectric resonators at millimeter wave frequencies,” J. Appl. Phys.104, 074111 (2008).
[CrossRef]

Sherwin, M. S.

S. Preu, S. Kim, R. Verma, P. G. Burke, M. S. Sherwin, and A. C. Gossard, “An improved model for non-resonant terahertz detection in field-effect transistors,” J. Appl. Phys.111, 024502 (2012).
[CrossRef]

S. Preu, H. Lu, M. S. Sherwin, and A. C. Gossard, “Detection of nanosecond-scale, high power THz pulses with a field effect transistor,” Rev. Sci. Instrum.83(2012).
[CrossRef] [PubMed]

Shin, D.-J.

S.-K. Kim, S.-H. Kim, G.-H. Kim, H.-G. Park, D.-J. Shin, and Y.-H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett.84, 861–863 (2004).
[CrossRef]

Sieber, M.

R. F. M. Hales, M. Sieber, and H. Waalkens, “Trace formula for a dielectric microdisk with a point scatterer,” J. Phys. A44, 155305 (2011).
[CrossRef]

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, “Unidirectional emission from circular dielectric microresonators with a point scatterer,” Phys. Rev. A80, 063813 (2009).
[CrossRef]

Sivco, D. L.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Song, Q.

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett.108, 243902 (2012).
[CrossRef] [PubMed]

Sorel, M.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. OBrien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

Stone, A. D.

H. G. L. Schwefel, N. B. Rex, H. E. Türeci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B21, 923–934 (2004).
[CrossRef]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

H. E. Türeci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” in “Progress in Optics” 47E. Wolf, ed. (Elsevier Science Bv, Amsterdam), pp. 75–137 (2005).
[CrossRef]

Strain, M. J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. OBrien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

Sun, F.-W.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

C.-L. Zou, H. G. L. Schwefel, F.-W. Sun, Z.-F. Han, and G.-C. Guo, “Quick root searching method for resonances of dielectric optical microcavities with the boundary element method,” Opt. Express19, 15669–15678 (2011).
[CrossRef] [PubMed]

Taflove, A.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol.15, 2154–2165 (1997).
[CrossRef]

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method,3rd ed. (Artech HouseBoston, 2005).

Thompson, M. G.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. OBrien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

Tredicucci, A.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics3, 46–49 (2009).
[CrossRef]

Türeci, H. E.

H. E. Türeci and H. G. L. Schwefel, “An efficient Fredholm method for the calculation of highly excited states of billiards,” J. Phys. A40, 13869–13882 (2007).
[CrossRef]

H. G. L. Schwefel, N. B. Rex, H. E. Türeci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B21, 923–934 (2004).
[CrossRef]

H. E. Türeci, H. G. L. Schwefel, P. Jacquod, and A. D. Stone, “Modes of wave-chaotic dielectric resonators,” in “Progress in Optics” 47E. Wolf, ed. (Elsevier Science Bv, Amsterdam), pp. 75–137 (2005).
[CrossRef]

Unterhinninghofen, J.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. U.S.A. (2010).

Verma, R.

S. Preu, S. Kim, R. Verma, P. G. Burke, M. S. Sherwin, and A. C. Gossard, “An improved model for non-resonant terahertz detection in field-effect transistors,” J. Appl. Phys.111, 024502 (2012).
[CrossRef]

Vitusevich, S. A.

E. N. Shaforost, N. Klein, S. A. Vitusevich, A. Offenhusser, and A. A. Barannik, “Nanoliter liquid characterization by open whispering-gallery mode dielectric resonators at millimeter wave frequencies,” J. Appl. Phys.104, 074111 (2008).
[CrossRef]

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods5, 591–596 (2008).
[CrossRef] [PubMed]

Waalkens, H.

R. F. M. Hales, M. Sieber, and H. Waalkens, “Trace formula for a dielectric microdisk with a point scatterer,” J. Phys. A44, 155305 (2011).
[CrossRef]

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, “Unidirectional emission from circular dielectric microresonators with a point scatterer,” Phys. Rev. A80, 063813 (2009).
[CrossRef]

Wächter, H.

H.-P. Loock, J. A. Barnes, G. Gagliardi, R. Li, R. D. Oleschuk, and H. Wächter, “Absorption detection using optical waveguide cavities,” Can. J. Chemistry88, 401–410 (2010).
[CrossRef]

Waldman, J.

Walther, C.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, B. Witzigmann, H. E. Beere, and D. A. Ritchie, “Vertically emitting microdisk lasers,” Nat. Photonics3, 46–49 (2009).
[CrossRef]

Wang, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. OBrien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science338, 363–366 (2012).
[CrossRef] [PubMed]

Wang, L. J.

S. Preu, G. H. Döhler, S. Malzer, L. J. Wang, and A. C. Gossard, “Tunable, continuous-wave terahertz photomixer sources and applications,” J. Appl. Phys.109, 061301 (2011).
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Supplementary Material (3)

» Media 1: MP4 (1480 KB)     
» Media 2: MP4 (1513 KB)     
» Media 3: MP4 (1439 KB)     

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Figures (5)

Fig. 1
Fig. 1

Schematic setup. The resonator is mounted at a fixed position in the center of a rotation stage. The detector (Golay cell, D1) scans the angular far field pattern of the disk. Two cylindrical lenses (horizontal lens, HL, and detector lens, DL) improve the signal to noise ratio by focusing the emitted power from the resonator on the detector. For most measurements, the lenses collect radiation within a 10° angle. Alternatively, the lenses can be replaced with a probe waveguide that touches the boundary of the disk to scan the near field. b Photograph of the resonator in the center of the ration mount. c Definition of variables used throughout the paper. Angles are defined with respect to the coupling position, the angle of incidence is defined as positive in the direction of the light. The thickness of the boundary between hole and disk circumference is labelled as b. The hole (radius rh) position relative to the coupling position is defined as αh. Parameters for the numerical calculation, such as the incidence angle of a light ray on the surface, χ, and the far field emission angle θ are also included.

Fig. 2
Fig. 2

The evanescent near field of a polyethylene WGM resonator (diameter 25 mm, in the following referenced as “large resonator”) without hole is probed with a waveguide. a) Transmission through the feed waveguide while the near field probe is scanned along the circumference of the resonator. b) Outcoupled power through the near field probe.

Fig. 3
Fig. 3

a) Q factors of several disks without and with a hole with a boundary thickness of b (see Fig. 1(c)). The closer the hole is drilled to the resonator circumference, the stronger are the perturbations of the mode and the stronger the reduction of the Q factor. The inset shows the extrapolated loss-limited Q factor in the limit of large frequencies. b) Modal structure of the disk with b = 0.38 mm before and after the hole was drilled. Despite a strong shift in the resonance frequency, the Q factor was only slightly altered.

Fig. 4
Fig. 4

Small Resonator (R = 5.2 mm) with a hole at 180° ± 5°. a) Snapshot of the FDTD calculation on a logarithmic scale. The small circle indicates the hole. A movie ( Media 1) is provided in the supplementary material. b) Result of the Poynting vector analysis. The background shows a snapshot of the FDTD simulation. The arrows are the Poynting vectors, originating from the point at which they are evaluated, respectively. The Poynting vectors clearly reflect the pattern of the radiated field. The distance between the resonator edge and the circle on which the Poynting vectors are calculated is ρ = 8 mm. c) Experimental data (black dots) as well as far-field radiation pattern predicted from the theoretical Poynting-analysis (red) on a linear scale. The dip in the theoretical emission intensity at 270° is due to the waveguide region which was excluded from the Poynting vector analysis. In the experiment, the waveguide is curved and thus does not lie in this direction.

Fig. 5
Fig. 5

Large Resonator, the hole with d = 12.5 mm sits at 315° ±5° (top row) and 47° ±5° (bottom row); a) snapshot of the FDTD calculation. A movie ( Media 2) is provided in the supplementary material. b) Result of the Poynting vector analysis, as in Fig. 4(c). The distance between the resonator edge and the circle on which the Poynting vectors are calculated is ρ = 4 mm. c) Experimental data (black dotted) as well as far-field radiation pattern predicted from the theoretical Poynting-analysis on a linear scale (red). While the second main lobe observed experimentally at 130° − 180° is more narrow in the theoretical prediction, good overall agreement is achieved. d) snapshot of the FDTD calculation, the emission direction can be anticipated visually. A movie ( Media 3) is provided in the supplementary material. e) Result of the Poynting vector analysis, as in Fig. 4. The distance between the resonator edge and the circle on which the Poynting vectors are calculated is ρ = 4 mm. f) Experimental data (black dotted) as well as far-field radiation pattern predicted from the theoretical Poynting-analysis on a linear scale (red). While the first main lobe predicted from the theoretical calculation around 120° is missing in the experimental data, experiment and theory agree well for the second lobe at 200°, most likely due to the slightly curved waveguide in the experiment.

Equations (1)

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Q ( ν ) Q loss Q 0 exp ( γ ν ) Q loss + Q 0 exp ( γ ν ) ,

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