Abstract

We investigate optical microresonators consisting of either one or two coupled rectangular strips between upper and lower slab waveguides. The cavities are evanescently excited under oblique angles by thin-film guided, in-plane unguided waves supported by one of the slab waveguides. Beyond a specific incidence angle, losses are fully suppressed. The interaction between the guided mode of the cavity-strip and the incoming slab modes leads to resonant behavior for specific incidence angles and gaps. For a single cavity, at resonance, the input power is equally split among each of the four output ports, while for two cavities an add-drop filter can be realized that, at resonance, routes the incoming power completely to the forward drop waveguide via the cavity. For both applications, the strength of the interaction is controlled by the gaps between cavities and waveguides.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
  5. D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc.-J: Optoelectron. 140(3), 177–188 (1993).
    [Crossref]
  6. M. K. Chin and S. T. Ho, “Design and modeling of waveguide-coupled single-mode microring resonators,” J. Lightwave Technol. 16(8), 1433–1446 (1998).
    [Crossref]
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    [Crossref]
  8. M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: The coupled guided mode perspective,” Opt. Commun. 214(1-6), 155–170 (2002).
    [Crossref]
  9. M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34(5-6), 541–557 (2002).
    [Crossref]
  10. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
    [Crossref]
  11. M. Hammer, L. Ebers, and J. Förstner, “Oblique evanescent excitation of a dielectric strip: A model resonator with an open optical cavity of unlimited Q,” Opt. Express 27(7), 9313–9320 (2019).
    [Crossref]
  12. E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Spatial integration and differentiation of optical beams in a slab waveguide by a dielectric ridge supporting high-q resonances,” Opt. Express 26(19), 25156–25165 (2018).
    [Crossref]
  13. E. A. Bezus, D. A. Bykov, and L. L. Doskolovich, “Bound states in the continuum and high-q resonances supported by a dielectric ridge on a slab waveguide,” Photonics Res. 6(11), 1084–1093 (2018).
    [Crossref]
  14. M. Hammer, L. Ebers, A. Hildebrandt, A. Alhaddad, and J. Förstner, “Oblique semi-guided waves: 2-d integrated photonics with negative effective permittivity,” 2018 IEEE 17th Int. Conf. on Math. Methods Electromagn. Theory (MMET), pp. 5–9 (2018).
  15. M. Hammer, L. Ebers, and J. Förstner, “Oblique quasi-lossless excitation of a thin silicon slab waveguide: A guided-wave-variant of an anti-reflection coating,” J. Opt. Soc. Am. B 36(9), 2395–2401 (2019).
    [Crossref]
  16. L. Ebers, M. Hammer, and J. Förstner, “Oblique incidence of semi-guided planar waves on slab waveguide steps: effects of rounded edges,” Opt. Express 26(14), 18621–18632 (2018).
    [Crossref]
  17. M. Hammer, A. Hildebrandt, and J. Förstner, “Full resonant transmission of semi-guided planar waves through slab waveguide steps at oblique incidence,” J. Lightwave Technol. 34(3), 997–1005 (2016).
    [Crossref]
  18. M. Hammer, “Oblique incidence of semi-guided waves on rectangular slab waveguide discontinuities: A vectorial QUEP solver,” Opt. Commun. 338, 447–456 (2015).
    [Crossref]
  19. M. Hammer, A. Hildebrandt, and J. Förstner, “How planar optical waves can be made to climb dielectric steps,” Opt. Lett. 40(16), 3711–3714 (2015).
    [Crossref]
  20. F. Çivitci, M. Hammer, and H. J. W. M. Hoekstra, “Semi-guided plane wave reflection by thin-film transitions for angled incidence,” Opt. Quantum Electron. 46(3), 477–490 (2014).
    [Crossref]
  21. H. A. Haus and Y. Lai, “Theory of cascaded quarter wave shifted distributed feedback resonators,” IEEE J. Quantum Electron. 28(1), 205–213 (1992).
    [Crossref]
  22. COMSOL Multiphysics GmbH, Göttingen, Germany. https://www.comsol.de .
  23. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
    [Crossref]
  24. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
    [Crossref]
  25. M. A. Popović, C. Manolatou, and M. R. Watts, “Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters,” Opt. Express 14(3), 1208–1222 (2006).
    [Crossref]
  26. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
    [Crossref]
  27. M. Hammer, A. Hildebrandt, and J. Förstner, “Full resonant transmission of semi-guided planar waves through slab waveguide steps at oblique incidence,” J. Lightwave Technol. 34(3), 997–1005 (2016).
    [Crossref]

2019 (2)

2018 (3)

2016 (2)

2015 (2)

M. Hammer, “Oblique incidence of semi-guided waves on rectangular slab waveguide discontinuities: A vectorial QUEP solver,” Opt. Commun. 338, 447–456 (2015).
[Crossref]

M. Hammer, A. Hildebrandt, and J. Förstner, “How planar optical waves can be made to climb dielectric steps,” Opt. Lett. 40(16), 3711–3714 (2015).
[Crossref]

2014 (1)

F. Çivitci, M. Hammer, and H. J. W. M. Hoekstra, “Semi-guided plane wave reflection by thin-film transitions for angled incidence,” Opt. Quantum Electron. 46(3), 477–490 (2014).
[Crossref]

2012 (1)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

2006 (1)

2002 (2)

M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: The coupled guided mode perspective,” Opt. Commun. 214(1-6), 155–170 (2002).
[Crossref]

M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34(5-6), 541–557 (2002).
[Crossref]

1999 (3)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

S. V. Boriskina and A. I. Nosich, “Radiation and absorption losses of the whispering-gallery-mode dielectric resonators excited by a dielectric waveguide,” IEEE Trans. Microwave Theory Tech. 47(2), 224–231 (1999).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[Crossref]

1998 (3)

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

1993 (1)

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc.-J: Optoelectron. 140(3), 177–188 (1993).
[Crossref]

1992 (1)

H. A. Haus and Y. Lai, “Theory of cascaded quarter wave shifted distributed feedback resonators,” IEEE J. Quantum Electron. 28(1), 205–213 (1992).
[Crossref]

1974 (1)

E. A. J. Marcatili, “Slab-coupled waveguides,” The Bell Syst. Tech. J. 53(4), 645–674 (1974).
[Crossref]

Alhaddad, A.

M. Hammer, L. Ebers, A. Hildebrandt, A. Alhaddad, and J. Förstner, “Oblique semi-guided waves: 2-d integrated photonics with negative effective permittivity,” 2018 IEEE 17th Int. Conf. on Math. Methods Electromagn. Theory (MMET), pp. 5–9 (2018).

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Bezus, E. A.

E. A. Bezus, D. A. Bykov, and L. L. Doskolovich, “Bound states in the continuum and high-q resonances supported by a dielectric ridge on a slab waveguide,” Photonics Res. 6(11), 1084–1093 (2018).
[Crossref]

E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Spatial integration and differentiation of optical beams in a slab waveguide by a dielectric ridge supporting high-q resonances,” Opt. Express 26(19), 25156–25165 (2018).
[Crossref]

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Boriskina, S. V.

S. V. Boriskina and A. I. Nosich, “Radiation and absorption losses of the whispering-gallery-mode dielectric resonators excited by a dielectric waveguide,” IEEE Trans. Microwave Theory Tech. 47(2), 224–231 (1999).
[Crossref]

Bykov, D. A.

E. A. Bezus, D. A. Bykov, and L. L. Doskolovich, “Bound states in the continuum and high-q resonances supported by a dielectric ridge on a slab waveguide,” Photonics Res. 6(11), 1084–1093 (2018).
[Crossref]

E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Spatial integration and differentiation of optical beams in a slab waveguide by a dielectric ridge supporting high-q resonances,” Opt. Express 26(19), 25156–25165 (2018).
[Crossref]

Chin, M. K.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Çivitci, F.

F. Çivitci, M. Hammer, and H. J. W. M. Hoekstra, “Semi-guided plane wave reflection by thin-film transitions for angled incidence,” Opt. Quantum Electron. 46(3), 477–490 (2014).
[Crossref]

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

De Heyn, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

De Vos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Doskolovich, L. L.

E. A. Bezus, D. A. Bykov, and L. L. Doskolovich, “Bound states in the continuum and high-q resonances supported by a dielectric ridge on a slab waveguide,” Photonics Res. 6(11), 1084–1093 (2018).
[Crossref]

E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Spatial integration and differentiation of optical beams in a slab waveguide by a dielectric ridge supporting high-q resonances,” Opt. Express 26(19), 25156–25165 (2018).
[Crossref]

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Ebers, L.

Fan, S.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
[Crossref]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Förstner, J.

Hammer, M.

M. Hammer, L. Ebers, and J. Förstner, “Oblique evanescent excitation of a dielectric strip: A model resonator with an open optical cavity of unlimited Q,” Opt. Express 27(7), 9313–9320 (2019).
[Crossref]

M. Hammer, L. Ebers, and J. Förstner, “Oblique quasi-lossless excitation of a thin silicon slab waveguide: A guided-wave-variant of an anti-reflection coating,” J. Opt. Soc. Am. B 36(9), 2395–2401 (2019).
[Crossref]

L. Ebers, M. Hammer, and J. Förstner, “Oblique incidence of semi-guided planar waves on slab waveguide steps: effects of rounded edges,” Opt. Express 26(14), 18621–18632 (2018).
[Crossref]

M. Hammer, A. Hildebrandt, and J. Förstner, “Full resonant transmission of semi-guided planar waves through slab waveguide steps at oblique incidence,” J. Lightwave Technol. 34(3), 997–1005 (2016).
[Crossref]

M. Hammer, A. Hildebrandt, and J. Förstner, “Full resonant transmission of semi-guided planar waves through slab waveguide steps at oblique incidence,” J. Lightwave Technol. 34(3), 997–1005 (2016).
[Crossref]

M. Hammer, “Oblique incidence of semi-guided waves on rectangular slab waveguide discontinuities: A vectorial QUEP solver,” Opt. Commun. 338, 447–456 (2015).
[Crossref]

M. Hammer, A. Hildebrandt, and J. Förstner, “How planar optical waves can be made to climb dielectric steps,” Opt. Lett. 40(16), 3711–3714 (2015).
[Crossref]

F. Çivitci, M. Hammer, and H. J. W. M. Hoekstra, “Semi-guided plane wave reflection by thin-film transitions for angled incidence,” Opt. Quantum Electron. 46(3), 477–490 (2014).
[Crossref]

M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: The coupled guided mode perspective,” Opt. Commun. 214(1-6), 155–170 (2002).
[Crossref]

M. Hammer, L. Ebers, A. Hildebrandt, A. Alhaddad, and J. Förstner, “Oblique semi-guided waves: 2-d integrated photonics with negative effective permittivity,” 2018 IEEE 17th Int. Conf. on Math. Methods Electromagn. Theory (MMET), pp. 5–9 (2018).

Haus, H. A.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

H. A. Haus and Y. Lai, “Theory of cascaded quarter wave shifted distributed feedback resonators,” IEEE J. Quantum Electron. 28(1), 205–213 (1992).
[Crossref]

Hildebrandt, A.

Ho, S. T.

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[Crossref]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[Crossref]

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[Crossref]

Kumar Selvaraja, S.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Lai, Y.

H. A. Haus and Y. Lai, “Theory of cascaded quarter wave shifted distributed feedback resonators,” IEEE J. Quantum Electron. 28(1), 205–213 (1992).
[Crossref]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Lohmeyer, M.

M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34(5-6), 541–557 (2002).
[Crossref]

Love, J. D.

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc.-J: Optoelectron. 140(3), 177–188 (1993).
[Crossref]

M. Hoekstra, H. J. W.

F. Çivitci, M. Hammer, and H. J. W. M. Hoekstra, “Semi-guided plane wave reflection by thin-film transitions for angled incidence,” Opt. Quantum Electron. 46(3), 477–490 (2014).
[Crossref]

Manolatou, C.

M. A. Popović, C. Manolatou, and M. R. Watts, “Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters,” Opt. Express 14(3), 1208–1222 (2006).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[Crossref]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Marcatili, E. A. J.

E. A. J. Marcatili, “Slab-coupled waveguides,” The Bell Syst. Tech. J. 53(4), 645–674 (1974).
[Crossref]

Nosich, A. I.

S. V. Boriskina and A. I. Nosich, “Radiation and absorption losses of the whispering-gallery-mode dielectric resonators excited by a dielectric waveguide,” IEEE Trans. Microwave Theory Tech. 47(2), 224–231 (1999).
[Crossref]

Popovic, M. A.

Rowland, D. R.

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc.-J: Optoelectron. 140(3), 177–188 (1993).
[Crossref]

Soifer, V. A.

Van Thourhout, D.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
[Crossref]

Watts, M. R.

IEE Proc.-J: Optoelectron. (1)

D. R. Rowland and J. D. Love, “Evanescent wave coupling of whispering gallery modes of a dielectric cylinder,” IEE Proc.-J: Optoelectron. 140(3), 177–188 (1993).
[Crossref]

IEEE J. Quantum Electron. (2)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

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Figures (8)

Fig. 1.
Fig. 1. Oblique evanescent excitation of a dielectric resonator with rectangular micro-strip cavity; schematic view (a) and cross section view (b). The incoming semi-guided wave propagates under an incidence angle $\theta$ normal to the cavity. Outgoing optical waves are either directly transmitted, forward or backward dropped, or reflected. $P_\textrm {A}, P_\textrm {B}, P_\textrm {C}$ and $P_\textrm {D}$ indicate the outgoing power at the respective ports. Material parameters correspond to a SOI design with refractive indices $n_\textrm {g} = 3.45$ in the guiding layers and $n_\textrm {b} = 1.45$ in the claddings and the gaps between the layers. Waveguide thicknesses are defined as $d=h=0.22\,\mu \textrm {m}$ with a cavity width of $w=0.5\,\mu \textrm {m}$ and variable gap distance $g$. Incoming wave is the TE mode for vacuum wavelength $\lambda = 1.55\,\mu \textrm {m}$.
Fig. 2.
Fig. 2. (a) Relative transmission / reflection power levels of a microresonator with a single cavity for different gaps $g\in \{200,300,400\}\,\textrm {nm}$ as a function of the incidence angle $\theta$; (b) field plots of the absolute electric field $\mathrm {log}_{10}{\boldsymbol {|E|}}$ at resonant angle $\theta _\textrm {r}$ for the corresponding fixed gap distances $g$ from (a). The contour lines indicate the levels of 2%, 5% and 10% of the overall absolute field maximum.
Fig. 3.
Fig. 3. Resonance angles $\theta _\textrm {r}$ with equal outgoing power on each port (a) and absolute square of the electric field maximum ${\boldsymbol {E}}_\textrm {c}$ in the center of the cavity relative to the absolute field maximum ${\boldsymbol {E}}_\textrm {0}$ of the isolated slab at $\theta =58.99^\circ$ (b) versus the gap $g$.
Fig. 4.
Fig. 4. Cross section view of a symmetric four-port configuration consisting of two identical cavities with dimensions $w\times h$ at distance $s$. Input and receiver slabs of thickness $d$ are separated by the distance $g$ from the cavities. Specific waveguide parameters are adopted from Figure 1. As before, the incoming semi-guided TE wave propagates at angle $\theta$ as demonstrated in Figure 1(a).
Fig. 5.
Fig. 5. (a) Field plots of the absolute electric field $\mathrm {log}_{10}|{\boldsymbol {E}}|$ at resonance $(\theta _\textrm {r},s_\textrm {r})$ for different gaps $g\in \{200,300,400\}\,\textrm {nm}$. Contour lines indicate the levels at 2%, 5% and 10% of the overall field maximum. (b) Outgoing power $P_\textrm {C}$ in the forward drop port over the incidence angle $\theta$ for different cavity distances $s$ around the resonance $(\theta _\textrm {r},s_\textrm {r})$ for the corresponding gaps from (a). The angles $\theta _\textrm {m,e}$ and $\theta _\textrm {m,o}$ associated with the even (e) and odd (o) supermodes of the coupled strips at $s=100\,\textrm {nm}$ are indicated.
Fig. 6.
Fig. 6. Real (a) and imaginary (b) part of the effective index $N_\textrm {s}$ for the even (solid line) and odd (dashed line) modes for the overall structure (including cavities and slabs) depending on the separation $s$ for different gaps $g\in \{200,300,400\}\,\textrm {nm}$.
Fig. 7.
Fig. 7. (a) Outgoing power scans $P_\textrm {C}$ over the wavelength $\lambda$ for different gap distances $g$ at resonance with the corresponding values $(\theta _\textrm {r},s_\textrm {r})$ adopted from Figure 5(a). (b) Enlargement of the resonance peak for a smaller range of wavelengths around the resonance wavelength $\lambda _\textrm {r}=1.55\,\mu \textrm {m}$.
Fig. 8.
Fig. 8. Outgoing power $P_\textrm {C}$ in the forward drop port over the cavity distance $s$ for fixed gap $g=200\,\textrm {nm}$ and incidence angle $\theta =57.56^\circ$ (a) and corresponding logarithmic field plots of the absolute electric field $\mathrm {log}_{10}|{\boldsymbol {E}}|$ at resonance (b).

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