Abstract

A rectangular dielectric strip at some distance above an optical slab waveguide is being considered, for evanescent excitation of the strip through the semi-guided waves supported by the slab, at specific oblique angles. The 2.5-D configuration shows resonant transmission properties with respect to variations of the angle of incidence, or of the excitation frequency, respectively. The strength of the interaction can be controlled by the gap between strip and slab. For increasing distance, our simulations predict resonant states with unit extremal reflectance of an angular or spectral width that tends to zero, i.e. resonances with a Q-factor that tends to infinity, while the resonance position approaches the level of the guided mode of the strip. This exceptionally simple system realizes what might be termed a “bound state coupled to the continuum”.

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

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References

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  5. M. Lohmeyer and R. Stoffer, “Integrated optical cross strip polarizer concept,” Opt. Quantum Electron. 33, 413–431 (2001).
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  6. M. Lohmeyer, L. Wilkens, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Integrated magnetooptic cross strip isolator,” Opt. Commun. 189, 251–259 (2001).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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  23. M. Maksimovic, M. Hammer, and E. van Groesen, “Coupled optical defect microcavities in 1D photonic crystals and quasi-normal modes,” Opt. Eng. 47, 1146011–12 (2008).
    [Crossref]
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  25. D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
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  26. C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
    [Crossref]
  27. L. Yuan and Y. Y. Lu, “Bound states in the continuum on periodic structures: perturbation theory and robustness,” Opt. Lett. 42, 4490–4493 (2017).
    [Crossref] [PubMed]
  28. L. Yuan and Y.-Y. Lu, “Bound states in the continuum on periodic structures surrounded by strong resonances,” Phys. Rev. A 97, 043828 (2018).
    [Crossref]
  29. C.-L. Zou, J.-M. Cui, F.-W. Sun, X. Xiong, X.-B. Zou, Z.-F. Han, and G.-C. Guo, “Guiding light through optical bound states in the continuum for ultrahigh-Q microresonators,” Laser & Photonics Rev. 9, 114–119 (2014).
    [Crossref]

2018 (4)

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, 1084–1093 (2018).
[Crossref]

L. Yuan and Y.-Y. Lu, “Bound states in the continuum on periodic structures surrounded by strong resonances,” Phys. Rev. A 97, 043828 (2018).
[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, 18621–18632 (2018).
[Crossref] [PubMed]

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, 25156–25165 (2018).
[Crossref] [PubMed]

2017 (2)

L. Yuan and Y. Y. Lu, “Bound states in the continuum on periodic structures: perturbation theory and robustness,” Opt. Lett. 42, 4490–4493 (2017).
[Crossref] [PubMed]

L. Ebers, M. Hammer, and J. Förstner, “Spiral modes supported by circular dielectric tubes and tube segments,” Opt. Quantum Electron. 49, 176 (2017).
[Crossref]

2016 (2)

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

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

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, 3711–3714 (2015).
[Crossref] [PubMed]

2014 (2)

C.-L. Zou, J.-M. Cui, F.-W. Sun, X. Xiong, X.-B. Zou, Z.-F. Han, and G.-C. Guo, “Guiding light through optical bound states in the continuum for ultrahigh-Q microresonators,” Laser & Photonics Rev. 9, 114–119 (2014).
[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, 477–490 (2014).
[Crossref]

2008 (3)

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
[Crossref] [PubMed]

M. Maksimovic, M. Hammer, and E. van Groesen, “Field representation for optical defect microcavities in multilayer structures using quasi-normal modes,” Opt. Commun. 281, 1401–1411 (2008).
[Crossref]

M. Maksimovic, M. Hammer, and E. van Groesen, “Coupled optical defect microcavities in 1D photonic crystals and quasi-normal modes,” Opt. Eng. 47, 1146011–12 (2008).
[Crossref]

2006 (1)

2004 (1)

M. Hammer, “Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics,” Opt. Commun. 235, 285–303 (2004).
[Crossref]

2002 (2)

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

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

2001 (2)

M. Lohmeyer and R. Stoffer, “Integrated optical cross strip polarizer concept,” Opt. Quantum Electron. 33, 413–431 (2001).
[Crossref]

M. Lohmeyer, L. Wilkens, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Integrated magnetooptic cross strip isolator,” Opt. Commun. 189, 251–259 (2001).
[Crossref]

2000 (1)

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photonics Technol. Lett. 12, 182–183 (2000).
[Crossref]

1999 (1)

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, 1322–1331 (1999).
[Crossref]

1992 (1)

A. S. Sudbø, “Why are accurate computations of mode fields in rectangular dielectric waveguides difficult?” J. Light. Technol. 10, 418–419 (1992).
[Crossref]

Alhaddad, S.

M. Hammer, L. Ebers, A. Hildebrandt, S. Alhaddad, and J. Förstner, “Oblique semi-guided waves: 2-D integrated photonics with negative effective permittivity,” in 2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic Theory (MMET), (2018), pp. 9–15.

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, 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, 25156–25165 (2018).
[Crossref] [PubMed]

Birks, T. A.

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photonics Technol. Lett. 12, 182–183 (2000).
[Crossref]

Borisov, A. G.

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
[Crossref] [PubMed]

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, 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, 25156–25165 (2018).
[Crossref] [PubMed]

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, 477–490 (2014).
[Crossref]

Cui, J.-M.

C.-L. Zou, J.-M. Cui, F.-W. Sun, X. Xiong, X.-B. Zou, Z.-F. Han, and G.-C. Guo, “Guiding light through optical bound states in the continuum for ultrahigh-Q microresonators,” Laser & Photonics Rev. 9, 114–119 (2014).
[Crossref]

Dimmick, T. E.

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photonics Technol. Lett. 12, 182–183 (2000).
[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, 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, 25156–25165 (2018).
[Crossref] [PubMed]

Dötsch, H.

M. Lohmeyer, L. Wilkens, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Integrated magnetooptic cross strip isolator,” Opt. Commun. 189, 251–259 (2001).
[Crossref]

Ebers, L.

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, 18621–18632 (2018).
[Crossref] [PubMed]

L. Ebers, M. Hammer, and J. Förstner, “Spiral modes supported by circular dielectric tubes and tube segments,” Opt. Quantum Electron. 49, 176 (2017).
[Crossref]

M. Hammer, L. Ebers, A. Hildebrandt, S. Alhaddad, and J. Förstner, “Oblique semi-guided waves: 2-D integrated photonics with negative effective permittivity,” in 2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic Theory (MMET), (2018), pp. 9–15.

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, 1322–1331 (1999).
[Crossref]

Förstner, J.

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, 18621–18632 (2018).
[Crossref] [PubMed]

L. Ebers, M. Hammer, and J. Förstner, “Spiral modes supported by circular dielectric tubes and tube segments,” Opt. Quantum Electron. 49, 176 (2017).
[Crossref]

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

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

M. Hammer, L. Ebers, A. Hildebrandt, S. Alhaddad, and J. Förstner, “Oblique semi-guided waves: 2-D integrated photonics with negative effective permittivity,” in 2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic Theory (MMET), (2018), pp. 9–15.

Guo, G.-C.

C.-L. Zou, J.-M. Cui, F.-W. Sun, X. Xiong, X.-B. Zou, Z.-F. Han, and G.-C. Guo, “Guiding light through optical bound states in the continuum for ultrahigh-Q microresonators,” Laser & Photonics Rev. 9, 114–119 (2014).
[Crossref]

Hammer, M.

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, 18621–18632 (2018).
[Crossref] [PubMed]

L. Ebers, M. Hammer, and J. Förstner, “Spiral modes supported by circular dielectric tubes and tube segments,” Opt. Quantum Electron. 49, 176 (2017).
[Crossref]

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

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

M. Hammer, “Oblique incidence of semi-guided waves on rectangular slab waveguide discontinuities: A vectorial QUEP solver,” Opt. Commun. 338, 447–456 (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, 477–490 (2014).
[Crossref]

M. Maksimovic, M. Hammer, and E. van Groesen, “Coupled optical defect microcavities in 1D photonic crystals and quasi-normal modes,” Opt. Eng. 47, 1146011–12 (2008).
[Crossref]

M. Maksimovic, M. Hammer, and E. van Groesen, “Field representation for optical defect microcavities in multilayer structures using quasi-normal modes,” Opt. Commun. 281, 1401–1411 (2008).
[Crossref]

M. Hammer, “Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics,” Opt. Commun. 235, 285–303 (2004).
[Crossref]

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

M. Hammer, L. Ebers, A. Hildebrandt, S. Alhaddad, and J. Förstner, “Oblique semi-guided waves: 2-D integrated photonics with negative effective permittivity,” in 2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic Theory (MMET), (2018), pp. 9–15.

Han, Z.-F.

C.-L. Zou, J.-M. Cui, F.-W. Sun, X. Xiong, X.-B. Zou, Z.-F. Han, and G.-C. Guo, “Guiding light through optical bound states in the continuum for ultrahigh-Q microresonators,” Laser & Photonics Rev. 9, 114–119 (2014).
[Crossref]

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, 1322–1331 (1999).
[Crossref]

Hertel, P.

M. Lohmeyer, L. Wilkens, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Integrated magnetooptic cross strip isolator,” Opt. Commun. 189, 251–259 (2001).
[Crossref]

Hildebrandt, A.

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

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

M. Hammer, L. Ebers, A. Hildebrandt, S. Alhaddad, and J. Förstner, “Oblique semi-guided waves: 2-D integrated photonics with negative effective permittivity,” in 2018 IEEE 17th International Conference on Mathematical Methods in Electromagnetic Theory (MMET), (2018), pp. 9–15.

Hoekstra, H. J. W. M.

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, 477–490 (2014).
[Crossref]

Hsu, C. W.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

Joannopoulos, J. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[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, 1322–1331 (1999).
[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, 1322–1331 (1999).
[Crossref]

Knight, J. C.

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photonics Technol. Lett. 12, 182–183 (2000).
[Crossref]

Lohmeyer, M.

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

M. Lohmeyer and R. Stoffer, “Integrated optical cross strip polarizer concept,” Opt. Quantum Electron. 33, 413–431 (2001).
[Crossref]

M. Lohmeyer, L. Wilkens, O. Zhuromskyy, H. Dötsch, and P. Hertel, “Integrated magnetooptic cross strip isolator,” Opt. Commun. 189, 251–259 (2001).
[Crossref]

Lu, Y. Y.

Lu, Y.-Y.

L. Yuan and Y.-Y. Lu, “Bound states in the continuum on periodic structures surrounded by strong resonances,” Phys. Rev. A 97, 043828 (2018).
[Crossref]

Maksimovic, M.

M. Maksimovic, M. Hammer, and E. van Groesen, “Coupled optical defect microcavities in 1D photonic crystals and quasi-normal modes,” Opt. Eng. 47, 1146011–12 (2008).
[Crossref]

M. Maksimovic, M. Hammer, and E. van Groesen, “Field representation for optical defect microcavities in multilayer structures using quasi-normal modes,” Opt. Commun. 281, 1401–1411 (2008).
[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, 1208–1222 (2006).
[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, 1322–1331 (1999).
[Crossref]

Marinica, D. C.

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
[Crossref] [PubMed]

Popovic, M. A.

Shabanov, S. V.

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
[Crossref] [PubMed]

Soifer, V. A.

Soljacic, M.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

Stoffer, R.

M. Lohmeyer and R. Stoffer, “Integrated optical cross strip polarizer concept,” Opt. Quantum Electron. 33, 413–431 (2001).
[Crossref]

Stone, A. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

Sudbø, A. S.

A. S. Sudbø, “Why are accurate computations of mode fields in rectangular dielectric waveguides difficult?” J. Light. Technol. 10, 418–419 (1992).
[Crossref]

Sun, F.-W.

C.-L. Zou, J.-M. Cui, F.-W. Sun, X. Xiong, X.-B. Zou, Z.-F. Han, and G.-C. Guo, “Guiding light through optical bound states in the continuum for ultrahigh-Q microresonators,” Laser & Photonics Rev. 9, 114–119 (2014).
[Crossref]

van Groesen, E.

M. Maksimovic, M. Hammer, and E. van Groesen, “Field representation for optical defect microcavities in multilayer structures using quasi-normal modes,” Opt. Commun. 281, 1401–1411 (2008).
[Crossref]

M. Maksimovic, M. Hammer, and E. van Groesen, “Coupled optical defect microcavities in 1D photonic crystals and quasi-normal modes,” Opt. Eng. 47, 1146011–12 (2008).
[Crossref]

Vassallo, C.

C. Vassallo, Optical Waveguide Concepts(Elsevier, 1991).

Villeneuve, P. R.

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Figures (4)

Fig. 1
Fig. 1 Oblique evanescent excitation of a dielectric strip, schematic (a), and cross section view (b). Cartesian coordinates x , y , z are oriented such that x is normal to the slab plane, while y is parallel to the strip axis. The incoming semi-guided wave propagates in the y-z-plane at an angle θ with respect to the strip normal. Outgoing waves with reflectance R and transmittance T are observed under the same angle. Parameters: refractive indices n g = 3.45 (guiding regions), n b = 1.45 (substrate, gap layer, and cladding), slab thicknesses d = h = 0.22 μ m, strip width w = 0.5 μ m, variable gap g. TE excitation around a vacuum wavelength λ = 1.55 μ m is considered.
Fig. 2
Fig. 2 Transmission properties of the strip-resonator of Fig. 1, for gaps g = 100 nm (dashed line), g = 200 nm (dash-dotted), and g = 300 nm (solid curve). The panels show the reflectance R as a function of theangle of incidence θ, for fixed vacuum wavelength λ (a), or as a function of the vacuum wavelength λ, for fixed angle of incidence (b), and for fixed wavenumber ky (c).
Fig. 3
Fig. 3 Absolute electric field strength | E | on the x-z-cross section plane, for the dielectric strip resonator of Fig. 1 with a gap of g = 200 nm, at angles of incidence θ = 0 (a, normal incidence), θ = 56 (b, still off resonance), θ = 58.02 (c, at “half maximum” of the resonance), and θ = 58.27 (d, at resonance). The color levels of the panels are comparable; the contours indicate the levels of 2%, 5%, and 10% of the overall field maximum.
Fig. 4
Fig. 4 Resonance characteristics for the strip resonator of Fig. 1. Positions θr, λr of the resonances and full-widths-at-half-maxima Δ θ r, Δ λ r are shown as functions of the gap distance g, for angular scans with constant vacuum wavelength (a), and for wavelength scans with either constant angle of incidence θ = θ m (continuous lines & markers) or constant wavenumber k y = k N m (dashed lines) (b). Uppermost logarithmic plots, (a): Absolute square of the electric field strength E c at the center of the strip cavity, relative to the field strength E 0 at the center of the lower slab (for incoming TE mode at an angle of 59°, at λ = 1.55 μ m), for absent strip. (b) Quality factor Q associated with the strip resonances. Lines: vQUEP results [11]; markers: FE-simulations (COMSOL [19]).

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