Abstract

We describe intricate cavity mode structures, that are possible in waveguide devices with two or more guided modes. The main element is interference between the scattered fields of two modes at the facets, resulting in multipole or mode cancelations. Therefore, strong coupling between the modes, such as around zero group velocity points, is advantageous to obtain high quality factors. We discuss the mechanism in three different settings: a cylindrical structure with and without negative group velocity mode, and a surface plasmon device. A general semi-analytical expression for the cavity parameters describes the phenomenon, and it is validated with extensive numerical calculations.

© 2007 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Microcavity confinement based on an anomalous zero group-velocity waveguide mode

Mihai Ibanescu, Steven G. Johnson, David Roundy, Yoel Fink, and J. D. Joannopoulos
Opt. Lett. 30(5) 552-554 (2005)

Tunable triple Fano resonances based on multimode interference in coupled plasmonic resonator system

Shilei Li, Yunyun Zhang, Xiaokang Song, Yilin Wang, and Li Yu
Opt. Express 24(14) 15351-15361 (2016)

Ultracompact photonic crystal polarization beam splitter based on multimode interference

Ming-Feng Lu, Shan-Mei Liao, and Yang-Tung Huang
Appl. Opt. 49(4) 724-731 (2010)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. K.J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
    [Crossref] [PubMed]
  2. M. Ibanescu, S.G. Johnson, D. Roundy, Y. Fink, and J.D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
    [Crossref] [PubMed]
  3. M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective,” Opt. Comm. 214, 155–170 (2002).
    [Crossref]
  4. M. Hammer, “Total multimode reflection at facets of planar high-contrast optical waveguides,” Journ. Lightw. Tech. 20, 1549–1555 (2002).
    [Crossref]
  5. S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
    [Crossref]
  6. P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33, 327–341 (2001).
    [Crossref]
  7. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J.D. Joannopoulos, S.G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006).
    [Crossref] [PubMed]
  8. A. Karalis, E. Lidorikis, M. Ibanescu, J.D. Joannopoulos, and M. Soljači*#x0107;, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
    [Crossref] [PubMed]
  9. H.A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984).
  10. M. Ibanescu, S.G. Johnson, D. Roundy, C. Luo, Y. Fink, and J.D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
    [Crossref] [PubMed]
  11. P.P.P. Debackere, P. Bienstman, and R. Baets “Adaptive Spatial Resolution: Application to Surface Plasmon Waveguide Modes,” accepted for publication in Opt. Quantum Electron.
  12. T.P. White, L.C. Botten, R.C. McPhedran, and C.M. de Sterke, “Ultracompact resonant filters in photonic crystals,” Opt. Lett. 28, 2452–2454 (2003).
    [Crossref] [PubMed]

2006 (1)

2005 (2)

A. Karalis, E. Lidorikis, M. Ibanescu, J.D. Joannopoulos, and M. Soljači*#x0107;, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, D. Roundy, Y. Fink, and J.D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[Crossref] [PubMed]

2004 (1)

M. Ibanescu, S.G. Johnson, D. Roundy, C. Luo, Y. Fink, and J.D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref] [PubMed]

2003 (2)

2002 (2)

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

M. Hammer, “Total multimode reflection at facets of planar high-contrast optical waveguides,” Journ. Lightw. Tech. 20, 1549–1555 (2002).
[Crossref]

2001 (2)

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[Crossref]

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33, 327–341 (2001).
[Crossref]

Baets, R.

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33, 327–341 (2001).
[Crossref]

P.P.P. Debackere, P. Bienstman, and R. Baets “Adaptive Spatial Resolution: Application to Surface Plasmon Waveguide Modes,” accepted for publication in Opt. Quantum Electron.

Bermel, P.

Bienstman, P.

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33, 327–341 (2001).
[Crossref]

P.P.P. Debackere, P. Bienstman, and R. Baets “Adaptive Spatial Resolution: Application to Surface Plasmon Waveguide Modes,” accepted for publication in Opt. Quantum Electron.

Botten, L.C.

Burr, G.

de Sterke, C.M.

Debackere, P.P.P.

P.P.P. Debackere, P. Bienstman, and R. Baets “Adaptive Spatial Resolution: Application to Surface Plasmon Waveguide Modes,” accepted for publication in Opt. Quantum Electron.

Fan, S.

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[Crossref]

Farjadpour, A.

Fink, Y.

M. Ibanescu, S.G. Johnson, D. Roundy, Y. Fink, and J.D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, D. Roundy, C. Luo, Y. Fink, and J.D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref] [PubMed]

Hammer, M.

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

M. Hammer, “Total multimode reflection at facets of planar high-contrast optical waveguides,” Journ. Lightw. Tech. 20, 1549–1555 (2002).
[Crossref]

Haus, H.A.

H.A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984).

Ibanescu, M.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J.D. Joannopoulos, S.G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006).
[Crossref] [PubMed]

A. Karalis, E. Lidorikis, M. Ibanescu, J.D. Joannopoulos, and M. Soljači*#x0107;, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, D. Roundy, Y. Fink, and J.D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, D. Roundy, C. Luo, Y. Fink, and J.D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref] [PubMed]

Joannopoulos, J.D.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J.D. Joannopoulos, S.G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, D. Roundy, Y. Fink, and J.D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[Crossref] [PubMed]

A. Karalis, E. Lidorikis, M. Ibanescu, J.D. Joannopoulos, and M. Soljači*#x0107;, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, D. Roundy, C. Luo, Y. Fink, and J.D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref] [PubMed]

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[Crossref]

Johnson, S.G.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J.D. Joannopoulos, S.G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, D. Roundy, Y. Fink, and J.D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, D. Roundy, C. Luo, Y. Fink, and J.D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref] [PubMed]

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[Crossref]

Karalis, A.

A. Karalis, E. Lidorikis, M. Ibanescu, J.D. Joannopoulos, and M. Soljači*#x0107;, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[Crossref] [PubMed]

Lidorikis, E.

A. Karalis, E. Lidorikis, M. Ibanescu, J.D. Joannopoulos, and M. Soljači*#x0107;, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[Crossref] [PubMed]

Luo, C.

M. Ibanescu, S.G. Johnson, D. Roundy, C. Luo, Y. Fink, and J.D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref] [PubMed]

McPhedran, R.C.

Mekis, A.

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[Crossref]

Rodriguez, A.

Roundy, D.

Soljaci*#x0107;, M.

A. Karalis, E. Lidorikis, M. Ibanescu, J.D. Joannopoulos, and M. Soljači*#x0107;, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[Crossref] [PubMed]

Vahala, K.J.

K.J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

White, T.P.

Appl. Phys. Lett. (1)

S.G. Johnson, S. Fan, A. Mekis, and J.D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[Crossref]

Journ. Lightw. Tech. (1)

M. Hammer, “Total multimode reflection at facets of planar high-contrast optical waveguides,” Journ. Lightw. Tech. 20, 1549–1555 (2002).
[Crossref]

Nature (1)

K.J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

Opt. Comm. (1)

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

Opt. Lett. (3)

Opt. Quantum Electron. (1)

P. Bienstman and R. Baets, “Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers,” Opt. Quantum Electron. 33, 327–341 (2001).
[Crossref]

Phys. Rev. Lett. (2)

A. Karalis, E. Lidorikis, M. Ibanescu, J.D. Joannopoulos, and M. Soljači*#x0107;, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[Crossref] [PubMed]

M. Ibanescu, S.G. Johnson, D. Roundy, C. Luo, Y. Fink, and J.D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92, 063903 (2004).
[Crossref] [PubMed]

Other (2)

P.P.P. Debackere, P. Bienstman, and R. Baets “Adaptive Spatial Resolution: Application to Surface Plasmon Waveguide Modes,” accepted for publication in Opt. Quantum Electron.

H.A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1.
Fig. 1.

(a) General picture of a system with two circulating modes. (b) Schematic of the cylindrical structure. The dashed line is the axis of the cylinder. (b) Dispersion of the HE11 mode.

Download Full Size | PPT Slide | PDF

Fig. 2.
Fig. 2.

(a) Q versus L of the resonances. Dots are data points from mode expansion (CAMFR), crosses present results from FDTD (MEEP). (b) ω versus L for the same cavity modes.

Download Full Size | PPT Slide | PDF

Fig. 3.
Fig. 3.

(a) Field plot of some resonances. The electric field along ϕ is shown. L n and ωn are L/a and ω ×(a/2πc), respectively. (b) Far-field on- and off-resonance. The magnetic field along the direction of the axis is shown. The cavity is located to the left of these plots.

Download Full Size | PPT Slide | PDF

Fig. 4.
Fig. 4.

Magnitudes of the reflection matrix elements for the cylindrical structure with the negative group velocity mode.

Download Full Size | PPT Slide | PDF

Fig. 5.
Fig. 5.

Magnitude squared of the two eigenvalues for the cylindrical structure in the frequency range with a negative group velocity mode.

Download Full Size | PPT Slide | PDF

Fig. 6.
Fig. 6.

Dispersion of the TE modes with angular momentum zero in the cylindrical structure. The frequency region with two guided modes is indicated.

Download Full Size | PPT Slide | PDF

Fig. 7.
Fig. 7.

(a) Q versus L of resonances. Dots are data points from mode expansion (CAMFR), crosses present checks with FDTD (MEEP). (b) ω versus L for the cavity modes in the cylindrical structure with two positive v g waveguide modes.

Download Full Size | PPT Slide | PDF

Fig. 8.
Fig. 8.

(a) Field plot of some resonances. The electric field along ϕ is shown; only one half is presented. Ln and ωn are L/a and ω ×(a/2πc), respectively. (b) Magnitudes of the reflection matrix elements for the cylindrical structure in the frequency range with two positive group velocity modes.

Download Full Size | PPT Slide | PDF

Fig. 9.
Fig. 9.

Magnitude squared of the two eigenvalues for the cylindrical structure in the frequency range with positive group velocity modes.

Download Full Size | PPT Slide | PDF

Fig. 10.
Fig. 10.

(a) Schematic of the two-dimensional, non-cylindrical plasmon structure. (b) Dispersion of the central waveguide (black), and of the outside waveguides (red).

Download Full Size | PPT Slide | PDF

Fig. 11.
Fig. 11.

(a) Q versus L of a resonance. Data calculated with mode expansion (CAMFR). (b) ω versus L for the plasmonic cavity.

Download Full Size | PPT Slide | PDF

Fig. 12.
Fig. 12.

(a) Depiction of the magnetic field at the peak of the resonance shown in Fig. 11(a) (L = 0.238L p and ω = 0.601ωp). (b) Magnitudes of the reflection matrix elements for the plasmonic structure.

Download Full Size | PPT Slide | PDF

Fig. 13.
Fig. 13.

Numerically calculated magnitude squared of an eigenvalue for the plasmonic structure.

Download Full Size | PPT Slide | PDF

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

Q = ω r L ∣ v g ∣ ( 1 − ∣ λ ∣ 2 ) .
P × R [ c 0 c 1 ] = λ [ c 0 c 1 ] ,
v g average = ∣ v g 0 ∣ ∣ c 0 ∣ 2 + ∣ v g 1 ∣ ∣ c 1 ∣ 2 .
P = [ exp ( − i k 0 L ) 0 0 exp ( − i k 1 L ) ] ,
R = [ r 00 r 01 r 10 r 11 ] ,
λ = exp ( − i Δ L ) [ d cos ⁡ ( kL ) − iδ sin ⁡ ( kL ) ± ( − id sin ⁡ ( kL ) + δ cos ⁡ ( kL ) ) 2 + r 01 2 ] .
∣ λ ∣ 2 ≈ ∣ r 01 ∣ 2 ± 2 cos ⁡ ( kL ) Re ( r 01 d * ) ∓ 2 sin ⁡ ( kL ) Im ( r 01 δ * ) ,
λ ≈ ± r 01 exp ( − i Δ L ) .
∣ λ ∣ 2 ≈ ∣ d ± δ ∣ 2 ± Re ( c 2 ( d * ± δ * ) exp ( ± i Δ L ) − id sin ⁡ ( Δ L ) + δ cos ⁡ ( Δ L ) ) .
∣ λ + ∣ 2 ≈ r 00 2 + 2 r 01 2 cos ⁡ ( 2 kL ) + r 01 4 r 00 2 .

Metrics