Abstract

Wavenumber matching is crucial to proper designs of optical devices such as ring-bus waveguides or planar cavities. In particular, the range of in-plane wavenumbers needs to be adequately determined along the coupling direction. Oftentimes, numerically intensive search is necessary for its accurate determination for surface plasmon resonances in particular nanostructures. In this paper, a method based on contour integrals is employed in order to provide a rough idea on the coupling capability of participating optical components. An example is provided for a semi-infinite metal–dielectric periodic multilayer bounded by another semi-infinite medium.

© 2011 IEEE

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  2. S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, S. Schulz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).
  3. N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 308, 534-537 (2005).
  4. H. Shin, S. Fan, "All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals," Appl. Phys. Lett. 89, 151102-1-151102-3 (2006).
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  6. I. R. Hooper, J. R. Sambles, "Surface plasmon polaritons on narrow-ridged short-pitch metal gratings," Phys. Rev. B 66, 205408 (2002).
  7. X. Yang, B. Zeng, C. Wang, X. Luo, "Breaking the feature sizes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer," Opt. Exp. 17, 21560-21565 (2009).
  8. Y. Gong, J. Vučković, "Design of plasmon cavities for solid-state cavity quantum electrodynamics applications," Appl. Phys. Lett. 90, 033113-1-033113-3 (2007).
  9. H.-I. Lee, "Wave propagation and resonance in four-layer systems for organic electro-luminescent diodes," J. Opt. Soc. Amer. A 24, 3017-3035 (2007).
  10. N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, "Designer spoof surface plasmon structures collimate terahertz laser beams," Nature Mater. 9, 730-735 (2010).
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  15. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999).
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  21. H. Walther, B. T. H. Varcoe, B.-G. Englert, T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325 (2006).
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  23. Q. Sun, M. Al-Amri, A. Kamli, M. S. Zubairy, "Lamb shift due to surface plasmon polariton modes," Phys. Rev. A 77, 062501-1-062501-6 (2008).
  24. L. M. Delves, J. N. Lyness, "A numerical method for locating the zeros of an analytic function," Math. Comput. 21, 543-560 (1967).
  25. J. Pritz, L. M. Woods, "Radiative electromagnetic modes in concentric cylindrical layers," Physica B: Cond. Matter 404, 1585-1590 (2009).

2010 (3)

H.-I. Lee, "Wave classification and resonant excitations in lossy metal-dielectric multilayers," Photon. Nanostruct.—Funda. Appl. 8, 183-197 (2010).

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, "Designer spoof surface plasmon structures collimate terahertz laser beams," Nature Mater. 9, 730-735 (2010).

M. Soltani, S. Yegnanarayanan, Q. Li, A. Adibi, "Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: Theory and experiment," IEEE J. Quantum Electron. 46, 1158-1169 (2010).

2009 (3)

M. Liscidini, J. E. Sipe, "Analysis of Bloch-surface-wave assisted diffraction-based biosensors," J. Opt. Soc. Amer. B 26, 279-289 (2009).

X. Yang, B. Zeng, C. Wang, X. Luo, "Breaking the feature sizes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer," Opt. Exp. 17, 21560-21565 (2009).

J. Pritz, L. M. Woods, "Radiative electromagnetic modes in concentric cylindrical layers," Physica B: Cond. Matter 404, 1585-1590 (2009).

2008 (1)

Q. Sun, M. Al-Amri, A. Kamli, M. S. Zubairy, "Lamb shift due to surface plasmon polariton modes," Phys. Rev. A 77, 062501-1-062501-6 (2008).

2007 (5)

C. Garcia-Segundo, H. Yan, M. S. Zhan, "Atom trap with surface plasmon and evanescent field," Phys. Rev. A 75, 030902(R)-1-030902(R)-4 (2007).

Y. Gong, J. Vučković, "Design of plasmon cavities for solid-state cavity quantum electrodynamics applications," Appl. Phys. Lett. 90, 033113-1-033113-3 (2007).

H.-I. Lee, "Wave propagation and resonance in four-layer systems for organic electro-luminescent diodes," J. Opt. Soc. Amer. A 24, 3017-3035 (2007).

D. E. Chang, A. S. Sørensen, E. A. Demler, M. D. Lukin, "A single-photon transistor using nanoscale surface plasmons," Nature Phys. 3, 807-812 (2007).

S. Darmawan, Y. M. Landobasa, M.-K. Chin, "Pole-zero dynamics of high-order ring resonator filters," J. Lightw. Technol. 25, 1568-1575 (2007).

2006 (3)

I. Breukelaar, P. Berini, "Long-range surface plasmon polariton mode cutoff and radiation in slab waveguide," J. Opt. Soc. Amer. A 23, 1971-1977 (2006).

H. Shin, S. Fan, "All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals," Appl. Phys. Lett. 89, 151102-1-151102-3 (2006).

H. Walther, B. T. H. Varcoe, B.-G. Englert, T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325 (2006).

2005 (1)

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 308, 534-537 (2005).

2003 (1)

D. T. Alves, F. A. Barone, C. Farina, A. C. Tort, "Influence of two parallel plates on atomic levels," Phys. Rev. A 67, 022103 (2003).

2002 (2)

I. R. Hooper, J. R. Sambles, "Surface plasmon polaritons on narrow-ridged short-pitch metal gratings," Phys. Rev. B 66, 205408 (2002).

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, S. Schulz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).

1999 (1)

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

1992 (1)

E. Anemogiannis, E. N. Glytsis, "Multilayer waveguides: Efficient numerical analysis of general structures," J. Lightw. Technol. 10, 1344-1351 (1992).

1985 (1)

C. A. Lütken, F. Ravndal, "Energy-level shifts in atoms between metallic planes," Phys. Rev. A 31, 2082-2090 (1985).

1984 (1)

G. W. Ford, W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).

1967 (1)

L. M. Delves, J. N. Lyness, "A numerical method for locating the zeros of an analytic function," Math. Comput. 21, 543-560 (1967).

1948 (1)

U. Fano, "The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's waves)," J. Opt. Soc. Amer. 31, 213-222 (1948).

Appl. Phys. Lett. (2)

H. Shin, S. Fan, "All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals," Appl. Phys. Lett. 89, 151102-1-151102-3 (2006).

Y. Gong, J. Vučković, "Design of plasmon cavities for solid-state cavity quantum electrodynamics applications," Appl. Phys. Lett. 90, 033113-1-033113-3 (2007).

IEEE J. Quantum Electron. (2)

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

M. Soltani, S. Yegnanarayanan, Q. Li, A. Adibi, "Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: Theory and experiment," IEEE J. Quantum Electron. 46, 1158-1169 (2010).

J. Lightw. Technol. (2)

S. Darmawan, Y. M. Landobasa, M.-K. Chin, "Pole-zero dynamics of high-order ring resonator filters," J. Lightw. Technol. 25, 1568-1575 (2007).

E. Anemogiannis, E. N. Glytsis, "Multilayer waveguides: Efficient numerical analysis of general structures," J. Lightw. Technol. 10, 1344-1351 (1992).

J. Mod. Opt. (1)

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, S. Schulz, "The asymmetric lossy near-perfect lens," J. Mod. Opt. 49, 1747-1762 (2002).

J. Opt. Soc. Amer. (1)

U. Fano, "The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's waves)," J. Opt. Soc. Amer. 31, 213-222 (1948).

J. Opt. Soc. Amer. A (2)

H.-I. Lee, "Wave propagation and resonance in four-layer systems for organic electro-luminescent diodes," J. Opt. Soc. Amer. A 24, 3017-3035 (2007).

I. Breukelaar, P. Berini, "Long-range surface plasmon polariton mode cutoff and radiation in slab waveguide," J. Opt. Soc. Amer. A 23, 1971-1977 (2006).

J. Opt. Soc. Amer. B (1)

M. Liscidini, J. E. Sipe, "Analysis of Bloch-surface-wave assisted diffraction-based biosensors," J. Opt. Soc. Amer. B 26, 279-289 (2009).

Math. Comput. (1)

L. M. Delves, J. N. Lyness, "A numerical method for locating the zeros of an analytic function," Math. Comput. 21, 543-560 (1967).

Nature Mater. (1)

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, F. Capasso, "Designer spoof surface plasmon structures collimate terahertz laser beams," Nature Mater. 9, 730-735 (2010).

Nature Phys. (1)

D. E. Chang, A. S. Sørensen, E. A. Demler, M. D. Lukin, "A single-photon transistor using nanoscale surface plasmons," Nature Phys. 3, 807-812 (2007).

Opt. Exp. (1)

X. Yang, B. Zeng, C. Wang, X. Luo, "Breaking the feature sizes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer," Opt. Exp. 17, 21560-21565 (2009).

Photon. Nanostruct.—Funda. Appl. (1)

H.-I. Lee, "Wave classification and resonant excitations in lossy metal-dielectric multilayers," Photon. Nanostruct.—Funda. Appl. 8, 183-197 (2010).

Phys. Rep. (1)

G. W. Ford, W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces," Phys. Rep. 113, 195-287 (1984).

Phys. Rev. A (4)

C. A. Lütken, F. Ravndal, "Energy-level shifts in atoms between metallic planes," Phys. Rev. A 31, 2082-2090 (1985).

D. T. Alves, F. A. Barone, C. Farina, A. C. Tort, "Influence of two parallel plates on atomic levels," Phys. Rev. A 67, 022103 (2003).

C. Garcia-Segundo, H. Yan, M. S. Zhan, "Atom trap with surface plasmon and evanescent field," Phys. Rev. A 75, 030902(R)-1-030902(R)-4 (2007).

Q. Sun, M. Al-Amri, A. Kamli, M. S. Zubairy, "Lamb shift due to surface plasmon polariton modes," Phys. Rev. A 77, 062501-1-062501-6 (2008).

Phys. Rev. B (1)

I. R. Hooper, J. R. Sambles, "Surface plasmon polaritons on narrow-ridged short-pitch metal gratings," Phys. Rev. B 66, 205408 (2002).

Physica B: Cond. Matter (1)

J. Pritz, L. M. Woods, "Radiative electromagnetic modes in concentric cylindrical layers," Physica B: Cond. Matter 404, 1585-1590 (2009).

Rep. Prog. Phys. (1)

H. Walther, B. T. H. Varcoe, B.-G. Englert, T. Becker, "Cavity quantum electrodynamics," Rep. Prog. Phys. 69, 1325 (2006).

Science (1)

N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 308, 534-537 (2005).

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