Abstract

We have theoretically studied the optical properties of a filled slot metamaterial waveguide with lateral slab regions consisting of alternating silver–silica multilayers. It is shown that this geometry improves the subwavelength confinement of guided light and that the particular metal–dielectric ratio of 15nm/10nm results in substantially enhanced transmission, as compared with metal–dielectric–metal slot waveguides having similar dimensions.

© 2014 Optical Society of America

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Corrections

Evgeny G. Mironov, Liming Liu, Haroldo T. Hattori, and Richard M. De La Rue, "Analysis of silica-filled slot waveguides based on hyperbolic metamaterials: erratum," J. Opt. Soc. Am. B 31, 2285-2285 (2014)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-31-10-2285

References

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2013 (3)

H. Nguyen, N. Yazawa, S. Hashimoto, S. Otsuka, and T. Baba, “Sub-100  μm photonic crystal Si optical modulators: spectral, athermal, and high speed performance,” IEEE J. Sel. Top. Quantum Electron. 19, 3400811 (2013).
[CrossRef]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[CrossRef]

E. G. Mironov, Z. Li, H. T. Hattori, K. Vora, H. H. Tan, and C. Jagadish, “Titanium nano-antenna for high-power pulsed operation,” J. Lightwave Technol. 31, 2459–2466 (2013).
[CrossRef]

2012 (1)

2009 (7)

Z. Wang, N. Zhu, Y. Tang, L. Wosinski, D. Dai, and S. He, “Ultracompact low-loss coupler between strip and slot waveguides,” Opt. Lett. 34, 1498–1500 (2009).
[CrossRef]

M. T. Hill, E. M. Marell, S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y. S. Oei, R. Nötzel, C. Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Opt. Express 17, 20878–20884 (2009).
[CrossRef]

H. J. Y. Allen, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 675–677 (2009).
[CrossRef]

J. Van Campehout, P. R. A. Binetti, P. R. Romeo, P. Regreny, C. Seassal, X. J. M. Leijtens, T. De Vries, Y. S. Oei, R. P. J. Van Veldhove, R. Nötzel, L. Di Cioccio, J. M. Fedeli, M. K. Smit, D. Van Thourhout, and R. Baets, “Low-footprint optical interconnect on an SOI chip through heterogeneous integration of InP-Based microdisk lasers and microdetectors,” IEEE Photon. Technol. Lett. 21, 522–524 (2009).
[CrossRef]

H. T. Hattori, D. Liu, H. H. Tan, and C. Jagadish, “Large square resonator laser with quasi single-mode operation,” IEEE Photon. Technol. Lett. 21, 359–361 (2009).
[CrossRef]

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, “Modal analysis and coupling in metal-insulator-metal waveguides,” Phys. Rev. B 79, 035120 (2009).
[CrossRef]

2008 (4)

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photonics 2, 365–370 (2008).
[CrossRef]

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsesquioxane electron-beam resist,” Electron. Lett. 44, 115–116 (2008).
[CrossRef]

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14, 1448–1461 (2008).
[CrossRef]

H. T. Hattori, “Analysis of optically pumped equilateral triangular microlasers with three mode-selective trenches,” Appl. Opt. 47, 2178–2185 (2008).
[CrossRef]

2007 (3)

G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers,” Opt. Lett. 32, 1495–1497 (2007).
[CrossRef]

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25, 2511–2521 (2007).
[CrossRef]

H. T. Hattori, I. McKerracher, H. H. Tan, C. Jagadish, and R. M. De La Rue, “In-plane coupling of light from InP-based photonic crystal band-edge lasers into single-mode waveguides,” IEEE J. Quantum Electron. 43, 279–286 (2007).
[CrossRef]

2006 (5)

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
[CrossRef]

L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31, 2133–2135 (2006).
[CrossRef]

P. U. Jepsen, B. M. Fischer, A. Thoman, H. Helm, J. Y. Suh, R. Lopez, and R. F. Haglund, “Metal-insulator phase transition in a VO2 thin film observed with terahertz spectroscopy,” Phys. Rev. B 74, 205103 (2006).
[CrossRef]

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

2004 (2)

2003 (2)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[CrossRef]

T. Asano, M. Mochizuki, S. Noda, M. Okano, and M. Imada, “A channel drop filter using a single-defect in a 2-D photonic crystal slab: defect engineering with respect to polarization mode and ratio of emissions from upper to lower sides,” J. Lightwave Technol. 21, 1370–1376 (2003).
[CrossRef]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

2000 (2)

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000).
[CrossRef]

H. T. Hattori, V. M. Schneider, and O. Lisboa, “Cantor set fiber Bragg grating,” J. Opt. Soc. Am. A 17, 1583–1589 (2000).
[CrossRef]

1999 (1)

M. Fujita, A. Sakai, and T. Baba, “Ultra-small and ultra-low threshold microdisk injection laser: design, fabrication, lasing characteristics and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673–681 (1999).
[CrossRef]

1998 (1)

1996 (1)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures at near infrared wavelength,” Nature 383, 699–702 (1996).
[CrossRef]

1994 (2)

D. Liu and C. Svensson, “Power consumption estimation in CMOS VLSI circuit,” IEEE J. Solid-State Circuits 29, 663–670 (1994).
[CrossRef]

C. A. Foss, G. L. Hornyak, J. A. Stockert, and C. R. Martin, “Template-synthesized nanoscopic gold particles: optical spectra and the effects of particle size and shape,” J. Phys. Chem. 98, 2963–2971 (1994).
[CrossRef]

1986 (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Allen, H. J. Y.

H. J. Y. Allen, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457, 675–677 (2009).
[CrossRef]

Almeida, V. R.

Antoniou, N.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[CrossRef]

Asano, T.

Atwater, H. A.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
[CrossRef]

Baba, T.

H. Nguyen, N. Yazawa, S. Hashimoto, S. Otsuka, and T. Baba, “Sub-100  μm photonic crystal Si optical modulators: spectral, athermal, and high speed performance,” IEEE J. Sel. Top. Quantum Electron. 19, 3400811 (2013).
[CrossRef]

M. Fujita, A. Sakai, and T. Baba, “Ultra-small and ultra-low threshold microdisk injection laser: design, fabrication, lasing characteristics and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673–681 (1999).
[CrossRef]

Baets, R.

J. Van Campehout, P. R. A. Binetti, P. R. Romeo, P. Regreny, C. Seassal, X. J. M. Leijtens, T. De Vries, Y. S. Oei, R. P. J. Van Veldhove, R. Nötzel, L. Di Cioccio, J. M. Fedeli, M. K. Smit, D. Van Thourhout, and R. Baets, “Low-footprint optical interconnect on an SOI chip through heterogeneous integration of InP-Based microdisk lasers and microdetectors,” IEEE Photon. Technol. Lett. 21, 522–524 (2009).
[CrossRef]

G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers,” Opt. Lett. 32, 1495–1497 (2007).
[CrossRef]

Barrios, C. A.

Benson, T. M.

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
[CrossRef]

Berini, P.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484–10503 (2000).
[CrossRef]

Binetti, P. R. A.

J. Van Campehout, P. R. A. Binetti, P. R. Romeo, P. Regreny, C. Seassal, X. J. M. Leijtens, T. De Vries, Y. S. Oei, R. P. J. Van Veldhove, R. Nötzel, L. Di Cioccio, J. M. Fedeli, M. K. Smit, D. Van Thourhout, and R. Baets, “Low-footprint optical interconnect on an SOI chip through heterogeneous integration of InP-Based microdisk lasers and microdetectors,” IEEE Photon. Technol. Lett. 21, 522–524 (2009).
[CrossRef]

Boriskina, S. V.

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
[CrossRef]

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures at near infrared wavelength,” Nature 383, 699–702 (1996).
[CrossRef]

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33, 5186–5201 (1986).
[CrossRef]

Capasso, F.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[CrossRef]

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14, 1448–1461 (2008).
[CrossRef]

Chen, L.

Chong, H.

L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Crozier, K. B.

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14, 1448–1461 (2008).
[CrossRef]

Cubukcu, E.

E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Top. Quantum Electron. 14, 1448–1461 (2008).
[CrossRef]

Dai, D.

De La Rue, R. M.

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsesquioxane electron-beam resist,” Electron. Lett. 44, 115–116 (2008).
[CrossRef]

H. T. Hattori, I. McKerracher, H. H. Tan, C. Jagadish, and R. M. De La Rue, “In-plane coupling of light from InP-based photonic crystal band-edge lasers into single-mode waveguides,” IEEE J. Quantum Electron. 43, 279–286 (2007).
[CrossRef]

L. O’Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42, 1454–1455 (2006).
[CrossRef]

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic bandgap structures at near infrared wavelength,” Nature 383, 699–702 (1996).
[CrossRef]

De Vries, T.

J. Van Campehout, P. R. A. Binetti, P. R. Romeo, P. Regreny, C. Seassal, X. J. M. Leijtens, T. De Vries, Y. S. Oei, R. P. J. Van Veldhove, R. Nötzel, L. Di Cioccio, J. M. Fedeli, M. K. Smit, D. Van Thourhout, and R. Baets, “Low-footprint optical interconnect on an SOI chip through heterogeneous integration of InP-Based microdisk lasers and microdetectors,” IEEE Photon. Technol. Lett. 21, 522–524 (2009).
[CrossRef]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

Di Cioccio, L.

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Figures (11)

Fig. 1.
Fig. 1.

Slot waveguide cross section.

Fig. 2.
Fig. 2.

Effective dielectric permittivity of the slab metal–dielectric regions (fAg=0.6) calculated using the Maxwell–Garnet theory [33,34].

Fig. 3.
Fig. 3.

Electric field profiles for (a) symmetric and (b) antisymmetric modes. Note that the field inside the slot is only amplified for the symmetric case.

Fig. 4.
Fig. 4.

(a) Ex profile for quasi-TE00 fundamental slot mode. (b) Ex profile for quasi-TE01 slot mode. (c) Ex profile for quasi-TE02 slot mode. (d) Ex profile for quasi-TE03 slot mode.

Fig. 5.
Fig. 5.

Real part of modal effective refractive index.

Fig. 6.
Fig. 6.

Imaginary part of modal effective refractive index.

Fig. 7.
Fig. 7.

Waveguide modal indices for different slot widths.

Fig. 8.
Fig. 8.

Dispersion for waveguide with 20 nm slot width.

Fig. 9.
Fig. 9.

Slot waveguide coupled with stripe waveguide.

Fig. 10.
Fig. 10.

Normalized transmission for the 20 nm gap width.

Fig. 11.
Fig. 11.

(a) Normalized Ex profile in logarithmic scale for 0nm/25nm silver/silicon layer thickness ratio. (b) Normalized Ex profile in logarithmic scale for 15nm/10nm silver/silicon layer thickness ratio. (c) Normalized Ex profile in logarithmic scale for 25nm/0nm silver/silicon layer thickness ratio.

Equations (6)

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εx=εz=fAgεAg+(1fAg)εSi,
εy=εAgεSifAgεSi+(1fAg)εAg,
εAg(ω)=εωp2ω2iωγc,
Ex=E0{neff,zcos(0.5kxLlateral+φ)Θ(x),(neff,z/εx)cos(kx(x0.5(Llateral+wslot)+φ),neff,zcos(0.5kxLside+φ)exp(γ(x0.5wslotLlateral)),0<x<0.5wslot0.5wslot<x<0.5wslot+Llateralx>0.5wslot+Llateral,
Θ(x)={cosh(γx)/cosh(0.5γwslot)sinh(γx)/sinh(0.5γwslot),
D(λ)=λ0c2neff,zλ02.

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