Abstract

Polaritonic slot waveguides have been explored as a means of manipulating nanoscale fields to compete in the race for the sub-diffractional confinement of light. Hexagonal boron nitride (h-BN), when incorporated into hyperbolic-insulator-hyperbolic (HIH) configurations, is a strong contender, with its naturally occurring anisotropy allowing it to strongly confine and enhance local fields. However, while the volumetric phonon polaritons of h-BN have been widely used for these means, its hyperbolic surface phonon polaritons (HSPhPs) or D’yakonov polaritons contain untapped potential and are widely unused. In this paper, we qualitatively discuss the hybridization of fundamental hyperbolic surface phonon polariton modes in an HIH slot waveguide. The resulting symmetric dark, or lower mode, is then used to design a patch antenn, which shows possibilities for applying the familiar microstrip transmission-line approach of antenna design to this HSPhP antenna.

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

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2018 (1)

Y. Yang, M. F. Finch, D. Xiong, and B. A. Lail, “Hybrid long-range hyperbolic phonon polariton waveguide using hexagonal boron nitride for mid-infrared subwavelength confinement,” Opt. Express 26(20), 26272–26282 (2018).
[Crossref] [PubMed]

2017 (3)

V. A. Zenin, S. Choudhury, S. Saha, V. M. Shalaev, A. Boltasseva, and S. I. Bozhevolnyi, “Hybrid plasmonic waveguides formed by metal coating of dielectric ridges,” Opt. Express 25(11), 12295–12302 (2017).
[Crossref] [PubMed]

F. J. Alfaro-Mozaz, P. Alonso-González, S. Vélez, I. Dolado, M. Autore, S. Mastel, F. Casanova, L. E. Hueso, P. Li, A. Y. Nikitin, and R. Hillenbrand, “Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas,” Nat. Commun. 8, 15624 (2017).
[Crossref] [PubMed]

P. Li, I. Dolado, F. J. Alfaro-Mozaz, A. Y. Nikitin, F. Casanova, L. E. Hueso, S. Vélez, and R. Hillenbrand, “Optical nanoimaging of hyperbolic surface polaritons at the edges of van der waals materials,” Nano Lett. 17(1), 228–235 (2017).
[Crossref] [PubMed]

2016 (7)

A. Nemilentsau, T. Low, and G. Hanson, “Anisotropic 2D materials for tunable hyperbolic plasmonics,” Phys. Rev. Lett. 116(6), 066804 (2016).
[Crossref] [PubMed]

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

G. Wang, W. Zhang, J. Lu, and H. Zhao, “Dispersion and optical gradient force from high-order mode coupling between two hyperbolic metamaterial waveguides,” Phys. Lett. A 380(35), 2774–2780 (2016).
[Crossref]

Y. Xu, N. Premkumar, Y. Yang, and B. A. Lail, “Hybrid surface phononic waveguide using hyperbolic boron nitride,” Opt. Express 24(15), 17183–17192 (2016).
[Crossref] [PubMed]

W. Adams, M. Sadatgol, and D. Ö. Güney, “Review of near-field optics and superlenses for sub-diffraction-limited nano-imaging,” AIP Adv. 6(10), 100701 (2016).
[Crossref]

B. Zhu, G. Ren, Y. Gao, H. Li, B. Wu, and S. Jian, “Strong light confinement and gradient force in a hexagonal boron nitride slot waveguide,” Opt. Lett. 41(21), 4991–4994 (2016).
[Crossref] [PubMed]

Z. Le, L. Yin, Y. Zou, and X. Wu, “Slab waveguide theory for general multi-slot waveguide,” J. Mod. Opt. 63(13), 1–10 (2016).
[Crossref]

2015 (3)

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Long-range plasmonic waveguides with hyperbolic cladding,” Opt. Express 23(24), 31109–31119 (2015).
[Crossref] [PubMed]

J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic plasmons and topological transitions over uniaxial metasurfaces,” Phys. Rev. Lett. 114(23), 233901 (2015).
[Crossref] [PubMed]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

2014 (4)

G. Yuan, L. Gao, Y. Chen, X. Liu, J. Wang, and Z. Wang, “Improvement of optical sensing performances of a double-slot-waveguide-based ring resonator sensor on silicon-on-insulator platform,” Optik (Stuttg.) 125(2), 850–854 (2014).
[Crossref]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. C. Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5(1), 5221 (2014).
[Crossref] [PubMed]

E. Cojocaru, “Comparative analysis of Dyakonov hybrid surface waves at dielectric–elliptic and dielectric–hyperbolic media interfaces,” J. Opt. Soc. Am. B 31(11), 2558–2564 (2014).
[Crossref]

2013 (2)

X. Li, X. Feng, K. Cui, F. Liu, and Y. Huang, “Designing low transmission loss silicon slot waveguide at wavelength band of high material absorption,” Opt. Commun. 306, 131–134 (2013).
[Crossref]

D. Li, N. M. Lawandy, and R. Zia, “Surface phonon-polariton enhanced optical forces in silicon carbide nanostructures,” Opt. Express 21(18), 20900–20910 (2013).
[Crossref] [PubMed]

2012 (2)

J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, O. Fedosenko, S. Machulik, A. Aleksandrova, G. Monastyrskyi, Y. Flores, and W. Ted Masselink, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51(28), 6789–6798 (2012).
[Crossref] [PubMed]

L. Yousefi and A. C. Foster, “Waveguide-fed optical hybrid plasmonic patch nano-antenna,” Opt. Express 20(16), 18326–18335 (2012).
[Crossref] [PubMed]

2011 (2)

J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11327–11331 (2011).
[Crossref] [PubMed]

S. Xiao, Y. Li, Y. Hao, X. Jiang, and J. Yang, “High-speed compact silicon digital optical switch with slot structure,” Optik (Stuttg.) 122(11), 955–959 (2011).
[Crossref]

2010 (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

2008 (3)

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
[Crossref]

2007 (4)

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007).
[Crossref]

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]

C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32(21), 3080–3082 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

2006 (1)

L. V. Alekseyev and E. Narimanov, “Slow light and 3D imaging with non-magnetic negative index systems,” Opt. Express 14(23), 11184–11193 (2006).
[Crossref] [PubMed]

2005 (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

2004 (2)

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[Crossref] [PubMed]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[Crossref]

2003 (1)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

1988 (1)

M. I. D’yakonov, “New type of electromagnetic wave propagating at an interface,” Zh. Eksp. Teor. Fiz 94, 119–123 (1988).

Adams, W.

W. Adams, M. Sadatgol, and D. Ö. Güney, “Review of near-field optics and superlenses for sub-diffraction-limited nano-imaging,” AIP Adv. 6(10), 100701 (2016).
[Crossref]

Aleksandrova, A.

J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, O. Fedosenko, S. Machulik, A. Aleksandrova, G. Monastyrskyi, Y. Flores, and W. Ted Masselink, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51(28), 6789–6798 (2012).
[Crossref] [PubMed]

Alekseyev, L. V.

L. V. Alekseyev and E. Narimanov, “Slow light and 3D imaging with non-magnetic negative index systems,” Opt. Express 14(23), 11184–11193 (2006).
[Crossref] [PubMed]

Alfaro-Mozaz, F. J.

F. J. Alfaro-Mozaz, P. Alonso-González, S. Vélez, I. Dolado, M. Autore, S. Mastel, F. Casanova, L. E. Hueso, P. Li, A. Y. Nikitin, and R. Hillenbrand, “Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas,” Nat. Commun. 8, 15624 (2017).
[Crossref] [PubMed]

P. Li, I. Dolado, F. J. Alfaro-Mozaz, A. Y. Nikitin, F. Casanova, L. E. Hueso, S. Vélez, and R. Hillenbrand, “Optical nanoimaging of hyperbolic surface polaritons at the edges of van der waals materials,” Nano Lett. 17(1), 228–235 (2017).
[Crossref] [PubMed]

Almeida, V. R.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[Crossref] [PubMed]

Alonso-Gonzalez, P.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Alonso-González, P.

F. J. Alfaro-Mozaz, P. Alonso-González, S. Vélez, I. Dolado, M. Autore, S. Mastel, F. Casanova, L. E. Hueso, P. Li, A. Y. Nikitin, and R. Hillenbrand, “Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas,” Nat. Commun. 8, 15624 (2017).
[Crossref] [PubMed]

Alù, A.

J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic plasmons and topological transitions over uniaxial metasurfaces,” Phys. Rev. Lett. 114(23), 233901 (2015).
[Crossref] [PubMed]

Autore, M.

F. J. Alfaro-Mozaz, P. Alonso-González, S. Vélez, I. Dolado, M. Autore, S. Mastel, F. Casanova, L. E. Hueso, P. Li, A. Y. Nikitin, and R. Hillenbrand, “Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas,” Nat. Commun. 8, 15624 (2017).
[Crossref] [PubMed]

Babicheva, V. E.

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Long-range plasmonic waveguides with hyperbolic cladding,” Opt. Express 23(24), 31109–31119 (2015).
[Crossref] [PubMed]

Barrios, C. A.

C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32(21), 3080–3082 (2007).
[Crossref] [PubMed]

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[Crossref] [PubMed]

Bartal, G.

J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11327–11331 (2011).
[Crossref] [PubMed]

Basov, D. N.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. C. Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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A. Nemilentsau, T. Low, and G. Hanson, “Anisotropic 2D materials for tunable hyperbolic plasmonics,” Phys. Rev. Lett. 116(6), 066804 (2016).
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F. J. Alfaro-Mozaz, P. Alonso-González, S. Vélez, I. Dolado, M. Autore, S. Mastel, F. Casanova, L. E. Hueso, P. Li, A. Y. Nikitin, and R. Hillenbrand, “Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas,” Nat. Commun. 8, 15624 (2017).
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A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
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J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5(1), 5221 (2014).
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P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
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B. Zhu, G. Ren, Y. Gao, H. Li, B. Wu, and S. Jian, “Strong light confinement and gradient force in a hexagonal boron nitride slot waveguide,” Opt. Lett. 41(21), 4991–4994 (2016).
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C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32(21), 3080–3082 (2007).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
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Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
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P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
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J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, O. Fedosenko, S. Machulik, A. Aleksandrova, G. Monastyrskyi, Y. Flores, and W. Ted Masselink, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51(28), 6789–6798 (2012).
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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. C. Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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Y. Yang, M. F. Finch, D. Xiong, and B. A. Lail, “Hybrid long-range hyperbolic phonon polariton waveguide using hexagonal boron nitride for mid-infrared subwavelength confinement,” Opt. Express 26(20), 26272–26282 (2018).
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Y. Xu, N. Premkumar, Y. Yang, and B. A. Lail, “Hybrid surface phononic waveguide using hyperbolic boron nitride,” Opt. Express 24(15), 17183–17192 (2016).
[Crossref] [PubMed]

Yao, J.

J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11327–11331 (2011).
[Crossref] [PubMed]

Yin, L.

Z. Le, L. Yin, Y. Zou, and X. Wu, “Slab waveguide theory for general multi-slot waveguide,” J. Mod. Opt. 63(13), 1–10 (2016).
[Crossref]

Yin, X.

J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11327–11331 (2011).
[Crossref] [PubMed]

Yousefi, L.

L. Yousefi and A. C. Foster, “Waveguide-fed optical hybrid plasmonic patch nano-antenna,” Opt. Express 20(16), 18326–18335 (2012).
[Crossref] [PubMed]

Yoxall, E.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Yuan, G.

G. Yuan, L. Gao, Y. Chen, X. Liu, J. Wang, and Z. Wang, “Improvement of optical sensing performances of a double-slot-waveguide-based ring resonator sensor on silicon-on-insulator platform,” Optik (Stuttg.) 125(2), 850–854 (2014).
[Crossref]

Zenin, V. A.

V. A. Zenin, S. Choudhury, S. Saha, V. M. Shalaev, A. Boltasseva, and S. I. Bozhevolnyi, “Hybrid plasmonic waveguides formed by metal coating of dielectric ridges,” Opt. Express 25(11), 12295–12302 (2017).
[Crossref] [PubMed]

Zettl, A.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. C. Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Zhang, W.

G. Wang, W. Zhang, J. Lu, and H. Zhao, “Dispersion and optical gradient force from high-order mode coupling between two hyperbolic metamaterial waveguides,” Phys. Lett. A 380(35), 2774–2780 (2016).
[Crossref]

Zhang, X.

J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11327–11331 (2011).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Zhao, H.

G. Wang, W. Zhang, J. Lu, and H. Zhao, “Dispersion and optical gradient force from high-order mode coupling between two hyperbolic metamaterial waveguides,” Phys. Lett. A 380(35), 2774–2780 (2016).
[Crossref]

Zhu, B.

B. Zhu, G. Ren, Y. Gao, H. Li, B. Wu, and S. Jian, “Strong light confinement and gradient force in a hexagonal boron nitride slot waveguide,” Opt. Lett. 41(21), 4991–4994 (2016).
[Crossref] [PubMed]

Zia, R.

D. Li, N. M. Lawandy, and R. Zia, “Surface phonon-polariton enhanced optical forces in silicon carbide nanostructures,” Opt. Express 21(18), 20900–20910 (2013).
[Crossref] [PubMed]

Zou, Y.

Z. Le, L. Yin, Y. Zou, and X. Wu, “Slab waveguide theory for general multi-slot waveguide,” J. Mod. Opt. 63(13), 1–10 (2016).
[Crossref]

ACS Photonics (1)

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

AIP Adv. (1)

W. Adams, M. Sadatgol, and D. Ö. Güney, “Review of near-field optics and superlenses for sub-diffraction-limited nano-imaging,” AIP Adv. 6(10), 100701 (2016).
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Appl. Opt. (1)

J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, O. Fedosenko, S. Machulik, A. Aleksandrova, G. Monastyrskyi, Y. Flores, and W. Ted Masselink, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51(28), 6789–6798 (2012).
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G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25(9), 2511–2521 (2007).
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Z. Le, L. Yin, Y. Zou, and X. Wu, “Slab waveguide theory for general multi-slot waveguide,” J. Mod. Opt. 63(13), 1–10 (2016).
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J. Opt. Soc. Am. B (1)

E. Cojocaru, “Comparative analysis of Dyakonov hybrid surface waves at dielectric–elliptic and dielectric–hyperbolic media interfaces,” J. Opt. Soc. Am. B 31(11), 2558–2564 (2014).
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P. Li, I. Dolado, F. J. Alfaro-Mozaz, A. Y. Nikitin, F. Casanova, L. E. Hueso, S. Vélez, and R. Hillenbrand, “Optical nanoimaging of hyperbolic surface polaritons at the edges of van der waals materials,” Nano Lett. 17(1), 228–235 (2017).
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Nat. Commun. (2)

J. D. Caldwell, A. V. Kretinin, Y. Chen, V. Giannini, M. M. Fogler, Y. Francescato, C. T. Ellis, J. G. Tischler, C. R. Woods, A. J. Giles, M. Hong, K. Watanabe, T. Taniguchi, S. A. Maier, and K. S. Novoselov, “Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride,” Nat. Commun. 5(1), 5221 (2014).
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F. J. Alfaro-Mozaz, P. Alonso-González, S. Vélez, I. Dolado, M. Autore, S. Mastel, F. Casanova, L. E. Hueso, P. Li, A. Y. Nikitin, and R. Hillenbrand, “Nanoimaging of resonating hyperbolic polaritons in linear boron nitride antennas,” Nat. Commun. 8, 15624 (2017).
[Crossref] [PubMed]

Nat. Mater. (1)

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008).
[Crossref] [PubMed]

Nat. Photonics (2)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Opt. Commun. (1)

X. Li, X. Feng, K. Cui, F. Liu, and Y. Huang, “Designing low transmission loss silicon slot waveguide at wavelength band of high material absorption,” Opt. Commun. 306, 131–134 (2013).
[Crossref]

Opt. Express (8)

V. A. Zenin, S. Choudhury, S. Saha, V. M. Shalaev, A. Boltasseva, and S. I. Bozhevolnyi, “Hybrid plasmonic waveguides formed by metal coating of dielectric ridges,” Opt. Express 25(11), 12295–12302 (2017).
[Crossref] [PubMed]

D. Li, N. M. Lawandy, and R. Zia, “Surface phonon-polariton enhanced optical forces in silicon carbide nanostructures,” Opt. Express 21(18), 20900–20910 (2013).
[Crossref] [PubMed]

Y. Xu, N. Premkumar, Y. Yang, and B. A. Lail, “Hybrid surface phononic waveguide using hyperbolic boron nitride,” Opt. Express 24(15), 17183–17192 (2016).
[Crossref] [PubMed]

Y. Yang, M. F. Finch, D. Xiong, and B. A. Lail, “Hybrid long-range hyperbolic phonon polariton waveguide using hexagonal boron nitride for mid-infrared subwavelength confinement,” Opt. Express 26(20), 26272–26282 (2018).
[Crossref] [PubMed]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Long-range plasmonic waveguides with hyperbolic cladding,” Opt. Express 23(24), 31109–31119 (2015).
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L. V. Alekseyev and E. Narimanov, “Slow light and 3D imaging with non-magnetic negative index systems,” Opt. Express 14(23), 11184–11193 (2006).
[Crossref] [PubMed]

L. Yousefi and A. C. Foster, “Waveguide-fed optical hybrid plasmonic patch nano-antenna,” Opt. Express 20(16), 18326–18335 (2012).
[Crossref] [PubMed]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

Opt. Lett. (3)

B. Zhu, G. Ren, Y. Gao, H. Li, B. Wu, and S. Jian, “Strong light confinement and gradient force in a hexagonal boron nitride slot waveguide,” Opt. Lett. 41(21), 4991–4994 (2016).
[Crossref] [PubMed]

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
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C. A. Barrios, K. B. Gylfason, B. Sánchez, A. Griol, H. Sohlström, M. Holgado, and R. Casquel, “Slot-waveguide biochemical sensor,” Opt. Lett. 32(21), 3080–3082 (2007).
[Crossref] [PubMed]

Optik (Stuttg.) (2)

G. Yuan, L. Gao, Y. Chen, X. Liu, J. Wang, and Z. Wang, “Improvement of optical sensing performances of a double-slot-waveguide-based ring resonator sensor on silicon-on-insulator platform,” Optik (Stuttg.) 125(2), 850–854 (2014).
[Crossref]

S. Xiao, Y. Li, Y. Hao, X. Jiang, and J. Yang, “High-speed compact silicon digital optical switch with slot structure,” Optik (Stuttg.) 122(11), 955–959 (2011).
[Crossref]

Phys. Lett. A (1)

G. Wang, W. Zhang, J. Lu, and H. Zhao, “Dispersion and optical gradient force from high-order mode coupling between two hyperbolic metamaterial waveguides,” Phys. Lett. A 380(35), 2774–2780 (2016).
[Crossref]

Phys. Rev. A (1)

Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
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D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
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J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic plasmons and topological transitions over uniaxial metasurfaces,” Phys. Rev. Lett. 114(23), 233901 (2015).
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A. Nemilentsau, T. Low, and G. Hanson, “Anisotropic 2D materials for tunable hyperbolic plasmonics,” Phys. Rev. Lett. 116(6), 066804 (2016).
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Proc. Natl. Acad. Sci. U.S.A. (1)

J. Yao, X. Yang, X. Yin, G. Bartal, and X. Zhang, “Three-dimensional nanometer-scale optical cavities of indefinite medium,” Proc. Natl. Acad. Sci. U.S.A. 108(28), 11327–11331 (2011).
[Crossref] [PubMed]

Science (4)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. C. Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
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M. F. Finch, C. A. B. S. Filho, N. Premkumar, Y. Yang, and B. A. Lail, “A 4H-SiC phonon polariton enhanced hybrid waveguide,” in Proceedings of IEEE International Symposium on Antennas and Propagation (APSURSI, 2016), pp. 987–988.
[Crossref]

D. M. Pozar, Microwave Engineering (Wiley Global Education, 2011).

C. A. Balanis, Antenna Theory: Analysis and Design (John Wiley & Sons, 2012).

K. F. Lee and K. M. Luk, Microstrip Patch Antenna (World Scientific, 2011).

R. Garg, P. Bhartia, I. J. Bahi, and A. Ittipiboon, Microstrip Antenna Design Handbook (Artech House, 2001).

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Figures (10)

Fig. 1
Fig. 1 (a) Dispersion curve of the SM0 mode of a semi-infinite h-BN slab with 0.6µm thickness. Inset shows the XY cross-sectional Re(Ey) of the waveguide which features the interaction between the two SM0 modes propagating along the Z direction on the YZ surfaces of h-BN waveguide at 1400cm−1. (b) Dispersion curve of the h-BN waveguide with 0.6µm thickness varied with the width of the waveguide from 0.1µm to 20µm at 1400cm−1.
Fig. 2
Fig. 2 Normalized spatial distribution of the Y-component of electrical field, Re(Ey) for the fundamental (a) SM0-S and (b) SM0-A modes.
Fig. 3
Fig. 3 Re(Ey) distribution of a slot waveguide with large separation between the h-BN waveguides (black rectangles) with (a) SM0-S lower, (b) SM0-S upper, (c) SM0-A lower and (d) SM0-A upper modes.
Fig. 4
Fig. 4 Re(Ey) of (a) SM0-S lower, (b) SM0-S upper, (c) SM0-A lower, (d) SM0-A upper at 1400cm−1 for H = 0.6µm and W = 1.6µm. Insets show the H-field vector (red arrows) and E-field vector (blue arrows) of each hybrid mode.
Fig. 5
Fig. 5 (a) Normalized energy density along x = 0 [dashed line in inset] for T = 50nm and H = 0.6µm shows the confinement and enhancement in the SiO2 layer. The shaded orange and blue areas represent the SiO2 and h-BN regions, respectively. (b) Re(Ey) of the hybrid SM0-S lower mode and (c) Re(Ey) of the hybrid volumetric mode with magnetic field vector (red arrows) and electric field vector (blue arrows).
Fig. 6
Fig. 6 (a) Real index nsemi-inf of the hybrid SM0-S lower mode of a semi-infinite h-BN slot waveguide when H = 0.6µm from 1380cm−1 to 1520cm−1. Inset shows the normalized Re(Ey) distribution of the SM0-S lower mode for a semi-infinite h-BN slot waveguide at 1400cm−1. (b) Analytically fitted and simulated real effective index neff of the SM0-S lower slot-waveguide mode versus the width, W1 for different values of h-BN waveguide thickness H (colored lines) and with SiO2 thickness T = 50nm at 1400cm−1.
Fig. 7
Fig. 7 Configuration of hybrid h-BN slot waveguide fed h-BN patch antenna. The SiO2 layer is shown in orange, while the h-BN layers are shown in blue with optical axis (OA) indicated by the red arrow. W1 and W2 are the widths of the h-BN slot waveguide and h-BN patch antenna, respectively, L is the length of h-BN patch antenna and H and T are the thicknesses of the h-BN layer and the SiO2 layer, respectively.
Fig. 8
Fig. 8 Re[Ey(z)] and Re[Ez(z)] at the center of the SiO2 layer along the Z-axis for the hybrid SM0-S lower slot waveguide with W1 = 1µm and H = 0.6µm at 1400cm−1.
Fig. 9
Fig. 9 Normalized Re(Ey) in the slot of the hybrid SM0-S lower slot waveguide fed h-BN patch antenna. Inset shows the electric field vectors in the SiO2 layer in the YZ plane.
Fig. 10
Fig. 10 (a) Radiation field of the h-BN slot waveguide fed h-BN patch antenna and (b) the ratio of the reflected wave power due to the impedance mismatch to the guided wave power in the slot waveguide, S11.

Equations (7)

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k 2 k e 2 ε + k 2 ε = k 0 2
θ( ω )=arctan ε ( ω ) ε ( ω )
n eff =n semi-inf ×f( H, W 1 )
f( H, W 1 )= 10.541.408 W 1 +12.36H+22.82 W 1 H 4.8010.8356 W 1 +23.91H+21.76 W 1 H
Z Waveguide = Z 0 n eff
Z Antenna = 1 2G rad
G rad = W 2 120λ 0 [ 1 1 24 ( 2πT λ 0 ) 2 ]

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