Abstract

Long propagation waveguides are critical for any photonic-on-chip applications. There has been an extensive investigation in using plasmon polaritons for near-infrared and optical networks, however, for mid- to long-wave IR applications phonon polaritons are required given that plasmonic polaritonic effects are negligible. In recent years, extensive research has been conducted on hexagonal boron nitride (h-BN), which has shown h-BN to have naturally occurring subwavelength, volumetrically confined hyperbolic phonon polaritons (HPhPs). This work presents numerical results for both long- and short-range phononic volumetric polariton modes in a slab of h-BN. A hybrid long-range phononic waveguide consisting of two identical dielectric cylinder wires symmetrically placed on each side of the h-BN slab is coupled to the long-range HPhP mode. Based on analytical coupled-mode theory and computational finite element analysis, we have investigated the modal characteristics of the hybrid long-range phonon polaritonic waveguide. Due to the strong coupling between the high index cylindrical-waveguide mode and the HPhPs in the h-BN thin film, subwavelength confinement can be achieved (modal area ranging from  102λo2 to  101λo2) while enabling long propagation distances (7λ0-370λ0).

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]

2017 (3)

P. Li, I. Dolado, F. J. Alfaro-Mozaz, A. Yu. 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]

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]

V. E. Babicheva, “Long-range propagation of plasmon and phonon polaritons in hyperbolic-metamaterial waveguides,” J. Opt. 19(12), 124013 (2017).
[Crossref]

2016 (4)

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]

F. Bigourdan, J. P. Hugonin, F. Marquier, C. Sauvan, and J. J. Greffet, “Nanoantenna for electrical generation of surface plasmon polaritons,” Phys. Rev. Lett. 116(10), 106803 (2016).
[Crossref] [PubMed]

T. Schädle and B. Mizaikoff, “Mid-infrared waveguides: a perspective,” Appl. Spectrosc. 70(10), 1625–1638 (2016).
[Crossref] [PubMed]

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface plasmon polariton graphene photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref] [PubMed]

2015 (4)

Z. Zhang and J. Wang, “Long-range hybrid wedge plasmonic waveguide,” Sci. Rep. 4(1), 6870 (2015).
[Crossref] [PubMed]

J. D. Caldwell, L. Lindsay, V. Giannini, I. Vurgaftman, T. L. Reinecke, S. A. Maier, and O. J. Glembocki, “Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons,” Nanophotonics 4(1), 44–68 (2015).
[Crossref]

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6(1), 6963 (2015).
[Crossref] [PubMed]

2014 (5)

E. Gil, V. G. Dubrovskii, G. Avit, Y. André, C. Leroux, K. Lekhal, J. Grecenkov, A. Trassoudaine, D. Castelluci, G. Monier, R. M. Ramdani, C. Robert-Goumet, L. Bideux, J. C. Harmand, and F. Glas, “Record pure zincblende phase in GaAs nanowires down to 5 nm in radius,” Nano Lett. 14(7), 3938–3944 (2014).
[Crossref] [PubMed]

B. G. Ghamsari, X. G. Xu, L. Gilburd, G. C. Walker, and P. Berini, “Mid-infrared surface phonon polaritons in boron-nitride nanotubes,” J. Opt. 16(11), 114008 (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. Castro 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]

Z. Jacob, “Hyperbolic phonon-polaritons,” Nat. Mater. 13(12), 1081–1083 (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]

2013 (1)

2012 (4)

L. Chen, X. Li, G. Wang, W. Li, S. Chen, L. Xiao, and D. Gao, “A silicon-based 3-D hybrid long-range plasmonic waveguide for nanophotonic integration,” J. Lightwave Technol. 30(1), 163–168 (2012).
[Crossref]

J. B. Khurgin and A. Boltasseva, “Reflecting upon the losses in plasmonics and metamaterials,” MRS Bull. 37(8), 768–779 (2012).
[Crossref]

L. Chen, T. Zhang, X. Li, and W. Huang, “Novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film,” Opt. Express 20(18), 20535–20544 (2012).
[Crossref] [PubMed]

S. A. Holmstrom, T. H. Stievater, M. W. Pruessner, D. Park, W. S. Rabinovich, J. B. Khurgin, C. J. K. Richardson, S. Kanakaraju, L. C. Calhoun, and R. Ghodssi, “Guided-mode phonon-polaritons in suspended waveguides,” Phys. Rev. B 86(16), 165120 (2012).
[Crossref]

2011 (1)

J. B. Khurgin and G. Sun, “Scaling of losses with size and wavelength in nanoplasmonics and metamaterials,” Appl. Phys. Lett. 99(21), 211106 (2011).
[Crossref]

2010 (2)

M. Ameen, A. Garcia-Etxarri, M. Schnell, R. Hillenbrand, and J. Aizpurua, “Infrared phononic nanoantennas: localized surface phonon polaritons in SiC disks,” Chin. Sci. Bull. 55(24), 2625–2628 (2010).
[Crossref]

H. C. Kim and X. Cheng, “Infrared dipole antenna enhanced by surface phonon polaritons,” Opt. Lett. 35(22), 3748–3750 (2010).
[Crossref] [PubMed]

2009 (3)

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1(3), 484–588 (2009).
[Crossref]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

J. C. Meyer, A. Chuvilin, G. Algara-Siller, J. Biskupek, and U. Kaiser, “Selective sputtering and atomic resolution imaging of atomically thin boron nitride membranes,” Nano Lett. 9(7), 2683–2689 (2009).
[Crossref] [PubMed]

2008 (4)

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]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10(10), 105018 (2008).
[Crossref]

Y. Joo, M. Jung, J. Yoon, S. Song, H. Won, S. Park, and J. Ju, “Long-range surface plasmon polaritons on asymmetric double-electrode structures,” Appl. Phys. Lett. 92(16), 161103 (2008).
[Crossref]

K. M. Pitman, A. M. Hofmeister, A. B. Corman, and A. K. Speck, “Optical properties of silicon carbide for astrophysical applications,” Astron. Astrophys. 483(2), 661–672 (2008).
[Crossref]

2007 (1)

R. Kirchain and L. Kimerling, “A road map for nanophotonics,” Nat. Photonics 1(6), 303–305 (2007).
[Crossref]

2004 (1)

N. Ocelic and R. Hillenbrand, “Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation,” Nat. Mater. 3(9), 606–609 (2004).
[Crossref] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

1991 (1)

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B Condens. Matter 44(11), 5855–5872 (1991).
[Crossref] [PubMed]

1986 (1)

L. Wendler and R. Haupt, “Long-range surface plasmon-phonon-polaritons,” J. Phys. C Solid State 19(11), 1871–1896 (1986).
[Crossref]

Aizpurua, J.

M. Ameen, A. Garcia-Etxarri, M. Schnell, R. Hillenbrand, and J. Aizpurua, “Infrared phononic nanoantennas: localized surface phonon polaritons in SiC disks,” Chin. Sci. Bull. 55(24), 2625–2628 (2010).
[Crossref]

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. Yu. 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]

Algara-Siller, G.

J. C. Meyer, A. Chuvilin, G. Algara-Siller, J. Biskupek, and U. Kaiser, “Selective sputtering and atomic resolution imaging of atomically thin boron nitride membranes,” Nano Lett. 9(7), 2683–2689 (2009).
[Crossref] [PubMed]

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]

Ameen, M.

M. Ameen, A. Garcia-Etxarri, M. Schnell, R. Hillenbrand, and J. Aizpurua, “Infrared phononic nanoantennas: localized surface phonon polaritons in SiC disks,” Chin. Sci. Bull. 55(24), 2625–2628 (2010).
[Crossref]

Andersen, T.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6(1), 6963 (2015).
[Crossref] [PubMed]

André, Y.

E. Gil, V. G. Dubrovskii, G. Avit, Y. André, C. Leroux, K. Lekhal, J. Grecenkov, A. Trassoudaine, D. Castelluci, G. Monier, R. M. Ramdani, C. Robert-Goumet, L. Bideux, J. C. Harmand, and F. Glas, “Record pure zincblende phase in GaAs nanowires down to 5 nm in radius,” Nano Lett. 14(7), 3938–3944 (2014).
[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]

Avit, G.

E. Gil, V. G. Dubrovskii, G. Avit, Y. André, C. Leroux, K. Lekhal, J. Grecenkov, A. Trassoudaine, D. Castelluci, G. Monier, R. M. Ramdani, C. Robert-Goumet, L. Bideux, J. C. Harmand, and F. Glas, “Record pure zincblende phase in GaAs nanowires down to 5 nm in radius,” Nano Lett. 14(7), 3938–3944 (2014).
[Crossref] [PubMed]

Babicheva, V. E.

V. E. Babicheva, “Long-range propagation of plasmon and phonon polaritons in hyperbolic-metamaterial waveguides,” J. Opt. 19(12), 124013 (2017).
[Crossref]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[Crossref] [PubMed]

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. 10(10), 105018 (2008).
[Crossref]

Basov, D. N.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6(1), 6963 (2015).
[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. Castro 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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Berini, P.

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Figures (7)

Fig. 1
Fig. 1 Schematic illustration of the proposed hybrid long-range phonon polariton waveguide which includes two identical GaAs cylinder wires with diameter d symmetrically placed on each side of a thin h-BN slab are separated with a spacer height h. The h-BN slab has thickness of t and this waveguide is embedded in air at mid-infrared wavelength λ 0 =6.6μm.
Fig. 2
Fig. 2 (a) The effective indices as a function of h-BN slab thickness t for hybrid and non-hybrid LRHPhP and SRHPhP waveguides. (b) The propagation distance for hybrid and non-hybrid LRHPhP and SRHPhP changing with t. The solid lines and broken lines represent long- and short-range HPhPs, respectively. The colored curves (red and green) represent hybrid waveguides for different spacer heights h. The black lines represent a h-BN thin slab embedded in low dielectric material exhibiting long and short range HPhPs.
Fig. 3
Fig. 3 (a) Normalized modal area ( A m / A 0 ) versus cylinder wire diameter d for different spacer height h (colored lines), compared with a pure cylinder mode (black line). (b) Hybrid propagation distance versus cylinder wire diameter d for different spacer height h (colored lines), compared with LRHPhP modes in Air-hBN-Air is denoted by the black dashed line.
Fig. 4
Fig. 4 The cross-sectional electromagnetic energy density distribution for (a) [d,h] = [2.5, 0.25] μm, (b) [d,h] = [1, 0.25] μm, (c) [d,h] = [1, 0.01] μm and (d) [d,h] = [1.5, 0.01] μm. The lower right-hand corner shows the magnetic field vectors for the hybrid LRHPhP waveguides.
Fig. 5
Fig. 5 Normalized energy density along x = 0 [dashed line in inset in (a)] for h = 0.01μm (a), 0.05µm (b), 0.1μm (c), 0.25µm (d) shows the confinement in the air spacer. The shaded grey and blue areas represent the two dielectric wires and h-BN slab regions, respectively. The energy density along y = ( t/2) + h [dashed line inset in (e)] for h = 0.01μm (e), 0.05µm (f), 0.1μm (g), 0.25μm (h).
Fig. 6
Fig. 6 Effective index of the hybrid LRHPhP waveguide for a range of spacer height h versus cylinder wire diameters d, n hyb (colored lines). For comparison, the effective indices of pure cylinder wire, n wire (black solid line), and pure LRHPhP, n LRHPhP (black dashed line) are plotted.
Fig. 7
Fig. 7 (a) The cylinder mode character | a + (d,h) | 2 depends on wire diameter d from Eq. (4) for different spacer height h. (b) The dependence of coupling strength κ on cylinder wire diameter d and spacer height h from Eq. (5).

Equations (5)

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

A m = W m max{ W( r ) } = 1 max{ W(r) } W( r ) d 2 r
W( r )= 1 2 Re{ d(ωε( r )) } | E( r ) | 2 + 1 2 μ 0 | H( r ) | 2
ψ ± ( d,h )= a ± ( d,h ) ψ wire ( d )+ b ± ( d,h ) ψ LRHPhP
| a + (d,h) | 2 = n hyb ( d,h ) n LRHPhP ( n hyb ( d,h ) n wire ( d ))+( n hyb ( d,h ) n LRHPhP )
κ(d,h)= ( n hyb ( d,h ) n LRHPhP )( n hyb ( d,h ) n wire ( d )) .

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