Abstract

We present a broadband and efficient short-range plasmonic directional coupler design, for the delivery and collection of deeply sub-wavelength radiation to tapered plasmonic nanowires. We show a proof-of-concept design using a planar geometry operating at wavelengths between 1.2 −2.4 μm, showing that the propagation characteristics predicted by an Eigenmode analysis are in excellent agreement with finite element simulations. This analytical formulation is straightforward to implement and immediately provides the power-exchange properties of hybrid plasmonic waveguides. An investigation of both waveguide delivery and collection performance to and from a plasmonic nano-tip is performed. We show that this design strategy can be straightforwardly adapted to a realistic hybrid fiber geometry, containing wire diameters more than one order of magnitude larger than the planar geometries, with important applications in all-fiber plasmonic superfocussing, and nonlinear plasmonics.

© 2016 Optical Society of America

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2016 (2)

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid Optical Fibers An Innovative Platform for In-Fiber Photonic Devices,” Adv. Opt. Mat. 4(1), 13–36 (2016).
[Crossref]

A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016).
[Crossref] [PubMed]

2015 (5)

C. Fisher, L. C. Botten, C. G. Poulton, R. C. McPhedran, and C. M. de Sterke, “Efficient end-fire coupling of surface plasmons in a metal waveguide,” J. Opt. Soc. Am. B 32(3), 412–425 (2015).
[Crossref]

R. Spittel, P. Uebel, H. Bartelt, and M. A. Schmidt, “Curvature-induced geometric momenta: the origin of waveguide dispersion of surface plasmons on metallic wires,” Opt. Express 23(9), 12174–12188 (2015).
[Crossref] [PubMed]

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-Chip Hybrid Photonic-Plasmonic Light Concentrator for Nanofocusing in an Integrated Silicon Photonics Platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

T. Wieduwilt, A. Tuniz, S. Linzen, S. Goerke, J. Dellith, U. Hübner, and Markus A. Schmidt, “Ultrathin niobium nanofilms on fiber optical tapers a new route towards low-loss hybrid plasmonic modes,” Sci. Rep. 5, 17060 (2015).
[Crossref]

B. N. Tugchin, N. Janunts, A. E. Klein, M. Steinert, S. Fasold, S. Diziain, M. Sison, E. Kley, A. Tünnermann, and T. Pertsch, “Plasmonic Tip Based on Excitation of Radially Polarized Conical Surface Plasmon Polariton for Detecting Longitudinal and Transversal Fields,” ACS Photonics 2(10), 1468–1475 (2015).
[Crossref]

2013 (3)

P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. St. J. Russell, “A Gold-Nanotip Optical Fiber for Plasmon-Enhanced Near-Field Detection,” Appl. Phys. Lett. 103(2), 021101 (2013).
[Crossref]

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” N. J. Phys. 15, 013033 (2013).
[Crossref]

M. S. Tame, K. R. McEnery, S. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Physics 9, 329–340 (2013).
[Crossref]

2012 (3)

2011 (6)

2010 (3)

2009 (3)

A. Degiron, S. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[Crossref]

R. Wan, F. Liu, X. Tang, Y. Huang, and J. Peng, “Vertical coupling between short range surface plasmon polariton mode and dielectric waveguide mode,” Appl. Phys. Lett. 94(14), 141104 (2009).
[Crossref]

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

2008 (4)

M. A. Schmidt and P. St. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16(18) 13617–13623 (2008).
[Crossref] [PubMed]

J. Ballato, T. Hawkins, P. Foy, R. Stolen, B. Kokuoz, M. Ellison, C. McMillen, J. Reppert, A. M. Rao, M. Daw, S. Sharma, R. Shori, O. Stafsudd, R. R. Rice, and D. R. Powers, “Silicon optical fiber,” Opt. Express 16(23), 18675–18683 (2008).
[Crossref]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

X. Tang, Y. Huang, Y. Wang, W. Zhang, and J. Peng, “Tunable surface plasmons for emission enhancement of silicon nanocrystals using Ag-poor cermet layer,” Appl. Phys. Lett. 92(25), 251116 (2008).
[Crossref]

2007 (4)

K. Kneipp, “Surface-enhanced Raman scattering,” Phys. Today 60, 40 (2007).
[Crossref]

P. Bharadwaj and L. Novotny, “Spectral dependence of single molecule fluorescence enhancement,” Opt. Express 15(21), 14266–14274 (2007).
[Crossref] [PubMed]

J. T. Hastings, J. Guo, P. D. Keathley, P. B. Kumaresh, Y. Wei, S. Law, and L. G. Bachas, “Optimal self-referenced sensing using long- and short- range surface plasmons,” Opt. Express 15(26), 17661–17672 (2007).
[Crossref] [PubMed]

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mat. 6(5), 336–347 (2007).
[Crossref]

2005 (1)

C. C. Neacsu, G. A. Steudle, and M. B. Raschke, “Plasmonic light scattering from nanoscopic metal tips,” Appl. Phys. B 80(3), 295–300 (2005).
[Crossref]

2004 (1)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[Crossref] [PubMed]

2003 (1)

E. Devaux, T. W. Ebbesen, J. Weeber, and A. Dereux, “Launching and decoupling surface plasmons via microgratings,” Appl. Phys. Lett. 83(24), 4936 (2003).
[Crossref]

2002 (2)

H. G. Frey, F. Keilmann, A. Kriele, and R. Guckenberger, “Enhancing the resolution of scanning near-field optical microscopy by a metal tip grown on an aperture probe,” Appl. Phys. Lett. 81(26), 5030 (2002).
[Crossref]

V. Stenger and F. R. Beyette, “Design and Analysis of an OpticalWaveguide Tap for Silicon CMOS Circuits,” J. Lightwave Technol. 20(2), 277–284 (2002)
[Crossref]

1998 (1)

1987 (2)

S. Chuang, “A Coupled Mode Formulation by Reciprocity and a Variational Principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[Crossref]

D. Marcuse, “Directional Couplers Made of Nonidentical Asymmetric Slabs. Part I: Synchronous Coupler,” J. Lightwave Technol. 5(1), 113–118 (1987).
[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(8), 5186–5201 (1986).
[Crossref]

1983 (1)

1968 (1)

A. Otto, “Excitation of Nonradiative Surface Plasmon Waves in Silver by Method of Frustrated Total Reflection,” Z. Phys. 216(4), 398–410 (1968).
[Crossref]

1965 (1)

1944 (1)

H. A. Bethe, “Theory of Diffraction by Small Holes’, Phys. Rev. 66(7), 163–182 (1944).
[Crossref]

Abouraddy, A. F.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mat. 6(5), 336–347 (2007).
[Crossref]

Adibi, A.

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-Chip Hybrid Photonic-Plasmonic Light Concentrator for Nanofocusing in an Integrated Silicon Photonics Platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

Agio, M.

X. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett. 9(11), 3756–3761 (2011).
[Crossref]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref] [PubMed]

Apuzzo, A.

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-Chip Hybrid Photonic-Plasmonic Light Concentrator for Nanofocusing in an Integrated Silicon Photonics Platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

Argyros, A.

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid Optical Fibers An Innovative Platform for In-Fiber Photonic Devices,” Adv. Opt. Mat. 4(1), 13–36 (2016).
[Crossref]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[Crossref] [PubMed]

Aubry, A.

A. Aubry, D. Z. Lei, S. A. Maier, and J. B. Pendry, “Plasmonic Hybridization between Nanowires and a Metallic Surface: A Transformation Optics Approach,” ACS Nano 5(4), 3293–3308 (2011).
[Crossref] [PubMed]

Bachas, L. G.

Ballato, J.

Bartelt, H.

Bauerschmidt, S. T.

P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. St. J. Russell, “A Gold-Nanotip Optical Fiber for Plasmon-Enhanced Near-Field Detection,” Appl. Phys. Lett. 103(2), 021101 (2013).
[Crossref]

Bayindir, M.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mat. 6(5), 336–347 (2007).
[Crossref]

Benoit, G.

A. F. Abouraddy, M. Bayindir, G. Benoit, S. D. Hart, K. Kuriki, N. Orf, O. Shapira, F. Sorin, B. Temelkuran, and Y. Fink, “Towards multimaterial multifunctional fibres that see, hear, sense and communicate,” Nat. Mat. 6(5), 336–347 (2007).
[Crossref]

Berini, P.

Bethe, H. A.

H. A. Bethe, “Theory of Diffraction by Small Holes’, Phys. Rev. 66(7), 163–182 (1944).
[Crossref]

Beyette, F. R.

Bharadwaj, P.

Biancalana, F.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” N. J. Phys. 15, 013033 (2013).
[Crossref]

Blaize, S.

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-Chip Hybrid Photonic-Plasmonic Light Concentrator for Nanofocusing in an Integrated Silicon Photonics Platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

Botten, L. C.

Bozhevolnyi, S. I.

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(8), 5186–5201 (1986).
[Crossref]

Chamanzar, M.

Y. Luo, M. Chamanzar, A. Apuzzo, R. Salas-Montiel, K. N. Nguyen, S. Blaize, and A. Adibi, “On-Chip Hybrid Photonic-Plasmonic Light Concentrator for Nanofocusing in an Integrated Silicon Photonics Platform,” Nano Lett. 15(2), 849–856 (2015).
[Crossref] [PubMed]

Chang, W.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” N. J. Phys. 15, 013033 (2013).
[Crossref]

Chen, X.

X. Chen, V. Sandoghdar, and M. Agio, “Highly efficient interfacing of guided plasmons and photons in nanowires,” Nano Lett. 9(11), 3756–3761 (2011).
[Crossref]

Cho, S.

A. Degiron, S. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[Crossref]

Chuang, S.

S. Chuang, “A Coupled Mode Formulation by Reciprocity and a Variational Principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[Crossref]

Conforti, M.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, Tr. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” N. J. Phys. 15, 013033 (2013).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1

(a) Scanning-electron micrographs of cleaved fibers containing a gold nanowire (left), showing a naturally-forming sharp nanotip (right). White scale bars are 10 and 0.5 μm (from left to right). Reproduced with permission from [35]. Copyright 2013, AIP Publishing LLC. (b) Schematic of a hybrid dielectric-plasmonic directional coupler with plasmonic nanotip. Light from the dielectric core (light blue), directionally couples into the SR-SPP mode on the gold nanowire (yellow), and focusses at the tip (magenta spot at the tip end). Dark blue: silica cladding. Comparison between (c) effective index neff and (d) loss for the SR-SPP modes of planar gold films (blue) and cylindrical gold wires (green) in a silica background at λ = 1.55 μm, where w is their width or diameter, respectively [inset in (c)].

Fig. 2
Fig. 2

Conceptual schematic of the planar directional coupler device for the excitation of the SR-SPP mode. (i) Directional coupling section: the fundamental isolated Eigenmode (IEM) of the dielectric core couples to the strongly bounded SR-SPP mode via the beating of the two even- and odd- hybrid Eigenmodes (HEMs) in the coupling section which is terminated after one coupling length (i.e. length at which the maximum power is transferred from the core to the plasmonic film). (ii) Plasmonic nanotip section: the excited SR-SPP mode travels down the nanotip and is focused to deep sub-wavelength dimensions, which can be used for nanoscale light delivery or collection.

Fig. 3
Fig. 3

Design principle and parameter choices for the dielectric-plasmonic directional coupler. Only the IEM dispersions are considered at this point of the design procedure. (a) Structural and material parameter selection: for a given wavelength (here: 1.55 μm), the parameters are selected by choosing the combination of dielectric core width d (dashed lines) and gold film thickness w (solid line) that leads to phase-matching between the fundamental dielectric core mode and the SR-SPP mode (vertical red dashed line). For example, a core index of ncore = 1.87 and width 500 nm requires a gold strip of width 15 nm. (b) Phase-matching map of dielectric waveguide thickness versus gold film thickness. For a constant dielectric core index, various combinations of d phase-match with a gold strip of width w. The arrows show the parameters chosen here, w = 15nm, d = 500nm, ncore = 1.87.

Fig. 4
Fig. 4

(a) Effective index of the TM core and SR-SPP IEMs (dashed lines) and of the HEMs, HEM 1 and HEM 2 (solid lines). (b) Real parts of the transverse magnetic field of each EM. Upper two plots: IEMs. Lower plot: HEMs. (c) Modal losses [same labeling as in (a)]. (d) Real and imaginary parts of a1 and a2 calculated using Eq. (4), setting Hin = Hcore, i.e. the TM core IEM.

Fig. 5
Fig. 5

Spatial distribution of Poynting vector component Sz(x, z) (normalized to the maximum in the window) calculated using (a) the EM ansatz and (b) FE-simulations at λ = 1.55μm. (c) Sz(z) in the middle of the dielectric waveguide [ S z core ( z ) = S z ( d / 2 , z ), blue] and upper edge of gold strip [ S z SPP ( z ) = S z ( x = d + t + w , z ), red], as indicated by the dotted lines in (a) and (b). (d) Fraction of power in dielectric core mode and SPP mode in the core (blue) and SPP mode (red) respectively, as defined in the text. In (c),(d) solid lines are from FE calculations, dashed lines result from the EM ansatz. In (d), the additional dash-dotted lines are obtained from Eq. (6), setting Hout = Hcore (blue) and Hout = HSPP (red), as defined in the text.

Fig. 6
Fig. 6

Spectral distribution of normalized Sz as defined in Fig. 5, in the center of the dielectric waveguide [ S z core, (a) and (c)] and upper edge of gold strip [ S z SPP, (b) and (d)] evaluated using EM analysis [(a) and (b)] and FE simulations [(c) and (d)]. Plasmonic power transfer efficiency η (blue) and coupling length Lc (red) as (e) a function of wavelength (t = 400nm) and (f) as a function of t for a fixed wavelength of λ = 1.55μm. Solid lines: EM analysis. Circles: FE simulations.

Fig. 7
Fig. 7

Distribution of the Poynting vector magnitude for the proposed planar superfocussing device (delivery mode operation) for three selected wavelengths [(a): 1.25 μm, (b): 1.55 μm, (c): 1.85 μm]. The fundamental TM mode of the dielectric waveguide is incident from the left. Right: close-up views of the apex of the nanotip. In all plots, the Poynting vector magnitude has been normalized to the same number for ease of comparison.

Fig. 8
Fig. 8

Delivery efficiency ηdelivery (blue) as a function of wavelength for two different tip lengths (solid line: 1 μm, dashed line: 1.5 μm). Red: power enhancement at the tip (tip length: 1 μm.

Fig. 9
Fig. 9

(a) Example simulation of the normalized Poynting vector magnitude for a dipole located at an axial distance of 1 nm from the apex of the nanotip (λ = 1.55μm). Red dashed line: integration region at output. Inset: schematic of the tip (yellow), point source (black circle), dipole orientation (green) and integration region for collection efficiency calculations (dashed blue circle). Scale bar:1 nm. (b) Corresponding normalized Poynting vector magnitude at the output of the dielectric waveguide as a function of relative lateral position (x-direction) of the dipole source point.

Fig. 10
Fig. 10

Lateral spatial resolution (Δx) and collection efficiency of the plasmonic directional coupler with tapered nanotip as functions of (a) wavelength (dipole/apex distance: 1 nm) and (b) of the dipole-apex distance (λ = 1.55μm). Structural parameters as in Fig. 9.

Fig. 11
Fig. 11

Fiber-based plasmonic directional mode coupler for the excitation of the short-range TM0 mode [inset schematic of (a), d = 1μm, t = 0.5μm, w = 0.5μm, silica cladding (dark blue), dielectric core with ncore = 1.67 (light blue), and gold satellite (yellow)]. The device consists of a cylindrical dielectric waveguide and a metallic nanowire. (a) neff and (b) loss of the various isolated and hybrid modes. In both plots, dashed lines are the IEMs, solid lines refer to the HEMs. (c) Axial component of the Poynting vector (normalized log scale) for IEMs (dielectric core mode and plasmonic TM0 mode) and for the HEMs (asymmetric and symmetric HEM 1 and HEM 2, respectively) at λ = 1.55μm. White arrows indicate the direction of the electric field at a fixed point of time. Scale bar: 1 μm

Fig. 12
Fig. 12

Axial Poynting vector component Sz(x, z) of the fiber-based superfocussing device consisting of a plasmonic directional fiber coupler, used to excite the TM0-mode at the beginning of the conical nanotip (λ = 1.55μm, ncore = 1.67, d = 1μm, t = 500nm, w = 500nm, silica background). All images refer to the xz plane defined in the inset of Fig. 11(a). (a) Sz(x, z) pattern of the coupler section, calculated using the EM approach and assuming the fundamental dielectric waveguide mode as input field. The vertical white dashed line indicates the location of maximum power transfer, i.e. the optimal location for the excitation of the TM0 mode on the nanowire. The remaining three images (b–d) have been calculated using a FE-method. (b) TM0-mode propagation along the nanotip. (c) Close-up view of the apex of the nanotip [white square in (b)]. (d) Poynting vector magnitude distribution (xy-plane) at a position 1 nm away from the apex of the tip, as highlighted by the black dotted lines. All plots have been normalized to the maximum value in each window.

Equations (10)

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H tot ( x , y , z ) a 1 H 1 ( x , y ) exp ( i β 1 z ) + a 2 H 2 ( x , y ) exp ( i β 2 z ) ,
E tot ( x , y , z ) a 1 E 1 ( x , y ) exp ( i β 1 z ) + a 2 E 2 ( x , y ) exp ( i β 2 z ) ,
1 2 A [ E i ( x , y ) × H j ( x , y ) ] z ^ d A = δ i , j ,
a i = 1 2 A [ E i ( x , y ) × H in ( x , y ) ] z ^ d A ,
b i = 1 2 A [ E i ( x , y ) × H out ( x , y ) ] z ^ d A .
f P = | a 1 b 1 | 2 exp ( 2 β 1 I z ) + | a 2 b 2 | 2 exp ( 2 β 2 I z ) + + 2 exp ( β I ¯ z ) { [ e ( a 1 b 1 ) e ( a 2 b 2 ) + m ( a 1 b 1 ) m ( a 2 b 2 ) ] cos ( Δ β R z ) + + [ e ( a 1 b 1 ) m ( a 2 b 2 ) m ( a 1 b 1 ) e ( a 2 b 2 ) ] sin ( Δ β R z ) } ,
P core ( z ) = d + t / 2 S z ( x , y ) d x ,
P SPP ( z ) = d + t / 2 S z ( x , y ) d x ,
f core ( z ) = P core ( z ) / [ P SPP ( 0 ) + P core ( 0 ) ] ,
f SPP ( z ) = P SPP ( z ) [ P SPP ( 0 ) + P core ( 0 ) ] .

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