Abstract

To enable multiple functions of plasmonic nanocircuits, it is of key importance to control the propagation properties and the modal distribution of the guided optical modes such that their impedance matches to that of nearby quantum systems and desired light-matter interaction can be achieved. Here, we present efficient mode converters for manipulating guided modes on a plasmonic two-wire transmission line. The mode conversion is achieved through varying the path length, wire cross section and the surrounding index of refraction. Instead of pure optical interference, strong near-field coupling of surface plasmons results in great momentum splitting and modal profile variation. We theoretically demonstrate control over nanoantenna radiation and discuss the possibility to enhance nanoscale light-matter interaction. The proposed converter may find applications in surface plasmon amplification, index sensing and enhanced nanoscale spectroscopy.

© 2012 OSA

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2012 (4)

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
[CrossRef] [PubMed]

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: Plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett.3(7), 945–952 (2012).
[CrossRef]

C. Rewitz, T. Keitzl, P. Tuchscherer, J.-S. Huang, P. Geisler, G. Razinskas, B. Hecht, and T. Brixner, “Ultrafast plasmon propagation in nanowires characterized by far-field spectral interferometry,” Nano Lett.12(1), 45–49 (2012).
[CrossRef] [PubMed]

A. Guerrero-Martínez, M. Grzelczak, and L. M. Liz-Marzán, “Molecular thinking for nanoplasmonic design,” ACS Nano6(5), 3655–3662 (2012).
[CrossRef] [PubMed]

2011 (8)

D. W. Pohl, S. G. Rodrigo, and L. Novotny, “Stacked optical antennas,” Appl. Phys. Lett.98(2), 023111–023113 (2011).
[CrossRef]

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics5(2), 83–90 (2011).
[CrossRef]

M. Schnell, P. Alonso Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics5(5), 283–287 (2011).
[CrossRef]

J. Wen, P. Banzer, A. Kriesch, D. Ploss, B. Schmauss, and U. Peschel, “Experimental cross-polarization detection of coupling far-field light to highly confined plasmonic gap modes via nanoantennas,” Appl. Phys. Lett.98(10), 101109 (2011).
[CrossRef]

A. V. Krasavin, T. P. Vo, W. Dickson, P. M. Bolger, and A. V. Zayats, “All-plasmonic modulation via stimulated emission of copropagating surface plasmon polaritons on a substrate with gain,” Nano Lett.11(6), 2231–2235 (2011).
[CrossRef] [PubMed]

P. Berini and I. De Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics6(1), 16–24 (2011).
[CrossRef]

S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett.107(9), 096801 (2011).
[CrossRef] [PubMed]

Y. Gao, Q. Gan, Z. Xin, X. Cheng, and F. J. Bartoli, “Plasmonic Mach-Zehnder interferometer for ultrasensitive on-chip biosensing,” ACS Nano5(12), 9836–9844 (2011).
[CrossRef] [PubMed]

2010 (11)

J.-S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett.10(6), 2105–2110 (2010).
[CrossRef] [PubMed]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett.10(6), 1991–1997 (2010).
[CrossRef] [PubMed]

E. Verhagen, L. K. Kuipers, and A. Polman, “Plasmonic nanofocusing in a dielectric wedge,” Nano Lett.10(9), 3665–3669 (2010).
[CrossRef] [PubMed]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics4(6), 382–387 (2010).
[CrossRef]

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics4(7), 457–461 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitry,” Nat. Commun.1(9), 150 (2010).
[CrossRef] [PubMed]

P. M. Krenz, R. L. Olmon, B. A. Lail, M. B. Raschke, and G. D. Boreman, “Near-field measurement of infrared coplanar strip transmission line attenuation and propagation constants,” Opt. Express18(21), 21678–21686 (2010).
[CrossRef] [PubMed]

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett.105(11), 117701 (2010).
[CrossRef] [PubMed]

N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett.10(5), 1741–1746 (2010).
[CrossRef] [PubMed]

M. Seo, J. Kyoung, H. Park, S. Koo, H.-S. Kim, H. Bernien, B. J. Kim, J. H. Choe, Y. H. Ahn, H.-T. Kim, N. Park, Q. H. Park, K. Ahn, and D.-S. Kim, “Active terahertz nanoantennas based on VO2 phase transition,” Nano Lett.10(6), 2064–2068 (2010).
[CrossRef] [PubMed]

2009 (7)

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J.-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A.-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett.9(11), 3914–3921 (2009).
[CrossRef] [PubMed]

J. Wen, S. Romanov, and U. Peschel, “Excitation of plasmonic gap waveguides by nanoantennas,” Opt. Express17(8), 5925–5932 (2009).
[CrossRef] [PubMed]

J.-S. Huang, D. V. Voronine, P. Tuchscherer, T. Brixner, and B. Hecht, “Deterministic spatiotemporal control of optical fields in nanoantennas and plasmonic circuits,” Phys. Rev. B79(19), 195441 (2009).
[CrossRef]

N. Yang, Y. Tang, and A. E. Cohen, “Spectroscopy in sculpted fields,” Nano Today4(3), 269–279 (2009).
[CrossRef]

J.-S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett.9(5), 1897–1902 (2009).
[CrossRef] [PubMed]

E. Verhagen, M. Spasenović, A. Polman, and L. K. Kuipers, “Nanowire plasmon excitation by adiabatic mode transformation,” Phys. Rev. Lett.102(20), 203904 (2009).
[CrossRef] [PubMed]

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3(1), 55–58 (2009).
[CrossRef]

2008 (2)

W. Dickson, G. A. Wurtz, P. R. Evans, R. J. Pollard, and A. V. Zayats, “Electronically controlled surface plasmon dispersion and optical transmission through metallic hole arrays using liquid crystal,” Nano Lett.8(1), 281–286 (2008).
[CrossRef] [PubMed]

M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express16(2), 1385–1392 (2008).
[CrossRef] [PubMed]

2007 (1)

D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys.3(11), 807–812 (2007).
[CrossRef]

2006 (5)

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett.97(5), 053002 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006).
[CrossRef] [PubMed]

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett.6(9), 1928–1932 (2006).
[CrossRef] [PubMed]

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett.97(1), 017402 (2006).
[CrossRef] [PubMed]

2005 (2)

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett.94(1), 017402 (2005).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett.95(4), 046802 (2005).
[CrossRef] [PubMed]

2004 (3)

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]

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

S. Y. Park and D. Stroud, “Splitting of surface plasmon frequencies of metal particles in a nematic liquid crystal,” Appl. Phys. Lett.85(14), 2920–2922 (2004).
[CrossRef]

2003 (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett.90(2), 027402 (2003).
[CrossRef] [PubMed]

2001 (2)

J. C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, and J. P. Goudonnet, “Near-field observation of surface plasmon polariton propagation on thin metal stripes,” Phys. Rev. B64(4), 045411 (2001).
[CrossRef]

A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition,” Phys. Rev. Lett.87(23), 237401 (2001).
[CrossRef] [PubMed]

1997 (1)

1996 (1)

A. M. Boiron, B. Lounis, and M. Orrit, “Single molecules of dibenzanthanthrene in n-hexadecane,” J. Chem. Phys.105(10), 3969–3974 (1996).
[CrossRef]

1994 (1)

L. Novotny and C. Hafner, “Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics50(5), 4094–4106 (1994).
[CrossRef] [PubMed]

1991 (1)

1989 (1)

S. Chandrasekhar, A. S. Vengurlekar, V. T. Karulkar, and S. K. Roy, “Temperature, light intensity and microstructure dependence of the refractive index of polycrystalline silicon films,” Thin Solid Films169(2), 205–212 (1989).
[CrossRef]

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P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
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M. Schnell, P. Alonso Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics5(5), 283–287 (2011).
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M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics4(7), 457–461 (2010).
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P. Berini and I. De Leon, “Surface plasmon-polariton amplifiers and lasers,” Nat. Photonics6(1), 16–24 (2011).
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I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics4(6), 382–387 (2010).
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D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys.3(11), 807–812 (2007).
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J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J.-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A.-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett.9(11), 3914–3921 (2009).
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W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett.95(4), 046802 (2005).
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J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett.6(9), 1928–1932 (2006).
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006).
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett.95(4), 046802 (2005).
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W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
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J.-S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett.10(6), 2105–2110 (2010).
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Y. Gao, Q. Gan, Z. Xin, X. Cheng, and F. J. Bartoli, “Plasmonic Mach-Zehnder interferometer for ultrasensitive on-chip biosensing,” ACS Nano5(12), 9836–9844 (2011).
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M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics4(7), 457–461 (2010).
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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett.94(1), 017402 (2005).
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P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
[CrossRef] [PubMed]

Science (1)

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Thin Solid Films (1)

S. Chandrasekhar, A. S. Vengurlekar, V. T. Karulkar, and S. K. Roy, “Temperature, light intensity and microstructure dependence of the refractive index of polycrystalline silicon films,” Thin Solid Films169(2), 205–212 (1989).
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FDTD solutions, Lumerical Solutions Inc., Vancouver, Canada. http://www.lumerical.com/ .

J. Kern, S. Grossmann, N. V. Tarakina, T. Häckel, M. Emmerling, M. Kamp, J.-S. Huang, P. Biagioni, J. C. Prangsma, and B. Hecht, “Atomic-scale confinement of optical fields,” arXiv, http://arxiv.org/abs/1112.5008v2 , (2011).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

W. E. M. T. Basché, M. Orrit, and U. P. Wild, Single-Molecule Optical Detection, Imaging and Spectroscopy (Wiley-VCH, 1997).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the plasmonic waveguide mode converter for manipulating the nanoscale light-matter interaction. Single terrylene molecules are used as an example for quantum systems integrated in the nanogap with well-aligned permanent dipole moment.

Fig. 2
Fig. 2

Propagation constant ( k , blue squares) and the propagation length ( [ k ' ] 1 , green circles) of the guided SPPs, i.e. the lowest order TM mode, on a solitary single metallic nanowire as functions of (a) the width of the nanowire and (b) the refractive index n of the surrounding medium. The height of the wire is fixed at 30 nm and the surrounding refractive index is set to 1.0 for (a). The wire cross section is fixed at 30 × 30 nm2 for (b). The red circles in both plots mark the propagation constant ( k =14.8 rad/μm ) of a nanowire with cross section of 30 × 30 nm2 embedded in a medium with n = 1.0. The inset shows a representative field intensity profile of the guided 0th-order TM mode on a single nanowire.

Fig. 3
Fig. 3

Coupling of the guided SPPs on individual wires of a nanosized plasmonic TWTL consisting of two gold nanowires (cross section: 30 × 30 nm2) separated by a nanogap varying from 10 nm to 300 nm. (a) Intensity modal profiles of the guided TE and TM modes on a TWTL as well as that of a solitary single nanowire. The propagation constant at a fixed frequency of 361.196 THz reveals the mode coupling with a gap-dependent splitting of k , in analogy to the energy splitting observed in strongly coupled nanoantennas [41]. (b) The propagation constant ( k , blue squares) and the propagation length ( [ k ' ] 1 , green circles) of the guided TE (hollow) and TM modes (solid) on a TWTL as a function of the gap size. All modal profiles are normalized to the same intensity color scale with red and blue colors meaning high and low field intensity, respectively.

Fig. 4
Fig. 4

Near-field intensity enhancement of the standing waves on a TWTL with a Y-split. The TWTL (cross section: 30 × 30 nm2, gap: 10 nm) splits into two single wires separated by a distance of 610 nm. Either TE or TM mode is injected from the left side of the TWTL. Field intensity of the injected TM mode (blue solid line) and TE mode (red solid line) before the Y-split is recorded 5 nm away from the outer surface of the TWTL and at the center of the gap, respectively, as depicted with blue and red solid lines in the upper panel. After the Y-split, field intensity distributions is recorded 5 nm away from the surface of the wires, as depicted with dotted line in the upper panel. Propagation constant ( k ) and the corresponding wavelength (λ) of each guided mode are marked. Regardless of the injected mode, after the Y-split, the wavevector and effective wavelength of the guided mode restore to the values of a single wire due to the vanishing near-field coupling.

Fig. 5
Fig. 5

(a) Schematic diagram of exemplary mode converters based on three working principles. Conversion of the input mode with propagation constant k in to the output mode with k out is accomplished through different path length ( r 1 = 648 nm and r 2 = 500 nm, top panel) and different propagation constant ( k 1 and k 2 ) due to different cross sectional width (σ1 = 13 nm and σ2 = 40 nm, middle panel) or different surrounding refractive index (n1 = 1.0 and n2 = 1.5, bottom panel). Green dashed square is the area in which the index of refraction is modified. The red dashed line indicates the position of the field monitor where modal profile and guided power flux are recorded. (b) Map of electric field intensity enhancement recorded at a frequency of 361.196 THz on a plane cutting the sample at the middle height. The phase difference between the displacement currents on individual nanowires is added an odd integer multiples of π after the converter. The injected TM modes with most of the power guided through the outer surface of the wires are successfully converted into a highly concentrated TE mode in the dielectric nanogap (10 nm). All intensity maps are normalized to the same color scale.

Fig. 6
Fig. 6

(a) Schematic diagram of a complex integrated plasmonic nanocircuit consisting of a single metal stripe (r1), the first section of TWTL (r2), a mode converter, the second section of TWTL (r3) and a nanoantenna. The cross section of the wires of TWTL and nanoantenna arms is 30 × 30 nm2 and the gap is 10 nm. The cross section of the single metal stripe is 30 × 70 nm2, exactly the same as that of the TWTL except that the gap is filled with gold. The surrounding index of refraction is 1.0 everywhere except for the tuning area indicated by the green dashed box, in which the refractive index is scanned from 1.0 to 2.0. (b) and (c) the field intensity enhancement map of the circuit obtained with a refractive index set to 1.0 and 1.5, respectively, corresponding to the case of no conversion and best conversion. (d) Cross sectional profile of field intensity enhancement at different section of the complex circuit and at the terminal antenna obtained at n = 1.0 and n = 1.5. (e) Mode (ηm, open circles), power (ηp, open squares) and overall conversion efficiency (ηoverall, open triangles) as well as the emitted power from the nanoantenna (Pout, solid squares dashed line) as a function of the refractive index of the material inside the green dashed box. The radiated power is normalized to the injected power. All simulation data are obtained at a frequency of 361.196 THz.

Equations (14)

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k ˜ = n ˜ eff k 0 .
k =Re{ n ˜ eff } 2π λ 0 .
L= [ k ' ] 1 = [ Im{ n ˜ eff } 2π λ 0 ] 1 .
ΔΦ= k ,1 r 1 k ,2 r 2 ,
ΔΦ= k Δr.
Δr= mπ θ c k ,
Δ k = mπ θ c R ,
MC= P total 2 P gap P total ,
η m = | MC out MC in | | MC TE |+| MC TM | ,
η p = P total ' P total ,
η overall = η p η m .
P out = η antenna ×( 1 Γ p2 )× e 2 k ,TE ' r 3 × η overall × e 2 k ,TM ' r 2 ×( 1 Γ p1 )× P S ,
η m = 1 2 [ cos( Δ k L c +π )+1 ]= 1 2 [ cos( sΔn L c +π )+1 ].
Eμ=| E || μ |cosϕ,

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