Abstract

In recent years, many nanophotonic devices have been developed. Much attention has been given to the waveguides carrying surface plasmon polariton modes with subwavelength confinement and long propagation length. However, coupling far field light into a nano structure is a significant challenge. In this work, we present an architecture that enables high efficiency excitation of nanoscale waveguides in the direction normal to the waveguide. Our approach employs a bowtie aperture to provide both field confinement and high transmission efficiency. More than six times the power incident on the open area of the bowtie aperture can be coupled into the waveguide. The intensity in the waveguide can be more than twenty times higher than that of the incident light, with mode localization better than λ 2/250. The vertical excitation of waveguide allows easy integration. The bowtie aperture/waveguide architecture presented in this work will open up numerous possibilities for the development of nanoscale optical systems for applications ranging from localized chemical sensing to compact communication devices.

© 2009 OSA

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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]

T. A. Mandviwala, B. A. Lail, and G. D. Boreman, “Characterization of microstrip transmission lines at IR frequencies – modeling, fabrication and measurements,” Microw. Opt. Technol. Lett. 50(5), 1232–1237 (2008).
[CrossRef]

S. A. Maier, “Waveguiding: The best of both worlds,” Nat. Photonics 2(8), 460–461 (2008).
[CrossRef]

N. Murphy-DuBay, L. Wang, E. C. Kinzel, S. M. V. Uppuluri, and X. Xu, “Nanopatterning using NSOM probes integrated with high transmission nanoscale bowtie aperture,” Opt. Express 16(4), 2584–2589 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-4-2584 .
[CrossRef] [PubMed]

2007 (3)

L. Wang and X. Xu, “L.; X. Xu, “High transmission nanoscale bowtie-shaped aperture probe for near-field optical imaging,” Appl. Phys. Lett. 90(26), 261105 (2007).
[CrossRef]

A. Hosseini, H. Nejati, and Y. Massoud, “Design of a maximally flat optical low pass filter using plasmonic nanostrip waveguides,” Opt. Express 15(23), 15280–15286 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?id=144685 .
[CrossRef] [PubMed]

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

2006 (6)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (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,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407–035415 (2006).
[CrossRef]

E. X. Jin and X. Xu, “Enhanced optical near field from a bowtie aperture,” Appl. Phys. Lett. 88(15), 153110–153112 (2006).
[CrossRef]

L. Wang, S. M. V. Uppuluri, E. X. Jin, and X. Xu, “Nanolithography using high transmission nanoscale bowtie apertures,” Nano Lett. 6(3), 361–364 (2006).
[CrossRef] [PubMed]

A. Degiron and D. R. Smith, “Numerical simulations of long-range plasmons,” Opt. Express 14(4), 1611–1625 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=OE-14-4-1611 .
[CrossRef] [PubMed]

2005 (1)

E. X. Jin and X. Xu, “Obtaining super resolution light spot using surface plasmon assisted sharp ridge nanoaperture,” Appl. Phys. Lett. 86(11), 111106–111108 (2005).
[CrossRef]

2004 (2)

K. Şendur, W. Challener, and C. Peng, “Ridge waveguide as a near field aperture for high density data storage,” J. Appl. Phys. 96(5), 2743–2752 (2004).
[CrossRef]

E. X. Jin and X. Xu, “Finite-Difference Time-Domain Studies on Optical Transmission through Planar Nano-Apertures in a Metal Film,” Jpn. J. Appl. Phys. 43(1), 407–417 (2004).
[CrossRef]

2003 (1)

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

2002 (2)

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[CrossRef]

X. Shi and L. Hesselink, “Mechanisms for Enhancing Power Throughput from Planar Nano-Apertures for Near-Field Optical Data Storage,” Jpn. J. Appl. Phys. 41(Part 1, No. 3B), 1632–1635 (2002).
[CrossRef]

1997 (1)

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70(11), 1354–1356 (1997).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1965 (1)

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407–035415 (2006).
[CrossRef]

Aussenegg, F. R.

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[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]

Boreman, G. D.

T. A. Mandviwala, B. A. Lail, and G. D. Boreman, “Characterization of microstrip transmission lines at IR frequencies – modeling, fabrication and measurements,” Microw. Opt. Technol. Lett. 50(5), 1232–1237 (2008).
[CrossRef]

Bozhevolnyi, S. I.

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,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Challener, W.

K. Şendur, W. Challener, and C. Peng, “Ridge waveguide as a near field aperture for high density data storage,” J. Appl. Phys. 96(5), 2743–2752 (2004).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Degiron, A.

Dereux, A.

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

Devaux, E.

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,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407–035415 (2006).
[CrossRef]

Ditlbacher, H.

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[CrossRef]

Ebbesen, T. W.

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,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

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

Felidj, N.

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[CrossRef]

Genov, D. A.

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]

Grober, R. D.

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70(11), 1354–1356 (1997).
[CrossRef]

Hesselink, L.

X. Shi and L. Hesselink, “Mechanisms for Enhancing Power Throughput from Planar Nano-Apertures for Near-Field Optical Data Storage,” Jpn. J. Appl. Phys. 41(Part 1, No. 3B), 1632–1635 (2002).
[CrossRef]

Hosseini, A.

Jin, E. X.

E. X. Jin and X. Xu, “Enhanced optical near field from a bowtie aperture,” Appl. Phys. Lett. 88(15), 153110–153112 (2006).
[CrossRef]

L. Wang, S. M. V. Uppuluri, E. X. Jin, and X. Xu, “Nanolithography using high transmission nanoscale bowtie apertures,” Nano Lett. 6(3), 361–364 (2006).
[CrossRef] [PubMed]

E. X. Jin and X. Xu, “Obtaining super resolution light spot using surface plasmon assisted sharp ridge nanoaperture,” Appl. Phys. Lett. 86(11), 111106–111108 (2005).
[CrossRef]

E. X. Jin and X. Xu, “Finite-Difference Time-Domain Studies on Optical Transmission through Planar Nano-Apertures in a Metal Film,” Jpn. J. Appl. Phys. 43(1), 407–417 (2004).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kimerling, L.

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

Kinzel, E. C.

Kirchain, R.

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

Krenn, J. R.

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[CrossRef]

Lail, B. A.

T. A. Mandviwala, B. A. Lail, and G. D. Boreman, “Characterization of microstrip transmission lines at IR frequencies – modeling, fabrication and measurements,” Microw. Opt. Technol. Lett. 50(5), 1232–1237 (2008).
[CrossRef]

Laluet, J. Y.

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,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Lamprecht, B.

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[CrossRef]

Leitner, A.

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[CrossRef]

Maier, S. A.

S. A. Maier, “Waveguiding: The best of both worlds,” Nat. Photonics 2(8), 460–461 (2008).
[CrossRef]

Malitson, I. H.

Mandviwala, T. A.

T. A. Mandviwala, B. A. Lail, and G. D. Boreman, “Characterization of microstrip transmission lines at IR frequencies – modeling, fabrication and measurements,” Microw. Opt. Technol. Lett. 50(5), 1232–1237 (2008).
[CrossRef]

Massoud, Y.

Murphy-DuBay, N.

Nejati, H.

Oulton, R. F.

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]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[CrossRef] [PubMed]

Peng, C.

K. Şendur, W. Challener, and C. Peng, “Ridge waveguide as a near field aperture for high density data storage,” J. Appl. Phys. 96(5), 2743–2752 (2004).
[CrossRef]

Pile, D. F. P.

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]

Prober, D. E.

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70(11), 1354–1356 (1997).
[CrossRef]

Salerno, M.

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[CrossRef]

Schider, G.

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[CrossRef]

Schoelkopf, R. J.

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70(11), 1354–1356 (1997).
[CrossRef]

Sendur, K.

K. Şendur, W. Challener, and C. Peng, “Ridge waveguide as a near field aperture for high density data storage,” J. Appl. Phys. 96(5), 2743–2752 (2004).
[CrossRef]

Shi, X.

X. Shi and L. Hesselink, “Mechanisms for Enhancing Power Throughput from Planar Nano-Apertures for Near-Field Optical Data Storage,” Jpn. J. Appl. Phys. 41(Part 1, No. 3B), 1632–1635 (2002).
[CrossRef]

Smith, D. R.

Sorger, V. J.

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]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407–035415 (2006).
[CrossRef]

Uppuluri, S. M. V.

Volkov, V. S.

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,” Nature 440(7083), 508–511 (2006).
[CrossRef] [PubMed]

Wang, L.

N. Murphy-DuBay, L. Wang, E. C. Kinzel, S. M. V. Uppuluri, and X. Xu, “Nanopatterning using NSOM probes integrated with high transmission nanoscale bowtie aperture,” Opt. Express 16(4), 2584–2589 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-4-2584 .
[CrossRef] [PubMed]

L. Wang and X. Xu, “L.; X. Xu, “High transmission nanoscale bowtie-shaped aperture probe for near-field optical imaging,” Appl. Phys. Lett. 90(26), 261105 (2007).
[CrossRef]

L. Wang, S. M. V. Uppuluri, E. X. Jin, and X. Xu, “Nanolithography using high transmission nanoscale bowtie apertures,” Nano Lett. 6(3), 361–364 (2006).
[CrossRef] [PubMed]

Xu, X.

N. Murphy-DuBay, L. Wang, E. C. Kinzel, S. M. V. Uppuluri, and X. Xu, “Nanopatterning using NSOM probes integrated with high transmission nanoscale bowtie aperture,” Opt. Express 16(4), 2584–2589 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-4-2584 .
[CrossRef] [PubMed]

L. Wang and X. Xu, “L.; X. Xu, “High transmission nanoscale bowtie-shaped aperture probe for near-field optical imaging,” Appl. Phys. Lett. 90(26), 261105 (2007).
[CrossRef]

L. Wang, S. M. V. Uppuluri, E. X. Jin, and X. Xu, “Nanolithography using high transmission nanoscale bowtie apertures,” Nano Lett. 6(3), 361–364 (2006).
[CrossRef] [PubMed]

E. X. Jin and X. Xu, “Enhanced optical near field from a bowtie aperture,” Appl. Phys. Lett. 88(15), 153110–153112 (2006).
[CrossRef]

E. X. Jin and X. Xu, “Obtaining super resolution light spot using surface plasmon assisted sharp ridge nanoaperture,” Appl. Phys. Lett. 86(11), 111106–111108 (2005).
[CrossRef]

E. X. Jin and X. Xu, “Finite-Difference Time-Domain Studies on Optical Transmission through Planar Nano-Apertures in a Metal Film,” Jpn. J. Appl. Phys. 43(1), 407–417 (2004).
[CrossRef]

Zhang, X.

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]

Appl. Phys. Lett. (5)

H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. 80(3), 404–406 (2002).
[CrossRef]

E. X. Jin and X. Xu, “Obtaining super resolution light spot using surface plasmon assisted sharp ridge nanoaperture,” Appl. Phys. Lett. 86(11), 111106–111108 (2005).
[CrossRef]

E. X. Jin and X. Xu, “Enhanced optical near field from a bowtie aperture,” Appl. Phys. Lett. 88(15), 153110–153112 (2006).
[CrossRef]

R. D. Grober, R. J. Schoelkopf, and D. E. Prober, “Optical antenna: towards a unity efficiency near-field optical probe,” Appl. Phys. Lett. 70(11), 1354–1356 (1997).
[CrossRef]

L. Wang and X. Xu, “L.; X. Xu, “High transmission nanoscale bowtie-shaped aperture probe for near-field optical imaging,” Appl. Phys. Lett. 90(26), 261105 (2007).
[CrossRef]

J. Appl. Phys. (1)

K. Şendur, W. Challener, and C. Peng, “Ridge waveguide as a near field aperture for high density data storage,” J. Appl. Phys. 96(5), 2743–2752 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (2)

X. Shi and L. Hesselink, “Mechanisms for Enhancing Power Throughput from Planar Nano-Apertures for Near-Field Optical Data Storage,” Jpn. J. Appl. Phys. 41(Part 1, No. 3B), 1632–1635 (2002).
[CrossRef]

E. X. Jin and X. Xu, “Finite-Difference Time-Domain Studies on Optical Transmission through Planar Nano-Apertures in a Metal Film,” Jpn. J. Appl. Phys. 43(1), 407–417 (2004).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

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Supplementary Material (1)

» Media 1: AVI (4272 KB)     

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Figures (6)

Fig. 1
Fig. 1

Bowtie aperture vertically coupled to a waveguide. (a) Three-dimensional rendering. The top gray line is the metal signal line. The bowtie aperture is fabricated in a metal layer (gray). (b) Definitions of the dimensions for the bowtie aperture in a metal film of thickness f and characterized by dimensions, a, b, s, and d. (c) Definitions of the dimensions of the nanoscale plasmonic waveguide, which has width and thickness, w and t, respectively. The center of the metal signal line is directly above the center of the bowtie aperture but separated by a layer of dielectric with thickness g.

Fig. 2
Fig. 2

Instantaneous electric field distribution showing coupling between a plane wave and the waveguide. A y-polarized plane wave incident on a 250 nm bowtie aperture (25 nm gap) coupling to a 100 wide transmission line separated from the bowtie aperture by a gap of 100 nm. The magnitudes of the electric fields are plotted: (a) (Media 1) yz plane through the centre of the aperture with inset showing xz plane. The black arrow of the incident wave vector points to the center of the bowtie aperture. (b) xy plane midway through the dielectric region (z = 50 nm). The magnitude of the incident electric field is 1 V/m in the fused silica substrate. In the figures, the field is saturated at 2.5 V/m for clarity. A movie of light propagation from far field into the waveguide is provided in supplementary information. (c) Peak and instantaneous values of the electric field along the centerline of the nanostrip (z = 50 nm) and the power carried in the line as a function of distance from the center of the aperture.

Fig. 3
Fig. 3

Coupling efficiency from a far field light source to the waveguide. The far field light source is assumed to be a diffraction limited spot incident on the bowtie aperture with a diameter of 945.5 nm. For the bowtie aperture, a = b is used. s = d = 25 nm, f = 100 nm, and t = 50 nm.

Fig. 4
Fig. 4

Properties of the nanostrip waveguide. (a) Magnitude of the Poynting vector along the waveguide with the size of w = 200 nm, g = 100 nm and t = 50 nm. Solid field lines show the direction of the electric field and dashed indicate the direction of the magnetic field. The waveguide is transmitting 1 nW total power. The intensity is saturated at 50 kW/m2 for clarity. (b) Mode area, defined as the ratio of the total power carried in the transmission line divided by the peak power intensity. (c) Propagation length for different geometries. (d) Ratio between the peak intensity in the waveguide at 4 μm away from the center (y = 4 μm) and the incident intensity.

Fig. 6
Fig. 6

Interaction between the bowtie aperture and nanostrip waveguide. The geometry parameters are a = b = 250 nm, f = 100 nm, s = d = 25 nm, w = 100 nm, g = 100 nm, and t = 50 nm. (a) Electric field on yz plane and (b) magnetic field on xz plane (both passing through the origin). The field lines and arrows show the directions of the fields.

Fig. 5
Fig. 5

Transmission through a bowtie aperture. Field distribution for a bowtie aperture (a = b = 250 nm, s = d = 25 nm, t = 100 nm) in a silver film on a fused silica substrate at one instant in time. (a) The electric field on the yz plane (saturated at 2.5 V/m for clarity). Field lines show the direction of the electric field. (b) The magnetic field on the xz plane (saturated at 10 mA/m for clarity). Field lines show the direction of the magnetic field. (c) The ratio of the intensity at the centre of the gap on the exit plane to the intensity of the incident plane wave for different bowties (s = d = 25 nm, f = 100 nm) as a function of wavelength, showing strong spectral dependence and resonance.

Equations (2)

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Am=ARe{E×H*}dARe{E×H*}max
Lm=1/2Im{k}

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