Abstract

The Taiji symbol is a very old schematic representation of two opposing but complementary patterns in oriental civilization. Using electron beam lithography, we fabricated an array of 70 × 70 gold Taiji marks with 30nm thickness and a total area of 50 × 50 µm2 on a fused silica substrate. The diameter of each Taiji mark is 500nm, while the period of the array is 700nm. Here we present experimental as well as numerical simulation results pertaining to plasmonic resonances of several Taiji nano-structures under normal illumination. We have identified a Taiji structure with a particularly interesting vortex-like Poynting vector profile, which could be attributed to the special shape and dimensions of the Taiji symbol.

© 2010 OSA

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2009 (1)

2008 (2)

G. D'Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77, 043825 (2008).
[CrossRef]

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[CrossRef]

2007 (1)

A. Ohta and Y. Kawata, “Analyses of radiation force and torque on a spherical particle near a substrate illuminated by a focused Laguerre-Gaussian beam,” Opt. Commun. 274(2), 269–273 (2007).
[CrossRef]

2006 (2)

Q. W. Zhan, “Properties of circularly polarized vortex beams,” Opt. Lett. 31(7), 867–869 (2006).
[CrossRef] [PubMed]

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97(26), 263902 (2006).
[CrossRef]

2005 (1)

2003 (1)

2002 (1)

G. Gbur, T. D. Visser, and E. Wolf, “Singular optics,” Opt. Photonics News 13(12), 55 (2002).
[CrossRef]

2000 (1)

Y. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Physics Reports-Review Section,” Phys. Lett. 331, 118–195 (2000).

1999 (1)

1998 (1)

M. S. Soskin and M. V. Vasnetsov, “Nonlinear singular optics,” Pure Appl. Opt. 7(2), 301–311 (1998).
[CrossRef]

1997 (1)

K. Rice, “Companion encyclopedia of Asian philosophy,” Ref. User Serv. Q. 37, 86 (1997).

1995 (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

1972 (1)

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

Anderson, M. H.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Bakker, R.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[CrossRef]

Bashevoy, M. V.

Bloemer, M.

G. D'Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77, 043825 (2008).
[CrossRef]

Blok, H.

Boltasseva, A.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[CrossRef]

Chang, Y. H.

Christy, R. W.

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

Cornell, E. A.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

D'Aguanno, G.

G. D'Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77, 043825 (2008).
[CrossRef]

Desyatnikov, A.

G. D'Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77, 043825 (2008).
[CrossRef]

Drachev, V. P.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[CrossRef]

Ensher, J. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Fedotov, V. A.

Gahagan, K. T.

Gbur, G.

Johnson, P. B.

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

Kawata, Y.

A. Ohta and Y. Kawata, “Analyses of radiation force and torque on a spherical particle near a substrate illuminated by a focused Laguerre-Gaussian beam,” Opt. Commun. 274(2), 269–273 (2007).
[CrossRef]

Kildishev, A. V.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Physics Reports-Review Section,” Phys. Lett. 331, 118–195 (2000).

Lenstra, D.

Liu, Z.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[CrossRef]

Lu, J. Y.

Luk’yanchuk, B. S.

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97(26), 263902 (2006).
[CrossRef]

Matthews, M. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Mattiucci, N.

G. D'Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77, 043825 (2008).
[CrossRef]

Ohta, A.

A. Ohta and Y. Kawata, “Analyses of radiation force and torque on a spherical particle near a substrate illuminated by a focused Laguerre-Gaussian beam,” Opt. Commun. 274(2), 269–273 (2007).
[CrossRef]

Pedersen, R. H.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[CrossRef]

Pelinovsky, D. E.

Y. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Physics Reports-Review Section,” Phys. Lett. 331, 118–195 (2000).

Rice, K.

K. Rice, “Companion encyclopedia of Asian philosophy,” Ref. User Serv. Q. 37, 86 (1997).

Schouten, H. F.

Shalaev, V. M.

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[CrossRef]

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, “Nonlinear singular optics,” Pure Appl. Opt. 7(2), 301–311 (1998).
[CrossRef]

Swartzlander, G. A.

Tribelsky, M. I.

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97(26), 263902 (2006).
[CrossRef]

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, “Nonlinear singular optics,” Pure Appl. Opt. 7(2), 301–311 (1998).
[CrossRef]

Visser, T. D.

Wieman, C. E.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Wolf, E.

G. Gbur, T. D. Visser, and E. Wolf, “Singular optics,” Opt. Photonics News 13(12), 55 (2002).
[CrossRef]

Zhan, Q. W.

Zheludev, N. I.

J. Opt. Soc. Am. B (1)

Metamaterials (Amst.) (1)

Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,” Metamaterials (Amst.) 2(1), 45–51 (2008).
[CrossRef]

Opt. Commun. (1)

A. Ohta and Y. Kawata, “Analyses of radiation force and torque on a spherical particle near a substrate illuminated by a focused Laguerre-Gaussian beam,” Opt. Commun. 274(2), 269–273 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Opt. Photonics News (1)

G. Gbur, T. D. Visser, and E. Wolf, “Singular optics,” Opt. Photonics News 13(12), 55 (2002).
[CrossRef]

Phys. Lett. (1)

Y. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Physics Reports-Review Section,” Phys. Lett. 331, 118–195 (2000).

Phys. Rev. A (1)

G. D'Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77, 043825 (2008).
[CrossRef]

Phys. Rev. B (1)

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

Phys. Rev. Lett. (1)

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett. 97(26), 263902 (2006).
[CrossRef]

Pure Appl. Opt. (1)

M. S. Soskin and M. V. Vasnetsov, “Nonlinear singular optics,” Pure Appl. Opt. 7(2), 301–311 (1998).
[CrossRef]

Ref. User Serv. Q. (1)

K. Rice, “Companion encyclopedia of Asian philosophy,” Ref. User Serv. Q. 37, 86 (1997).

Science (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of bose-einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[CrossRef] [PubMed]

Other (1)

J. F. Nye, and M. V. Berry, “Dislocation in wave trains,” Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences 336, 165–190 (1974).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic diagram showing the process of e-beam lithography. Our samples were fabricated without any adhesion layer (such as Ti or Cr) between the gold film and the glass substrate. A 3 nm film of gold was sputter-deposited on the developed resist layer, followed by the thermal evaporation of another 27 nm of gold. (b) SEM image of a small region from the fabricated sample, showing diameter of tails. (c) The ideal Taiji mark designed for the studies reported in this paper. (d) Magnified view of a single cell in the SEM image of frame (b), showing the fitting curves of a fabricated Taiji mark (R 1 = 275 nm, R 2 = 250 nm, D 1 = 100 nm, diameter of the tangent circle D 2 = 60 nm).

Fig. 2
Fig. 2

(Top row) Experimental and simulated transmittance spectra for (a) x-polarized illumination; (b) y-polarized illumination. The illumination wavelengths available in our experiments ranged from λmin = 900 nm to λmax = 1900 nm. (Bottom row) Evolution of the simulated transmittance spectra upon varying the diameter of the tangent circle: (c) x-polarized illumination; (d) y-polarized illumination.

Fig. 3
Fig. 3

(a) Vortex-like profile of the time-averaged Poynting vector (red arrows) at different planes in the near-field region of the illuminated Taiji structure for the case of y-polarized illumination at λ = 1615 nm. (b) Schematic diagram of the physical model used to explain the origin of the vortex-like profile. The vortex in this diagram is produced by a horizontal electric dipole and a vertical surface current.

Fig. 4
Fig. 4

Simulated results corresponding to the interface region between air and gold (Taiji mark), obtained for the case of y-polarized illumination at λ = 1615 nm, i.e., second dip in the transmittance spectrum of Fig. 2(b). (a) Surface charge density in arbitrary units (color-coded) and surface current density (red arrows). (b) Vertical magnetic field in arbitrary units (color-coded) and horizontal electric field (red arrows). (c) Vertical electric field in arbitrary units (color-coded) and horizontal magnetic field (red arrows); shown on the right-hand-side in each case are the resulting time-averaged Poynting vector profiles.

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