Abstract

Topological insulators (TI) are new phases of matter with topologically protected surface states (SS) possessing novel physical properties such as spin-momentum locking. Coupling optical angular momentum to the SS is of interest for both fundamental understanding and applications in future spintronic devices. However, due to the nanoscale thickness of the surface states, the light matter interaction is dominated by the bulk. Here we propose and experimentally demonstrate a plasmonic cavity enabling both nanoscale light confinement and control of surface plasmon-polariton (SPP) spin angular momentum (AM) – towards coupling to topological-insulator SS. The resulting SPP field components within the cavity are arranged in a chess-board-like pattern. Each chess-board square exhibits approximately a uniform circular polarization (spin AM) of the local in-plane field interleaved by out-of-plane field vortices (orbital AM). As the first step, we demonstrate the predicted pattern experimentally by near-field measurements on a gold-air interface, with excellent agreement to our theory. Our results pave the way towards efficient optical access to topological-insulator surface states using plasmonics.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]

2014 (3)

Z.-H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S.-Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron spin-polarization control in the topological insulator Bi2Se3.,” Phys. Rev. Lett. 112(7), 076802 (2014).
[Crossref] [PubMed]

H. Koc, H. Ozisik, E. Deligöz, A. M. Mamedov, and E. Ozbay, “Mechanical, electronic, and optical properties of Bi2S3 and Bi2Se3 compounds: first principle investigations,” J. Mol. Model. 20(4), 1–12 (2014).
[Crossref] [PubMed]

Y. Yadin, J. Scheuer, Y. Gross, and M. Orenstein, “Spontaneous locking of optical vortices in coupled semiconductor lasers,” Phys. Rev. A 90(3), 033803 (2014).
[Crossref]

2013 (2)

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref] [PubMed]

C. Jozwiak, C.-H. Park, K. Gotlieb, C. Hwang, D.-H. Lee, S. G. Louie, J. D. Denlinger, C. R. Rotundu, R. J. Birgeneau, Z. Hussain, and A. Lanzara, “Photoelectron spin-flipping and texture manipulation in a topological insulator,” Nat. Phys. 9(5), 293–298 (2013).
[Crossref]

2012 (5)

R. Warmbier, G. S. Manyali, and A. Quandt, “Surface plasmon polaritons in lossy uniaxial anisotropic materials,” Phys. Rev. B 85(8), 085442 (2012).
[Crossref]

Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, “Topological States and adiabatic pumping in quasicrystals,” Phys. Rev. Lett. 109(10), 106402 (2012).
[Crossref] [PubMed]

A. Quandt, “Viewpoint: quasicrystals, meet topological insulators,” Physics (College Park Md.) 5, 99 (2012).
[Crossref]

S.-W. Cho, J. Park, S.-Y. Lee, H. Kim, and B. Lee, “Coupling of spin and angular momentum of light in plasmonic vortex,” Opt. Express 20(9), 10083–10094 (2012).
[Crossref] [PubMed]

Y. Sharma, P. Srivastava, A. Dashora, L. Vadkhiya, M. Bhayani, R. Jain, A. Jani, and B. Ahuja, “Electronic structure, optical properties and Compton profiles of Bi2S3 and Bi2Se3,” Solid State Sci. 14(2), 241–249 (2012).
[Crossref]

2011 (4)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

J. W. McIver, D. Hsieh, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, “Control over topological insulator photocurrents with light polarization,” Nat. Nanotechnol. 7(2), 96–100 (2011).
[Crossref] [PubMed]

S. Souma, K. Kosaka, T. Sato, M. Komatsu, A. Takayama, T. Takahashi, M. Kriener, K. Segawa, and Y. Ando, “Direct measurement of the out-of-plane spin texture in the Dirac-cone surface state of a topological insulator,” Phys. Rev. Lett. 106(21), 216803 (2011).
[Crossref] [PubMed]

P. Hosur, “Circular photogalvanic effect on topological insulator surfaces: Berry-curvature-dependent response,” Phys. Rev. B 83(3), 035309 (2011).
[Crossref]

2010 (3)

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[Crossref] [PubMed]

M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[Crossref]

J. E. Moore, “The birth of topological insulators,” Nature 464(7286), 194–198 (2010).
[Crossref] [PubMed]

2009 (5)

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. Hor, R. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009).
[Crossref]

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.-L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

L. Fu, “Hexagonal warping effects in the surface states of the topological insulator Bi2Te3.,” Phys. Rev. Lett. 103(26), 266801 (2009).
[Crossref] [PubMed]

T. V. Teperik, A. Archambault, F. Marquier, and J.-J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[Crossref] [PubMed]

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Observation of optical spin symmetry breaking in nanoapertures,” Nano Lett. 9(8), 3016–3019 (2009).
[Crossref] [PubMed]

2008 (1)

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref] [PubMed]

2006 (2)

J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, “Resonant and non-resonant generation and focusing of surface plasmons with circular gratings,” Opt. Express 14(12), 5664–5670 (2006).
[Crossref] [PubMed]

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

1954 (1)

W. H. McMaster, “Polarization and the Stokes parameters,” Am. J. Phys. 22(6), 351–362 (1954).
[Crossref]

Ahuja, B.

Y. Sharma, P. Srivastava, A. Dashora, L. Vadkhiya, M. Bhayani, R. Jain, A. Jani, and B. Ahuja, “Electronic structure, optical properties and Compton profiles of Bi2S3 and Bi2Se3,” Solid State Sci. 14(2), 241–249 (2012).
[Crossref]

Analytis, J. G.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.-L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

Ando, Y.

S. Souma, K. Kosaka, T. Sato, M. Komatsu, A. Takayama, T. Takahashi, M. Kriener, K. Segawa, and Y. Ando, “Direct measurement of the out-of-plane spin texture in the Dirac-cone surface state of a topological insulator,” Phys. Rev. Lett. 106(21), 216803 (2011).
[Crossref] [PubMed]

Archambault, A.

Bansil, A.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. Hor, R. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009).
[Crossref]

Bhayani, M.

Y. Sharma, P. Srivastava, A. Dashora, L. Vadkhiya, M. Bhayani, R. Jain, A. Jani, and B. Ahuja, “Electronic structure, optical properties and Compton profiles of Bi2S3 and Bi2Se3,” Solid State Sci. 14(2), 241–249 (2012).
[Crossref]

Birgeneau, R. J.

C. Jozwiak, C.-H. Park, K. Gotlieb, C. Hwang, D.-H. Lee, S. G. Louie, J. D. Denlinger, C. R. Rotundu, R. J. Birgeneau, Z. Hussain, and A. Lanzara, “Photoelectron spin-flipping and texture manipulation in a topological insulator,” Nat. Phys. 9(5), 293–298 (2013).
[Crossref]

Bretner, I.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Observation of optical spin symmetry breaking in nanoapertures,” Nano Lett. 9(8), 3016–3019 (2009).
[Crossref] [PubMed]

Cava, R.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. Hor, R. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009).
[Crossref]

Chen, Y. L.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.-L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

Cho, S.-W.

S.-W. Cho, J. Park, S.-Y. Lee, H. Kim, and B. Lee, “Coupling of spin and angular momentum of light in plasmonic vortex,” Opt. Express 20(9), 10083–10094 (2012).
[Crossref] [PubMed]

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10(2), 529–536 (2010).
[Crossref] [PubMed]

Chu, J.-H.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.-L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

Dai, X.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.-L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

Damascelli, A.

Z.-H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S.-Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron spin-polarization control in the topological insulator Bi2Se3.,” Phys. Rev. Lett. 112(7), 076802 (2014).
[Crossref] [PubMed]

Dashora, A.

Y. Sharma, P. Srivastava, A. Dashora, L. Vadkhiya, M. Bhayani, R. Jain, A. Jani, and B. Ahuja, “Electronic structure, optical properties and Compton profiles of Bi2S3 and Bi2Se3,” Solid State Sci. 14(2), 241–249 (2012).
[Crossref]

Deligöz, E.

H. Koc, H. Ozisik, E. Deligöz, A. M. Mamedov, and E. Ozbay, “Mechanical, electronic, and optical properties of Bi2S3 and Bi2Se3 compounds: first principle investigations,” J. Mol. Model. 20(4), 1–12 (2014).
[Crossref] [PubMed]

Denlinger, J. D.

C. Jozwiak, C.-H. Park, K. Gotlieb, C. Hwang, D.-H. Lee, S. G. Louie, J. D. Denlinger, C. R. Rotundu, R. J. Birgeneau, Z. Hussain, and A. Lanzara, “Photoelectron spin-flipping and texture manipulation in a topological insulator,” Nat. Phys. 9(5), 293–298 (2013).
[Crossref]

Dreisow, F.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature 496(7444), 196–200 (2013).
[Crossref] [PubMed]

Elfimov, I. S.

Z.-H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S.-Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron spin-polarization control in the topological insulator Bi2Se3.,” Phys. Rev. Lett. 112(7), 076802 (2014).
[Crossref] [PubMed]

Fang, Z.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.-L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

Fisher, I. R.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.-L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

Fu, L.

L. Fu, “Hexagonal warping effects in the surface states of the topological insulator Bi2Te3.,” Phys. Rev. Lett. 103(26), 266801 (2009).
[Crossref] [PubMed]

Gedik, N.

J. W. McIver, D. Hsieh, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, “Control over topological insulator photocurrents with light polarization,” Nat. Nanotechnol. 7(2), 96–100 (2011).
[Crossref] [PubMed]

Gorodetski, Y.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Observation of optical spin symmetry breaking in nanoapertures,” Nano Lett. 9(8), 3016–3019 (2009).
[Crossref] [PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref] [PubMed]

Gotlieb, K.

C. Jozwiak, C.-H. Park, K. Gotlieb, C. Hwang, D.-H. Lee, S. G. Louie, J. D. Denlinger, C. R. Rotundu, R. J. Birgeneau, Z. Hussain, and A. Lanzara, “Photoelectron spin-flipping and texture manipulation in a topological insulator,” Nat. Phys. 9(5), 293–298 (2013).
[Crossref]

Grauer, D.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. Hor, R. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009).
[Crossref]

Greffet, J.-J.

Gross, Y.

Y. Yadin, J. Scheuer, Y. Gross, and M. Orenstein, “Spontaneous locking of optical vortices in coupled semiconductor lasers,” Phys. Rev. A 90(3), 033803 (2014).
[Crossref]

Hasan, M. Z.

M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[Crossref]

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. Hor, R. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009).
[Crossref]

Hasman, E.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Observation of optical spin symmetry breaking in nanoapertures,” Nano Lett. 9(8), 3016–3019 (2009).
[Crossref] [PubMed]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref] [PubMed]

Haverkort, M. W.

Z.-H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S.-Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron spin-polarization control in the topological insulator Bi2Se3.,” Phys. Rev. Lett. 112(7), 076802 (2014).
[Crossref] [PubMed]

Hillenbrand, R.

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89(10), 101124 (2006).
[Crossref]

Hor, Y.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. Hor, R. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5(6), 398–402 (2009).
[Crossref]

Hosur, P.

P. Hosur, “Circular photogalvanic effect on topological insulator surfaces: Berry-curvature-dependent response,” Phys. Rev. B 83(3), 035309 (2011).
[Crossref]

Hsieh, D.

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Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.-L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
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Zhang, X.

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Z.-H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S.-Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron spin-polarization control in the topological insulator Bi2Se3.,” Phys. Rev. Lett. 112(7), 076802 (2014).
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Adv. Opt. Photonics (1)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Am. J. Phys. (1)

W. H. McMaster, “Polarization and the Stokes parameters,” Am. J. Phys. 22(6), 351–362 (1954).
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Appl. Phys. Lett. (1)

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J. Mol. Model. (1)

H. Koc, H. Ozisik, E. Deligöz, A. M. Mamedov, and E. Ozbay, “Mechanical, electronic, and optical properties of Bi2S3 and Bi2Se3 compounds: first principle investigations,” J. Mol. Model. 20(4), 1–12 (2014).
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Nat. Nanotechnol. (1)

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Nat. Phys. (2)

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Opt. Express (3)

Phys. Rev. A (1)

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[Crossref] [PubMed]

Z.-H. Zhu, C. N. Veenstra, S. Zhdanovich, M. P. Schneider, T. Okuda, K. Miyamoto, S.-Y. Zhu, H. Namatame, M. Taniguchi, M. W. Haverkort, I. S. Elfimov, and A. Damascelli, “Photoelectron spin-polarization control in the topological insulator Bi2Se3.,” Phys. Rev. Lett. 112(7), 076802 (2014).
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Solid State Sci. (1)

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Other (1)

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Supplementary Material (2)

NameDescription
» Visualization 1: MOV (13222 KB)      media files
» Visualization 2: MOV (10900 KB)      media files

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Figures (4)

Fig. 1
Fig. 1 (a) Permittivity values of Bi2Se3 as given by Ref. 20. (b) Penetration depth of SPP into the TI. The inset is FDTD simulation of the setup at 1.5[μm] illumination wavelength. Highly confined SPPs are evident. (c) IP to OP SPP field components ratio inside the TI. (d) SPP wavelength (blue) and figure of merit (red) as a function of illumination wavelength.
Fig. 2
Fig. 2 Square cavity construction (c) from parallel vertical (a) and horizontal (b) slit pairs. The red arrows represent the illumination polarization. (d) Scanning electron microscope image of a resonantly enhanced cavity milled by FIB in gold.
Fig. 3
Fig. 3 Square cavity milled in gold on top of Bi2Se3 FDTD simulation (a,b) Phase difference, E y E x between the IP components in radians, under LHC (a) and RHC (b) illuminations. (c) Absolute value of the total SPP field under circularly polarized illumination. (d,e) Phase of the OP field under LHC (d) and RHC (e) showing the vortex array. (f) Absolute value of the OP SPP field. Maxima of the IP field (c) overlap with zeros of the OP field (f). The insets represent the same spatial region capturing four “chess board” cells. Solid white arrows represent the direction of field rotation within a cell; dashed black arrows represent the direction of phase accumulation of the vortices. Switching the illumination flips the rotation direction of a given cell or vortex, (a,d) versus (b,e). (c). For time dependent vector field simulation see Visualization 1 and Visualization 2.
Fig. 4
Fig. 4 Experimental (top) and simulation (bottom) results of the phase (a,b) and amplitude (c,d) of the OP field in the inner square of the cavity in Fig. 2(d) Dashed arrows represent increasing phase direction around 4 of the vortices in the array.

Equations (2)

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E ± spp = C ω ( i k z 0 k spp )exp( i k spp x )exp( k z z )
p Square | 2Im[ E x ( x,y ) E * y ( x,y ) ] | | E x ( x,y ) | 2 + | E y ( x,y ) | 2 ×W( x,y )dxdy = 8 π 2 0.8106

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