Abstract

Manipulation of surface plasmon polaritons (SPPs) on metal surfaces is important for constructing ultracompact integrated micro/nano optical devices and systems. We employ the method of surface electromagnetic wave holography (SWH) to design holographic groove patterns for managing the transport of broadband SPPs on metal surface. Several sets of groove patterns corresponding to different wavelengths are etched on the same region on metal surface to form a broadband SPP hologram. The incident SPPs are scattered by the composite hologram and interfere with each other to focus at different or the same positions for SPPs of different wavelengths. Finite-difference time-domain simulations show that broadband demultiplexing of SPPs is realized by the designed plasmonic holographic structures. In addition, the broadband SPPs can be focused to a pre-designated spot by a designed plasmonic hologram and as a result focusing of an ultrashort plasmonic pulse can be achieved. The results show that the SWH can successfully handle design of plasmonic holographic structures for SPPs wavelength management on metal surface.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2014 (2)

Y. G. Chen, Y. H. Chen, and Z. Y. Li, “Direct method to control surface plasmon polaritons on metal surfaces,” Opt. Lett. 39(2), 339–342 (2014).
[CrossRef] [PubMed]

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

2013 (3)

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated plasmon beam: nondiffracting versus linearly focused,” Phys. Rev. Lett. 110(4), 046807 (2013).
[CrossRef]

B. Wang, X. Wu, and Y. Zhang, “Multiple-wavelength focusing and demultiplexing plasmonic lens based on asymmetric nanoslit arrays,” Plasmonics 8(4), 1535–1541 (2013).
[CrossRef]

Y. H. Chen, M. Q. Zhang, L. Gan, X. Y. Wu, L. Sun, J. Liu, J. Wang, and Z. Y. Li, “Holographic plasmonic lenses for surface plasmons with complex wavefront profile,” Opt. Express 21(15), 17558–17566 (2013).
[CrossRef] [PubMed]

2012 (3)

Y. H. Chen, L. Huang, L. Gan, and Z. Y. Li, “Wave-Front Shaping of Infrared Light through a Subwavelength Hole,” Light: Science & Applications 1(8), e26 (2012).
[CrossRef]

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Z. Y. Li, “Nanophotonics in China: overviews and highlights,” Frontiers of Physics 7(6), 601–631 (2012).
[CrossRef]

2011 (6)

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[CrossRef] [PubMed]

T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011).
[CrossRef] [PubMed]

G. Wang, H. Lu, X. Liu, D. Mao, and L. Duan, “Tunable multi-channel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunication regime,” Opt. Express 19(4), 3513–3518 (2011).
[CrossRef] [PubMed]

Y. H. Chen, J. X. Fu, and Z. Y. Li, “Surface electromagnetic wave holography,” Opt. Express 19, 23908–23920 (2011).
[CrossRef] [PubMed]

F. Hu, H. Yi, and Z. Zhou, “Wavelength demultiplexing structure based on arrayed plasmonic slot cavities,” Opt. Lett. 36(8), 1500–1502 (2011).
[CrossRef] [PubMed]

L. Li, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[CrossRef] [PubMed]

2010 (2)

2009 (1)

G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
[CrossRef] [PubMed]

2007 (2)

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett. 7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

2005 (2)

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]

G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30(24), 3359–3361 (2005).
[CrossRef] [PubMed]

2004 (2)

B. Wang and G. P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85(16), 3599–3601 (2004).
[CrossRef]

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (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. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martìn-Moreno, F. J. Garcìa-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

1996 (1)

Absil, P. P.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Albrecht, M.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Aussenegg, F. R.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett. 7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Bai, B. F.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Balram, K. C.

T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011).
[CrossRef] [PubMed]

Barnes, W. L.

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

Baron, A.

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[CrossRef] [PubMed]

Bartal, G.

G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
[CrossRef] [PubMed]

Bashaw, M. C.

Bozhevolnyi, S. I.

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]

Brongersma, M. L.

T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011).
[CrossRef] [PubMed]

Chen, W. T.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Chen, X. Z.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Chen, Y. G.

Chen, Y. H.

Chiang, I.-D.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Chu, S. T.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martìn-Moreno, F. J. Garcìa-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

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.

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[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]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martìn-Moreno, F. J. Garcìa-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Drezet, A.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett. 7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Duan, L.

Ebbesen, T. W.

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[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]

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

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martìn-Moreno, F. J. Garcìa-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Elsaesser, T.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Fan, S.

Fu, J. X.

Gan, L.

Y. H. Chen, M. Q. Zhang, L. Gan, X. Y. Wu, L. Sun, J. Liu, J. Wang, and Z. Y. Li, “Holographic plasmonic lenses for surface plasmons with complex wavefront profile,” Opt. Express 21(15), 17558–17566 (2013).
[CrossRef] [PubMed]

Y. H. Chen, L. Huang, L. Gan, and Z. Y. Li, “Wave-Front Shaping of Infrared Light through a Subwavelength Hole,” Light: Science & Applications 1(8), e26 (2012).
[CrossRef]

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Garcìa-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martìn-Moreno, F. J. Garcìa-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Genet, C.

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[CrossRef] [PubMed]

Gill, D.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Heanue, J. F.

Hesselink, L.

Hohenau, A.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett. 7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Hryniewicz, J. V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Hsu, W. L.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Hu, F.

Huang, L.

Y. H. Chen, L. Huang, L. Gan, and Z. Y. Li, “Wave-Front Shaping of Infrared Light through a Subwavelength Hole,” Light: Science & Applications 1(8), e26 (2012).
[CrossRef]

Huang, L. L.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Huang, X. G.

Huang, Y.-W.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Hugonin, J. P.

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[CrossRef] [PubMed]

Jin, G. F.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Johnson, F. G.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

King, O.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Koller, D.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett. 7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Krenn, J. R.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett. 7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Lalanne, P.

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[CrossRef] [PubMed]

Lande, D.

Leitner, A.

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett. 7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

Lerosey, G.

G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
[CrossRef] [PubMed]

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martìn-Moreno, F. J. Garcìa-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Li, G. X.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Li, L.

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated plasmon beam: nondiffracting versus linearly focused,” Phys. Rev. Lett. 110(4), 046807 (2013).
[CrossRef]

L. Li, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[CrossRef] [PubMed]

Li, T.

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated plasmon beam: nondiffracting versus linearly focused,” Phys. Rev. Lett. 110(4), 046807 (2013).
[CrossRef]

L. Li, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[CrossRef] [PubMed]

Li, Z. Y.

Liao, C. Y.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Lienau, C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Lin, H. T.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martìn-Moreno, F. J. Garcìa-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Little, B. E.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Liu, A. Q.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Liu, J.

Liu, X.

Lu, H.

Ly-Gagnon, D. S.

T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011).
[CrossRef] [PubMed]

Mao, D.

Martin-Moreno, L.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Martìn-Moreno, L.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martìn-Moreno, F. J. Garcìa-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Matheu, P.

G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
[CrossRef] [PubMed]

Miller, D. A. B.

T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011).
[CrossRef] [PubMed]

Mühlenbernd, H.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Neacsu, C. C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Pile, D. F. P.

G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
[CrossRef] [PubMed]

Raschke, M. B.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Rodier, J. C.

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[CrossRef] [PubMed]

Ropers, C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Rousseau, E.

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[CrossRef] [PubMed]

Seiferth, F.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Sun, G.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Sun, L.

Sun, S.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Tan, Q. F.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Tanemura, T.

T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011).
[CrossRef] [PubMed]

Tao, J.

Trakalo, M.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Tsai, D. P.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Van, V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Veronis, G.

Volkov, V. S.

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]

Wahl, P.

T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011).
[CrossRef] [PubMed]

Wang, B.

B. Wang, X. Wu, and Y. Zhang, “Multiple-wavelength focusing and demultiplexing plasmonic lens based on asymmetric nanoslit arrays,” Plasmonics 8(4), 1535–1541 (2013).
[CrossRef]

B. Wang and G. P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85(16), 3599–3601 (2004).
[CrossRef]

Wang, C.-M.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Wang, G.

Wang, G. P.

B. Wang and G. P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85(16), 3599–3601 (2004).
[CrossRef]

Wang, J.

Wang, S. M.

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated plasmon beam: nondiffracting versus linearly focused,” Phys. Rev. Lett. 110(4), 046807 (2013).
[CrossRef]

L. Li, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[CrossRef] [PubMed]

White, J. S.

T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011).
[CrossRef] [PubMed]

Wu, X.

B. Wang, X. Wu, and Y. Zhang, “Multiple-wavelength focusing and demultiplexing plasmonic lens based on asymmetric nanoslit arrays,” Plasmonics 8(4), 1535–1541 (2013).
[CrossRef]

Wu, X. Y.

Yang, K. Y.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Yi, H.

Zentgraf, T.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Zhang, J. S.

C. L. Zhao and J. S. Zhang, “Plasmonic demultiplexer and guiding,” ACS Nano 4(11), 6433–6438 (2010).
[CrossRef] [PubMed]

Zhang, M. Q.

Zhang, S.

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

Zhang, X.

L. Li, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[CrossRef] [PubMed]

G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
[CrossRef] [PubMed]

Zhang, Y.

B. Wang, X. Wu, and Y. Zhang, “Multiple-wavelength focusing and demultiplexing plasmonic lens based on asymmetric nanoslit arrays,” Plasmonics 8(4), 1535–1541 (2013).
[CrossRef]

Zhao, C. L.

C. L. Zhao and J. S. Zhang, “Plasmonic demultiplexer and guiding,” ACS Nano 4(11), 6433–6438 (2010).
[CrossRef] [PubMed]

Zhou, L.

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

Zhou, Z.

Zhu, J. H.

Zhu, S. N.

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated plasmon beam: nondiffracting versus linearly focused,” Phys. Rev. Lett. 110(4), 046807 (2013).
[CrossRef]

L. Li, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[CrossRef] [PubMed]

ACS Nano (1)

C. L. Zhao and J. S. Zhang, “Plasmonic demultiplexer and guiding,” ACS Nano 4(11), 6433–6438 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

B. Wang and G. P. Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85(16), 3599–3601 (2004).
[CrossRef]

Frontiers of Physics (1)

Z. Y. Li, “Nanophotonics in China: overviews and highlights,” Frontiers of Physics 7(6), 601–631 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004).
[CrossRef]

Light: Science & Applications (1)

Y. H. Chen, L. Huang, L. Gan, and Z. Y. Li, “Wave-Front Shaping of Infrared Light through a Subwavelength Hole,” Light: Science & Applications 1(8), e26 (2012).
[CrossRef]

Nano Lett. (8)

W. T. Chen, K. Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014).
[CrossRef] [PubMed]

L. L. Huang, X. Z. Chen, H. Mühlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for dontrolling dight propagation,” Nano Lett. 12, 5750–5755 (2012).

L. Li, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011).
[CrossRef] [PubMed]

A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Plasmonic crystal demultiplexer and multiports,” Nano Lett. 7(6), 1697–1700 (2007).
[CrossRef] [PubMed]

T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011).
[CrossRef] [PubMed]

G. Lerosey, D. F. P. Pile, P. Matheu, G. Bartal, and X. Zhang, “Controlling the phase and amplitude of plasmon sources at a subwavelength scale,” Nano Lett. 9(1), 327–331 (2009).
[CrossRef] [PubMed]

A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, “Compact antenna for efficient and unidirectional launching and decoupling of surface plasmons,” Nano Lett. 11(10), 4207–4212 (2011).
[CrossRef] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, “Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source,” Nano Lett. 7(9), 2784–2788 (2007).
[CrossRef] [PubMed]

Nature (1)

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

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. Lett. (2)

L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated plasmon beam: nondiffracting versus linearly focused,” Phys. Rev. Lett. 110(4), 046807 (2013).
[CrossRef]

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]

Plasmonics (1)

B. Wang, X. Wu, and Y. Zhang, “Multiple-wavelength focusing and demultiplexing plasmonic lens based on asymmetric nanoslit arrays,” Plasmonics 8(4), 1535–1541 (2013).
[CrossRef]

Science (2)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martìn-Moreno, F. J. Garcìa-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Other (1)

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford Publishing Pte. Ltd, 2008).

Supplementary Material (1)

» Media 1: MOV (2158 KB)     

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Figures (6)

Fig. 1
Fig. 1

Schematic of multiple-wavelength surface holography, (a) writing process, (b) reading process.

Fig. 2
Fig. 2

Design of two-wavelength metallic holographic pattern for SPPs demultiplexing on metal surface. (a) Field pattern of the reference wave. (b) Field pattern of the object wave. (c) Interference fringe pattern. (d) Geometric configuration of holographic groove pattern corresponding to λ 1 . (e) Geometric configuration of holographic groove pattern corresponding to λ 2 . (f) The composite holographic groove patterns.

Fig. 3
Fig. 3

Simulation results of SPPs reconstructions of individual holograms and composite holograms for demultiplexing applications. Intensity distribution of SPPs in the focusing region on metal surface for (a) the individual hologram shown in Fig. 2(d) with incident wavelength λ = 1.1 μ m and (b) the individual hologram shown in Fig. 2(e) with incident wavelength λ = 1.0 μ m . (c) The spectra of coupling efficiency of focal areas with 3 μ m y 1 μ m for individual hologram shown in Fig. 2(d) and 1 μ m y 3 μ m for individual hologram shown in Fig. 2(e). Figure 3(d-h) SPPs demultiplexing with two-wavelength composite hologram [shown in Fig. 2(f)]. Intensity distribution of SPPs with λ = 1.1 μ m in the focusing region (d) on x y plane and (g) on focal plane y z plane with x = 8 μ m . Intensity distribution of SPPs with λ = 1.0 μ m in the focusing region (e) on x y plane and (h) on focal plane y z plane with x = 8 μ m . (f) The spectra of coupling efficiency of two focal areas with 3 μ m y 1 μ m and 1 μ m y 3 μ m .

Fig. 4
Fig. 4

Holographic patterns designed to focus SPPs with three wavelengths to the same point on metal surface. (a) The composite groove pattern. Intensity distribution of SPPs in the focusing region on metal surface with wavelength (b) λ = 0.93 μ m , (c) λ = 1.0 μ m , (d) λ = 1.1 μ m . (e) The spectrum of coupling efficiency of the focal area with 1 μ m y 1 μ m .

Fig. 5
Fig. 5

The focusing of other non-designed wavelength through the holographic patterns shown in Fig. 4(a). Intensity distribution of SPPs in the focusing region on metal surface with wavelength (a) λ = 0.90 μ m , (b) λ = 0.95 μ m , (c) λ = 1.05 μ m , (d) λ = 1.15 μ m .

Fig. 6
Fig. 6

The focusing of an ultrashort plasmonic pulse to a point through the holographic patterns shown in Fig. 4(a). (a) The incident pulse, (b)he incident spectrum, (c) the focal pulse, (d) the focal spectrum, (e-h) four frame excerpted from video in turn (see Media 1). Here the white point F indicates the position of the pre-designed focus spot and the rectangular region denotes the hologram region.

Equations (6)

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ψ O1 ψ W1 + φ 01 =2 m 1 π,
H 1 (x,y)=α m δ( ψ O1 ψ W1 + φ 01 =2 m 1 π) .
ψ O2 ψ W2 + φ 02 =2 m 2 π,
H 2 (x,y)=α m δ( ψ O 2 ψ W2 + φ 02 =2 m 2 π) .
H(x,y)= H 1 (x,y)+ H 2 (x,y).
H(x,y)= H 1 (x,y)+ H 2 (x,y)++ H n (x,y).

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