Abstract

Conventional optical lenses enable precise foci but suffer from the diffraction limit due to the cutoff of spatial frequencies. Development of a super-oscillatory phenomenon offers an alternative approach to realize far-field sub-diffraction focusing. However, most super-oscillatory lenses exhibit a strong dependence on incident wavelengths, resulting in a narrow-band working frequency due to a fragile super-oscillatory field. Here, for the first time, achromatic super-oscillatory metasurfaces (ASOMs) are proposed to simultaneously steer optical fields at visible wavelengths of 473 nm, 532 nm and 632.8 nm and to achieve focusing at the same axial position with a resolution beyond the diffraction limit. These metasurface-based devices provide dispersionless phase profiles so that the material dispersion can be neglected in the optimization process. In addition, the design strategy can effectively circumvent the axial chromatic aberration observed in previously demonstrated metasurfaces. Constructed ASOMs are further verified numerically and simulated results for one ASOM with spot sizes of 0.706, 0.722 and 0.750 times the diffraction limit at the preset plane are consistent with the designs. Furthermore, benefiting from flexible and arbitrary phase modulations of the metasurface, the proposed method gives more freedom for a design of a super-oscillatory field and enables a lightweight, low-cost and compact optical element to replace the bulky doublet/triplet lens in a conventional optical system.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (5)

W. Zhang, W. Tan, Q. Yang, T. Zhou, and J. Liu, “Subwavelength focusing in visible light band by a Fibonacci photonic quasi-crystal plano-concave lens,” J. Opt. Soc. Am. B 35(10), 2364–2367 (2018).
[Crossref]

C. Zhang, Z. Jiang, W. Tan, R. Ge, and J. Liu, “Non-near-field sub-diffraction focusing in the visible wavelength range by a Fibonacci subwavelength circular grating,” J. Opt. Soc. Am. A 35(10), 1701–1704 (2018).
[Crossref] [PubMed]

J. Liu and Z. Fan, “Size Limits for Focusing of Two-Dimensional Photonic Quasicrystal Lenses,” IEEE Photonics Technol. Lett. 30(11), 1001–1004 (2018).
[Crossref]

Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic Broadband Super-Resolution Imaging by Super-Oscillatory Metasurface,” Laser Photonics Rev. 12, 1800064 (2018).
[Crossref]

X. Zhang, X. Li, J. Jin, M. Pu, X. Ma, J. Luo, Y. Guo, C. Wang, and X. Luo, “Polarization-independent broadband meta-holograms Via polarization-dependent nanoholes,” Nanoscale 10(19), 9304–9310 (2018).
[Crossref] [PubMed]

2017 (3)

F. Qin, K. Huang, J. Wu, J. Teng, C.-W. Qiu, and M. Hong, “A Supercritical Lens Optical Label-Free Microscopy: Sub-Diffraction Resolution and Ultra-Long Working Distance,” Adv. Mater. 29(8), 1602721 (2017).
[Crossref] [PubMed]

G. H. Yuan, E. T. Rogers, and N. I. Zheludev, “Achromatic super-oscillatory lenses with sub-wavelength focusing,” Light Sci. Appl. 6(9), e17036 (2017).
[Crossref] [PubMed]

J. Wu, Z. Wu, Y. He, A. Yu, Z. Zhang, Z. Wen, and G. Chen, “Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator,” Opt. Express 25(6), 6274–6282 (2017).
[Crossref] [PubMed]

2016 (3)

C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, and X. Luo, “Super-resolution optical telescopes with local light diffraction shrinkage,” Sci. Rep. 5(1), 18485 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Z. Jiang and J. Liu, “Progress in far-field focusing and imaging with super-oscillation,” Wuli Xuebao 65(23), 234203 (2016).

2015 (6)

G. Yuan, E. T. F. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2015).
[Crossref] [PubMed]

X. G. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. Astron. 58(9), 594201 (2015).
[Crossref]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

J. Liu, E. Liu, Z. Fan, and X. Zhang, “Dielectric refractive index dependence of the focusing properties of a dielectric-cylinder-type decagonal photonic quasicrystal flat lens and its photon localization,” Appl. Phys. Express 8(11), 112003 (2015).
[Crossref]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

2014 (3)

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

X. Chen, Y. Zhang, L. Huang, and S. Zhang, “Ultrathin Metasurface Laser Beam Shaper,” Adv. Opt. Mater. 2(10), 978–982 (2014).
[Crossref]

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

2013 (5)

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

T. Liu, J. Tan, J. Liu, and H. Wang, “Vectorial design of super-oscillatory lens,” Opt. Express 21(13), 15090–15101 (2013).
[Crossref] [PubMed]

A. M. H. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3(1), 1715 (2013).
[Crossref] [PubMed]

E. T. F. Rogers and N. I. Zheludev, “Optical super-oscillations: Sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15(9), 094008 (2013).
[Crossref]

2012 (2)

E. T. F. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
[Crossref] [PubMed]

2008 (1)

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

2007 (2)

K. I. Willig, B. Harke, R. Medda, and S. W. Hell, “STED microscopy with continuous wave beams,” Nat. Methods 4(11), 915–918 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

2006 (2)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. Math. Gen. 39(22), 6965–6977 (2006).
[Crossref]

2003 (1)

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67, 046611 (2003).
[Crossref] [PubMed]

2000 (1)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1994 (1)

1991 (1)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the Diffraction Barrier: Optical Microscopy on a Nanometric Scale,” Science 251(5000), 1468–1470 (1991).
[Crossref] [PubMed]

1977 (1)

Adamo, G.

G. Yuan, E. T. F. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2015).
[Crossref] [PubMed]

Bai, B.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
[Crossref] [PubMed]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. Math. Gen. 39(22), 6965–6977 (2006).
[Crossref]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the Diffraction Barrier: Optical Microscopy on a Nanometric Scale,” Science 251(5000), 1468–1470 (1991).
[Crossref] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref] [PubMed]

Capasso, F.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Chad, J. E.

E. T. F. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Cheah, K.-W.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

Chen, G.

Chen, S.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

Chen, W. T.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Chen, X.

X. Chen, Y. Zhang, L. Huang, and S. Zhang, “Ultrathin Metasurface Laser Beam Shaper,” Adv. Opt. Mater. 2(10), 978–982 (2014).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
[Crossref] [PubMed]

Courjon, D.

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67, 046611 (2003).
[Crossref] [PubMed]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Dennis, M. R.

E. T. F. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Devlin, R. C.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Eleftheriades, G. V.

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G. Yuan, E. T. F. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2015).
[Crossref] [PubMed]

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

E. T. F. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Savo, S.

E. T. F. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Shen, Z.

G. Yuan, E. T. F. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2015).
[Crossref] [PubMed]

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

Siegman, A. E.

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Tan, J.

Tan, Q.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
[Crossref] [PubMed]

Tan, W.

Tang, D.

C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, and X. Luo, “Super-resolution optical telescopes with local light diffraction shrinkage,” Sci. Rep. 5(1), 18485 (2016).
[Crossref] [PubMed]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

Teng, J.

F. Qin, K. Huang, J. Wu, J. Teng, C.-W. Qiu, and M. Hong, “A Supercritical Lens Optical Label-Free Microscopy: Sub-Diffraction Resolution and Ultra-Long Working Distance,” Adv. Mater. 29(8), 1602721 (2017).
[Crossref] [PubMed]

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
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E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the Diffraction Barrier: Optical Microscopy on a Nanometric Scale,” Science 251(5000), 1468–1470 (1991).
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Wang, C.

X. Zhang, X. Li, J. Jin, M. Pu, X. Ma, J. Luo, Y. Guo, C. Wang, and X. Luo, “Polarization-independent broadband meta-holograms Via polarization-dependent nanoholes,” Nanoscale 10(19), 9304–9310 (2018).
[Crossref] [PubMed]

Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic Broadband Super-Resolution Imaging by Super-Oscillatory Metasurface,” Laser Photonics Rev. 12, 1800064 (2018).
[Crossref]

C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, and X. Luo, “Super-resolution optical telescopes with local light diffraction shrinkage,” Sci. Rep. 5(1), 18485 (2016).
[Crossref] [PubMed]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Wang, H.

Wang, J.

C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, and X. Luo, “Super-resolution optical telescopes with local light diffraction shrinkage,” Sci. Rep. 5(1), 18485 (2016).
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Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy,” Science 319(5864), 810–813 (2008).
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Wang, Y.

Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic Broadband Super-Resolution Imaging by Super-Oscillatory Metasurface,” Laser Photonics Rev. 12, 1800064 (2018).
[Crossref]

C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, and X. Luo, “Super-resolution optical telescopes with local light diffraction shrinkage,” Sci. Rep. 5(1), 18485 (2016).
[Crossref] [PubMed]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

Weiner, J. S.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the Diffraction Barrier: Optical Microscopy on a Nanometric Scale,” Science 251(5000), 1468–1470 (1991).
[Crossref] [PubMed]

Wen, Z.

Wichmann, J.

Willig, K. I.

K. I. Willig, B. Harke, R. Medda, and S. W. Hell, “STED microscopy with continuous wave beams,” Nat. Methods 4(11), 915–918 (2007).
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Wong, A. M. H.

A. M. H. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3(1), 1715 (2013).
[Crossref] [PubMed]

Wu, J.

F. Qin, K. Huang, J. Wu, J. Teng, C.-W. Qiu, and M. Hong, “A Supercritical Lens Optical Label-Free Microscopy: Sub-Diffraction Resolution and Ultra-Long Working Distance,” Adv. Mater. 29(8), 1602721 (2017).
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J. Wu, Z. Wu, Y. He, A. Yu, Z. Zhang, Z. Wen, and G. Chen, “Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator,” Opt. Express 25(6), 6274–6282 (2017).
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Wu, Z.

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Yan, W.

C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, and X. Luo, “Super-resolution optical telescopes with local light diffraction shrinkage,” Sci. Rep. 5(1), 18485 (2016).
[Crossref] [PubMed]

Yang, J.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

Yang, Q.

Ye, H.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Yeo, S. P.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Yu, A.

Yuan, G.

G. Yuan, E. T. F. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2015).
[Crossref] [PubMed]

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

Yuan, G. H.

G. H. Yuan, E. T. Rogers, and N. I. Zheludev, “Achromatic super-oscillatory lenses with sub-wavelength focusing,” Light Sci. Appl. 6(9), e17036 (2017).
[Crossref] [PubMed]

Zentgraf, T.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
[Crossref] [PubMed]

Zhang, C.

Zhang, H.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

Zhang, J.

Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic Broadband Super-Resolution Imaging by Super-Oscillatory Metasurface,” Laser Photonics Rev. 12, 1800064 (2018).
[Crossref]

Zhang, S.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref] [PubMed]

X. Chen, Y. Zhang, L. Huang, and S. Zhang, “Ultrathin Metasurface Laser Beam Shaper,” Adv. Opt. Mater. 2(10), 978–982 (2014).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
[Crossref]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
[Crossref] [PubMed]

Zhang, T.

Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic Broadband Super-Resolution Imaging by Super-Oscillatory Metasurface,” Laser Photonics Rev. 12, 1800064 (2018).
[Crossref]

Zhang, W.

Zhang, X.

X. Zhang, X. Li, J. Jin, M. Pu, X. Ma, J. Luo, Y. Guo, C. Wang, and X. Luo, “Polarization-independent broadband meta-holograms Via polarization-dependent nanoholes,” Nanoscale 10(19), 9304–9310 (2018).
[Crossref] [PubMed]

J. Liu, E. Liu, Z. Fan, and X. Zhang, “Dielectric refractive index dependence of the focusing properties of a dielectric-cylinder-type decagonal photonic quasicrystal flat lens and its photon localization,” Appl. Phys. Express 8(11), 112003 (2015).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Zhang, Y.

C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, and X. Luo, “Super-resolution optical telescopes with local light diffraction shrinkage,” Sci. Rep. 5(1), 18485 (2016).
[Crossref] [PubMed]

X. Chen, Y. Zhang, L. Huang, and S. Zhang, “Ultrathin Metasurface Laser Beam Shaper,” Adv. Opt. Mater. 2(10), 978–982 (2014).
[Crossref]

Zhang, Z.

Zhao, Z.

C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, and X. Luo, “Super-resolution optical telescopes with local light diffraction shrinkage,” Sci. Rep. 5(1), 18485 (2016).
[Crossref] [PubMed]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).
[Crossref]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

Zheludev, N. I.

G. H. Yuan, E. T. Rogers, and N. I. Zheludev, “Achromatic super-oscillatory lenses with sub-wavelength focusing,” Light Sci. Appl. 6(9), e17036 (2017).
[Crossref] [PubMed]

G. Yuan, E. T. F. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2015).
[Crossref] [PubMed]

G. Yuan, E. T. F. Rogers, T. Roy, Z. Shen, and N. I. Zheludev, “Flat super-oscillatory lens for heat-assisted magnetic recording with sub-50 nm resolution,” Opt. Express 22(6), 6428–6437 (2014).
[Crossref] [PubMed]

E. T. F. Rogers and N. I. Zheludev, “Optical super-oscillations: Sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15(9), 094008 (2013).
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E. T. F. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

Zheng, G.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
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Zhu, A. Y.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
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Zhuang, X.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

Adv. Mater. (1)

F. Qin, K. Huang, J. Wu, J. Teng, C.-W. Qiu, and M. Hong, “A Supercritical Lens Optical Label-Free Microscopy: Sub-Diffraction Resolution and Ultra-Long Working Distance,” Adv. Mater. 29(8), 1602721 (2017).
[Crossref] [PubMed]

Adv. Opt. Mater. (1)

X. Chen, Y. Zhang, L. Huang, and S. Zhang, “Ultrathin Metasurface Laser Beam Shaper,” Adv. Opt. Mater. 2(10), 978–982 (2014).
[Crossref]

Appl. Phys. Express (1)

J. Liu, E. Liu, Z. Fan, and X. Zhang, “Dielectric refractive index dependence of the focusing properties of a dielectric-cylinder-type decagonal photonic quasicrystal flat lens and its photon localization,” Appl. Phys. Express 8(11), 112003 (2015).
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IEEE Photonics Technol. Lett. (1)

J. Liu and Z. Fan, “Size Limits for Focusing of Two-Dimensional Photonic Quasicrystal Lenses,” IEEE Photonics Technol. Lett. 30(11), 1001–1004 (2018).
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E. T. F. Rogers and N. I. Zheludev, “Optical super-oscillations: Sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15(9), 094008 (2013).
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J. Opt. Soc. Am. A (1)

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

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M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. Math. Gen. 39(22), 6965–6977 (2006).
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Laser Photonics Rev. (3)

Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic Broadband Super-Resolution Imaging by Super-Oscillatory Metasurface,” Laser Photonics Rev. 12, 1800064 (2018).
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K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

D. Tang, C. Wang, Z. Zhao, Y. Wang, M. Pu, X. Li, P. Gao, and X. Luo, “Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing,” Laser Photonics Rev. 9(6), 713–719 (2015).
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Light Sci. Appl. (1)

G. H. Yuan, E. T. Rogers, and N. I. Zheludev, “Achromatic super-oscillatory lenses with sub-wavelength focusing,” Light Sci. Appl. 6(9), e17036 (2017).
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Nano Lett. (1)

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband Focusing Flat Mirrors Based on Plasmonic Gradient Metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
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Nanoscale (1)

X. Zhang, X. Li, J. Jin, M. Pu, X. Ma, J. Luo, Y. Guo, C. Wang, and X. Luo, “Polarization-independent broadband meta-holograms Via polarization-dependent nanoholes,” Nanoscale 10(19), 9304–9310 (2018).
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Nat. Commun. (2)

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013).
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X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012).
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Nat. Mater. (1)

E. T. F. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
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Nat. Methods (1)

K. I. Willig, B. Harke, R. Medda, and S. W. Hell, “STED microscopy with continuous wave beams,” Nat. Methods 4(11), 915–918 (2007).
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Nat. Nanotechnol. (1)

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
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Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

T. Grosjean and D. Courjon, “Polarization filtering induced by imaging systems: effect on image structure,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67, 046611 (2003).
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Sci. Adv. (1)

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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X. G. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mech. Astron. 58(9), 594201 (2015).
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Sci. Rep. (3)

G. Yuan, E. T. F. Rogers, T. Roy, G. Adamo, Z. Shen, and N. I. Zheludev, “Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths,” Sci. Rep. 4(1), 6333 (2015).
[Crossref] [PubMed]

C. Wang, D. Tang, Y. Wang, Z. Zhao, J. Wang, M. Pu, Y. Zhang, W. Yan, P. Gao, and X. Luo, “Super-resolution optical telescopes with local light diffraction shrinkage,” Sci. Rep. 5(1), 18485 (2016).
[Crossref] [PubMed]

A. M. H. Wong and G. V. Eleftheriades, “An optical super-microscope for far-field, real-time imaging beyond the diffraction limit,” Sci. Rep. 3(1), 1715 (2013).
[Crossref] [PubMed]

Science (5)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the Diffraction Barrier: Optical Microscopy on a Nanometric Scale,” Science 251(5000), 1468–1470 (1991).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging Intracellular Fluorescent Proteins at Nanometer Resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy,” Science 319(5864), 810–813 (2008).
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[Crossref] [PubMed]

Wuli Xuebao (1)

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Figures (6)

Fig. 1
Fig. 1 Schematic of a metasurface for achromatic sub-diffraction focusing. ASOM: achromatic super-oscillatory metasurface; R: red light; G: green light; B: blue light.
Fig. 2
Fig. 2 Light response of a high-aspect-ratio TiO2 nanofin. (a) Schematic of the TiO2 nanofin. The rectangular structure rotates an angle (φ) with respect to the x axis. (b) Phase and amplitude modulations of the cross-polarization light with various orientations at wavelengths of 473 nm, 532 nm and 632.8 nm. Average amplitudes of the LCP/RCP conversion are 0.86, 0.978 and 0.823, respectively.
Fig. 3
Fig. 3 Optimized results through GA algorithm. (a) Transmission of the ASOM1, containing binary phase modulations, either 0 or π. (b) ASOM1 is 20 μm diameter; the zoom-in section shows the central region of ASOM1 with only two orientations: 0° or 90°, corresponding to a phase change of π. (c-e) Distributions of the spot (solid lines) and local wavevector (dashed lines) across z = 10 μm at wavelengths of 473 nm, 532 nm and 632.8 nm.
Fig. 4
Fig. 4 (a-c) Intensity distributions along the propagating direction and (d-f) Intensity profiles across z = 10 μm for ASOM1 at wavelengths of 473 nm, 532 nm and 632.8 nm.
Fig. 5
Fig. 5 (a-c) Intensity distributions of ASOM2 along the propagating direction, the shaded region represents the constrained region of the energy concentration. An artificial scale bar is used for a clear display near the foci. (d-f) Intensity profiles across z = 10 μm at the wavelengths of 473 nm, 532 nm and 632.8 nm.
Fig. 6
Fig. 6 (a) Transmission of the ASOM3, containing four phase modulations in [0, 2π]: 0, π/2, π and 3π/2. (b-d) Intensity profiles across z = 10 μm at wavelengths of 473 nm, 532 nm and 632.8 nm.

Tables (1)

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Table 1 Performance of optimized ASOMs. The incident intensity is 1.

Equations (4)

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min { I λ1 ( FWH M λ1 2 ;f;T)/ I λ1 (0;f;T) I λ2 ( FWH M λ2 2 ;f;T)/ I λ2 (0;f;T) I λ3 ( FWH M λ3 2 ;f;T)/ I λ3 (0;f;T)
{ I λ1 (r;f;T)/ I λ1 (0;f;T)M I λ2 (r;f;T)/ I λ2 (0;f;T)M I λ3 (r;f;T)/ I λ3 (0;f;T)M T=[ t 1 , t 2 ,..., t N ] {0,π} or {0,π/2 ,π, 3π/2 } ... L 1 r L 2 ,
min n=1,2,3 w n * I λn ( FWH M λn 2 ;f;T)/ I λn (0;f;T) .
I λn (r;z;T) I λn (0;f;T) fDzf+D,

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