Abstract

Metasurfaces composed of artificially fabricated nano-sized structures have shown extraordinary potential for the precise control of light. Here, we demonstrate for the first time, a metasurface application to reduce the axial size of the point spread function in laser scanning microscopy. The all-dielectric metasurface has wavelength selectivity over the whole visible range, and confinement of the excitation point spread function of the electromagnetic field. These two unique features allow the metasurface to be applied to laser scanning microscope systems. Numerical and experimental demonstrations of the proposed all-dielectric metasurface are reported, showing sharp implicit spectral filtering in the visible range and enhanced axial confinement by observing actin filaments in NIH3T3 cells. We believe that our approach can provide a useful insight on the practicality of using metasurfaces as an imaging platform.

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

Full Article  |  PDF Article
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2018 (3)

G. Yoon, D. Lee, K. T. Nam, and J. Rho, “Pragmatic metasurface hologram at visible wavelength: the balance between diffraction efficiency and fabrication compatibility,” ACS Photonics 5(5), 1643–1647 (2018).
[Crossref]

G. Yoon, D. Lee, K. T. Nam, and J. Rho, ““Crypto-display” in dual-mode metasurfaces by simultaneous control of phase and spectral responses,” ACS Nano 12(7), 6421–6428 (2018).
[Crossref]

S. Sun, W. Yang, C. Zhang, J. Jing, Y. Gao, X. Yu, Q. Song, and S. Xiao, “Real-time tunable colors from microfluidic reconfigurable all-dielectric metasurfaces,” ACS Nano 12(3), 2151–2159 (2018).
[Crossref]

2017 (8)

V. Flauraud, M. Reyes, R. Paniagua-Dominguez, A. I. Kuznetsov, and J. Brugger, “Silicon nanostructures for bright field full color prints,” ACS Photonics 4(8), 1913–1919 (2017).
[Crossref]

Z. Dong, J. Ho, Y. F. Yu, Y. H. Fu, R. Paniagua-Dominguez, S. Wang, A. I. Kuznetsov, and J. K. Yang, “Printing beyond sRGB color gamut by mimicking silicon nanostructures in free-space,” Nano Lett. 17(12), 7620–7628 (2017).
[Crossref]

Z. Li, I. Kim, L. Zhang, M. Q. Mehmood, M. S. Anwar, M. Saleem, D. Lee, K. T. Nam, S. Zhang, B. Luk’yanchuk, Y. Wang, G. Zheng, J. Rho, and C.-W. Qiu, “Dielectric meta-holograms enabled with dual magnetic resonances in visible light,” ACS Nano 11(9), 9382–9389 (2017).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358(6367), eaam8100 (2017).
[Crossref]

A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11(7), 415–420 (2017).
[Crossref]

A. Trache and G. A. Meininger, “Total internal reflection fluorescence (TIRF) microscopy,” Curr. Protoc. Microbiol. 10, 2A–2 (2017).

S. Nasrollahi, S. Banerjee, B. Qayum, P. Banerjee, and A. Pathak, “Nanoscale matrix topography influences microscale cell motility through adhesions, actin organization, and cell shape,” ACS Biomater. Sci. Eng. 3(11), 2980–2986 (2017).
[Crossref]

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

2016 (4)

X. Yang, H. Xie, E. Alonas, Y. Liu, X. Chen, P. J. Santangelo, Q. Ren, P. Xi, and D. Jin, “Mirror-enhanced super-resolution microscopy,” Light: Sci. Appl. 5(6), e16134 (2016).
[Crossref]

S. Dobbenga, L. E. Fratila-Apachitei, and A. A. Zadpoor, “Nanopattern-induced osteogenic differentiation of stem cells–a systematic review,” Acta Biomater. 46, 3–14 (2016).
[Crossref]

J. Proust, F. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

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]

2015 (5)

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref]

X. Ni, Z. J. Wong, M. Mrejen, Y. Wang, and X. Zhang, “An ultrathin invisibility skin cloak for visible light,” Science 349(6254), 1310–1314 (2015).
[Crossref]

L. Huang, H. Mühlenbernd, X. Li, X. Song, B. Bai, Y. Wang, and T. Zentgraf, “Broadband hybrid holographic multiplexing with geometric metasurfaces,” Adv. Mater. 27(41), 6444–6449 (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]

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

2014 (2)

J. Lu, F. Zheng, Y. Cheng, H. Ding, Y. Zhao, and Z. Gu, “Hybrid inverse opals for regulating cell adhesion and orientation,” Nanoscale 6(18), 10650–10656 (2014).
[Crossref]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref]

2013 (3)

L. C. Hsu, J. Fang, D. A. Borca-Tasciuc, R. W. Worobo, and C. I. Moraru, “Effect of micro-and nanoscale topography on the adhesion of bacterial cells to solid surfaces,” Appl. Environ. Microbiol. 79(8), 2703–2712 (2013).
[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. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013).
[Crossref]

2012 (3)

B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E.-B. Kley, F. Lederer, A. Tünnermann, and T. Pertsch, “Spatial and spectral light shaping with metamaterials,” Adv. Mater. 24(47), 6300–6304 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

2011 (1)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

2006 (3)

R.-Y. He, G.-L. Chang, H.-L. Wu, C.-H. Lin, K.-C. Chiu, Y.-D. Su, and S.-J. Chen, “Enhanced live cell membrane imaging using surface plasmon-enhanced total internal reflection fluorescence microscopy,” Opt. Express 14(20), 9307–9316 (2006).
[Crossref]

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[Crossref]

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222(2), 105–117 (2006).
[Crossref]

2005 (1)

2004 (2)

1999 (1)

M. G. Gustafsson, D. Agard, and J. Sedat, “I5M: 3D widefield light microscopy with better than 100nm axial resolution,” J. Microsc. 195(1), 10–16 (1999).
[Crossref]

1994 (1)

S. W. Hell, S. Lindek, C. Cremer, and E. H. Stelzer, “Measurement of the 4Pi-confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64(11), 1335–1337 (1994).
[Crossref]

1993 (1)

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[Crossref]

Agard, D.

M. G. Gustafsson, D. Agard, and J. Sedat, “I5M: 3D widefield light microscopy with better than 100nm axial resolution,” J. Microsc. 195(1), 10–16 (1999).
[Crossref]

Aieta, F.

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Alonas, E.

X. Yang, H. Xie, E. Alonas, Y. Liu, X. Chen, P. J. Santangelo, Q. Ren, P. Xi, and D. Jin, “Mirror-enhanced super-resolution microscopy,” Light: Sci. Appl. 5(6), e16134 (2016).
[Crossref]

Anwar, M. S.

Z. Li, I. Kim, L. Zhang, M. Q. Mehmood, M. S. Anwar, M. Saleem, D. Lee, K. T. Nam, S. Zhang, B. Luk’yanchuk, Y. Wang, G. Zheng, J. Rho, and C.-W. Qiu, “Dielectric meta-holograms enabled with dual magnetic resonances in visible light,” ACS Nano 11(9), 9382–9389 (2017).
[Crossref]

Arbabi, A.

A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11(7), 415–420 (2017).
[Crossref]

Arbabi, E.

A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, “Planar metasurface retroreflector,” Nat. Photonics 11(7), 415–420 (2017).
[Crossref]

Bai, B.

L. Huang, H. Mühlenbernd, X. Li, X. Song, B. Bai, Y. Wang, and T. Zentgraf, “Broadband hybrid holographic multiplexing with geometric metasurfaces,” Adv. Mater. 27(41), 6444–6449 (2015).
[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]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012).
[Crossref]

Bailey, B.

B. Bailey, D. L. Farkas, D. L. Taylor, and F. Lanni, “Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation,” Nature 366(6450), 44–48 (1993).
[Crossref]

Banerjee, P.

S. Nasrollahi, S. Banerjee, B. Qayum, P. Banerjee, and A. Pathak, “Nanoscale matrix topography influences microscale cell motility through adhesions, actin organization, and cell shape,” ACS Biomater. Sci. Eng. 3(11), 2980–2986 (2017).
[Crossref]

Banerjee, S.

S. Nasrollahi, S. Banerjee, B. Qayum, P. Banerjee, and A. Pathak, “Nanoscale matrix topography influences microscale cell motility through adhesions, actin organization, and cell shape,” ACS Biomater. Sci. Eng. 3(11), 2980–2986 (2017).
[Crossref]

Bedu, F.

J. Proust, F. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

Bewersdorf, J.

J. Bewersdorf, R. Schmidt, and S. W. Hell, “Comparison of I5M and 4Pi-microscopy,” J. Microsc. 222(2), 105–117 (2006).
[Crossref]

Bianco, F.

Birks, T.

Blanchard, R.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

Bonod, N.

J. Proust, F. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

Borca-Tasciuc, D. A.

L. C. Hsu, J. Fang, D. A. Borca-Tasciuc, R. W. Worobo, and C. I. Moraru, “Effect of micro-and nanoscale topography on the adhesion of bacterial cells to solid surfaces,” Appl. Environ. Microbiol. 79(8), 2703–2712 (2013).
[Crossref]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref]

Brugger, J.

V. Flauraud, M. Reyes, R. Paniagua-Dominguez, A. I. Kuznetsov, and J. Brugger, “Silicon nanostructures for bright field full color prints,” ACS Photonics 4(8), 1913–1919 (2017).
[Crossref]

Capasso, F.

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358(6367), eaam8100 (2017).
[Crossref]

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]

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015).
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S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
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ACS Biomater. Sci. Eng. (1)

S. Nasrollahi, S. Banerjee, B. Qayum, P. Banerjee, and A. Pathak, “Nanoscale matrix topography influences microscale cell motility through adhesions, actin organization, and cell shape,” ACS Biomater. Sci. Eng. 3(11), 2980–2986 (2017).
[Crossref]

ACS Nano (5)

S. Sun, Z. Zhou, C. Zhang, Y. Gao, Z. Duan, S. Xiao, and Q. Song, “All-dielectric full-color printing with TiO2 metasurfaces,” ACS Nano 11(5), 4445–4452 (2017).
[Crossref]

G. Yoon, D. Lee, K. T. Nam, and J. Rho, ““Crypto-display” in dual-mode metasurfaces by simultaneous control of phase and spectral responses,” ACS Nano 12(7), 6421–6428 (2018).
[Crossref]

J. Proust, F. Bedu, B. Gallas, I. Ozerov, and N. Bonod, “All-dielectric colored metasurfaces with silicon mie resonators,” ACS Nano 10(8), 7761–7767 (2016).
[Crossref]

Z. Li, I. Kim, L. Zhang, M. Q. Mehmood, M. S. Anwar, M. Saleem, D. Lee, K. T. Nam, S. Zhang, B. Luk’yanchuk, Y. Wang, G. Zheng, J. Rho, and C.-W. Qiu, “Dielectric meta-holograms enabled with dual magnetic resonances in visible light,” ACS Nano 11(9), 9382–9389 (2017).
[Crossref]

S. Sun, W. Yang, C. Zhang, J. Jing, Y. Gao, X. Yu, Q. Song, and S. Xiao, “Real-time tunable colors from microfluidic reconfigurable all-dielectric metasurfaces,” ACS Nano 12(3), 2151–2159 (2018).
[Crossref]

ACS Photonics (3)

G. Yoon, D. Lee, K. T. Nam, and J. Rho, “Pragmatic metasurface hologram at visible wavelength: the balance between diffraction efficiency and fabrication compatibility,” ACS Photonics 5(5), 1643–1647 (2018).
[Crossref]

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[Crossref]

Y. Shen, V. Rinnerbauer, I. Wang, V. Stelmakh, J. D. Joannopoulos, and M. Soljacic, “Structural colors from Fano resonances,” ACS Photonics 2(1), 27–32 (2015).
[Crossref]

Acta Biomater. (1)

S. Dobbenga, L. E. Fratila-Apachitei, and A. A. Zadpoor, “Nanopattern-induced osteogenic differentiation of stem cells–a systematic review,” Acta Biomater. 46, 3–14 (2016).
[Crossref]

Adv. Mater. (2)

B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E.-B. Kley, F. Lederer, A. Tünnermann, and T. Pertsch, “Spatial and spectral light shaping with metamaterials,” Adv. Mater. 24(47), 6300–6304 (2012).
[Crossref]

L. Huang, H. Mühlenbernd, X. Li, X. Song, B. Bai, Y. Wang, and T. Zentgraf, “Broadband hybrid holographic multiplexing with geometric metasurfaces,” Adv. Mater. 27(41), 6444–6449 (2015).
[Crossref]

Appl. Environ. Microbiol. (1)

L. C. Hsu, J. Fang, D. A. Borca-Tasciuc, R. W. Worobo, and C. I. Moraru, “Effect of micro-and nanoscale topography on the adhesion of bacterial cells to solid surfaces,” Appl. Environ. Microbiol. 79(8), 2703–2712 (2013).
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Figures (10)

Fig. 1.
Fig. 1. (a) Schematic of MAIT. Source light is illuminated to the image plane, and the emitted fluorescence is captured by PMT through a pinhole and optics system (Obj: objective lens, DM: dichroic mirror, M: mirror, L1-L2: lenses, P: pinhole). The specimen is placed directly onto a dielectric metasurface with a-Si:H nanodiscs. Inset shows the magnified view of the black box. Constructive interference is formed inside the specimen with a small axial excitation region (red ellipse). The beam profile of the source light and narrow PSF is shown in the inset (i) and (ii), respectively. (b) Schematic of the designed dielectric metasurface. On an SiO$_2$ substrate, a-Si:H nanodiscs are arranged in an array with period $P$. Each nanodisc has radius $r$ and thickness $T$. The metasurface selectively and efficiently reflects a narrow range of wavelengths.
Fig. 2.
Fig. 2. (a) Reflection from the metasurface as affected by the nanodisc radius $r$ and wavelength $\lambda$. An increase in $r$ causes an increase in the $\lambda$ that is reflected with high efficiency and a narrow FWHM. (b) Plots of normalized selected $\lambda$ in Fig. 2(a). Each reflection spectrum shows a narrow bandwidth, which is selectively reflected at a desired $\lambda$. Simulated and measured reflection spectra of (c) $r$ = 75 nm and (d) $r$ = 94 nm. (e) Field profile for the ED resonance, (f) field profile for the MD resonance and (g) current density in xz plane at $\lambda$ = 488 nm.
Fig. 3.
Fig. 3. Electric field amplitude profiles in the y-z plane of MAIT using metasurfaces that have reflection peaks at: (a) 488 nm, (b) 556 nm, (c) 596 nm and (d) 647 nm. (e) Normal confocal PSF at 488 nm. (f) Distance of PSF from the metasurface according to different wavelength.
Fig. 4.
Fig. 4. NIH3T3 cell images of normal confocal microscopy and MAIT for comparison of normal confocal microscopy and MAIT. Captured cell image stained with green fluorescent dye from (a) the normal confocal microscopy and (b) MAIT. (c) Intensity profile of the dashed lines in Fig. 4(a)–4(b). Captured cell image stained with red fluorescent dye from (d) the normal confocal microscopy and (e) MAIT. (f) Intensity profile of the dashed line in Fig. 4(d)-(e), as in Fig. 4(c). The red and blue lines in Fig. 4(c) and 4(f) represent the fitted intensity profiles from normal confocal microscopy and MAIT, respectively. Scale bars are 5 $\mu$m. (g) Image obtained by normal confocal microscopy with out-of-focus signal, blurring the image. Cell images stained with (h) green and (i) red fluorescent dye are captured by MAIT with high SBNR and contrast. (j) Intensity profile of the yellow indicators showing single filament structure in Fig. 4(h) and 4(i).
Fig. 5.
Fig. 5. Refractive index $n$ (black lines) and extinction coefficient $k$ (red lines) of: (a) a-Si:H and (b) a-Si.
Fig. 6.
Fig. 6. SEM images of fabricated dielectric metasurfaces composed of a-Si:H nanodiscs array. Each metasurface has different geometrical parameters: (a) $r$ = 75 nm, $P$ = 334 nm, (b) $r$ = 94 nm, $P$ = 380 nm. PT was coated to acquire SEM images.
Fig. 7.
Fig. 7. (a) Scaling factor $F=P/r$ used in numerical simulation and fabrication. (b) Quality factor (Q-factor) when $P$ = 442 nm, which yields a maximum reflectance peak at 647 nm. This term is considered to ensure that $F$ sharpens the reflectance spectrum. The reflectance peak sharpens as the space between nanodiscs increases. (c) Reflectance spectra at $P$ = 442 nm with $F$ = 3.2, 3.5 and 3.8.
Fig. 8.
Fig. 8. The phase difference of the incident and the reflected beam (red) and amplitude of the interference pattern (black) along the propagation axis at wavelength of 488 nm.
Fig. 9.
Fig. 9. Gaussian beam profiles on the x-y plane. (a) Normal Gaussian beam profile and (b) Gaussian beam profile on the metasurface. The refractive index of surrounding is 1 (air). (c) Normal Gaussian beam profile and (d) Gaussian beam profile on the metasurface. The refractive index of surrounding is 1.33 (water). The wavelength is 488 nm. As shown in the figures, there is no difference in spatial resolution. The Gaussian beam waist decreased when the surrounding refractive index increased.
Fig. 10.
Fig. 10. (a) Axial confinement according to the reflection coefficient. (b) Field amplitude along the propagating axis. In the calculation, two Gaussian beams were illuminated along the propagation direction with opposite direction. One Gaussian beam is adjusted to have various amplitude which can be considered as the effective reflector having different reflection. The axial confinement is defined as a full-width half-maximum of the field amplitude in one cycle, normalized by wavelength.