Abstract

We demonstrate theoretically a 2D subwavelength silicon-grating reflector with strong focusing capability and the potential application to an optical dipole trap of cold molecules such as MgF. We study the dependence of the focusing properties of this reflector on its structural parameters, numerical aperture, and fabrication-error tolerance. Our study shows that the reflector delivers high reflectivity and strong focusing performances with the maximum intensity at the focal point over 200 times the incident one. Such a focusing field on the reflector can provide a deep potential to trap cold MgF molecules from a standard magneto-optical trap.

© 2018 Optical Society of America

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References

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2018 (1)

S. M. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. L. Wang, S. N. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

2017 (10)

O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite functional metasurfaces for multispectral achromatic optics,” Nat. Commun. 8, 14992 (2017).
[Crossref]

J. P. McGilligan, P. F. Griffin, R. Elvin, S. J. Ingleby, E. Riis, and A. S. Arnold, “Grating chips for quantum technologies,” Sci. Rep. 7, 384 (2017).
[Crossref]

E. Imhof, B. K. Stuhl, B. Kasch, B. Kroese, S. E. Olson, and M. B. Squires, “Two-dimensional grating magneto-optical trap,” Phys. Rev. A 96, 033636 (2017).
[Crossref]

Y. N. Yin, S. P. Xu, T. Li, Y. L. Yin, Y. Xia, and J. P. Yin, “2D surface optical lattice formed by plasmon polaritons with application to nanometer-scale molecular deposition,” Sci. Rep. 7, 7788 (2017).
[Crossref]

D. L. Gao, W. Q. Ding, M. N. Vesperinas, X. M. Ding, M. Rahman, T. H. Zhang, C. T. Lim, and C. W. Qiu, “Optical manipulation from the microscale to the nanoscale: fundamentals, advances, and prospects,” Light: Sci. Appl. 6, e17039 (2017).
[Crossref]

T. H. Zhang, M. R. C. Mahdy, Y. M. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. W. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
[Crossref]

S. M. Wang, P. C. Wu, V. C. Su, Y. C. Lai, C. H. Chu, J. W. Chen, S. H. Lu, J. Chen, B. B. Xu, C. H. Kuan, T. Li, S. N. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

X. X. Yang, C. L. Li, Y. N. Yin, S. P. Xu, X. J. Li, Y. Xia, and J. P. Yin, “Bichromatic slowing of MgF molecules in multilevel systems,” J. Phys. B 50, 015001 (2017).
[Crossref]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

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

2016 (3)

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnology 11, 23–36 (2016).
[Crossref]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
[Crossref]

H. Zhang, T. Li, Y. L. Yin, X. J. Li, Y. Xia, and J. P. Yin, “Microtrap on a concave grating reflector for atom trapping,” Chin. Phys. B. 25, 087802 (2016).
[Crossref]

2015 (6)

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength- thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

X. F. Duan, G. R. Zhou, Y. Q. Huang, Y. F. Shang, and X. M. Ren, “Theoretical analysis and design guideline for focusing subwavelength gratings,” Opt. Express 23, 2639–2646 (2015).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High” efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Y. N. Yin, Y. Xia, X. J. Li, X. X. Yang, S. P. Xu, and J. P. Yin, “Narrow- linewidth and stable-frequency light source for laser cooling of magnesium fluoride molecules,” Appl. Phys. Express 8, 092701 (2015).
[Crossref]

M. M. Rahman, A. A. Sayem, M. R. C. Mahdy, M. E. Haque, R. Islam, S. T. Chowdhury, and M. A. Matin, “Tractor beam for fully immersed multiple objects: Long distance pulling, trapping, and rotation with a single optical set-up,” Ann. Phys. 527, 777–793 (2015).
[Crossref]

C. W. Qiu, W. Q. Ding, M. R. C. Mahdy, D. L. Gao, T. H. Zhang, F. C. Cheong, A. Dogariu, Z. Wang, and C. T. Lim, “Photon momentum transfer in inhomogeneous dielectric mixtures and induced tractor beams,” Light: Sci. Appl. 4, e278 (2015).
[Crossref]

2014 (1)

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

2013 (7)

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
[Crossref]

S. Person, M. Jain, Z. Lapin, J. J. Saenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13, 1806–1809 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref]

M. R. Tarbutt, B. E. Sauer, J. J. Hudson, and E. A. Hinds, “Design for a fountain of YbF molecules to measure the electron’s electric dipole moment,” New J. Phys. 15, 053034 (2013).
[Crossref]

C. C. Nshii, M. Vangeleyn, J. P. Cotter, P. F. Griffin, E. A. Hinds, C. N. Ironside, P. See, A. G. Sinclair, E. Riis, and A. S. Arnold, “A surface-patterned chip as a strong source of ultracold atoms for quantum technologies,” Nat. Nanotechnology 8, 321–324 (2013).
[Crossref]

2010 (2)

2007 (1)

F. M. Huang, N. Zheludev, Y. Chen, and F. Javier Garcia de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90, 091119 (2007).
[Crossref]

2006 (1)

J. P. Yin, “Realization and research of optically-trapped quantum degenerate gases,” Phys. Rep. 430, 1–116 (2006).
[Crossref]

2005 (2)

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5, 1399–1402 (2005).
[Crossref]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726–1729 (2005).
[Crossref]

2000 (1)

R. Grimm, M. Weidemuller, and Y. B. Ovchinnikov, “Optical dipole traps for neutral atoms,” Adv. At. Mol. Opt. Phys. 42, 95–170 (2000).
[Crossref]

1989 (1)

1987 (1)

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[Crossref]

Aieta, F.

Almeida, E.

O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite functional metasurfaces for multispectral achromatic optics,” Nat. Commun. 8, 14992 (2017).
[Crossref]

Alù, A.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength- thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Arnold, A. S.

J. P. McGilligan, P. F. Griffin, R. Elvin, S. J. Ingleby, E. Riis, and A. S. Arnold, “Grating chips for quantum technologies,” Sci. Rep. 7, 384 (2017).
[Crossref]

C. C. Nshii, M. Vangeleyn, J. P. Cotter, P. F. Griffin, E. A. Hinds, C. N. Ironside, P. See, A. G. Sinclair, E. Riis, and A. S. Arnold, “A surface-patterned chip as a strong source of ultracold atoms for quantum technologies,” Nat. Nanotechnology 8, 321–324 (2013).
[Crossref]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[Crossref]

Avayu, O.

O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite functional metasurfaces for multispectral achromatic optics,” Nat. Commun. 8, 14992 (2017).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength- thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Ball, A. J.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength- thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Beausoleil, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref]

Brener, I.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High” efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Brongersma, M. L.

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
[Crossref]

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

Brown, D. E.

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5, 1399–1402 (2005).
[Crossref]

Capasso, F.

Chang-Hasnain, C. J.

Chase, C.

Chen, B. H.

S. M. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. L. Wang, S. N. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Chen, J.

S. M. Wang, P. C. Wu, V. C. Su, Y. C. Lai, C. H. Chu, J. W. Chen, S. H. Lu, J. Chen, B. B. Xu, C. H. Kuan, T. Li, S. N. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Chen, J. W.

S. M. Wang, P. C. Wu, V. C. Su, Y. C. Lai, C. H. Chu, J. W. Chen, S. H. Lu, J. Chen, B. B. Xu, C. H. Kuan, T. Li, S. N. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Chen, M. K.

S. M. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. L. Wang, S. N. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Chen, Y.

F. M. Huang, N. Zheludev, Y. Chen, and F. Javier Garcia de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90, 091119 (2007).
[Crossref]

Chen, Y. H.

S. M. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. L. Wang, S. N. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Cheong, F. C.

C. W. Qiu, W. Q. Ding, M. R. C. Mahdy, D. L. Gao, T. H. Zhang, F. C. Cheong, A. Dogariu, Z. Wang, and C. T. Lim, “Photon momentum transfer in inhomogeneous dielectric mixtures and induced tractor beams,” Light: Sci. Appl. 4, e278 (2015).
[Crossref]

Chowdhury, S. T.

M. M. Rahman, A. A. Sayem, M. R. C. Mahdy, M. E. Haque, R. Islam, S. T. Chowdhury, and M. A. Matin, “Tractor beam for fully immersed multiple objects: Long distance pulling, trapping, and rotation with a single optical set-up,” Ann. Phys. 527, 777–793 (2015).
[Crossref]

Chu, C. H.

S. M. Wang, P. C. Wu, V. C. Su, Y. C. Lai, C. H. Chu, J. W. Chen, S. H. Lu, J. Chen, B. B. Xu, C. H. Kuan, T. Li, S. N. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Cotter, J. P.

C. C. Nshii, M. Vangeleyn, J. P. Cotter, P. F. Griffin, E. A. Hinds, C. N. Ironside, P. See, A. G. Sinclair, E. Riis, and A. S. Arnold, “A surface-patterned chip as a strong source of ultracold atoms for quantum technologies,” Nat. Nanotechnology 8, 321–324 (2013).
[Crossref]

Decker, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High” efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Devlin, R.

Ding, W. Q.

D. L. Gao, W. Q. Ding, M. N. Vesperinas, X. M. Ding, M. Rahman, T. H. Zhang, C. T. Lim, and C. W. Qiu, “Optical manipulation from the microscale to the nanoscale: fundamentals, advances, and prospects,” Light: Sci. Appl. 6, e17039 (2017).
[Crossref]

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ACS Nano (1)

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M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High” efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
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Appl. Opt. (1)

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Figures (5)

Fig. 1.
Fig. 1. (a) Structure layout of the concentric circular grating proposed with strong focusing ability. The red arrows represent the incident light direction, and the blue ones show the polarization direction of radially polarized illumination. The inset is the schematic diagram of the circular grating configuration. (b) 2D intensity distribution of the focused beam on the x o z plane. (c)–(e) Dependence of the reflectivity (red line) and phase shift (black line) in the reflected plane of 1D infinitely long grating on the (c) grating thickness, (d) period, and (e) width. (f) 1D relative intensity distribution on the x axis at the focusing point z = 10.15    μm for panel (b).
Fig. 2.
Fig. 2. Focusing properties of the grating reflectors with 10 μm focal length and different numerical aperture. (a) Reflectivity of different NA reflectors. (b) The black line shows the relative maximum optical intensity at different NA, and the red line shows the corresponding FWHM.
Fig. 3.
Fig. 3. Influence of the missing number of grating strips on the focusing characteristics of the reflector. The red and black lines depict the relative maximum optical intensity of the reflector with a focal length of 10 μm and 20 μm at the missing of the grating strips, respectively.
Fig. 4.
Fig. 4. Optical potential, dipole force, and scattering rate of optically trapped MgF molecules on the reflector with a focal length of 10 μm and a numerical aperture of 0.91 without missing grating strips. Inset: dipole force exerted on molecules in the laser field along the x direction.
Fig. 5.
Fig. 5. Schematic of the grating MOT and the optical dipole trap of MgF molecules. Linearly polarized light (violet) at a wavelength of 359 nm and linearly polarized light (red) at a wavelength of 1550 nm are collimated by a beamsplitter, and circularly polarized light (gray arrows) by a quarter waveplate (green). An input beam of 359 nm is diffracted by three identical gratings on the periphery to create the MgF MOT (violet arrow indicates reflected MOT beams). An input beam of 1550 nm is reflected by the concentric grating in the center, resulting in a smaller trapping volume above the reflector (red arrow indicates reflected trapping beams).

Equations (5)

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ϕ ( x ) = 2 π λ ( x 2 + f 2 f ) + φ 0 ,
{ x n + 1 = x n + 1 2 ( Λ n + Λ n + 1 ) , n = 0 , 1 , 2 , ϕ ( x n + 1 ) = ϕ ( x n + 1 2 ( Λ n + Λ n + 1 ) ) = 2 π λ ( x n + 1 2 + f 2 f ) + φ 0 , n = 1 , 2 , .
U dip = 1 2 p E = 1 2 ϵ 0 c Re ( α ) I ( r ) ,
F dip ( r ) = U dip ( r ) = 1 2 ϵ 0 c Re ( α ) I ( r ) ,
R = I / ( 5 I sat ) 1 + I / ( 5 I sat ) + 4 ( ( ω ω 0 ) / Γ ) 2 1 10.5 Γ .

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