Abstract

A metal slit array arranged along a semicircular surface achieving subwavelength optical beam focusing along the lateral direction is proposed. Taking into consideration surface plasmon polaritons that pass through a metal slit array, we design the array with a curvature. By use of a genetic algorithm, the size of the metal slit and the corresponding curvature are to be determined. Based on our metal slit array configuration, the full width at half-maximum can be achieved on a subwavelength scale.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
    [CrossRef]
  5. S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
    [CrossRef]
  6. R. Merlin, “Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing,” Science 317, 927-929 (2007).
    [CrossRef] [PubMed]
  7. R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102, 207402 (2009).
    [CrossRef] [PubMed]
  8. X. B. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as plasmon lenses,” Opt. Lett. 31, 1322-1324(2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  14. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
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    [CrossRef] [PubMed]
  16. R. K. Kupka, Y. Chen, F. Rousseaux, A. M. Haghirigosnet, and H. Launois, “Properties of electromagnetic-fields in x-ray lithographic masks - guided modes and beam-propagation calculus,” J. Vac. Sci. Technol. B 11, 667-680(1993).
    [CrossRef]
  17. R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young's double-slit experiment,” Nature Nanotechnol. 2, 426-429 (2006).
    [CrossRef]
  18. H. F. Shi, X. G. Luo, and C. L. Du, “Young's interference of double metallic nanoslit with different widths,” Opt. Express 15, 11321-11327 (2007).
    [CrossRef] [PubMed]
  19. P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Phys. 2, 551-556 (2006).
    [CrossRef]
  20. Z. Michalewicz, Genetic Algorithms Plus Data Structures Equal Evolution Programs (Springer-Verlag, 1996).

2009

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102, 207402 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235-238 (2009).
[CrossRef]

W. M. Saj, “Light focusing on a stack of metal-insulator-metal waveguides sharp edge,” Opt. Express 17, 13615-13623(2009).
[CrossRef] [PubMed]

2008

B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schoenle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express 16, 4154-4162 (2008).
[CrossRef] [PubMed]

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

2007

R. Merlin, “Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing,” Science 317, 927-929 (2007).
[CrossRef] [PubMed]

H. F. Shi, X. G. Luo, and C. L. Du, “Young's interference of double metallic nanoslit with different widths,” Opt. Express 15, 11321-11327 (2007).
[CrossRef] [PubMed]

2006

X. B. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as plasmon lenses,” Opt. Lett. 31, 1322-1324(2006).
[CrossRef] [PubMed]

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young's double-slit experiment,” Nature Nanotechnol. 2, 426-429 (2006).
[CrossRef]

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Phys. 2, 551-556 (2006).
[CrossRef]

2005

2004

Z. J. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642-644 (2004).
[CrossRef]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1994

1993

R. K. Kupka, Y. Chen, F. Rousseaux, A. M. Haghirigosnet, and H. Launois, “Properties of electromagnetic-fields in x-ray lithographic masks - guided modes and beam-propagation calculus,” J. Vac. Sci. Technol. B 11, 667-680(1993).
[CrossRef]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235-238 (2009).
[CrossRef]

Bose, R.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Brolo, A. G.

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235-238 (2009).
[CrossRef]

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young's double-slit experiment,” Nature Nanotechnol. 2, 426-429 (2006).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235-238 (2009).
[CrossRef]

Chen, Y.

R. K. Kupka, Y. Chen, F. Rousseaux, A. M. Haghirigosnet, and H. Launois, “Properties of electromagnetic-fields in x-ray lithographic masks - guided modes and beam-propagation calculus,” J. Vac. Sci. Technol. B 11, 667-680(1993).
[CrossRef]

Dong, X. C.

Du, C. L.

Fan, S. H.

L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235-238 (2009).
[CrossRef]

Fan, X. B.

Gao, H. T.

Gordon, R.

R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102, 207402 (2009).
[CrossRef] [PubMed]

R. Gordon and A. G. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13, 1933-1938 (2005).
[CrossRef] [PubMed]

Haghirigosnet, A. M.

R. K. Kupka, Y. Chen, F. Rousseaux, A. M. Haghirigosnet, and H. Launois, “Properties of electromagnetic-fields in x-ray lithographic masks - guided modes and beam-propagation calculus,” J. Vac. Sci. Technol. B 11, 667-680(1993).
[CrossRef]

Harke, B.

Hell, S. W.

Hong, B. H.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Hugonin, J. P.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Phys. 2, 551-556 (2006).
[CrossRef]

Hwang, I. C.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Jouravlev, M. V.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Kaufman, L. J.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Keller, J.

Kim, H.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Kim, H. K.

Z. J. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642-644 (2004).
[CrossRef]

Kim, K. S.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Kim, P.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Kim, S.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Kim, W. Y.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Kim, Y.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Kupka, R. K.

R. K. Kupka, Y. Chen, F. Rousseaux, A. M. Haghirigosnet, and H. Launois, “Properties of electromagnetic-fields in x-ray lithographic masks - guided modes and beam-propagation calculus,” J. Vac. Sci. Technol. B 11, 667-680(1993).
[CrossRef]

Lalanne, P.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Phys. 2, 551-556 (2006).
[CrossRef]

Launois, H.

R. K. Kupka, Y. Chen, F. Rousseaux, A. M. Haghirigosnet, and H. Launois, “Properties of electromagnetic-fields in x-ray lithographic masks - guided modes and beam-propagation calculus,” J. Vac. Sci. Technol. B 11, 667-680(1993).
[CrossRef]

Lee, B.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Lee, J. Y.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Lim, Y.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Luo, X. G.

Merlin, R.

R. Merlin, “Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing,” Science 317, 927-929 (2007).
[CrossRef] [PubMed]

Michalewicz, Z.

Z. Michalewicz, Genetic Algorithms Plus Data Structures Equal Evolution Programs (Springer-Verlag, 1996).

Min, S. K.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Palik, E.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Park, J.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Rousseaux, F.

R. K. Kupka, Y. Chen, F. Rousseaux, A. M. Haghirigosnet, and H. Launois, “Properties of electromagnetic-fields in x-ray lithographic masks - guided modes and beam-propagation calculus,” J. Vac. Sci. Technol. B 11, 667-680(1993).
[CrossRef]

Saj, W. M.

Schoenle, A.

Shi, H. F.

Sun, Z. J.

Z. J. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642-644 (2004).
[CrossRef]

Ullal, C. K.

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235-238 (2009).
[CrossRef]

Wang, C. T.

Wang, G. P.

Westphal, V.

White, J. S.

L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235-238 (2009).
[CrossRef]

Wichmann, J.

Wong, C. W.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Yu, Z. F.

L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235-238 (2009).
[CrossRef]

Zia, R.

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young's double-slit experiment,” Nature Nanotechnol. 2, 426-429 (2006).
[CrossRef]

Appl. Phys. Lett.

S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, “Optical beam focusing by a single subwavelength metal slit surrounded by chirped dielectric surface gratings,” Appl. Phys. Lett. 92, 013103 (2008).
[CrossRef]

Z. J. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85, 642-644 (2004).
[CrossRef]

J. Vac. Sci. Technol. B

R. K. Kupka, Y. Chen, F. Rousseaux, A. M. Haghirigosnet, and H. Launois, “Properties of electromagnetic-fields in x-ray lithographic masks - guided modes and beam-propagation calculus,” J. Vac. Sci. Technol. B 11, 667-680(1993).
[CrossRef]

Nano Lett.

L. Verslegers, P. B. Catrysse, Z. F. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. H. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235-238 (2009).
[CrossRef]

Nature

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. C. Hwang, L. J. Kaufman, C. W. Wong, and P. Kim, “Near-field focusing and magnification through self-assembled nanoscale spherical lenses,” Nature 460, 498-501 (2009).
[CrossRef]

Nature Nanotechnol.

R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young's double-slit experiment,” Nature Nanotechnol. 2, 426-429 (2006).
[CrossRef]

Nature Phys.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nature Phys. 2, 551-556 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102, 207402 (2009).
[CrossRef] [PubMed]

Science

R. Merlin, “Radiationless electromagnetic interference: evanescent-field lenses and perfect focusing,” Science 317, 927-929 (2007).
[CrossRef] [PubMed]

Other

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Z. Michalewicz, Genetic Algorithms Plus Data Structures Equal Evolution Programs (Springer-Verlag, 1996).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the proposed optical beam focusing structure. A metal slit array consists of five slits embedded in the metal slab with a curved surface. A p-polarized light ( λ = 633 nm ) is incident behind the bottom of the metal slab. Transmitted light through a metal slit array is focused on the spot.

Fig. 2
Fig. 2

(a) Normalized time-averaged Poynting vector distribution for the five metal slits in the indented metal surface. The values of the slit widths and gaps are all 200 nm . Focal length f is 543 nm . (b) Normalized time-averaged Poynting vector distribution for the five point sources placed in free space. The phase distribution at each pointlike source is, respectively, 109.7 ° , 315.1 ° , 285.3 ° , 315.1 ° , and 109.7 ° from left to right. The five black circles indicate the point sources.

Fig. 3
Fig. 3

Flow of the genetic algorithm to optimize our optical beam focusing structure.

Fig. 4
Fig. 4

(a) Normalized time-averaged Poynting vector distribution of the first case: weighting factors a 1 through a 4 are 1, 1, 1, and 1, respectively. r, w 1 ( = w 5 ) , w 2 ( = w 4 ) , w 3 , g 1 ( = g 4 ) , and g 2 ( = g 3 ) are, respectively, 975, 80, 282, 315, 259, and 175 nm . Focal length f is 1.647 μm . (b) Cross-sectional plot along the lateral direction at focal point f of 1.647 μm ; its FWHM is 332 nm . (c) Convergence plot of the objective value in the genetic algorithm of the first case.

Fig. 5
Fig. 5

(a) Normalized time-averaged Poynting vector distribution of the second case: weighting factors a 1 through a 4 are 1, 2, 2, and 2, respectively. r, w 1 ( = w 5 ) , w 2 ( = w 4 ) , w 3 , g 1 ( = g 4 ) , and g 2 ( = g 3 ) are, respectively, 1262, 311, 212, 263, 340, and 224 nm . Focal length f is 1.308 μm . (b) Cross-sectional plot along the lateral direction at focal point f of 1.308 μm ; its FWHM is 299 nm on the subwavelength scale.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

tanh ( w 2 β 2 k 0 2 ε d ) = ε d β 2 k 0 2 ε m ε m β 2 k 0 2 ε d ,
Δ ϕ = Re ( β h ) + arg [ 1 ( 1 β / k 0 1 + β / k 0 ) 2 exp ( 2 j β h ) ] ,
b i = { | y i y i _ ref y i _ ref | ( i = 1 , 2 ) | y i y i _ ref | ( i = 3 , 4 ) ,
f > d h 3 ,
f d h 3 ,

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