Abstract

A method for producing optical structures using rotationally symmetric pyramids is proposed. Two-dimensional structures can be achieved using acute prisms. They form by multi-beam interference of plane waves that impinge from directions distributed symmetrically around the axis of rotational symmetry. Flat-topped pyramids provide an additional beam along the axis thus generating three-dimensional structures. Experimental results are consistent with the results of numerical simulations. The advantages of the method are simplicity of operation, low cost, ease of integration, good stability, and high transmittance. Possible applications are the fabrication of photonic micro-structures such as photonic crystals or array waveguides as well as multi-beam optical tweezers.

© 2006 Optical Society of America

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  1. E. Yablonovitch, "Photonic band-gap structures," J. Opt. Soc. Am. B 10,283-295 (1993).
    [CrossRef]
  2. U. Gruning, V. Lehmann, S. Ottow, and K. Busch, "Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm," Appl. Phys. Lett. 68, 747-749 (1996).
    [CrossRef]
  3. K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
    [CrossRef]
  4. K. Wang, A. Chelnokov, S. Rowson, P. Garoche, and J-M Lourtioz, "Focused-ion-beam etching in macroporous silicon to realize three-dimensional photonic crystals," J. Phys. D: Appl. Phys. 33, L119-L123 (2000).
    [CrossRef]
  5. H. Sun, Y. Xu, S. Juodkazis, K. Sun, M. Watanabe, S. Matsuo, H. Misawa, and J. Nishii, "Arbitrary-lattice photonic crystals created by multiphoton microfabrication," Opt. Lett. 26, 325-327 (2001).
    [CrossRef]
  6. M. J. Escuti, and G. P. Crawford, "Holographic photonic crystals," Opt. Eng. 43, 1973-1987 (2004).
    [CrossRef]
  7. V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
    [CrossRef]
  8. T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
    [CrossRef]
  9. T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, "Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses," Appl. Phys. Lett. 82, 2758-2760 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
    [CrossRef]
  14. V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
    [CrossRef] [PubMed]
  15. M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
    [CrossRef] [PubMed]

2005 (1)

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

2004 (1)

M. J. Escuti, and G. P. Crawford, "Holographic photonic crystals," Opt. Eng. 43, 1973-1987 (2004).
[CrossRef]

2003 (2)

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, "Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses," Appl. Phys. Lett. 82, 2758-2760 (2003).
[CrossRef]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

2002 (2)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

L. Cai, X. Yang, and Y. Wang, "All fourteen Bravais lattices can be formed by interference of four noncoplanar beams," Opt. Lett. 27, 900-902 (2002).
[CrossRef]

2001 (3)

H. Sun, Y. Xu, S. Juodkazis, K. Sun, M. Watanabe, S. Matsuo, H. Misawa, and J. Nishii, "Arbitrary-lattice photonic crystals created by multiphoton microfabrication," Opt. Lett. 26, 325-327 (2001).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

2000 (1)

K. Wang, A. Chelnokov, S. Rowson, P. Garoche, and J-M Lourtioz, "Focused-ion-beam etching in macroporous silicon to realize three-dimensional photonic crystals," J. Phys. D: Appl. Phys. 33, L119-L123 (2000).
[CrossRef]

1997 (1)

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

1996 (1)

U. Gruning, V. Lehmann, S. Ottow, and K. Busch, "Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm," Appl. Phys. Lett. 68, 747-749 (1996).
[CrossRef]

1995 (1)

1993 (1)

1991 (1)

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Atatüre, M.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

Badolato, A.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

Berger, V.

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

Busch, K.

U. Gruning, V. Lehmann, S. Ottow, and K. Busch, "Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm," Appl. Phys. Lett. 68, 747-749 (1996).
[CrossRef]

Cai, L.

Chelnokov, A.

K. Wang, A. Chelnokov, S. Rowson, P. Garoche, and J-M Lourtioz, "Focused-ion-beam etching in macroporous silicon to realize three-dimensional photonic crystals," J. Phys. D: Appl. Phys. 33, L119-L123 (2000).
[CrossRef]

Cheng, B.

Costard, E.

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

Crawford, G. P.

M. J. Escuti, and G. P. Crawford, "Holographic photonic crystals," Opt. Eng. 43, 1973-1987 (2004).
[CrossRef]

Dholakia, K.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Dreiser, J.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

Escuti, M. J.

M. J. Escuti, and G. P. Crawford, "Holographic photonic crystals," Opt. Eng. 43, 1973-1987 (2004).
[CrossRef]

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Garoche, P.

K. Wang, A. Chelnokov, S. Rowson, P. Garoche, and J-M Lourtioz, "Focused-ion-beam etching in macroporous silicon to realize three-dimensional photonic crystals," J. Phys. D: Appl. Phys. 33, L119-L123 (2000).
[CrossRef]

Gauthier-Lafaye, O.

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

Gruning, U.

U. Gruning, V. Lehmann, S. Ottow, and K. Busch, "Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm," Appl. Phys. Lett. 68, 747-749 (1996).
[CrossRef]

Hennessy, K.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

Herman, R. M.

Hu, E.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

Hu, W.

Imamoðlu, A.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

Juodkazis, S.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, "Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses," Appl. Phys. Lett. 82, 2758-2760 (2003).
[CrossRef]

H. Sun, Y. Xu, S. Juodkazis, K. Sun, M. Watanabe, S. Matsuo, H. Misawa, and J. Nishii, "Arbitrary-lattice photonic crystals created by multiphoton microfabrication," Opt. Lett. 26, 325-327 (2001).
[CrossRef]

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

Kondo, T.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, "Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses," Appl. Phys. Lett. 82, 2758-2760 (2003).
[CrossRef]

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

Lehmann, V.

U. Gruning, V. Lehmann, S. Ottow, and K. Busch, "Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm," Appl. Phys. Lett. 68, 747-749 (1996).
[CrossRef]

Li, H.

Li, Z.

Lourtioz, J-M

K. Wang, A. Chelnokov, S. Rowson, P. Garoche, and J-M Lourtioz, "Focused-ion-beam etching in macroporous silicon to realize three-dimensional photonic crystals," J. Phys. D: Appl. Phys. 33, L119-L123 (2000).
[CrossRef]

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

Matsuo, S.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, "Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses," Appl. Phys. Lett. 82, 2758-2760 (2003).
[CrossRef]

H. Sun, Y. Xu, S. Juodkazis, K. Sun, M. Watanabe, S. Matsuo, H. Misawa, and J. Nishii, "Arbitrary-lattice photonic crystals created by multiphoton microfabrication," Opt. Lett. 26, 325-327 (2001).
[CrossRef]

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

McGloin, D.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

Misawa, H.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, "Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses," Appl. Phys. Lett. 82, 2758-2760 (2003).
[CrossRef]

H. Sun, Y. Xu, S. Juodkazis, K. Sun, M. Watanabe, S. Matsuo, H. Misawa, and J. Nishii, "Arbitrary-lattice photonic crystals created by multiphoton microfabrication," Opt. Lett. 26, 325-327 (2001).
[CrossRef]

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

Mizeikis, V.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, "Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses," Appl. Phys. Lett. 82, 2758-2760 (2003).
[CrossRef]

Nishii, J.

Ottow, S.

U. Gruning, V. Lehmann, S. Ottow, and K. Busch, "Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm," Appl. Phys. Lett. 68, 747-749 (1996).
[CrossRef]

Petroff, P. M.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

Rowson, S.

K. Wang, A. Chelnokov, S. Rowson, P. Garoche, and J-M Lourtioz, "Focused-ion-beam etching in macroporous silicon to realize three-dimensional photonic crystals," J. Phys. D: Appl. Phys. 33, L119-L123 (2000).
[CrossRef]

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

Sun, H.

Sun, K.

Tamboli, A.

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

Wang, K.

K. Wang, A. Chelnokov, S. Rowson, P. Garoche, and J-M Lourtioz, "Focused-ion-beam etching in macroporous silicon to realize three-dimensional photonic crystals," J. Phys. D: Appl. Phys. 33, L119-L123 (2000).
[CrossRef]

Wang, Y.

Watanabe, M.

Wiggins, T. A.

Xu, J.

Xu, Y.

Yablonovitch, E.

Yang, J.

Yang, X.

Zhang, D.

Appl. Phys. Lett. (4)

U. Gruning, V. Lehmann, S. Ottow, and K. Busch, "Macroporous silicon with a complete two-dimensional photonic band gap centered at 5 μm," Appl. Phys. Lett. 68, 747-749 (1996).
[CrossRef]

K. Hennessy, A. Badolato, A. Tamboli, P. M. Petroff, E. Hu, M. Atatüre, J. Dreiser, and A. Imamoðlu, "Tuning photonic crystal nanocavity modes by wet chemical digital etching," Appl. Phys. Lett. 87, 021108 (2005).
[CrossRef]

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, "Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses," Appl. Phys. Lett. 82, 2758-2760 (2003).
[CrossRef]

J. Appl. Phys. (1)

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

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

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

J. Phys. D: Appl. Phys. (1)

K. Wang, A. Chelnokov, S. Rowson, P. Garoche, and J-M Lourtioz, "Focused-ion-beam etching in macroporous silicon to realize three-dimensional photonic crystals," J. Phys. D: Appl. Phys. 33, L119-L123 (2000).
[CrossRef]

Nature (2)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, "Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam," Nature 419, 145-147 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Opt. Eng. (1)

M. J. Escuti, and G. P. Crawford, "Holographic photonic crystals," Opt. Eng. 43, 1973-1987 (2004).
[CrossRef]

Opt. Lett. (3)

Supplementary Material (6)

» Media 1: AVI (2265 KB)     
» Media 2: AVI (2317 KB)     
» Media 3: AVI (2402 KB)     
» Media 4: AVI (501 KB)     
» Media 5: AVI (984 KB)     
» Media 6: AVI (925 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Multi-beam interference by a four-faceted symmetric acute pyramid (a) and its flattopped analogue (b)

Fig. 2.
Fig. 2.

Plane geometrical scheme of a collimated beam passing through a glass pyramid

Fig. 3.
Fig. 3.

Simulations of 2D patterns in the x-y plane behind n-faceted acute pyramids (λ=633nm, θ=2.50)

Fig. 4.
Fig. 4.

Experimental observation of optical lattices formed (a) by a 3-faceted acute pyramid with γ=5° (imaged with a 25X objective) and (b) by a 4-faceted pyramid with γ=2° (imaged with a 10X objective). The scale in the figures is 10µm/div.

Fig. 5.
Fig. 5.

Comparison of the experimentally measured intensity pattern of an axicon (a) with the one of the simulated intensity pattern from a 40-faceted acute pyramid (b). In (c) the radial distribution of the simulation is compared with the zero-order Bessel function.

Fig. 6.
Fig. 6.

Simulations of the 3D intensity distribution resulting from flat-topped pyramids (λ=633nm, θ=2.50)

Fig. 7.
Fig. 7.

Z-scan videos of the structure of 3D optical lattices using (a) a flat-topped prism with n=2 and γ=5°(imaged with a 25X objective), (b) a flat-topped pyramid with n=3 and γ=5° (imaged with a 25X objective), (c) a flat-topped pyramid with n=4 and γ=2° (imaged with a 10X objective). The corresponding videos of the simulations are shown in (d) for n=2, (e) for n=3 and (f) for n=4, respectively. [Media 1] [Media 2] [Media 3] [Media 4] [Media 5] [Media 6]

Equations (5)

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

E exp ( i δ ) exp ( i k · r ) ,
ψ ( z , ρ , φ ) = E 0 exp ( i k z i δ ) + E exp ( i k z z i δ ) j = 1 n exp [ i k ρ ρ cos ( φ φ j ) ] ,
I ( z , ρ , φ ) = E 0 2 + nE 2 + 2 E 2 i = 1 n j > i n cos ( k ρ ρ [ cos ( φ φ i ) cos ( φ φ j ) ] )
+ 2 EE 0 i = 1 n cos [ k ρ ρ cos ( φ φ i ) Kz ] .
ψ lim n j = 1 n exp ( i k ρ ρ cos ( φ φ j ) ) = 1 2 π 0 2 π exp ( i k ρ ρ cos α ) d α = J 0 ( ρ ) .

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