Abstract

The size of bright structures in traveling-wave light fields is limited by diffraction. This in turn limits a number of technologies, for example, optical trapping. One way to beat the diffraction limit is to use evanescent waves instead of traveling waves. Here we apply a holographic algorithm, direct search, to the shaping of complex evanescent-wave fields. We simulate three-dimensional intensity shaping of evanescent-wave fields using this approach, and we investigate some of its limitations.

© 2008 Optical Society of America

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  1. The size and separation of extrema can be arbitrarily small, provided their visibility is also arbitrarily small .
  2. P. J. Reece, V. Garcés-Chávez, and K. Dholakia, “Near-field optical micromanipulation with cavity enhanced evanescent waves,” Appl. Phys. Lett. 88, 221116 (2006).
    [CrossRef]
  3. T. Cizmár, M. Siler, M. Serý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
    [CrossRef]
  4. V. Garcés-Chávez, K. Dholakia, and G. C. Spalding, “Extended-area optically induced organization of microparticies on a surface,” Appl. Phys. Lett. 86, 031106 (2005).
    [CrossRef]
  5. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  6. Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, J. P. Samluk, and D. W. Prather, “Perfect lens makes a perfect trap,” Opt. Express 14, 2228-2235 (2006).
    [CrossRef] [PubMed]
  7. L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10, 023015 (2008).
    [CrossRef]
  8. L. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1-8 (2006).
    [CrossRef]
  9. R. F. Wallis and G. I. Stegeman, eds., Electromagnetic Surface Excitations (Springer-Verlag, 1986).
    [CrossRef]
  10. O. Bryngdahl, “Holography with evanescent waves,” J. Opt. Soc. Am. 59, 1645-1650 (1969).
    [CrossRef]
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    [CrossRef] [PubMed]
  12. P. S. Ramanujam, “Evanescent polarization holographic recording of sub-200-nm gratings in an azobenzene polyester,” Opt. Lett. 28, 2375-2377 (2003).
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  13. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy,” Opt. Lett. 30, 468-470 (2005).
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  14. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788-2798 (1987).
    [CrossRef] [PubMed]
  15. A. Tarantola, Inverse Problem Theory (Society for Industrial and Applied Mathematics, 2005).
  16. M. Mazilu and K. Dholakia, “Subwavelength trapping volumes created using negative refraction,” presented at SPIE Optics & Photonics Meeting 2006, San Diego, Calif., August 13-17, 2006.
  17. M. Mazilu and K. Dholakia, “Limits and possibilities in subwavelength imaging using negative refraction,” presented at Photon06, Manchester, UK, September 4-7, 2006.
  18. M. Clark and R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150-164 (1996).
    [CrossRef]
  19. M. Berry, “Faster than Fourier,” in Fundamental Problems in Quantum Theory, J.A.Anandan and J.Safko, eds. (World Scientific, 1994).

2008 (1)

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10, 023015 (2008).
[CrossRef]

2006 (4)

L. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1-8 (2006).
[CrossRef]

Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, J. P. Samluk, and D. W. Prather, “Perfect lens makes a perfect trap,” Opt. Express 14, 2228-2235 (2006).
[CrossRef] [PubMed]

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, “Near-field optical micromanipulation with cavity enhanced evanescent waves,” Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

T. Cizmár, M. Siler, M. Serý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

2005 (2)

2003 (1)

2000 (1)

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

1996 (2)

S. I. Bozhevolnyi and B. Vohnsen, “Near-field optical holography,” Phys. Rev. Lett. 77, 3351-3354 (1996).
[CrossRef] [PubMed]

M. Clark and R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150-164 (1996).
[CrossRef]

1987 (1)

1969 (1)

Allebach, J. P.

Berry, M.

M. Berry, “Faster than Fourier,” in Fundamental Problems in Quantum Theory, J.A.Anandan and J.Safko, eds. (World Scientific, 1994).

Boissel, Y.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10, 023015 (2008).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi and B. Vohnsen, “Near-field optical holography,” Phys. Rev. Lett. 77, 3351-3354 (1996).
[CrossRef] [PubMed]

Bryngdahl, O.

Cizmár, T.

T. Cizmár, M. Siler, M. Serý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Clark, M.

M. Clark and R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150-164 (1996).
[CrossRef]

Colomb, T.

Courtial, J.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10, 023015 (2008).
[CrossRef]

Cuche, E.

Depeursinge, C.

Dholakia, K.

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, “Near-field optical micromanipulation with cavity enhanced evanescent waves,” Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

T. Cizmár, M. Siler, M. Serý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

V. Garcés-Chávez, K. Dholakia, and G. C. Spalding, “Extended-area optically induced organization of microparticies on a surface,” Appl. Phys. Lett. 86, 031106 (2005).
[CrossRef]

M. Mazilu and K. Dholakia, “Subwavelength trapping volumes created using negative refraction,” presented at SPIE Optics & Photonics Meeting 2006, San Diego, Calif., August 13-17, 2006.

M. Mazilu and K. Dholakia, “Limits and possibilities in subwavelength imaging using negative refraction,” presented at Photon06, Manchester, UK, September 4-7, 2006.

Emery, Y.

Garcés-Chávez, V.

T. Cizmár, M. Siler, M. Serý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, “Near-field optical micromanipulation with cavity enhanced evanescent waves,” Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

V. Garcés-Chávez, K. Dholakia, and G. C. Spalding, “Extended-area optically induced organization of microparticies on a surface,” Appl. Phys. Lett. 86, 031106 (2005).
[CrossRef]

Helseth, L.

L. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1-8 (2006).
[CrossRef]

Lu, Z.

Magistretti, P. J.

Marquet, P.

Mazilu, M.

M. Mazilu and K. Dholakia, “Subwavelength trapping volumes created using negative refraction,” presented at SPIE Optics & Photonics Meeting 2006, San Diego, Calif., August 13-17, 2006.

M. Mazilu and K. Dholakia, “Limits and possibilities in subwavelength imaging using negative refraction,” presented at Photon06, Manchester, UK, September 4-7, 2006.

Murakowski, J. A.

Pendry, J. B.

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

Prather, D. W.

Ramanujam, P. S.

Rappaz, B.

Reece, P. J.

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, “Near-field optical micromanipulation with cavity enhanced evanescent waves,” Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

Samluk, J. P.

Schneider, G. J.

Schuetz, C. A.

Seldowitz, M. A.

Serý, M.

T. Cizmár, M. Siler, M. Serý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Shi, S.

Siler, M.

T. Cizmár, M. Siler, M. Serý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Smith, R.

M. Clark and R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150-164 (1996).
[CrossRef]

Spalding, G. C.

V. Garcés-Chávez, K. Dholakia, and G. C. Spalding, “Extended-area optically induced organization of microparticies on a surface,” Appl. Phys. Lett. 86, 031106 (2005).
[CrossRef]

Stegeman, G. I.

R. F. Wallis and G. I. Stegeman, eds., Electromagnetic Surface Excitations (Springer-Verlag, 1986).
[CrossRef]

Sweeney, D. W.

Tarantola, A.

A. Tarantola, Inverse Problem Theory (Society for Industrial and Applied Mathematics, 2005).

Thomson, L. C.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10, 023015 (2008).
[CrossRef]

Vohnsen, B.

S. I. Bozhevolnyi and B. Vohnsen, “Near-field optical holography,” Phys. Rev. Lett. 77, 3351-3354 (1996).
[CrossRef] [PubMed]

Wallis, R. F.

R. F. Wallis and G. I. Stegeman, eds., Electromagnetic Surface Excitations (Springer-Verlag, 1986).
[CrossRef]

Whyte, G.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10, 023015 (2008).
[CrossRef]

Yao, E.

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10, 023015 (2008).
[CrossRef]

Zemánek, P.

T. Cizmár, M. Siler, M. Serý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

P. J. Reece, V. Garcés-Chávez, and K. Dholakia, “Near-field optical micromanipulation with cavity enhanced evanescent waves,” Appl. Phys. Lett. 88, 221116 (2006).
[CrossRef]

V. Garcés-Chávez, K. Dholakia, and G. C. Spalding, “Extended-area optically induced organization of microparticies on a surface,” Appl. Phys. Lett. 86, 031106 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

New J. Phys. (1)

L. C. Thomson, Y. Boissel, G. Whyte, E. Yao, and J. Courtial, “Simulation of superresolution holography for optical tweezers,” New J. Phys. 10, 023015 (2008).
[CrossRef]

Opt. Commun. (2)

L. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1-8 (2006).
[CrossRef]

M. Clark and R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150-164 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (1)

T. Cizmár, M. Siler, M. Serý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Optical sorting and detection of sub-micron objects in a motional standing wave,” Phys. Rev. B 74, 035105 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

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

S. I. Bozhevolnyi and B. Vohnsen, “Near-field optical holography,” Phys. Rev. Lett. 77, 3351-3354 (1996).
[CrossRef] [PubMed]

Other (6)

A. Tarantola, Inverse Problem Theory (Society for Industrial and Applied Mathematics, 2005).

M. Mazilu and K. Dholakia, “Subwavelength trapping volumes created using negative refraction,” presented at SPIE Optics & Photonics Meeting 2006, San Diego, Calif., August 13-17, 2006.

M. Mazilu and K. Dholakia, “Limits and possibilities in subwavelength imaging using negative refraction,” presented at Photon06, Manchester, UK, September 4-7, 2006.

The size and separation of extrema can be arbitrarily small, provided their visibility is also arbitrarily small .

R. F. Wallis and G. I. Stegeman, eds., Electromagnetic Surface Excitations (Springer-Verlag, 1986).
[CrossRef]

M. Berry, “Faster than Fourier,” in Fundamental Problems in Quantum Theory, J.A.Anandan and J.Safko, eds. (World Scientific, 1994).

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Figures (8)

Fig. 1
Fig. 1

Geometry of the creation of evanescent waves by total internal reflection of a prism surface. A plane wave of vacuum wavelength λ is incident on a prism surface with angle of incidence α. The transverse wavelength along the prism surface, Λ, is given by the equation Λ sin ( α ) = λ n .

Fig. 2
Fig. 2

Glass hemisphere configuration creating an evanescent-wave field in the center of the flat surface. Illuminating the sphere with a point light source, A, which can be for example the end of a single-mode fiber, can create a collimated beam inside the glass, which in turn can create an evanescent plane wave above the center of the hemisphere’s flat side. Illuminating with two or more coherent point light sources at different positions can create a superposition of evanescent waves.

Fig. 3
Fig. 3

Example of the transverse k-space distribution of evanescent-plane-wave components used in our simulation. The dots represent evanescent-plane-wave components. They all lie outside the shaded area in the center, which represents traveling waves.

Fig. 4
Fig. 4

Shaping of the transverse intensity distribution of an evanescent-wave superposition, here directly above the prism surface ( z = 0 ) . “+” symbols indicate positions where the intensity was maximized. The k-space components are those shown in Fig. 3.

Fig. 5
Fig. 5

(a) Transverse and (b) longitudinal intensity cross section after optimization of the intensity at two trap positions (+ signs). The trap positions are 300 nm above the prism surface. The k-space distribution is that shown in Fig. 3.

Fig. 6
Fig. 6

Intensity resulting from an attempt to force the creation of two 3D intensity maxima. The algorithm tries to maximize the intensity at the trap positions, which are indicated by + signs (green in the online version); it tries to minimize the intensity at the points marked with “−” signs (red in the online version). k-space distribution as in Fig. 3.

Fig. 7
Fig. 7

Demonstration of intensity maxima away from the prism interface. The intensity was maximized in two points, each marked with a +, on the line x = y = 0 . The intensity is shown in two planes that both include the line: (a) y = 0 and (b) x = 0 . What appears to be a 3D maximum in (a) turns out to be a saddle point in (b). The intensity was calculated for a k-space distribution different from that shown in Fig. 3.

Fig. 8
Fig. 8

Local maximum in the field, u, which is the sum of two evanescent waves, u 1 ( z ) = exp ( z ) and u 2 ( z ) = exp ( 2 z ) , where z is the propagation distance (dimensionless units).

Equations (9)

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u ( x , y , z ) = exp ( i ( k x x + k z z ) ) ,
f = r n 1 .
u i ( x , y , z ) = exp ( i ( k x , i x + k y , i y + k z , i z ) ) ,
= exp ( i ( k x , i x + k y , i y ) ) exp ( β i z ) ,
k z , i = ( 2 π λ ) 2 k x , i 2 k y , i 2 ,
v ( x , y , z ) = i = 1 N exp ( i ϕ i ) u i ( x , y , z ) ,
I j = v ( x j , y j , z j ) 2 ,
Q = j ln ( I j + 1 ) .
Q = j = 1 M ln ( I j + 1 ) j = M + 1 M + L ln ( I j + 1 ) .

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