Abstract

We present analysis of forward optical scattering spectra of a single spherical object illuminated with tightly focused white light supercontinuum based on angular spectrum decomposition and Mie’s scattering theory. The experimental results agree with the theoretical calculations.

©2005 Optical Society of America

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References

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  4. K. Lindfors , T. Kalkbrenner , P. Stoller , and V. Sandoghdar , “ Detection and Spectroscopy of Gold Nanoparticles Using SupercontinuumWhite Light Confocal Microscopy ,” Phys. Rev. Lett.   93 , 037401 ( 2004 ).
    [Crossref] [PubMed]
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  9. G. Gouesbet , G. Grehan , and B. Maheu , “ Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism ,” J. Optics (Paris)   16 , 83 – 93 ( 1985 ).
    [Crossref]
  10. J. T. Hodges , G. Grehan , G. Gouesbet , and C. Presser , “ Forward scattering of a Gaussian beam by a nonabsorbing sphere ,” Appl. Opt.   34 , 2120 – 2132 ( 1995 ).
    [Crossref] [PubMed]
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  12. A. Rohrbach and E. H. K. Steler , “ Three-dimensional position detection of optically trapped dielectric particles ,” J. Appl. Phys.   91 , 5474 – 5488 ( 2002 ).
    [Crossref]
  13. L. Novotny , R. D. Grober , and K. Karrai , “ Reflected image of a strongly focused spot ,” Opt. Lett.   26 , 789 – 791 ( 2002 ).
    [Crossref]
  14. P. Torok , P. D. Higdon , R. Juskaitis , and T. Wilson , “ Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers ,” Opt. Comm.   155 , 335 – 341 ( 1998 ).
    [Crossref]
  15. L. Mandel and E. Wolf , Optical Coherence and Quantum Optics ( Cambridge U. Press, New York , 1995 ), pp. 144 .
  16. H. C. Van de Hulst , Light Scattering by Small Particles , ( Dover Publications, Inc., New York , 1981 ).

2005 (1)

2004 (2)

M. Y. Sfeir et.al., “ Probing electronic transitions in individual carbon nanotubes ,” Science   306 , 1540 – 1543 ( 2004 ).
[Crossref] [PubMed]

K. Lindfors , T. Kalkbrenner , P. Stoller , and V. Sandoghdar , “ Detection and Spectroscopy of Gold Nanoparticles Using SupercontinuumWhite Light Confocal Microscopy ,” Phys. Rev. Lett.   93 , 037401 ( 2004 ).
[Crossref] [PubMed]

2002 (2)

A. Rohrbach and E. H. K. Steler , “ Three-dimensional position detection of optically trapped dielectric particles ,” J. Appl. Phys.   91 , 5474 – 5488 ( 2002 ).
[Crossref]

L. Novotny , R. D. Grober , and K. Karrai , “ Reflected image of a strongly focused spot ,” Opt. Lett.   26 , 789 – 791 ( 2002 ).
[Crossref]

2000 (1)

1998 (1)

P. Torok , P. D. Higdon , R. Juskaitis , and T. Wilson , “ Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers ,” Opt. Comm.   155 , 335 – 341 ( 1998 ).
[Crossref]

1996 (1)

1995 (1)

1987 (1)

1986 (1)

1985 (1)

G. Gouesbet , G. Grehan , and B. Maheu , “ Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism ,” J. Optics (Paris)   16 , 83 – 93 ( 1985 ).
[Crossref]

1977 (2)

Atkin, D. M.

Birks, T. A.

Casperson, L. W.

Chevaillier, J. P.

Chew, H.

Cooke, D. D.

Fabre, J.

Gouesbet, G.

J. T. Hodges , G. Grehan , G. Gouesbet , and C. Presser , “ Forward scattering of a Gaussian beam by a nonabsorbing sphere ,” Appl. Opt.   34 , 2120 – 2132 ( 1995 ).
[Crossref] [PubMed]

G. Gouesbet , G. Grehan , and B. Maheu , “ Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism ,” J. Optics (Paris)   16 , 83 – 93 ( 1985 ).
[Crossref]

Grehan, G.

J. T. Hodges , G. Grehan , G. Gouesbet , and C. Presser , “ Forward scattering of a Gaussian beam by a nonabsorbing sphere ,” Appl. Opt.   34 , 2120 – 2132 ( 1995 ).
[Crossref] [PubMed]

G. Gouesbet , G. Grehan , and B. Maheu , “ Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism ,” J. Optics (Paris)   16 , 83 – 93 ( 1985 ).
[Crossref]

Grober, R. D.

Hamelin, P.

Higdon, P. D.

P. Torok , P. D. Higdon , R. Juskaitis , and T. Wilson , “ Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers ,” Opt. Comm.   155 , 335 – 341 ( 1998 ).
[Crossref]

Hodges, J. T.

Juskaitis, R.

P. Torok , P. D. Higdon , R. Juskaitis , and T. Wilson , “ Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers ,” Opt. Comm.   155 , 335 – 341 ( 1998 ).
[Crossref]

Kalkbrenner, T.

K. Lindfors , T. Kalkbrenner , P. Stoller , and V. Sandoghdar , “ Detection and Spectroscopy of Gold Nanoparticles Using SupercontinuumWhite Light Confocal Microscopy ,” Phys. Rev. Lett.   93 , 037401 ( 2004 ).
[Crossref] [PubMed]

Karrai, K.

Kerker, M.

Knight, J. C.

Lee, S. S.

Li, P.

Lindfors, K.

K. Lindfors , T. Kalkbrenner , P. Stoller , and V. Sandoghdar , “ Detection and Spectroscopy of Gold Nanoparticles Using SupercontinuumWhite Light Confocal Microscopy ,” Phys. Rev. Lett.   93 , 037401 ( 2004 ).
[Crossref] [PubMed]

Liu, Z.

Maheu, B.

G. Gouesbet , G. Grehan , and B. Maheu , “ Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism ,” J. Optics (Paris)   16 , 83 – 93 ( 1985 ).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf , Optical Coherence and Quantum Optics ( Cambridge U. Press, New York , 1995 ), pp. 144 .

Novotny, L.

Park, S. O.

Presser, C.

Ranka, J. K.

Rohrbach, A.

A. Rohrbach and E. H. K. Steler , “ Three-dimensional position detection of optically trapped dielectric particles ,” J. Appl. Phys.   91 , 5474 – 5488 ( 2002 ).
[Crossref]

Russell, P. S.

Sandoghdar, V.

K. Lindfors , T. Kalkbrenner , P. Stoller , and V. Sandoghdar , “ Detection and Spectroscopy of Gold Nanoparticles Using SupercontinuumWhite Light Confocal Microscopy ,” Phys. Rev. Lett.   93 , 037401 ( 2004 ).
[Crossref] [PubMed]

Sfeir, M. Y.

M. Y. Sfeir et.al., “ Probing electronic transitions in individual carbon nanotubes ,” Science   306 , 1540 – 1543 ( 2004 ).
[Crossref] [PubMed]

Shi, K.

Steler, E. H. K.

A. Rohrbach and E. H. K. Steler , “ Three-dimensional position detection of optically trapped dielectric particles ,” J. Appl. Phys.   91 , 5474 – 5488 ( 2002 ).
[Crossref]

Stentz, A. J.

Stoller, P.

K. Lindfors , T. Kalkbrenner , P. Stoller , and V. Sandoghdar , “ Detection and Spectroscopy of Gold Nanoparticles Using SupercontinuumWhite Light Confocal Microscopy ,” Phys. Rev. Lett.   93 , 037401 ( 2004 ).
[Crossref] [PubMed]

Torok, P.

P. Torok , P. D. Higdon , R. Juskaitis , and T. Wilson , “ Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers ,” Opt. Comm.   155 , 335 – 341 ( 1998 ).
[Crossref]

Van de Hulst, H. C.

H. C. Van de Hulst , Light Scattering by Small Particles , ( Dover Publications, Inc., New York , 1981 ).

Wilson, T.

P. Torok , P. D. Higdon , R. Juskaitis , and T. Wilson , “ Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers ,” Opt. Comm.   155 , 335 – 341 ( 1998 ).
[Crossref]

Windeler, R. S.

Wolf, E.

L. Mandel and E. Wolf , Optical Coherence and Quantum Optics ( Cambridge U. Press, New York , 1995 ), pp. 144 .

Yeh, C.

Yeung, W. F.

Appl. Opt. (3)

J. Appl. Phys. (1)

A. Rohrbach and E. H. K. Steler , “ Three-dimensional position detection of optically trapped dielectric particles ,” J. Appl. Phys.   91 , 5474 – 5488 ( 2002 ).
[Crossref]

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

J. Optics (1)

G. Gouesbet , G. Grehan , and B. Maheu , “ Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism ,” J. Optics (Paris)   16 , 83 – 93 ( 1985 ).
[Crossref]

Opt. Comm. (1)

P. Torok , P. D. Higdon , R. Juskaitis , and T. Wilson , “ Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers ,” Opt. Comm.   155 , 335 – 341 ( 1998 ).
[Crossref]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

K. Lindfors , T. Kalkbrenner , P. Stoller , and V. Sandoghdar , “ Detection and Spectroscopy of Gold Nanoparticles Using SupercontinuumWhite Light Confocal Microscopy ,” Phys. Rev. Lett.   93 , 037401 ( 2004 ).
[Crossref] [PubMed]

Science (1)

M. Y. Sfeir et.al., “ Probing electronic transitions in individual carbon nanotubes ,” Science   306 , 1540 – 1543 ( 2004 ).
[Crossref] [PubMed]

Other (2)

L. Mandel and E. Wolf , Optical Coherence and Quantum Optics ( Cambridge U. Press, New York , 1995 ), pp. 144 .

H. C. Van de Hulst , Light Scattering by Small Particles , ( Dover Publications, Inc., New York , 1981 ).

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Figures (5)

Fig. 1.
Fig. 1. Schematic diagram of optical scattering by using tightly focused supercontinuum. A linearly-polarized incoming supercontinuum is tightly focused by objective lens L1. The scattered light produced by a spherical scatterer is collected by objective lens L2 and analyzed by a spectrometer.
Fig. 2.
Fig. 2. Schematic diagram of experiment setup
Fig. 3
Fig. 3 Dependence of scattering efficiency on axial position (a) and (b) are the scattering efficiencies of the 1.5- and 2-μm diameter microspheres respectively at λ0=600nm as a function of axial position. Red lines are theoretical calculation results. Blue dots are experiment results.
Fig. 4.
Fig. 4. Measured chromatic aberration of the experimental system. Circles and pluses represent the results using 1.5 and 2.0-μm-diameter microspheres respectively. The blue line is the fitted curve.
Fig. 5.
Fig. 5. Scattering spectra of a 1.5-μm-diameter microsphere at two different positions. Dotted red lines are theoretical calculation results while solid blue lines are experiment data.

Equations (13)

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E ( r ) = E ͂ ( k i ) e j k i · r d k x d k y = 0 2 π 0 θ m E ͂ ( k i ) e j k i · r k 2 sin θ cos θ d θ d ϕ
E ͂ ( k i ) = j λ 0 ( 2 π ) 2 n ( 1 cos θ ) f e j k f E f ( θ , ϕ )
E f ( θ , ϕ ) = E 0 cos θ [ ( cos θ cos 2 ϕ + sin 2 ϕ ) x ̂ + ( cos θ 1 ) cos ϕ sin ϕ y ̂ sin θ cos ϕ z ̂ ]
E ͂ ( k i ) = j T λ 0 e j ψ ( 2 π ) 2 n c 1 cos [ sin 1 ( n sin θ n c ) ] f e j k f E f ( sin 1 ( n sin θ n c ) , ϕ )
M = ( cos θ cos 2 ϕ + sin 2 ϕ ( cos θ 1 ) cos ϕ sin ϕ sin θ cos ϕ ( cos θ 1 ) cos ϕ sin ϕ cos θ sin 2 ϕ + cos 2 ϕ sin θ sin ϕ sin θ cos ϕ sin θ sin ϕ cos θ )
E ' s ( r ' ) = j e j k r ' e j k i · r 0 k r ' ( sin 2 β ' S 1 ( cos α ' ) + cos α ' cos 2 β ' S 2 ( cos α ' ) cos β ' sin β ' S 1 ( cos α ' ) + cos α ' cos β ' sin β ' S 2 ( cos α ' ) sin α ' cos β ' S 2 ( cos α ' ) ) E ͂ ( k i )
E s ( r ; k i ) = M · E ' ̂ s ( M 1 r ) = E s ( α , β ; θ , ϕ )
E s ( α , β ) = 0 2 π 0 θ m E s ( α , β ; θ , ϕ ) k 2 sin θ cos θ d θ d ϕ
E r ( α , β ) = j E ͂ ( k o ) e j k o · r 0 ( 2 π ) 2 n λ 0 cos α e j k r r
p ( λ 0 ) 0 2 π d β 0 α m sin α d α { 0 2 π 0 θ m E s ( α , β ; θ , ϕ ) k 2 sin θ cos θ d θ d ϕ } + E r ( α , β ) 2
f ( λ ) = f ( λ 0 ) + Δ f
d ( λ ) = d ( λ 0 ) + Δ f
r 0 ( λ ) = r 0 ( λ 0 ) Δ f z ̂

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