Abstract

Dipole models are one of the simplest numerical models to understand nonlinear scattering. Existing dipole model for second harmonic generation, third harmonic generation and coherent anti-Stokes Raman scattering assume that the dipoles which make up a scatterer do not interact with one another. Thus, this dipole model can be called the uncoupled dipole model. This dipole model is not sufficient to describe the effects of refractive index of a scatterer or to describe scattering at the edges of a scatterer. Taking into account the interaction between dipoles overcomes these short comings of the uncoupled dipole model. Coupled dipole model has been primarily used for linear scattering studies but it can be extended to predict nonlinear scattering. The coupled and uncoupled dipole models have been compared to highlight their differences. Results of nonlinear scattering predicted by coupled dipole model agree well with previously reported experimental results.

© 2012 OSA

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2011

2010

2009

2008

G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P.-F. Brevet, “Multipolar second-harmonic generation in noble metal nanoparticles,” J. Opt. Soc. Am. B25(6), 955–960 (2008).
[CrossRef]

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J.95(10), 4908–4914 (2008).
[CrossRef] [PubMed]

2007

2006

2005

2004

J.-X. Cheng and X. S. Xie, “Coherent Anti-Stokes Raman Scattering microscopy: instrumentation, theory, and applications,” J. Phys. Chem. B108(3), 827–840 (2004).
[CrossRef]

S.-W. Chu, S.-Y. Chen, G.-W. Chern, T.-H. Tsai, Y.-C. Chen, B.-L. Lin, and C.-K. Sun, “Studies of X(2)/X(3) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy,” Biophys. J.86(6), 3914–3922 (2004).
[CrossRef] [PubMed]

2003

E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med.9(6), 796–801 (2003).
[CrossRef] [PubMed]

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A.100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

2002

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J.82(1), 493–508 (2002).
[CrossRef] [PubMed]

A. Zoumi, A. Yeh, and B. J. Tromberg, “Imaging cells and extracellular matrix in vivo by using second-harmonic generation and two-photon excited fluorescence,” Proc. Natl. Acad. Sci. U.S.A.99(17), 11014–11019 (2002).
[CrossRef] [PubMed]

J.-X. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, “Laser-scanning coherent Anti-Stokes Raman scattering microscopy and applications to cell biology,” Biophys. J.83(1), 502–509 (2002).
[CrossRef] [PubMed]

J.-X. Cheng and X. S. Xie, “Green's function formulation for third-harmonic generation microscopy,” J. Opt. Soc. Am. B19(7), 1604–1610 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B19(6), 1363–1375 (2002).
[CrossRef]

2000

1999

D. Yelin and Y. Silberberg, “Laser scanning third-harmonic-generation microscopy in biology,” Opt. Express5(8), 169–175 (1999).
[CrossRef] [PubMed]

P. J. Campagnola, M. D. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J.77(6), 3341–3349 (1999).
[CrossRef] [PubMed]

1998

1994

1992

K. Takeda, Y. Ito, and C. Munakata, “Simultaneous measurement of size and refractive index of a fine particle in flowing liquid,” Meas. Sci. Technol.3(1), 27–32 (1992).
[CrossRef]

1991

1990

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science248(4951), 73–76 (1990).
[CrossRef] [PubMed]

1988

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J.333, 848–872 (1988).
[CrossRef]

1978

J. N. Gannaway and C. J. R. Sheppard, “Second-harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron.10(5), 435–439 (1978).
[CrossRef]

1973

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J.186, 705–714 (1973).
[CrossRef]

1959

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Bachelier, G.

Balla, N. K.

Beaurepaire, E.

Benichou, E.

Bonn, M.

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J.95(10), 4908–4914 (2008).
[CrossRef] [PubMed]

Boucher, Y.

E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med.9(6), 796–801 (2003).
[CrossRef] [PubMed]

Brakenhoff, G.

Brevet, P.-F.

Brown, E.

E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med.9(6), 796–801 (2003).
[CrossRef] [PubMed]

Burger, K. N. J.

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J.95(10), 4908–4914 (2008).
[CrossRef] [PubMed]

Campagnola, P. J.

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J.90(2), 693–703 (2006).
[CrossRef] [PubMed]

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J.82(1), 493–508 (2002).
[CrossRef] [PubMed]

P. J. Campagnola, M. D. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J.77(6), 3341–3349 (1999).
[CrossRef] [PubMed]

Chen, S.-Y.

S.-W. Chu, S.-Y. Chen, G.-W. Chern, T.-H. Tsai, Y.-C. Chen, B.-L. Lin, and C.-K. Sun, “Studies of X(2)/X(3) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy,” Biophys. J.86(6), 3914–3922 (2004).
[CrossRef] [PubMed]

Chen, Y.-C.

S.-W. Chu, S.-Y. Chen, G.-W. Chern, T.-H. Tsai, Y.-C. Chen, B.-L. Lin, and C.-K. Sun, “Studies of X(2)/X(3) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy,” Biophys. J.86(6), 3914–3922 (2004).
[CrossRef] [PubMed]

Cheng, J.-X.

J.-X. Cheng and X. S. Xie, “Coherent Anti-Stokes Raman Scattering microscopy: instrumentation, theory, and applications,” J. Phys. Chem. B108(3), 827–840 (2004).
[CrossRef]

J.-X. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, “Laser-scanning coherent Anti-Stokes Raman scattering microscopy and applications to cell biology,” Biophys. J.83(1), 502–509 (2002).
[CrossRef] [PubMed]

J.-X. Cheng and X. S. Xie, “Green's function formulation for third-harmonic generation microscopy,” J. Opt. Soc. Am. B19(7), 1604–1610 (2002).
[CrossRef]

J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterization of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B19(6), 1363–1375 (2002).
[CrossRef]

Chern, G.-W.

S.-W. Chu, S.-Y. Chen, G.-W. Chern, T.-H. Tsai, Y.-C. Chen, B.-L. Lin, and C.-K. Sun, “Studies of X(2)/X(3) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy,” Biophys. J.86(6), 3914–3922 (2004).
[CrossRef] [PubMed]

Christie, R.

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A.100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Chu, S.-W.

S.-W. Chu, S.-Y. Chen, G.-W. Chern, T.-H. Tsai, Y.-C. Chen, B.-L. Lin, and C.-K. Sun, “Studies of X(2)/X(3) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy,” Biophys. J.86(6), 3914–3922 (2004).
[CrossRef] [PubMed]

Débarre, D.

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science248(4951), 73–76 (1990).
[CrossRef] [PubMed]

diTomaso, E.

E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med.9(6), 796–801 (2003).
[CrossRef] [PubMed]

Djaker, N.

Draine, B. T.

Flatau, P. J.

Gachet, D.

Gannaway, J. N.

J. N. Gannaway and C. J. R. Sheppard, “Second-harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron.10(5), 435–439 (1978).
[CrossRef]

Goodman, J. J.

Hoppe, P. E.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J.82(1), 493–508 (2002).
[CrossRef] [PubMed]

Huang, Z.

Hutmacher, D. W.

Hyman, B. T.

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A.100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Ito, Y.

K. Takeda, Y. Ito, and C. Munakata, “Simultaneous measurement of size and refractive index of a fine particle in flowing liquid,” Meas. Sci. Technol.3(1), 27–32 (1992).
[CrossRef]

Jain, R. K.

E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med.9(6), 796–801 (2003).
[CrossRef] [PubMed]

Jia, Y. K.

J.-X. Cheng, Y. K. Jia, G. Zheng, and X. S. Xie, “Laser-scanning coherent Anti-Stokes Raman scattering microscopy and applications to cell biology,” Biophys. J.83(1), 502–509 (2002).
[CrossRef] [PubMed]

Jonin, C.

Kauranen, M.

Lenne, P.-F.

Lewis, A.

P. J. Campagnola, M. D. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J.77(6), 3341–3349 (1999).
[CrossRef] [PubMed]

Lin, B.-L.

S.-W. Chu, S.-Y. Chen, G.-W. Chern, T.-H. Tsai, Y.-C. Chen, B.-L. Lin, and C.-K. Sun, “Studies of X(2)/X(3) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy,” Biophys. J.86(6), 3914–3922 (2004).
[CrossRef] [PubMed]

Lin, J.

Liu, C.

Loew, L. M.

P. J. Campagnola, M. D. Wei, A. Lewis, and L. M. Loew, “High-resolution nonlinear optical imaging of live cells by second harmonic generation,” Biophys. J.77(6), 3341–3349 (1999).
[CrossRef] [PubMed]

Lu, F.

Mäkitalo, J.

Malone, C. J.

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J.82(1), 493–508 (2002).
[CrossRef] [PubMed]

McKee, T.

E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med.9(6), 796–801 (2003).
[CrossRef] [PubMed]

Mertz, J.

Millard, A. C.

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J.90(2), 693–703 (2006).
[CrossRef] [PubMed]

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J.82(1), 493–508 (2002).
[CrossRef] [PubMed]

Mohler, W. A.

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J.90(2), 693–703 (2006).
[CrossRef] [PubMed]

P. J. Campagnola, A. C. Millard, M. Terasaki, P. E. Hoppe, C. J. Malone, and W. A. Mohler, “Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues,” Biophys. J.82(1), 493–508 (2002).
[CrossRef] [PubMed]

Moreaux, L.

Muller, M.

Müller, M.

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J.95(10), 4908–4914 (2008).
[CrossRef] [PubMed]

Munakata, C.

K. Takeda, Y. Ito, and C. Munakata, “Simultaneous measurement of size and refractive index of a fine particle in flowing liquid,” Meas. Sci. Technol.3(1), 27–32 (1992).
[CrossRef]

Nikitin, A. Y.

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A.100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J.186, 705–714 (1973).
[CrossRef]

Plotnikov, S. V.

S. V. Plotnikov, A. C. Millard, P. J. Campagnola, and W. A. Mohler, “Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres,” Biophys. J.90(2), 693–703 (2006).
[CrossRef] [PubMed]

Pluen, A.

E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med.9(6), 796–801 (2003).
[CrossRef] [PubMed]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J.186, 705–714 (1973).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. ii. structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Rigneault, H.

Rinia, H. A.

H. A. Rinia, K. N. J. Burger, M. Bonn, and M. Müller, “Quantitative label-free imaging of lipid composition and packing of individual cellular lipid droplets using multiplex CARS microscopy,” Biophys. J.95(10), 4908–4914 (2008).
[CrossRef] [PubMed]

Russier-Antoine, I.

Sandeau, N.

Sandre, O.

Seed, B.

E. Brown, T. McKee, E. diTomaso, A. Pluen, B. Seed, Y. Boucher, and R. K. Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation,” Nat. Med.9(6), 796–801 (2003).
[CrossRef] [PubMed]

Sheppard, C.

Sheppard, C. J. R.

N. K. Balla, P. T. C. So, and C. J. R. Sheppard, “Second harmonic scattering from small particles using Discrete Dipole Approximation,” Opt. Express18(21), 21603–21611 (2010).
[CrossRef] [PubMed]

J. N. Gannaway and C. J. R. Sheppard, “Second-harmonic imaging in the scanning optical microscope,” Opt. Quantum Electron.10(5), 435–439 (1978).
[CrossRef]

Silberberg, Y.

So, P. T. C.

Squier, J.

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science248(4951), 73–76 (1990).
[CrossRef] [PubMed]

Sun, C.-K.

S.-W. Chu, S.-Y. Chen, G.-W. Chern, T.-H. Tsai, Y.-C. Chen, B.-L. Lin, and C.-K. Sun, “Studies of X(2)/X(3) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy,” Biophys. J.86(6), 3914–3922 (2004).
[CrossRef] [PubMed]

Supatto, W.

Suuriniemi, S.

Takeda, K.

K. Takeda, Y. Ito, and C. Munakata, “Simultaneous measurement of size and refractive index of a fine particle in flowing liquid,” Meas. Sci. Technol.3(1), 27–32 (1992).
[CrossRef]

Terasaki, M.

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[CrossRef] [PubMed]

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A. Zoumi, A. Yeh, and B. J. Tromberg, “Imaging cells and extracellular matrix in vivo by using second-harmonic generation and two-photon excited fluorescence,” Proc. Natl. Acad. Sci. U.S.A.99(17), 11014–11019 (2002).
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[CrossRef] [PubMed]

W. R. Zipfel, R. M. Williams, R. Christie, A. Y. Nikitin, B. T. Hyman, and W. W. Webb, “Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation,” Proc. Natl. Acad. Sci. U.S.A.100(12), 7075–7080 (2003).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic of x-polarized light being focused on a thin layer of actin fibers oriented along x-axis.

Fig. 2
Fig. 2

Distribution of second order polarization component Px(2) induced in a thin layer of actin fiber bundles. Results predicted by UDM (a) and CMD (b&c). Refractive indices of samples (b) and (c) are 1.42 and 1.6 respectively.

Fig. 3
Fig. 3

Distribution of second order polarization components Py(2) (a & c)and Pz(2) (b & d) induced in a thin layer of actin fiber bundles. Results predicted by UDM (a & b) and CMD (c & d). Refractive index of 1.6 was used in CDM calculations.

Fig. 4
Fig. 4

Comparison of forward THG from axial scan of a 1.5 µm polystyrene bead as predicted by UDM and CDM.

Fig. 5
Fig. 5

Comparison of forward (-) and backward (- -) CARS from axial scan of a 1.5 µm polystyrene bead as predicted by a) CDM and b) UDM.

Equations (13)

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P i (1) = α ω,i ( E inc,i ji N A ij (1) P j (1) )
A ij (1) P j (1) = exp(ik r ij ) r ij 3 [ k 2 r ij ×( r ij × P j (1) )+ (1ik r ij ) r ij 2 { r ij 2 P j (1) 3 r ij ( r ij . P j (1) ) }], for ji; A ij (1) = α ω,i 1 , for j=i. }
j=1 N A ij (1) P j (1) = E inc,i
E loc,i (1) = α i 1 P i (1) =( E inc,i ji N A ij (1) P j (1) )
E SHG,i (2) = β i E loc,i (1) E loc,i (1) / α 2ω,i
E THG,i (3) = γ i E loc,i (1) E loc,i (1) E loc,i (1) / α 3ω,i
E CARS,i (3) = γ i E loc pump,i (1) E loc probe,i (1) E loc Stokes,i (1) / α ω CARS ,i
j=1 N A ij (n) P x,j (n) = E x,i (n) where(n,x)=(2,SHG) or (3,THG) or (3,CARS)
P i (1) =α E inc,i
P SHG,i (2) = β i E inc,i E inc,i
P THG,i (3) = γ i E inc,i E inc,i E inc,i
P CARS,i (3) = γ i E inc pump,i E inc probe,i E inc Stokes,i
P SHG = χ (2) EE =[ 0.09 1 1 0 0 0 0 0 0 0 0 1.15 0 0 0 0 1.15 0 ][ E x E x E y E y E z E z E y E z E x E z E x E y ]

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