Abstract

Image formation in Coherent Anti-Stokes Raman Scattering (CARS) microscopy of sub-wavelength objects is investigated via a combined experimental, numerical and theoretical study. We consider a resonant spherical object in the presence of a nonresonant background, using tightly focused laser pulses. When the object is translated along the laser propagation axis, we find the CARS signal to be asymmetric about the laser focal plane. When the object is located before the focus, there is a distinct shadow within the image, whereas the brightest signal is obtained when the object is behind the focus. This behaviour is caused by interference between resonant and nonresonant signals, and the Gouy phase shift is responsible for the observed asymmetry within the image.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-Dimensional Vibrational Imaging by Coherent Anti-Stokes Raman Scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
    [CrossRef]
  2. J.-X. Cheng and X. S. Xie, “Coherent Anti-Stokes Raman Scattering: Instrumentation, Theory, and Applications,” J. Phys. Chem. B 108, 827–840 (2004).
    [CrossRef]
  3. C. Evans and X. S. Xie, “Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine,” Annu. Rev. Anal. Chem. 1, 883–909 (2008).
    [CrossRef]
  4. E. O. Potma and X. S. Xie, “Theory of Spontaneous and Coherent Raman scattering,” in Handbook of Biological Nonlinear Optical Microscopy, B. R. Masters and P. T. C. So, eds. (Oxford University Press, 2008), pp. 164–185.
  5. M. D. Duncan, J. Reintjes, and T. J. Manuccia, “Scanning coherent anti-Stokes Raman microscope,” Opt. Lett. 7, 350–352 (1982).
    [CrossRef] [PubMed]
  6. C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
    [CrossRef] [PubMed]
  7. A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, Y. Jia, J. P. Pezacki, and A. Stolow, “Optimally chirped multimodal CARS microscopy based on a single Ti:sapphire oscillator,” Opt. Express 17, 2984–2996 (2009).
    [CrossRef] [PubMed]
  8. M. Rivard, M. Laliberté, A. Bertrand-Grenier, C. Harnagea, C. P. Pfeffer, M. Valliéres, Y. St-Pierre, A. Pignolet, M. A. El Khakani, and F. Légaré, “The structural origin of second harmonic generation in fascia,” Biomed. Opt. Express 2, 26–36 (2011).
    [CrossRef] [PubMed]
  9. J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterisation of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19, 1363–1375 (2002).
    [CrossRef]
  10. A. D. Slepkov, A. Ridsdale, A. F. Pegoraro, D. J. Moffatt, and A. Stolow, “Multimodal CARS microscopy of structured carbohydrate biopolymers,” Biomed. Opt. Express 1, 1347–1357 (2010).
    [CrossRef]
  11. A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd ed. (Artech House, 2005), pp. 58–79.
  12. M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-Order FDTD and Auxiliary Differential Equation Formulation of Optical Pulse Propagation in 2-D Kerr and Raman Nonlinear Dispersive Media,” IEEE J. Quantum Electron. 40, 175–182 (2004).
    [CrossRef]
  13. K. I. Popov, C. McElcheran, K. Briggs, S. Mack, and L. Ramunno, “Morphology of femtosecond laser modification of bulk dielectrics,” Opt. Express 19, 271–282 (2011).
    [CrossRef] [PubMed]
  14. A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd. ed. (Artech House, 2005), pp. 186–212.
  15. G. Mur, “Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
    [CrossRef]
  16. A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd ed. (Artech House, 2005), pp. 329–343.
  17. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, 2003), p. 194.

2011

2010

2009

2008

C. Evans and X. S. Xie, “Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine,” Annu. Rev. Anal. Chem. 1, 883–909 (2008).
[CrossRef]

2005

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[CrossRef] [PubMed]

2004

J.-X. Cheng and X. S. Xie, “Coherent Anti-Stokes Raman Scattering: Instrumentation, Theory, and Applications,” J. Phys. Chem. B 108, 827–840 (2004).
[CrossRef]

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-Order FDTD and Auxiliary Differential Equation Formulation of Optical Pulse Propagation in 2-D Kerr and Raman Nonlinear Dispersive Media,” IEEE J. Quantum Electron. 40, 175–182 (2004).
[CrossRef]

2002

1999

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-Dimensional Vibrational Imaging by Coherent Anti-Stokes Raman Scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[CrossRef]

1982

1981

G. Mur, “Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

Bertrand-Grenier, A.

Briggs, K.

Cheng, J.-X.

J.-X. Cheng and X. S. Xie, “Coherent Anti-Stokes Raman Scattering: Instrumentation, Theory, and Applications,” J. Phys. Chem. B 108, 827–840 (2004).
[CrossRef]

J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterisation of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19, 1363–1375 (2002).
[CrossRef]

Côté, D.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[CrossRef] [PubMed]

Duncan, M. D.

El Khakani, M. A.

Evans, C.

C. Evans and X. S. Xie, “Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine,” Annu. Rev. Anal. Chem. 1, 883–909 (2008).
[CrossRef]

Evans, C. L.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[CrossRef] [PubMed]

Freude, W.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-Order FDTD and Auxiliary Differential Equation Formulation of Optical Pulse Propagation in 2-D Kerr and Raman Nonlinear Dispersive Media,” IEEE J. Quantum Electron. 40, 175–182 (2004).
[CrossRef]

Fujii, M.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-Order FDTD and Auxiliary Differential Equation Formulation of Optical Pulse Propagation in 2-D Kerr and Raman Nonlinear Dispersive Media,” IEEE J. Quantum Electron. 40, 175–182 (2004).
[CrossRef]

Harnagea, C.

Holtom, G. R.

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-Dimensional Vibrational Imaging by Coherent Anti-Stokes Raman Scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[CrossRef]

Jia, Y.

Laliberté, M.

Légaré, F.

Lin, C. P.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[CrossRef] [PubMed]

Mack, S.

Manuccia, T. J.

McElcheran, C.

Moffatt, D. J.

Mur, G.

G. Mur, “Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

Pegoraro, A. F.

Pezacki, J. P.

Pfeffer, C. P.

Pignolet, A.

Popov, K. I.

Potma, E. O.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[CrossRef] [PubMed]

Puoris’haag, M.

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[CrossRef] [PubMed]

Ramunno, L.

Reintjes, J.

Ridsdale, A.

Rivard, M.

Russer, P.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-Order FDTD and Auxiliary Differential Equation Formulation of Optical Pulse Propagation in 2-D Kerr and Raman Nonlinear Dispersive Media,” IEEE J. Quantum Electron. 40, 175–182 (2004).
[CrossRef]

Sakagami, I.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-Order FDTD and Auxiliary Differential Equation Formulation of Optical Pulse Propagation in 2-D Kerr and Raman Nonlinear Dispersive Media,” IEEE J. Quantum Electron. 40, 175–182 (2004).
[CrossRef]

Slepkov, A. D.

Stolow, A.

St-Pierre, Y.

Tahara, M.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-Order FDTD and Auxiliary Differential Equation Formulation of Optical Pulse Propagation in 2-D Kerr and Raman Nonlinear Dispersive Media,” IEEE J. Quantum Electron. 40, 175–182 (2004).
[CrossRef]

Valliéres, M.

Volkmer, A.

Xie, X. S.

C. Evans and X. S. Xie, “Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine,” Annu. Rev. Anal. Chem. 1, 883–909 (2008).
[CrossRef]

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[CrossRef] [PubMed]

J.-X. Cheng and X. S. Xie, “Coherent Anti-Stokes Raman Scattering: Instrumentation, Theory, and Applications,” J. Phys. Chem. B 108, 827–840 (2004).
[CrossRef]

J.-X. Cheng, A. Volkmer, and X. S. Xie, “Theoretical and experimental characterisation of coherent anti-Stokes Raman scattering microscopy,” J. Opt. Soc. Am. B 19, 1363–1375 (2002).
[CrossRef]

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-Dimensional Vibrational Imaging by Coherent Anti-Stokes Raman Scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[CrossRef]

Zumbusch, A.

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-Dimensional Vibrational Imaging by Coherent Anti-Stokes Raman Scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[CrossRef]

Annu. Rev. Anal. Chem.

C. Evans and X. S. Xie, “Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine,” Annu. Rev. Anal. Chem. 1, 883–909 (2008).
[CrossRef]

Biomed. Opt. Express

IEEE J. Quantum Electron.

M. Fujii, M. Tahara, I. Sakagami, W. Freude, and P. Russer, “High-Order FDTD and Auxiliary Differential Equation Formulation of Optical Pulse Propagation in 2-D Kerr and Raman Nonlinear Dispersive Media,” IEEE J. Quantum Electron. 40, 175–182 (2004).
[CrossRef]

IEEE Trans. Electromagn. Compat.

G. Mur, “Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem. B

J.-X. Cheng and X. S. Xie, “Coherent Anti-Stokes Raman Scattering: Instrumentation, Theory, and Applications,” J. Phys. Chem. B 108, 827–840 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-Dimensional Vibrational Imaging by Coherent Anti-Stokes Raman Scattering,” Phys. Rev. Lett. 82, 4142–4145 (1999).
[CrossRef]

Proc. Natl. Acad. Sci. USA

C. L. Evans, E. O. Potma, M. Puoris’haag, D. Côté, C. P. Lin, and X. S. Xie, “Chemical imaging of tissue in vivo with video-rate coherent anti-Stokes Raman scattering microscopy,” Proc. Natl. Acad. Sci. USA 102, 16807–16812 (2005).
[CrossRef] [PubMed]

Other

E. O. Potma and X. S. Xie, “Theory of Spontaneous and Coherent Raman scattering,” in Handbook of Biological Nonlinear Optical Microscopy, B. R. Masters and P. T. C. So, eds. (Oxford University Press, 2008), pp. 164–185.

A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd. ed. (Artech House, 2005), pp. 186–212.

A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd ed. (Artech House, 2005), pp. 58–79.

A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd ed. (Artech House, 2005), pp. 329–343.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, 2003), p. 194.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(Color online). (a) Measured axial response of suspended polystyrene beads as a function of normalized displacement from the laser focus. The TPEF signal maximum is taken as the optimal focal position. The CARS signal is measured on resonance at ∼2850 cm−1. (b) Far-field integrated CARS signal vs. scatterer position relative to the best focus as calculated via FDTD, for scatterers of varying radius R, and for no scatterer. (c) FDTD calculated CARS signal for R = 0.4μm as in (b), including the cases where the background is index matched, and the background has no nonresonant nonlinear response. x0 is the position of the bead, xR is the Rayleigh length of the laser beam focusing lens (∼ 4μm in experiment, ∼ 2μm in simulations) at the pump frequency.

Fig. 2
Fig. 2

CARS images of 1μm diameter polystyrene beads embedded in agarose gel taken (a) 12.8 μm and (b) 8.8 μm deep into the sample. The CARS images were taken at a Raman shift of 2850 cm−1. The arrows show examples of dark spot artefacts in image (a), which correspond to bright spots in image (b).

Fig. 3
Fig. 3

The stages of the numerical experiment: (a) for each source pulse, a broad Gaussian beam is incident onto the surface of a high-NA paraboloidal perfectly reflecting macroscopic-sized mirror; (b) the electromagnetic field of the mirror is evaluated numerically at the boundary of the microscopic-sized simulation domain and is used as a boundary condition; (c) the laser pulses interact with the nonlinear media in the domain; (d) the scattered light is collected by the far-field probes and integrated over the appropriate solid angle; (e) the source pulses are absorbed by the absorbing boundaries of the simulation domain.

Fig. 4
Fig. 4

(Color online). Intensity of the total far field signal as evaluated by Eq. (6) for ρ = 0.4, 1, 2 (a); for ρ = 1, δϕL = π/8, 0 and: ϕG ≠ 0 (b); and ϕG ≡ 0 (c).

Equations (16)

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

D = [ 1 + 4 π ( χ ( 1 ) ( r ) + χ k ( 3 ) ( r ) E 2 ) ] E + 4 π P R , H = B ,
P R ( r , t ) = 1 4 π E ( χ R ( r , t ) * E 2 ( t ) ) .
χ R ( r , t ) = χ R ( 3 ) ( r ) 1 ( ω R 2 ω R 2 ω 2 + 2 j ω γ R ) .
E N R ( t ) = E 0 N R cos ( ω a s t + ϕ 0 ) , E R ( x 0 , t ) = E 0 R [ 1 + ( x 0 / x R ) ] 3 / 2 cos ( ω a s t + ϕ 0 + π / 2 + δ ϕ L + ϕ G ( x 0 ) ) ,
ϕ G ( x 0 ) = arctan ( x 0 / x R ) .
I I 0 ( 1 + ρ 2 [ 1 + ( x 0 / x R ) 2 ] 3 2 ρ sin ( δ ϕ L + ϕ G ) [ 1 + ( x 0 / x R ) 2 ] 3 / 2 ) ,
δ ϕ L k ( n n 0 ) R ,
E x p , s ( x , r ) = 0 , E y p , s ( x , r ) = E 0 p , s 1 + ( x / x R ) 2 exp ( r 2 w 0 2 ( 1 + ( x / x R ) 2 ) + i ( k p , s x ω p , s t + ϕ G ( x , r ) + ϕ 0 ) ) , E z p , s ( x , r ) = 0 , ϕ G ( x , r ) = arctan ( x / x R ) + x r 2 x R w 0 2 ( 1 + ( x / x R ) 2 ) ,
k a s = 2 k p k s = ( 2 ω p ω s ) n / c ,
P x a s N R ( 3 ) ( x , r ) = 0 , P y a s N R ( 3 ) ( x , r ) = χ N R ( 3 ) E y p 2 ( x , r ) E y s * ( x , r ) = χ N R ( 3 ) E 0 p 2 E 0 s [ 1 + ( x / x R ) 2 ] 3 / 2 exp ( 3 r 2 w 0 2 ( 1 + ( x / x R ) 2 ) ) e i ( k a s x ω a s t + ϕ G ( x , r ) + ϕ 0 ) , P z a s N R ( 3 ) ( x , r ) = 0 ,
E x a s N R ( P ) = 0 , E y a s N R ( P ) = ω a s 2 c 2 exp ( i k a s x P ) x P d x 0 2 π r d r exp ( k a s x ) P y a s N R ( 3 ) ( x , r ) = ω a s 2 c 2 exp ( i ( k a s x P ω a s t + ϕ 0 ) ) x P d x 0 2 π r d r × χ N R ( 3 ) E 0 p 2 E 0 s [ 1 + ( x / x R ) 2 ] 3 / 2 exp ( 3 r 2 w 0 2 ( 1 + ( x / x R ) 2 ) ) e i ϕ G ( x , r ) = ω a s 2 c 2 exp ( i ( k a s x P ω a s t + ϕ 0 ) ) x P w 0 2 x R π 2 2 χ N R ( 3 ) E 0 p 2 E 0 s , E z a s N R ( P ) = 0 ,
E y a s N R ( P ) = E 0 N R exp ( i ( k a s x P ω a s t + ϕ 0 ) ) ,
P y a s R ( 3 ) ( x , r ) = { i χ R ( 3 ) E 0 p 2 E 0 s [ 1 + ( x 0 / x R ) 2 ] 3 / 2 e i ( k a s x ω a s t + ϕ G ( x 0 , 0 ) + ϕ 0 ) , if ( x x 0 ) 2 + r 2 R 2 0 , otherwise .
E y a s R ( P ) = ω a s 2 c 2 exp ( i k a s x P ) x P d x 0 2 π r d r exp ( k a s x ) P y a s R ( 3 ) ( x , r ) = ω a s 2 c 2 exp ( i ( k a s x P ω a s t + ϕ G ( x 0 , 0 ) + ϕ 0 + π 2 ) ) x P 4 π 3 R 3 χ R ( 3 ) E 0 p 2 E 0 s [ 1 + ( x 0 / x R ) 2 ] 3 / 2 ,
E y a s R ( P ) = E 0 R [ 1 + ( x 0 / x R ) 2 ] 3 / 2 exp ( i ( k a s x P ω a s t + ϕ G ( x 0 , 0 ) + ϕ 0 + π 2 ) ) ,
E y ω a s R ( P ) = E 0 R [ 1 + ( x 0 / x R ) 2 ] 3 / 2 exp ( i ( k a s x P ω a s t + ϕ G ( x 0 , 0 ) + ϕ 0 + π 2 + δ ϕ L ) ) ,

Metrics